Referring to the figure, the polygons shown are similar. Findthe ratio (large to small) of their perimeters and areas.
Answers
SOLUTION
Consider the image below
The ratio of the side is given by
[tex]\begin{gathered} \text{large to small} \\ \frac{\text{large}}{small}=\frac{length\text{ of the side of the large triangle}}{Length\text{ of the side of small triangle }}=\frac{10}{5}=\frac{2}{1} \\ \\ \end{gathered}[/tex]Since the ratio of the side is the scale factor
[tex]\text{the scale factor =}\frac{2}{1}[/tex]hence The raio of the perimeters is the scale factor
Therefore
The ratio of their parimeter is 2 : 1
The ratio of the Areas is square of the scale factor
[tex]\text{Ratio of Area =(scale factor )}^2[/tex]
Hence
[tex]\begin{gathered} \text{ Since scale factor=}\frac{2}{1} \\ \text{Ratio of Area=}(\frac{2}{1})^2=\frac{2^2}{1^2}=\frac{4}{1} \\ \text{Hence} \\ \text{Ratio of their areas is 4 : 1} \end{gathered}[/tex]Therefore
The ratio of their Areas is 4 :1
Related Questions
discriminant for 2n^2+8n+1=-7
Answers
The given equation is
[tex]\begin{gathered} 2n^2+8n+1=-7 \\ 2n^2+8n+1+7=0 \\ 2n^2+8n+8=0 \end{gathered}[/tex]Where a = 2, b = 8, and c = 8.
The discriminant formula is
[tex]D=b^2-4ac[/tex]Let's replace the values
[tex]D=(8)^2-4(2)(8)=64-64=0[/tex]The equation has one real solution.Consider the two polynomials p(x), q(x) in Z[x] by p(x) = 1+2x+3x2, q(x) = 4+5x+7x3. Then p(x) + q(x) is
Answers
The solution for polynomials p(x) + q(x) is 7x³ + 3x² + 7x + 5
Given,
The polynomials
p(x) = 1 + 2x + 3x²
q(x) = 4 + 5x + 7x³
We have to find the solution for p(x) + q(x)
Then,
p(x) + q(x) = (1 + 2x + 3x²) + ( 4 + 5x + 7x³)
p(x) + q(x) = 7x³ + 3x² + 2x + 5x + 1 + 5
p(x) + q(x) = 7x³ + 3x² + 7x + 5
That is,
The solution for polynomials p(x) + q(x) is 7x³ + 3x² + 7x + 5
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Aaquib can buy 25 liters of regular gasoline for $58.98 or 25 liters of permimum gasoline for 69.73. How much greater is the cost for 1 liter of premimum gasolinz? Round your quotient to nearest hundredth. show your work :)
Answers
The cost for 1 liter of premium gasoline is $0.43 greater than the regular gasoline.
What is Cost?This is referred to as the total amount of money and resources which are used by companies in other to produce a good or service.
In this scenario, we were given 25 liters of regular gasoline for $58.98 or 25 liters of premium gasoline for $69.73.
Cost per litre of premium gasoline is = $69.73 / 25 = $2.79.
Cost per litre of regular gasoline is = $58.98/ 25 = $2.36.
The difference is however $2.79 - $2.36 = $0.43.
Therefore the cost for 1 liter of premimum gasoline is $0.43 greater than the regular gasoline.
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In the figure below, ZYZA and _YZX are right angles and _XYZ and ZAYZ arecongruent. Which of the following can be concluded about the distance frompoint A from point Z using Thales's method?O A. The distance between points A and Z is the same as the distancebetween points X and Z.B. The distance between points A and Z is the same as the distancebetween points A and Y.O C. The distance between points A and Z is the same as the distancebetween points Yand Z.D. The distance between points A and Z is the same as the distancebetween points X and Y.
Answers
Let's begin by identifying key information given to us:
[tex]\begin{gathered} \angle YZA=90^{\circ} \\ \angle YZX=90^{\circ} \\ \angle XYZ\cong\angle AYZ \end{gathered}[/tex]Thale's method shows that angles in a triangle opposite two sides of equal length are equal
[tex]undefined[/tex]As such, the answer is A (The distance between points A and Z is the same as the distance between X and Z)
Use a graph to predict the value of jewelry in 7 years.
Answers
Solution:
Given that the initial cost price of the jewelry is $2,200.
The rate at which it decreases each year is 12%.
Thus, the exponential decay function is;
[tex]\begin{gathered} y(t)=2200(1-0.12)^t \\ \\ \text{ Where }t\text{ is the time in years.} \end{gathered}[/tex]The graph of the function is;
From the graph;
CORRECT OPTION:
[tex]\approx899.09[/tex]Jordan wants to use the Starz princess hall, the Dynamic DJ's as his music And Roscoe's for his equipment. If Jordan has a total of $800 and wants the music to play for 4 hours, how many people can Jordan party?
Answers
The number of people that can attend Jordan's party would be; 50 people.
What is equation?The equation that represents the total amount that would be spent at the party would be a linear equation. A linear equation increases at a constant rate.
The form of the linear equation will be;
The Total amount = rental fee + (charge per hour of the Dynamic DJ x number of hours he plays) + (cost per person of Roscoe's rentals x number of people)
Now substitute;
$800 = $400 + ($50 x 4) + ($4 x p)
$800 = $400 + $200 + 4p
$800 = $600 + 4p
$800 - $600 = 4p
$200 = 4p
p = $200 / $4
p = 50 people
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a storage container for oil is in the shape of a cylinder with a diameter of 10ft and a height of 17ft. what is the volume if the storage container in cubic feet?
Answers
To calculate the volume, w will use the formula:
[tex]V=\pi r^2h[/tex]where r is the radius and h is the height
From the question,
diameter = 10
This implies that; r=d/2 = 10/2 = 5
h = 17
susbtitute the values into the formula
[tex]V=\pi\times5^2\times17[/tex][tex]=425\pi\text{ cubic feet}[/tex]If we substitute the value of pie= 22/7
[tex]V=\frac{22}{7}\times425[/tex][tex]\approx1335.71\text{ cubic f}eet[/tex]Andrea invites 12 cousins 6 aunts 4 brothers 2 sisters what fraction of her party guests are cousins?
Answers
To determine the fraction of cousins, you have to divide the number of cousins she invited by the total number of guests.
She invited 12 cousins, 6 aunts, 4 brothers, and 2 sisters, a total of 24 guests.
Then:
[tex]\frac{nº\text{cousins}}{\text{total guests}}=\frac{12}{24}[/tex]Both, 12 and 24 are divisible by 12, to simplify the fraction, divide the numerator and denominator by 12
[tex]\frac{12\div12}{24\div12}=\frac{1}{2}[/tex]The fraction
Simplify (v2 + 10v + 11)(v2 + 3v – 4) using the distributive property of multiplication ove addition(DPMA)
Answers
Given:
[tex](v^2+10v+11)(v^2+3v-4)[/tex]To find- the simplification.
Explanation-
We know that the distribution property of multiplication over addition says
[tex]a(b+c)=ab+ac[/tex]Use this property to simplify, and we get
[tex]\begin{gathered} =(v^2+10v+11)(v^2+3v-4) \\ =v^2(v^2+3v-4)+10v(v^2+3v-4)+11(v^2+3v-4) \end{gathered}[/tex]Multiply by opening the bracket, and we get
[tex]=(v^4+3v^3-4v^2)+(10v^3+30v^2-40v)+(11v^2+33v-44)[/tex]Now, open the bracket and combine the like terms.
[tex]\begin{gathered} =v^4+3v^3-4v^2+10v^3+30v^2-40v+11v^2+33v-44 \\ =v^4+(3v^3+10v^3)+(11v^2-4v^2+30v^2)-40v+33v-44 \end{gathered}[/tex]On further solving, we get
[tex]=v^4+13v^3+37v^2-7v-44[/tex]Thus, from the distributive property of multiplication over addition, we get v⁴+13v³+37v²-7v-44.
The answer is v⁴ + 13v³ + 37v² - 7v - 44.
I need help with my math homework question please. Plus it has a second part of the question
Answers
The given quadratic equation is
y = - x^2 + 25
a) The leading coeffiecient is the coefficient of the term with the highest exponent. Thus, the leading coefficient is the coefficient of x^2.
Leading coefficient = - 1
Since the leading coefficient is negative, the graph would open downwards. Thus, the correct option is
Down
b) The standard form of a quadratic equation is
y = ax^2 + bx + c
By comparing both equations,
a = - 1
b = 0
c = 25
The formula for calculating the x coordinate of the vertex of the graph is
x = - b/2a
By substituting the given values,
x = - 0/2 * - 1 = 0
We would calculate the y coordinate of the vertex by substituting x = 0 into the original equation. We have
y = - 0^2 + 25
y = 25
The coordinate of the vertex is (0, 25)
c) To find the x intercepts, we would equate the original equation to zero and solve for x. We have
- x^2 + 25 = 0
x^2 = 25
Taking the square root of both sides,
x = square root of 25
x = ± 5
Thus, the x intercepts are
(5, - 5)
d) The y intercept is the value of y when x = 0
Substituting x = 0 into the orignal equation,
y = - 0^2 + 25
y = 25
y intercept = (0, 25)
e) We would find another point on the graph. Let us substitute x = 6 into the equation. We have
y = - (6)^2 + 25 = - 36 + 25
y = - 11
We would plot (6, - 11) and (0, 25) on the graph. The graph is shown below
Jenny wants to earn $1,300by the end of the summer. How much more will she need to earn to meet her goal?
Answers
The most appropriate choice for subtraction of natural numbers will be given by-
Jenny needs $1172.95 to earn her goal.
What is subtraction?
At first, it is important to know about natural numbers.
Natural numbers are integers which are greater than or equal to 1
One of the operations on natural number is subtraction
The process of reducing one number from another number is called subtraction. Subtraction is used to find the difference between two numbers. The larger number is called minuend and the smaller number is called subtrehend.
Amount of money Jennyy had before = $127.05
Amount of money Jenny wants to earn = $1300
Amount of money Jenny needs to earn her goal = $(1300 - 127.05)
= $1172.95
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Complete Question
Jenny wants to earn $1,300 by the end of the summer. How much more will she need to meet her goal?
(Jenny had $127.05 before.)
For a standard normal distribution,Find P(-1.21 < Z< 2.26)
Answers
Answer:
The range of z-score is given below as
[tex]P(-1.21Using a graphing calculator, we will have the image be[tex]\begin{gathered} P(z<-1.21)=0.11314 \\ P(z<2.26)=0.9881 \\ P(-1.21Hence,The final answer is
[tex]P(-1.21\lt z\lt2.26)=0.8750[/tex]Jan draws a card from the set below, replaces it and then draws another card. Which of the following tree diagrams correctly shows the sample space?
Answers
Given the word problem, we can deduce the following information:
1. Jan draws a card from the set below, replaces it and then draws another card.
Based on the given information, there is a replacement happening. It means that Jan put a card back in the set before selecting another card. So the tree diagram that shows all the possible outcomes is Diagram A.
Therefore, the answer is A.
4. (A.20) Natasha and her friends go out for ice cream. They decide to create their own ice cream, which costs $1.60 plus 8 cents per topping. If x represents the number of toppings on the ice cream, then which'equation describes y, the total cost for the ice cream?A. y = 0.08 + 1.60)x B. y = .08 + 1.60x C. y = 1.60 +.08x D. y = 8x + 1.60
Answers
Answer:
C. y = 1.60 +.08x
Explanation:
The cost of the ice cream will be equal to the fixed cost of $1.60 plus the cost that depends on the number of toppings. So, if Natasha chooses x number of topping, the total cost of the toppings will be 8 cents times x or $0.08x
So, the total cost for the ice cream is represented by the equation:
y = 1.60 +.08x
Solve.Draw a rectangular fraction model to explain yourthinking.Then, write a number sentence.1/3of3/7=
Answers
We are asked to find 1/3 of 3/7 using a rectangular fraction model.
Let us draw a rectangular fraction model.
1/3 means make 3 rows
3/7 means make 7 columns
[tex]\frac{1}{3}\times\frac{3}{7}=\frac{3}{21}[/tex]Three 3 filled boxes represent the numerator and the total 21 boxes represent the denominator.
Therefore, the result is 3/21
the difference of four times a number and seven is 13
Answers
ExplanatIon
Step 1
let x represents the number
hence,
four times a number =4*x=4x
the difference of four times a number and seven=4x-7
is can be written as equal or "="",so
the difference of four times a number and seven is 13
[tex]4x-7=13[/tex]Step 2
solve for x
[tex]\begin{gathered} 4x-7=13 \\ \text{add 7 in both sides} \\ 4x-7+7=13+7 \\ 4x=20 \\ \text{divide both sides by 4} \\ \frac{4x}{4}=\frac{20}{4} \\ x=5 \end{gathered}[/tex]so, the number is 5.
I hope this helps you
the lettuce i have is 25 calories per serving. serving size is 85 grams. i had 27 grams . how many calories would this be? if you don’t know , don’t respond
Answers
There would be 91.8 calories in 27 grams.
Define unitary method.The unitary approach involves determining the value of a single unit, from which we can calculate the values of the necessary number of units. We must first determine the number of objects at the unit level in order to answer questions based on the unitary technique, after which we must determine it for higher values. For instance, if the price of 5 chocolates is $10, it is preferable to first determine the price of 1 chocolate in order to get the price of 6 chocolates. Once we get the price for 6 chocolates, we multiply it by 6.
Given,
Calories per serving = 25
Serving size = 85 grams
Calories per serving using unitary method:
Dividing,
[tex]\frac{85}{25}[/tex]
3.4
Calories per serving using unitary method is 3.4 calories.
Now, we have 27 grams,
Multiplying:
27 (3.4)
91.8
There would be 91.8 calories in 27 grams.
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Write the following linear equation in function notation. Y = 2x + 5a.) f(y) = 2x+ 5b.) f = 2x + 5c.)f(x) = 2x + 5d.)It is already written in function notation
Answers
Answer
Option C is correct.
The function notation
Explanation
can anyone help me?
solve using system of linear equations using elimination
x – y - 3z = 4
2x + 3y – 3z = -2
x + 3y – 2z = -4
Answers
The values of the variables are x = 2, y = -2 and z =0
How to solve the system of equations?From the question, the system of equations is given as
x – y - 3z = 4
2x + 3y – 3z = -2
x + 3y – 2z = -4
Subtract the second equation from the third
This action will eliminate (y)
So, we have
x + 3y – 2z = -4 - (2x + 3y – 3z = -2)
Evaluate
-x + z = -2
Make x the subject
x = z + 2
Substitute x = z + 2 in x – y - 3z = 4 and x + 3y – 2z = -4
z + 2 – y - 3z = 4
z + 2 + 3y – 2z = -4
Evaluate
-2z - y = 2
-z + 3y = -6
Double -z + 3y = -6
-2z + 6y = -12
Subtract -2z + 6y = -12 from -2z - y = 2 to eliminate z
7y = -14
Divide
y = -2
Substitute y = -2 in -z + 3y = -6
-z + 3(-2) = -6
Evaluate
-z - 6 = -6
Evaluate
z = 0
Recall that x – y - 3z = 4
So, we have
x + 2 - 3(0) = 4
Evaluate
x = 2
Hence, the solution is x = 2, y = -2 and z =0
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what is the approximation of 3√200
Answers
Given the expression:
[tex]\text{ }\sqrt[3]{200}[/tex]Let's simplify the expression and convert its decimal form to get its approximation.
We get,
[tex]\text{ }\sqrt[3]{200}\text{ = }\sqrt[3]{8\text{ x 25}}[/tex][tex]\text{ =2 }\sqrt[3]{25}[/tex]In decimal form:
[tex]\text{ 2 }\sqrt[3]{25}\text{ = 2 x 2.92401773821 = 5.84803547643 }\approx\text{ 5.8}[/tex]Therefore, the approximate equivalent of 3√200 is 5.8.
Determine the shape when the following points are graphed one a coordinate plane. A(-3, 1), B(2, 1), C(2, 4), D(-3, 4)
Answers
The given points are A(-3, 1), B(2, 1), C(2, 4), D(-3, 4).
The image below shows the figure formed by these points.
As you can observe, the shape formed by the given points is a rectangle with dimensions 5 times 3.
Therefore, the answer is "rectangle".You need a quarter of a pumpkin
to make a pie. How many pies
can you make with three and a
half pumpkins?
Answers
Answer: 14
Step-by-step explanation:
1/4 of a pumpkin is required to make a pie. The easiest way to complete this is to convert 3.5 pumpkins into the same fraction.
1 pumpkin = 4/4
3.5 pumpkins = 14/4
If only 1/4 of a pumpkin is required to make a pie and we have 14/4 then we can make 14 pumpkin pies.
Why might you use a different power of 10 instead of leaving bothnumbers in scientific notation?
Answers
Why might you use a different power of 10 instead of leaving both
numbers in scientific notation?
Because scintific notation is a simplification for large or small numbers, so a big number with a lot of zeros can be writen by a power of 10 multiplied by a number. But we cannot make substractions using this, because the powers ten represents very different values, for instance
[tex]\begin{gathered} 1\times10^1=10 \\ 1\times10^2=100 \end{gathered}[/tex][tex]1\times10^2-1\times10^1=100-10=90,[/tex]But if they have the same power, we can use the distibutive law to make the substraction
[tex]1\times10^2-1\times10^1=10\times10^1-1\times10^1=(10-1)\times10^1=9\times10^1^{}[/tex]which is the same thing. No matter the power of 10, if the power is the same you can use the same argument I've made before.
of a sample of 200 students surveyed,38 students said the soccer was their favorite sport what percent of the students in the sample prefer soccer 19% 38%40%76%
Answers
Out of 200 students surveyed, 38 said that soccer was their favorite sport.
The total number of students surveyed represents 100% of the sample, to determine which percentage does 38 represent, you can use cross multiplication:
200 students____100%
38 students _____ x%
Both relationships are at the same ratio so that:
[tex]\frac{100}{200}=\frac{x}{38}[/tex]To determine the percentage multiply both sides by 38:
[tex]\begin{gathered} 38\cdot\frac{100}{200}=38\cdot\frac{x}{38} \\ 19=x \end{gathered}[/tex]The percentage of students surveyed that like soccer is 19%
The average adult heart pumps about 84. mL/s of blood at 72 beats per minute. Suppose you need to calculate how long it would take the average heart tocirculate 6300. mL of blood.Set the math up. But don't do any of it. Just leave your answer as a math expressionAlso, be sure your answer includes all the correct unit symbols.
Answers
There are two ways to interpret the problem.
1) One is that a heart circulates 84ml of blood per second, although this makes the information of the beats per minute unnecessary.
In that case, an average heart would circulate 6300 ml of blood as shown in the next expression:
[tex]\begin{gathered} 6300=84t \\ \Rightarrow t=\frac{6300}{84} \end{gathered}[/tex]Where t is the time expressed in seconds
2) A second approach, and the one that makes better sense, is that each beat of the heart pumps 84ml per beat. Then, the expression that gives us the time needed to reach 6300ml of blood is:
[tex]\begin{gathered} \frac{84ml}{\text{beat}},\frac{72beats}{\min } \\ \Rightarrow84\cdot\frac{72ml}{\min}=\frac{6048ml}{\min } \end{gathered}[/tex]In that case, the equation that expresses the time needed by the heart to bump 6300ml of blood is:
[tex]\begin{gathered} 6300=6048\cdot t \\ \Rightarrow t=\frac{6300}{6048} \end{gathered}[/tex]With t being the time given in minutes
Find all solutions to the equationin the interval [O, 27). Enter thesolutions in increasing order.cos 2x = cos X[?]Tx = 0,2Remember: cos 20 = cos20 – sin20
Answers
SOLUTION
From
[tex]\begin{gathered} \cos 2x=\cos x \\ \cos ^2x-\sin ^2x=\cos x \\ \cos ^2x-(1-\cos ^2x)=\cos x \\ 2\cos ^2x-1=\cos x \\ 2\cos ^2x-\cos x-1=0 \\ \text{From the quadratic formula} \\ \cos x=\frac{1\pm\sqrt[]{1-(-8)}}{4} \\ \\ \cos x=\frac{1\pm3}{4} \\ \cos x=\text{ 1 or -}\frac{1}{2} \\ \text{Taking the cos}^{-1}of\text{ 1 and -}\frac{1}{2} \\ We\text{ have }\theta\text{ = 0, }\frac{2\pi}{3},\frac{4\pi}{3},\frac{8\pi}{3}\ldots\ldots\ldots2\pi \end{gathered}[/tex]So your answer is
[tex]0,\text{ }\frac{2\pi}{3},\text{ }\frac{4\pi}{3}[/tex]Find an equation for the line that passes through the points (2,2) and (-6,4)
Answers
Answer:
y=-1x/4+5/2
Step-by-step explanation:
use the slope formula
sarah spent a total of 10 on oranges and apples at the supet market. if she spent 3 dollars less for oranges than she did on apples how much did sarah spend on oranges
Answers
Let's write 2 equations from the two statements given.
Sarah spent 10 dollars on both oranges and apples
Let the price of oranges be "x" and price of apples be "y", thus we can write:
[tex]x+y=10[/tex]Oranges cost 3 less than apples, thus we can say:
[tex]y-3=x[/tex]We can substitute this into the first equation and solve for y:
[tex]\begin{gathered} x+y=10 \\ y-3+y=10 \\ 2y=10+3 \\ 2y=13 \\ y=\frac{13}{2} \\ y=6.5 \end{gathered}[/tex]Thus, let's solve for x now,
[tex]\begin{gathered} x=y-3 \\ x=6.5-3 \\ x=3.5 \end{gathered}[/tex]We want the price of oranges (x), thus,
Price of Oranges = $3.50
Reflect the following figure across the x-axis: S: (0, -3), T: (3, 1), U: (4, -3)
Answers
We are given the following coordinates.
[tex]\begin{gathered} S(0,-3) \\ T(3,1) \\ U(4,-3) \end{gathered}[/tex]We are asked to reflect them across the x-axis.
Recall that the rule for reflection across the x-axis is given by
[tex](x,y)\rightarrow(x,-y)[/tex]As you can see, the y-coordinate gets reversed.
Let us apply this rule on the given coordinates S, T, U
[tex]\begin{gathered} S(0,-3)\rightarrow U^{\prime}(0,3) \\ T(3,1)\rightarrow T^{\prime}(3,-1) \\ U(4,-3)\rightarrow U^{\prime}(4,3) \end{gathered}[/tex]Therefore, the above coordinates are reflected over the x-axis.
solve for x. z=5x-9y
Answers
ANSWER:
[tex]x=\frac{z+9y}{5}[/tex]STEP-BY-STEP EXPLANATION:
We have the following equation:
[tex]z=5x-9y[/tex]We solve for x as follows:
[tex]\begin{gathered} z+9y=5x \\ 5x=z+9y \\ x=\frac{z+9y}{5} \end{gathered}[/tex]