The bottom whiskers cover all data values from the smallest value to Q1, which is the lowest 25% of data values. The upper whiskers cover all data values between Q3 and the maximum value.
The horizontal axis covers all possible data values. The boxed portion of the box-and-whisker plot covers the middle 50% of the values in the data set.
Each whisker covers 25% of the data values.
The lower whisker covers all data values from the minimum value to Q1, i.e. the lowest 25% of data values. The upper whisker
covers all data values between Q3 and the maximum value, i.e. the highest 25% of data values.
The median is inside the box and represents the center of the data. 50% of data values are above the median and 50% of data values are below the median. Outliers or outliers in a dataset are often indicated by a "star" symbol on a box-and-whisker plot. If there are one or more outliers in the dataset, in order to draw a boxplot chart, we take the minimum and maximum values as the minimum and maximum values of the dataset, and exclude the values aberrant.
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find the point on the line y=3x + 4 that is closest to the origin
Therefore, the point on the line y = 3x + 4 that is closest to the origin is: (x, y) = (3/5, -2/5).
What is equation?An equation is a mathematical statement that shows the equality of two expressions, usually with an equal sign "=" in between them. An equation can contain variables, constants, and operators. The variables are represented by letters and can take on different values, while constants are fixed values that do not change. Operators include mathematical symbols like plus, minus, multiplication, and division, as well as exponents and logarithms.
Here,
To find the point on the line y=3x + 4 that is closest to the origin, we can use the distance formula between a point and a line. The point on the line that is closest to the origin will lie on the perpendicular line that passes through the origin and intersects the given line.
First, let's find the slope of the perpendicular line. Since the given line has a slope of 3, the perpendicular line will have a slope of -1/3 (the negative reciprocal of 3). Therefore, the equation of the perpendicular line is:
y = (-1/3)x + b
where b is the y-intercept.
Next, we need to find the point where the perpendicular line intersects the given line y=3x + 4. To do this, we can set the two equations equal to each other and solve for x and y:
(-1/3)x + b = 3x + 4
Multiplying both sides by 3 gives:
-x + 3b = 9x + 12
Rearranging gives:
10x = 3b - 12
x = (3/10)b - 6/5
Substituting this expression for x into either equation gives the corresponding value of y:
y = 3((3/10)b - 6/5) + 4 = (9/10)b - 14/5
Now, we need to find the value of b that makes the point (x, y) on the line y = 3x + 4 closest to the origin. The distance between the origin (0, 0) and any point (x, y) on the line y = (-1/3)x + b is given by the distance formula:
distance = √(x² + y²)
Substituting the expressions for x and y in terms of b gives:
distance = √((3/10)b - 6/5)² + ((9/10)b - 14/5)²)
To minimize the distance, we can take the derivative of the distance formula with respect to b and set it equal to zero:
d(distance)/db = (3/5)b - 12/5 = 0
Solving for b gives:
b = 4
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Tamika leans a 30-foot ladder against a wall so that it forms an angle of 65 degrees
with the ground. How high up the wall does the ladder reach? Round your answer to the nearest hundredth of a foot if necessary.
The ladder reaches approximately 26.11 feet up the wall.
What is trigonometric equations ?
Trigonometric equations are equations that involve trigonometric functions of one or more variables. The most common trigonometric functions are sine, cosine, tangent, cotangent, secant, and cosecant.
We can use trigonometry to solve this problem. The ladder, the wall, and the ground form a right triangle, where the ladder is the hypotenuse, the distance we want to find is one leg, and the angle between the ground and the ladder is the angle opposite the leg we want to find. We can use the sine function to solve for the height h:
sin(65) = h/30
Multiplying both sides by 30, we get:
h = 30 * sin(65)
Using a calculator, we find:
h ≈ 26.11
Therefore, the ladder reaches approximately 26.11 feet up the wall.
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What is 20% of 75?
pls help, tyy!!
After calculating the questiοn, we get that the value οf 20% οf 75 is 15.
What is percentage?A value οr ratiο that may be stated as a fractiοn οf 100 is referred tο in mathematics as a percentage. Divide the number by the tοtal and multiply by 100 tο find the percent οf a given number. Therefοre, the percentage refers tο a pοrtiοn per hundred. Per 100 is what the wοrd percentage signifies. The letter "%" stands fοr it.
Percent changes applied sequentially dο nοt add up in the usual way. Fοr example, if the 10% increase in price cοnsidered earlier (οn the $200 item, raising its price tο $220) is fοllοwed by a 10% decrease in the price (a decrease οf $22), then the final price will be $198—nοt the οriginal price οf $200.
Here the given is,
=> 20% of 75
=> 20% [tex]\times[/tex]75
=> [tex]\frac{20}{100}\times 75[/tex]
=> 5[tex]\times 3[/tex]
=> 15.
Hence the value of 20% of 75 is 15.
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help please I really appreciate it
Answer:
f(x) = -3(x -(-1))² +7
Step-by-step explanation:
You want the equation of the quadratic function that matches the given table.
LookThe first step in solving the problem is to look at the given information. To use the given equation, you need to know the vertex of the function, and its vertical scale factor.
VertexA quadratic function is symmetrical about the line through its vertex. That means we can locate the vertex by looking for x-values where the y-value is the same. The x-value of the vertex is halfway between those x-values.
Here, f(x) = 4 for both x=-2 and x=0. That means the x-value of the vertex is ...
(-2 +0)/2 = -1
This value of x is in the table, and f(-1) is given as 7. This means the vertex is (-1, 7) and these are the values that go in the two rightmost boxes.
f(x) = ( )(x -(-1))² + 7
Scale factor
The scale factor in the first box can be found by considering the difference between the f(x) value at the vertex, and the f(x) value at a point that is 1 unit either side:
( ) = f(-2) -f(-1) = 4 -7 = -3
The scale factor is -3, so the equation is ...
f(x) = -3(x -(-1))² +7
989+ 45
7) Jacky has 120 text messages on his phone.
Every day he gets 15 more. How many text
messages will Jacky have after 22 days?
Answer:490
Step-by-step explanation:15 times 22 +120=490
car A travelled 315km for 3 hours . if car B uses the same speed as Car A ,calculate how far Car B will travell for 2hrs 30 Minutes
In response to the given question, we can state that As a result, at the expressions same pace as automobile A, car B will go 262.5 kilometres in 2 hours and 30 minutes.
what is expression ?In mathematics, you can multiply, divide, add, or subtract. An expression is formed as follows: Expression, number, and math operator Numbers, parameters, and functions make up a mathematical expression. It is possible to contrast phrases and expressions. Every mathematical statement that comprises variables, numbers, and a mathematical action between them is referred to as an expression. For example, the phrase 4m + 5 is made up of the phrases 4m and 5, as well as the variable m from the provided equation, all separated by the mathematical symbol +.
We can use the following formula:
distance = time x speed
We know the distance is 315 km and the time is 3 hours for automobile A. As a result, we can compute its speed as follows:
speed = distance / time = 315 kilometres / 3 hours = 105 kilometres per hour
So we know that car B has the same speed as automobile A, which is 105 km/h. Car B takes 2 hours and 30 minutes, which is comparable to 2.5 hours. Hence, we can apply the same procedure to calculate the distance travelled by automobile B:
Distance is speed multiplied by time = 105 km/h multiplied by 2.5 hours = 262.5 kilometres
As a result, at the same pace as automobile A, car B will go 262.5 kilometres in 2 hours and 30 minutes.
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find end behavior of the polynomial
[tex] - 2x^4 - 3x^2 + x - 5[/tex]
the end behavior of the polynomial [tex]$-2 x^4-3 x^2-x+5$[/tex] is: The polynomial decreases without bound as [tex]$x$[/tex] get closer to positive infinity. The polynomial grows without bound as [tex]$x$[/tex] gets closer to negative infinity.
what is a polynomial?Algebraic expressions called polynomials include coefficients and variables. Indeterminates are another name for variables. For polynomial expressions, we can do mathematical operations like addition, subtraction, multiplication, and positive integer exponents but not division by variables. [tex]$x^2+x-12$[/tex] is an illustration of a polynomial with a single variable.
from the question:
The degree and leading coefficient of the polynomial [tex]$-2 x^4-3 x^2-x+5$[/tex]must be examined in order to determine its final behavior.
As the polynomial has a degree of 4 , it will expand or decay at a pace dictated by the leading coefficient as x gets closer to positive or negative infinity. The negative (leading) coefficient is -2 .
As in this instance, the final behavior of a polynomial with a negative leading coefficient and an even degree is as follows:
- The polynomial will decrement without bound as x approaches positive infinity, causing the y values to decrement steadily. This is due to the fact that as x increases significantly, the term with the highest degree takes over the polynomial, and since the leading coefficient is negative, the polynomial reduces.
- The polynomial will grow without bound as x gets closer to negative infinity, which causes the y-values to get steadily increasingly positive. This is because as x gets very tiny and negative, the term with the highest degree dominates the polynomial, and since the leading coefficient is negative, the polynomial rises.
Hence, the polynomial [tex]$-2 x^4-3 x^2-x+5$[/tex] has the following final behavior:
- The polynomial decreases without bound as x get closer to positive infinity.
- The polynomial grows without bound as x gets closer to negative infinity.
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m^2 + 4m+3=0 solve by completing the square
Answer:m=0,m=-2
Step-by-step explanation:
[tex]m^{2} + 4m+3=0\\(m+2)^{2} -1=0\\(m+2)^{2}=1\\1)m+1=1\\m=0\\1)m+1=-1\\m=-2[/tex]
Determine the period
Answer:
14
Step-by-step explanation:
Answer:
I believe your answer would be 14
In the rolling of two fair dice calculate the following: P( Sum of the two dice is 8 )= P( Sum of the two dice is 6 )= P( Sum of the two dice is not 4 )= P(Sum of the two dice is 5 or 9 )= P( Sum of the two dice is not 10 and not 7 )= Note: You can earn partial credit on this problem. You have attempted this problem 0 times. You have unlimited attempts remaining.
(Sum of the two dice is not 10 and not 7) = 1 - P(3, 4) - P(4, 3) - P(5, 2) - P(2, 5)= 1 - (2/36) - (2/36) - (4/36) - (4/36)= 20/36.
In the rolling of two fair dice, the following probabilities are calculated: P(Sum of the two dice is 8) = 5/36P(Sum of the two dice is 6) = 5/36P(Sum of the two dice is not 4) = 33/36P(Sum of the two dice is 5 or 9) = 10/36P(Sum of the two dice is not 10 and not 7) = 20/36
Note: We can earn partial credit on this problem. We have attempted this problem 0 times. We have unlimited attempts remaining.The step-by-step explanation of how these probabilities are calculated is given below:P(Sum of the two dice is 8) = P(2, 6) + P(3, 5) + P(4, 4) + P(5, 3) + P(6, 2)= (1/36) + (2/36) + (1/36) + (2/36) + (1/36)= 5/36P(Sum of the two dice is 6) = P(1, 5) + P(2, 4) + P(3, 3) + P(4, 2) + P(5, 1)= (1/36) + (1/36) + (1/36) + (1/36) + (1/36)= 5/36P(Sum of the two dice is not 4) = 1 - P(1, 3) - P(2, 2) - P(3, 1)= 1 - (1/36) - (1/36) - (1/36)= 33/36P(Sum of the two dice is 5 or 9) = P(1, 4) + P(2, 3) + P(3, 2) + P(4, 1) + P(3, 6) + P(4, 5) + P(5, 4) + P(6, 3)= (1/36) + (2/36) + (2/36) + (1/36) + (2/36) + (1/36) + (1/36) + (2/36)= 10/36P(Sum of the two dice is not 10 and not 7) = 1 - P(3, 4) - P(4, 3) - P(5, 2) - P(2, 5)= 1 - (2/36) - (2/36) - (4/36) - (4/36)= 20/36.
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Common pictures sizes (in inches) are 4 × 6, 5 × 7, 8 × 10, 9 × 12, 11 × 14, 14 × 18, and 16 × 20.
Are any of these picture sizes similar? Use similarity transformations.
The picture sizes that are similar are blank and blank. Dilating the smaller picture size using a scale factor of blank results in the larger picture size.
What does your conclusion indicate about resizing pictures?
Because most of the common picture sizes (select) similar, when resizing pictures one of two things will occur: the picture will be distorted or part of the picture will need to be cropped out.
Therefore , the solution of the given problem of expression comes out to be not proportional to the original size.
What exactly does an expression mean?Calculations like random multiplication, division, joining, and presently removing are necessary. They would result in the following if combined: An equation, some statistics, and a mathematical formula. A statement of veracity is composed of values, components, mathematical processes like additions, subtractions, blunders, and segments, as well as formulae. Words and phrases can be evaluated and analysed.
Here,
In terms of image sizes,
=> 4x6 and 8x10, 5x7 and 14x18, and 11x14 and 16x20 are comparable.
The bigger picture size is produced by diluting the smaller picture size by a scale factor of two.
This finding suggests that scaling images can be challenging if the new scale does not match the original.
When an image is resized, it will become distorted if the aspect ratios of the two sizes are different.
A portion of the image must be cropped out to suit the new size if the angles are identical but the new size is not proportional to the original size.
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Aaron has 2 pizzas left over from a
He ate of the leftover pizza
sleepover.
for lunch. How much of the pizza did he
eat? How much is left?
Pls help!!
Answer: 1/8
Step-by-step explanation:
valor aproximado de 25 m2 de cerámica de azulejos es de C$3 125 en una ferretería local. Cuál será la cantidad (m2) de azulejos que se puede comprar con un presupuesto
de C$ 15 625?
According to the question we can say that with a budget of T$15,625, you can purchase approximately 5.5 square meters of ceramic tiles at the given price of C$3,125 for 25 m2.
What is division?Among the four fundamental arithmetic operations, or ways to mix numbers to create new ones, is division. Multiplication, addition, as well as subtraction make up the remaining operations.
To find the quantity of tiles that can be purchased with a budget of T$15,625, we need to calculate the cost per square meter of the tiles and then divide the budget by this cost.
The cost per square meter of the tiles is given by:
C$3,125 / 25 m2 = C$125/m2
To convert C$125/m2 to T$, we need to use the current exchange rate. Let's assume that the current exchange rate is 1 CAD = 0.75 USD and 1 USD = T$30.
C$125/m2 * 0.75 USD/CAD * 30 T/USD = T$2,812.50/m2
Now we can calculate the quantity of tiles that can be purchased with a budget of T$15,625:
Quantity of tiles = Budget / Cost per square meter
Quantity of tiles = T$15,625 / T$2,812.50/m2
Quantity of tiles = 5.5 m2 (rounded to the nearest 0.5 m2)
Therefore, with a budget of T$15,625, you can purchase approximately 5.5 square meters of ceramic tiles at the given price of C$3,125 for 25 m2.
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A neighborhood depanneur has determined that daily demand for milk cartons has an approximate normal distribution, with a mean of 65 cartons and a standard deviation of 7 cartons. On Saturdays, the demand for milk is known to exceed 71 cartons. On the coming Saturday, what is the probability that it will be at least 81 cartons?
There is a 0.011 = 1.1% probability that the demand will be of at least 81 cartons on the next Saturday.
How to obtain probabilities using the normal distribution?The z-score of a measure X of a variable that has mean symbolized by [tex]\mu[/tex] and standard deviation symbolized by [tex]\sigma[/tex] is obtained by the rule presented as follows:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score represents how many standard deviations the measure X is above or below the mean of the distribution, depending if the obtained z-score is positive or negative.Using the z-score table, the p-value associated with the calculated z-score is found, and it represents the percentile of the measure X in the distribution.The mean and the standard deviation for this problem are given as follows:
[tex]\mu = 65, \sigma = 7[/tex]
The probability that there will be at least 81 cartoons is one subtracted by the p-value of Z when X = 81, hence:
Z = (81 - 65)/7
Z = 2.29
Z = 2.29 has a p-value of 0.989.
(we can consider this for any Saturday as outcomes of the normal distribution are independent).
Hence the probability is obtained as follows:
1 - 0.989 = 0.011 = 1.1%.
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4. Tshering claims that if she triples the side length of a square (s), the area of the square will also be tripled. Do you agree? Explain your thinking.
Tshering's claim is incorrect because the area is not trippled, but it is multiplied by a factor of 9
How to determine if Tshering's claim is correctGiven the the side length is
Side length, s = s
So, the area is
Area = s²
When the side length is trippled, we have
New side length, S = 3s
So, the area is
New area = (3s²)
New area = 9s²
Divide the new area by the initial area
Factor = 9s²/s²
So, we have
Factor = 9
This means that the area is multiplied by 9 and not tripled
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1.
Carolanne was adding the two polynomials shown below.
(3x2 – 4x – 1) + (8x2 – x + 6)
Which of the following best describes her answer in simplest form?
11x2
11x2 – 5x + 5
68x2 + 5
6x2 + 5
Answer:
[tex]11x^2 - 5x + 5[/tex] (Option 2)
Step-by-step explanation:
Equation:
[tex](3x^2 - 4x -1) +(8x^2 - x + 6)[/tex]
We can drop the parenthesis since there is nothing to distribute
[tex]3x^2 - 4x -1 +8x^2 - x + 6[/tex]
Combine like terms
[tex]3x^2 + 8x^2 -4x -x -1 +6\\\\11x^2 - 5x + 5[/tex]
Question -1 Solve n^(2)+13n+30=0 by factoring. Enter your answers as a list separated by
Answer:
(n+3)(n+10)
Step-by-step explanation:
n^2+13n+30
n^2+10n+3n+30
n(n+10)+3n+30
n(n+10)+3(n+10)
(n+3)(n+10)
the sonoma apple products company purchases apples from local growers and makes applesauce and apple juice. it costs $0.90 to produce a jar of applesauce and $0.65 to produce a bottle of apple juice. the company has a policy that at least 20 percent but no more than 65 percent of its output must be applesauce. the company wants to meet but not exceed the demand for each product. the marketing manager estimates that the demand for applesauce is 5000 jars, plus an additional 4 jars for each $1 spent on advertising for applesauce. the demand for apple juice is estimated to be 4000 bottles, plus an additional 5 bottles for every $1 spent on advertising for apple juice. the company has $19,750 to spend on producing and advertising its two products. applesauce sells for $2 per jar, and apple juice sells for $1.50 per bottle. formulate a linear optimization model to help the company determine how many units of each product to produce, and how much advertising to spend on each product, in order to maximize profit. (you do not need to find the optimal solution).
The linear optimization model is:
maximize 2x1 + 1.5x2 - 0.9x1 - 0.65x2 - x3 - x4
subject to:
0.2(x1 + x2) <= x1 <= 0.65(x1 + x2)
x1 <= 5000 + 4x3
x2 <= 4000 + 5x4
0.9x1 + 0.65x2 + x3 + x4 <= 19750
x1 >= 0
x2 >= 0
x3 >= 0
x4 >= 0
To formulate a linear optimization model for the Sonoma Apple Products Company, we need to define the decision variables, the objective function, and the constraints.
Decision variables:
- Let x1 be the number of jars of applesauce produced
- Let x2 be the number of bottles of apple juice produced
- Let x3 be the amount spent on advertising for applesauce
- Let x4 be the amount spent on advertising for apple juice
Objective function:
- The company wants to maximize profit, which is the difference between revenue and cost.
- The revenue from applesauce is $2 per jar, and the revenue from apple juice is $1.50 per bottle.
- The cost of producing applesauce is $0.90 per jar, and the cost of producing apple juice is $0.65 per bottle.
- The cost of advertising is x3 for applesauce and x4 for apple juice.
- Therefore, the objective function is:
maximize 2x1 + 1.5x2 - 0.9x1 - 0.65x2 - x3 - x4
Constraints:
- The company has a policy that at least 20% but no more than 65% of its output must be applesauce:
0.2(x1 + x2) <= x1 <= 0.65(x1 + x2)
- The company wants to meet but not exceed the demand for each product:
x1 <= 5000 + 4x3
x2 <= 4000 + 5x4
- The company has $19,750 to spend on producing and advertising its two products:
0.9x1 + 0.65x2 + x3 + x4 <= 19750
- The decision variables must be non-negative:
x1 >= 0
x2 >= 0
x3 >= 0
x4 >= 0
The linear optimization model is:
maximize 2x1 + 1.5x2 - 0.9x1 - 0.65x2 - x3 - x4
subject to:
0.2(x1 + x2) <= x1 <= 0.65(x1 + x2)
x1 <= 5000 + 4x3
x2 <= 4000 + 5x4
0.9x1 + 0.65x2 + x3 + x4 <= 19750
x1 >= 0
x2 >= 0
x3 >= 0
x4 >= 0
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#6. To raise money a club sells slices of pizza after school. Pepperoni slices cost $3 and cheese slices
cost $2. 12. 7 slices are sold and $326 are raised. How many of each slice were sold?
Answer:
pepperoni slices : 72
cheese slices: 55
Step-by-step explanation:
p is the number of pepperoni slices
c is the number of cheese slices
so p + c = 127 => c = 127 - p
3p + 2c = 326
3p + 2(127 - p) = 326
3p + 254 - 2p = 326
p = 326 - 254 = 72
c = 127 - 72 = 55
1. The cost of a peanut butter bar is $0.07 more than the cost of a chocolate bar. If you buy 5 peanut butter bars and 6 chocolate bars, the total cost is $6.40. How much does the chocolate bar cost?
A. $0.61
B. $0.55
C. $0.54
D. $0.62
Pls help!!! i need this done tonight
Answer:
The cost of the chocolate bar is $0.54. You can calculate this by subtracting the total cost of the peanut butter bars ($3.50) from the total cost of the 5 peanut butter bars and 6 chocolate bars ($6.40), resulting in $2.90 for the cost of the chocolate bars, which is then divided by 6 to get $0.54.
Determine if there is a proportional relationship between the length of the diagonals and the areas of the squares.
Area is the amount of space inside a shape. You can multiply the length of a rectangle by the width of a rectangle to find the area. If s represents each side length and a represents the area, which formula can you use to find the area of a square?
Square A with side length 4.8, Square B with side length 5.2, Square C with side length 6.4, Square D with side length 3.6
Square (cm) Side lengths (cm) Area (cm
2
)
A 4.8 ?
B 5.2 ?
C 6.4 ?
D 3.6 ?
s·2=a
s·s=a
s·a=a
Good work!
Let's start by finding the area of square A. The side length, s, is 4.8 centimeters. Use the formula to find 4.8·4.8.
to find the area.
Square A with side length of 4.8
The ratiοs are nοt equal fοr all the squares, which means there is nοt a prοpοrtiοnal relatiοnship between diagοnal length and area.
Using the fοrmula fοr finding the area οf a square, we have:
Area οf square A = side length squared
Area οf square A = 4.8 x 4.8
Area οf square A = 23.04 square cm
Similarly, we can find the areas οf squares B, C, and D:
Area οf square B = 5.2 x 5.2 = 27.04 square cm
Area οf square C = 6.4 x 6.4 = 40.96 square cm
Area οf square D = 3.6 x 3.6 = 12.96 square cm
Nοw, let's find the lengths οf the diagοnals οf each square using the Pythagοrean theοrem:
Diagοnal οf square A = √(4.8² + 4.8²) = 6.77 cm
Diagοnal οf square B = √(5.2² + 5.2²) = 7.35 cm
Diagοnal οf square C = √(6.4² + 6.4²) = 9.06 cm
Diagοnal οf square D = √(3.6² + 3.6²) = 5.09 cm
Tο determine if there is a prοpοrtiοnal relatiοnship between the length οf the diagοnals and the areas οf the squares, we need tο cοmpare the ratiοs οf the diagοnals tο the areas fοr each square.
Fοr example, the ratiο οf diagοnal length tο area fοr square A is:
Ratiο οf diagοnal length tο area fοr square A = diagοnal length / area
Ratiο οf diagοnal length tο area fοr square A = 6.77 cm / 23.04 square cm
Ratiο οf diagοnal length tο area fοr square A = 0.294
We can repeat this fοr the οther squares and cοmpare the ratiοs. If the ratiοs are apprοximately equal fοr all the squares, then there is a prοpοrtiοnal relatiοnship between diagοnal length and area.
Ratiο οf diagοnal length tο area fοr square B = 0.272
Ratiο οf diagοnal length tο area fοr square C = 0.221
Ratiο οf diagοnal length tο area fοr square D = 0.393
As we can see, the ratiοs are nοt equal fοr all the squares, which means there is nοt a prοpοrtiοnal relatiοnship between diagοnal length and area.
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find the missing angle
answer as soon as possible <3
ANSWER
31 is answer !!!!
Answer:
31
Step-by-step explanation:
180-35-23=122
180-122-27=31
I need help with my math homework please
Answer:
C, D and E
Step-by-step explanation:
2(4f+2g)
8f+4g
so it's C, D and E
One edge of a painting is 6 in. longer than the other edge. The painting has a 2-inch-wide frame. The function f(x) = x2 + 14x + 40 represents the total area of the painting and frame. Find the total area of the painting and the frame if the longer side of the frame is 14 inches long.
A rectangle that has a length of X plus 6 and a width of X, surrounded by a 2 inch frame on all sides.
area: _____in.2
The total area of the painting and frame is 248 inches squared.
What is area?Area is the size of a two-dimensional surface, typically defined by its length and width. It is an important concept in mathematics and is used to measure different shapes and figures. Area is also commonly used to measure the size of land, such as a city block or a region of a country. Areas can be measured in square meters, square kilometers, hectares, square feet, and many other units. Knowing the area of a shape or space can be helpful when planning a project or understanding how much space something requires.
Using the given equation, f(x) = x2 + 14x + 40, we can solve for the area of the painting and frame.
f(x) = x2 + 14x + 40
f(x) = (x + 6)2 + 2(x + 6)(2) + 2(2)(2)
f(x) = x2 + 12x + 36 + 4x + 24 + 16
f(x) = x2 + 16x + 56
We are told that the longer side of the frame is 14 inches long, so x = 8.
f(8) = 8^2 + 16(8) + 56
f(8) = 64 + 128 + 56
f(8) = 248 in.2
Therefore, the total area of the painting and frame is 248 inches squared.
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Find the work done by the force field F on a particle moving along the given path.
F(x, y) = x^2i − xyj
C: x = cos^3(t), y = sin^3(t) from (1, 0) to (0, 1)
The answer of the given question based on the finding the work done by the force, is field F on a particle moving along the path C is 1/6.
What is Force?A force is defined as influence that causes object to undergo change in motion. It is vector quantity, means it has both magnitude and direction.
To find the work done by the force field F on a particle moving along the given path, we need to evaluate the line integral of F along the path C.
The line integral of a vector field F along a curve C parameterized by r(t) is given by:
∫ F(r(t)) ⋅ r'(t) dt
where r'(t) is the derivative of r(t) with respect to t.
In this case, the force field F(x, y) = x²i − xyj, and the path C is given by x = cos³(t), y = sin³(t) from (1, 0) to (0, 1).
First, we need to parameterize the path C in terms of t. Since x = cos³(t) and y = sin³(t), we can express the path C as a vector function r(t) = ⟨cos³(t), sin³(t)⟩, where t goes from 0 to π/2.
we need to find derivative of r(t) with the respect of t:
r'(t) = ⟨-3cos³(t)sin(t), 3sin²(t)cos(t)⟩
Now, we can evaluate the line integral of F along C:∫ F(r(t)) ⋅ r'(t) dt
= ∫ (cos⁶(t)i - cos³(t)sin⁴(t)j) ⋅ (-3cos²(t)sin(t)i + 3sin²(t)cos(t)j) dt
= ∫ (-3cos⁸(t)sin(t) + 3cos³(t)sin⁵(t)) dt
= [-3/9cos⁹(t) - 3/6cos⁴(t)cos²(t)]_0^(π/2)
= 0 - (-3/9 - 3/12)
= 1/6
Therefore, the work done by the force field F on a particle moving along the path C is 1/6.
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solve x thereunder dnnd
Answer:
65.1
Step-by-step explanation:
cos(37)=[tex]\frac{52}{x}[/tex]
[tex]x=\frac{52}{cos(37)}[/tex]
[tex]x=65.111....\\x=65.1[/tex]
Identify the similar triangles
The similar triangles are-
ΔNMQ ≈ ΔNQP ≈ ΔQMP
Explain about the similar triangles?Triangles with the same shape but different sizes are said to be similar triangles.In other words, whenever two triangles appear similar, their corresponding sides are proportionately equal and their corresponding angles remain congruent.Three ways can be used to determine whether two triangles resemble similar: SSS, SAS, and AA
Triangles are similar if they have two identical kinds of angle type, or AA (Angle-Angle).Triangles are identical if they have two sets of proportional sides with equal included angles, or SAS (Side-Angle-Side).Triangles are similar if the ratio of the third side of one triangle to the third side of another triangle is known as SSS (Side-Side-Side).For the given figure:
Thus, the similar triangles are-
ΔNMQ ≈ ΔNQP ≈ ΔQMP
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if a rectangle the area of 16 square unit, would could the measure of the sides be?
Answer:
See below.
Step-by-step explanation:
We are asked to find measures of the unknown sides for the given area.
Let's keep in mind that a rectangle's area is; [tex]Area = (width) \times (height)[/tex]
One simple way to find all of the possible side lengths is to find all of the factors of 16.
What are Factors?
Factors are 2 whole numbers that multiply together to have the product of that given number.
Think of how many ways we can get to 16 by multiplying 2 numbers.
[tex]f_{1} \times f_{2} = 16\\f \ represents \ a \ factor.[/tex]
Here's all of the possible ways we can get to 16 with whole numbers.
[tex]8 \times 2 = 16\\4 \times 4 = 16\\2 \times 8 = 16\\1 \times 16 = 16\\16 \times 1 = 16[/tex]
Remember that the Width and Length of a Rectangle can have different values even with the same numbers multiplied.
[tex](8 \times 2) \ and \ (2 \times 8)\\Length \ can \ equal \ 2, \ or \ 8.\\Width \ can \ equal \ 8, \ or \ 2.[/tex]
These are all of the possible answers.
Bonsoir pouvez vous maider, merci d'avance.
On s’intéresse à la partie III. de l’activité Python « Vecteurs et repérage ». Écrire une fonction triangle_rectangle qui prend en arguments les coordonnées de trois points A, B etC et affiche, selon les
cas, le message « Le triangle ABC est rectangle en A. », « Le triangle ABC est rectangle en
B. », « Le triangle ABC est rectangle en C. » ou « Le triangle ABC n’est pas rectangle. ».
Pour A(2;−2), B(7;3) et C(5; 5), vérifier, avec votre programme, que le triangle ABC est rectangle en B.
Answer:
Voici une solution possible en Python:
def triangle_rectangle(A, B, C):
# Calcul des carrés des longueurs des côtés
AB2 = (B[0] - A[0])**2 + (B[1] - A[1])**2
BC2 = (C[0] - B[0])**2 + (C[1] - B[1])**2
AC2 = (C[0] - A[0])**2 + (C[1] - A[1])**2
# Vérification si le triangle est rectangle et affichage du résultat
if AB2 + BC2 == AC2 or AB2 + AC2 == BC2 or BC2 + AC2 == AB2:
if AB2 + BC2 == AC2:
print("Le triangle ABC est rectangle en A.")
elif AB2 + AC2 == BC2:
print("Le triangle ABC est rectangle en C.")
else:
print("Le triangle ABC est rectangle en B.")
else:
print("Le triangle ABC n'est pas rectangle.")
# Exemple avec A(2,-2), B(7,3) et C(5,5)
A = (2,-2)
B = (7,3)
C = (5,5)
triangle_rectangle(A, B, C) # affiche "Le triangle ABC est rectangle en B."
-
Explications :
La fonction triangle_rectangle prend en argument les coordonnées des points A, B et C sous forme de tuples (x,y). Elle commence par calculer les carrés des longueurs des côtés AB, BC et AC à l'aide de la formule de distance entre deux points.
Ensuite, elle vérifie si le triangle est rectangle en comparant la somme des carrés des longueurs de deux côtés avec le carré de la longueur du troisième côté. Si c'est le cas, elle affiche le message correspondant en précisant le point d'angle droit. Sinon, elle affiche le message indiquant que le triangle n'est pas rectangle.
Finalement, un exemple est donné avec les points A(2,-2), B(7,3) et C(5,5) pour vérifier que le triangle est rectangle en B, conformément à l'énoncé.
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Question 2: Three friends, Izzy, Lydia, & Jenna are collecting canned pet food for the animal shelter. Their goal is represented by the expression 6x^2 - 2xy + 8.
Izzy: 3x^2 - 2
Lydia: x^2
Jenna: 2xy + 5
Part A: Create an expression to represent the amount of canned food collected so far by the three friends.
Part B: Fill in the blanks to create an expression that represents the number of cans the friends still need to collect their goal. SHOW YOUR WORK!
Answer: __x^2 - __xy + __ (REMEMBER TO FILL IN THE BLANKS, MANDATORY)
By answering the above question, we may state that The missing values are "5" for the constant term, "-2" for the "xy" coefficient, and "2" for the "x²" coefficient.
What is expression?In mathematics, yοu can multiply, divide, add, οr take away. The fοllοwing is hοw an expressiοn is put tοgether: Numeric value, expressiοn, and math οperatοr The elements οf a mathematical expressiοn include numbers, parameters, and functiοns. It is feasible tο use cοntrasting wοrds and expressiοns. Any mathematical statement cοntaining variables, numbers, and a mathematical actiοn between them is knοwn as an expressiοn, οften knοwn as an algebraic expressiοn. As an example, the expressiοn 4m + 5 is cοmpοsed οf the expressiοns 4m and 5, as well as the variable m frοm the abοve equatiοn, which are all separated by the mathematical symbοl +.
Part A: We must add the expressiοns fοr each οf the three friends in οrder tο build an expressiοn tο reflect the tοtal amοunt οf canned fοοd that the three friends have sο far cοllected:
= (4x² + 2xy + 3) = (3x² - 2) + x2 + (2xy + 5)
Part B: We must deduct the amοunt acquired frοm the gοal expressiοn in οrder tο determine hοw many cans the buddies still need tο gather tο reach their gοal.
Aim - Amοunt gathered equals (6x² - 2xy + 8) - (4x² + 2xy + 3) = 2x² - 5 in terms οf the number οf cans required.
As a result, the expressiοn fοr hοw many mοre cans the buddies need tο gather tο reach their οbjective is 2x² - 5. The missing values are "5" fοr the cοnstant term, "-2" fοr the "xy" cοefficient, and "2" fοr the "x²" cοefficient.
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