Answers
1. The mathematical expression for the length is C. 2x + 5.
2. The quadratic equation is A. 2x² + 5x - 18 = 0.
3. The width of the tarpaulin is A. 2 ft.
4. The length of the tarpaulin is D. 9 ft.
5. The perimeter of the tarpaulin is C. 22 feet.
How to calculate the value?From the information, the following can be deduced:
Width = x
Length = (2 × x) + 5 = 2x + 5
Area = 18 ft²
The equation will be:
Length × Width =Area
(2x + 5)x = 18
2x² + 5x = 18
2x² + 5x - 18 = 0
2x² - 4x + 9x - 18 = 0
2x(x - 2) + 9(x - 2)
Therefore, x - 2 = 0
x = 0 + 2 = 2
Width = 2
Length = 2x + 5 = 2(2) + 5 = 9ft
Perimeter = 2( Length + Width)
= 2(2 + 9)
= 22 feet.
This illustrates the concept of addition to calculate the perimeter.
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Related Questions
In 2022, a company made a profit of $1.38 million. That amount is $2.54 million more than the profit from 2021.
What is the profit from 2021? Write & solve an Algebraic Equation.
Answers
Answer: 6x+2xz*52-35^5=
Step-by-step explanation: rs:p=4436x
Answer: The profit from 2021 = $ -1.16 Million ($1.16 Million loss)
Step-by-step explanation:
Profit for 2022 = $ 1.38 Million
Profit for 2021 = Profit for 2022 - $ 2.54 Million
Algebraic equation:
p2021 = p2022 -$ 2.54 Million
p2021 = $ 1.38 Million - $ 2.54 Million
p2021 = $ -1.16 Million
Please help me anwser this
Answers
Answer:
(x + 3)² + (y - 6)² = 9
Step-by-step explanation:
the equation of a circle in standard form is
(x - h)² + (y - k)² = r²
where (h, k ) are the coordinates of the centre and r is the radius
here (h, k ) = (- 3, 6 ) and r = 3 , then
(x - (- 3 )² + (y - 6)² = 3² , that is
(x + 3)² + (y - 6)² = 9
An artist is going to cut four similar righttriangles from a rectangular piece of paperlike the one shown to the right. What is thedistance from B and D to the diagonal AC?Write an equation and solve, showing ALLthe work.
Answers
First let's find the length of AC using the Pythagorean theorem in the right triangle with legs of 5 and 12:
[tex]\begin{gathered} AC^2=5^2+12^2 \\ AC^2=25+144 \\ AC^2=169 \\ AC=13 \end{gathered}[/tex]So the diagonal of the rectangle is 13 units. Now, since the area of a triangle is calculated as the product of a base and the corresponding height, we can use the legs as base and height or we can use the segment AC and the corresponding height, and the result is the same, so we have:
[tex]\begin{gathered} A=\frac{b\cdot h}{2} \\ A=\frac{5\cdot12}{2} \\ A=\frac{13\cdot h}{2} \\ \\ \frac{5\cdot12}{2}=\frac{13\cdot h}{2} \\ 60=13h \\ h=\frac{60}{13} \end{gathered}[/tex]So the distance from B or D to the diagonal AC is 60/13 units.
in Italy the leaning Tower of Pisa currently leans at 13 ft. off the vertical. the tower is 183 ft tall. what is the angle of inclination
Answers
The required inclination of the tower of Pisa as 85.95°.
Given that,
in Italy the leaning Tower of Pisa currently leans at 13 ft. off the vertical. the tower is 183 ft tall. what is the angle of inclination is to be determiend.
These are the equation that contains trigonometric operators such as sin, cos.. etc.. In algebraic operations.
Here,
base length is 13 ft,
Hypotenuse length of the tower = 183
According to the question,
Cosx = 13/ 183
x = 85.98°
Thus, the required inclination of the tower of pisa as 85.95°.
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If f(x)=x²-x³ + x² and g(x) = -x², where x # 0, what is (f/g)(x)?
Answers
The value of f(x)/g(x)=x-2 for f(x)=x²-x³ + x² and g(x) = -x² and where x # 0 and the definition of function defines "function, in mathematics, an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable)".
What is function?A function is a type of rule that produces one output for a single input. This is illustrated by the equation y=x². Any input for x results in a single output for y. Considering that x is the input value, we would say that y is a function of x. The property that every input is related to exactly one output defines a function as a relationship between a set of inputs and a set of allowable outputs. A mapping from A to B will only be a function if every element in set A has one end and only one image in set B. Let A & B be any two non-empty sets.
Here,
f(x)=2x²-x³
g(x)=-x²
f(x)/g(x)=(2x²-x³)/-x²
=x²(2-x)/-x²
f(x)/g(x)=x-2
The definition of function defines "function, in mathematics, an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable)". The value of f(x)/g(x)=x-2 for f(x)=x²-x³ + x² and g(x) = -x² and where x # 0.
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I need help with my mathWrite the slope-intercept form of the equation of each line
Answers
Answer:
y = -1
Explanation:
The slope-intercept form of the equation of a line has the form:
y = mx + b
Where m is the slope and b is the y-intercept.
The slope can be calculated as:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]Where (x1, y1) and (x2, y2) are the coordinates of two points in the line.
So, replacing (x1, y1) by (1, -1) and (x2, y2) by (2, -1), we get:
[tex]m=\frac{-1-(-1)}{2-1}=\frac{-1+1}{1}=\frac{0}{1}=0[/tex]On the other hand, the y-intercept is the point where the line crosses the y-axis. So, the y-intercept is -1.
Finally, the equation of the line in the slope-intercept form is:
y = 0x - 1
y = -1
So, the answer is y = -1
PLEASE HELP ASAP!!!!!!!!!!!!!!!!!!!!!!!!!
1. The quadratic function f(x) has roots of −4 and 2 and point (1, −5) lies on f(x). What is the equation of f(x)?
f(x) = (x − 2)(x + 4)
f(x) = (x − 2)(x − 4)
f(x) = 4(x − 2)(x + 4)
f(x) = 4(x − 2)(x − 4)
2. What is the standard form of the equation of a quadratic function with roots of 2 and −5 that passes through (1, −3)?
y = −0.5x2 + 1.5x − 5
y = −0.5x2 + 1.5x + 5
y = 0.5x2 + 1.5x − 5
y = 0.5x2 + 1.5x + 5
Answers
Answer: For 1 it is A - f(x)=(x-2)(x+4) and for 2 it is C - y = 0.5x^2 + 1.5x − 5
Step-by-step explanation:
Just use Desmos
graph of this equation x=3/5y
Answers
Step by step
Solve
3/5y = 1x
Divide both sides by 3/5 to isolate y
When you divide by a fraction, flip your fraction and multiply
3/5 * 5/3 y = 5/3 * 1x
y = 5/3x
There is no y intercept so your line passes through (0,0)
Your slope is 5/3, so from zero, you plot your point at rise 5 run 3, or up 5 and right 3, or x y pair ( 3, 5) and (0, 0)
17. A container is partially filled with 12 liters of whole milk containing 4% butterfat. How
much 1% milk must be added to get a mixture that is 2% butterfat? Construct a table,
then solve.
Answers
Step-by-step explanation:
a table ? why? what kind ?
it is relatively simple to solve :
x liters of 1% had to be mixed with 12 liters of 4% to get 12+x liters of 2%
x×0.01 + 12×0.04 = (12+x)×0.02 = 12×0.02 + x×0.02
12×0.02 = x×0.01
x = 12×0.02/0.01 = 12×2 = 24 liters
so, 24 liters of 1% had to be added to the 12 liters of 4% to get a 2% mixture (12 + 24 = 36 liters).
What is 4325 + 970 step by step explanation pls
Answers
you write out 4325 then put 970 below it,
4325
+970
5 plus 0 is 5, 7 plus 2 is 9, 9 plus 3 is 12 so put the 2 and carry the one on top of the 4, 4 plus the one we just carried over is 5
5295.
1/2 n + 3/4 n = 1/2
Solve for n =
Answers
Answer:
n=2/5
Step-by-step explanation:
Please look at the image below! :D
Answer:
[tex]\frac{2}{5}[/tex]
Step-by-step explanation:
[tex]\frac{1}{2}[/tex] n + [tex]\frac{3}{4}[/tex] n = [tex]\frac{1}{2}[/tex] [tex]\frac{1}{2}[/tex] means the same as [tex]\frac{2}{4}[/tex]
[tex]\frac{2}{4}[/tex] n + [tex]\frac{3}{4}[/tex] n = [tex]\frac{1}{2}[/tex]
[tex]\frac{5}{4}[/tex] n = [tex]\frac{1}{2}[/tex] multiply each side by [tex]\frac{4}{5}[/tex]
[tex](\frac{4}{5})[/tex][tex]\frac{5}{4}[/tex] n = [tex](\frac{4}{5})[/tex][tex]\frac{1}{2}[/tex]
n = [tex]\frac{4}{10}[/tex] = [tex]\frac{2}{5}[/tex]
(3x³ - 8x² + 16x - 1) ÷ (x − 1) answer ?
Answers
Answer:
[tex]= \frac{-125x^3-1}{x-1}[/tex]
find the area of this shape. 100pts
Answers
Answer:
A = 540 m²
Step-by-step explanation:
consider the shape split into 3 rectangles
the length is divided into 3 congruent sections
single dash = 30 m ÷ 3 = 10 m
the width is divided into 3 congruent sections
double dash = 27 m ÷ 3 = 9 m
then area (A) is the total of the 3 rectangular areas
A of left rectangle = 10 × 9 = 90 m²
A of middle rectangle = 10 × (9 + 9) = 10 × 18 = 180 m²
A of right rectangle = 10 × 27 = 270 m²
total area = 90 + 180 + 270 = 540 m²
Write a linear equation to represent the given problem and then solve the problem.
The perimeter of a rectangle is 150 cm. The length is 15 cm greater than the width. Find the dimensions.
Perimeter = 2 x Length + 2 x Width
Answers
w=L+15
p=(L+w)
150cm=L+L+15
150cm=2L+15
2L=150cm-15
2L=135cm
2L÷2=135cm÷2
L=67.5
w=67.5+15
w=82.5
Lines a and b are parallel. Line c is perpendicular to line a. Must it also be perpendicular to line b? Explain your thinking.
Answers
Line c is also perpendicular to line a.
Suppose that c and b are perpendicular. This implies that:
option 1) b and a are the same line or,
option 2) b is parallel to a
Since we know that a and b are different lines, hence, the option 2 is the correct.
derek enjoys going to the movies. he budgets a month for movies. admissions for one movie cost 7.25. how many movies can he see in one month and stay within budget
Answers
Derek can watch a maximum of (M/7.25) number of movies, where $M represents his budget for movie.
What is an inequality?In mathematics, an inequality is a relation which makes a non-equal comparison between two numbers or other mathematical expressions. There are two types of inequalities namely strict and slack inequalities.
Given is Derek who enjoys going to the movies. He budgets a month for movies and admissions for one movie cost $7.25.
Assume that the budget for movies is $M.
The cost of admission in one movie = $7.25
Suppose that Derek can watch [x] number of movies. Then, the given inequality will represent the number of movies Derek can watch -
7.25x ≤ M
x ≤ (M/7.25)
Therefore, Derek can watch a maximum of (M/7.25) number of movies, where $M represents his budget for movie.
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in a certain school district in a large metropolitan area, the sat scores over that past five years are normally distributed with a mean of 1468. furthermore, p 20 p20 is 1216. what is the p 98 p98 score for this population?
Answers
Using the normal distribution, the 98th percentile of the distribution of scores is of 2084.
Normal Probability DistributionThe 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 given 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 calculated 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 of the scores is given as follows:
[tex]\mu = 1468´[/tex]
The 20th percentile is of 1216, meaning that when X = 1216, Z = -0.84, hence the standard deviation is calculated as follows:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]-0.84 = \frac{1216 - 1468}{\sigma}[/tex]
[tex]0.84\sigma = 252[/tex]
[tex]\sigma = \frac{252}{0.84}[/tex]
[tex]\sigma = 300[/tex]
The 98th percentile is X when Z = 2.054, hence it is calculated as follows:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
2.054 = (X - 1468)/300
X - 1468 = 300 x 2.054
X = 2084.
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What is 2c - 5 = 15? Step by step please!!!
Answers
Answer:
c=10
Step-by-step explanation:
2c-5= 15
+5 +5
2c=20
/2 /2
c=10
Hello!
The solution to the problem 2c - 5 = 15 is
c = 10
Step-by-step explanation:
The first step is to add 5 to both sides of the equation.
2c - 5 = 15
2c - 5 + 5 = 15 + 5
The second step is to simplify by adding the numbers.
2c - 5 + 5 = 15 + 5
2c = 20
The third step is to divide both sides of the equation by the same factor.
2c = 20
2c ÷ 2 = 20 ÷ 2
The fourth step is to simply by canceling out the numbers which are present in both the denominator and numerator, then divide.
2c ÷ 2 = 20 ÷ 2
c = 10
Hope this helped!
Complete the ratio table.
13 11
22
52 44
55
91 77
Answers
The complete table using ratios is:
13, 39, 52, 72, and 91. What is the ratio?An ordered pair of numbers a and b, represented as a / b, is a ratio if b is not equal to 0. A proportion is an equation that sets two ratios at the same value.For instance, you could express the ratio as follows: 1: 3 if there is 1 boy and 3 girls (for every one boy there are 3 girls) There are 1 in 4 boys and 3 in 4 girls.In mathematics, a ratio shows how frequently one number appears in another.For instance, if a dish of the fruit contains eight oranges and six lemons, the ratio of oranges to lemons is eight to six.In, the column we can notice the pattern of (×2):
11×2 = 2222×2 = 44Now calculate similarly:
This is a ratio method 13, 39, 52, 72, and 91.Therefore, the complete table using ratios is:
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Gabrielle and Joni each wrote a fraction equivalent to 60/105 using the
greatest common factor. Gabrielle says the equivalent fraction is 12/21
Joni says the equivalent fraction is 4/7. Who is correct? Explain. Use the
GCF of the numerator and denominator of 60/105 to justify your answer.
Answers
Gabrielle is the correct one.
What are greatest common factor?The largest positive integer m that divides both x and y is the GCF of two or more non-zero integers, x, and y. The GCF stands for the greatest common factor. Here, greatest might be changed to highest, and factor to divisor. Therefore, the greatest common factor is often referred to as the highest common divisor )(HCD), highest common factor (HCF), or greatest common divisor (GCD.
Fractions, which are frequently employed in daily life, are almost always utilized with GCF. Finding the GCF of the denominator and numerator will allow you to obtain the necessary reduced form for simplifying a fraction or ratio. The greatest number that can divide two numbers x and y is their GCF.
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our football team has members, of which only are strong enough to play offensive lineman, while all other positions can be played by anyone. in how many ways can we choose a starting lineup consisting of a quarterback, a running back, an offensive lineman, and a wide receiver?
Answers
By using Permutation, the total number of ways in which we can choose a starting lineup consisting of a quarterback, a running back, an offensive lineman, and a wide receiver is 1512.
Permutation is defined as the arrangement of items in a specific or a particular order.
Since there are 3 choices for the position of offensive lineman, and for the next position there are 9 choices, similarly 8 choices for the next position and 7 choices remain for the last position.
So we get, 3x9x8x7 =1512, by the concept of Permutation.
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13 FUNDRAISER The Cougar Pep Squad wants to sell T-shirts in the bookstore for
the spring dance. The cost in dollars to order T-shirts in their school colors is
represented by the equation C = 2t + 3.
a. Make a table of values that represents this relationship.
b. Rewrite the equation in function notation.
c. Graph the function.
d. Describe the relationship between the number of T-shirts and the cost.
Answers
Answer:
See attached worksheet.
Step-by-step explanation:
See attached worksheet for the table and graph.
I assume that "functation notation: simply means using x and y:
y = 2x + 3
The relationship between the number of T-shirts and cost is defined by y = 2t + 3, where:
y is the total cost,
x is the number of t-shirts,
the 2 is the cost for 1 t-shirt ($/t-shirt), and
3 is a one=time charge of $3 for each order.
The graph (attached) shows a straight line with a y-intercept of 3, the initial order fee. It is linear since the cost of a t-shirt remains the same egardless of order size.
Use your number sense to find the values for x and y that satisfy the equations.-6x = -30
Answers
x = 5
Explanations:Given the equation shown:
[tex]-6x=-30[/tex]To get the value of "x", we will divide both sides by -6 to have:
[tex]\begin{gathered} \frac{\cancel{-6}x}{\cancel{-6}}=\frac{\cancel{-30}^5}{\cancel{-6}} \\ x=5 \end{gathered}[/tex]Hence the value of x that satisfies the equation is 5
if the expected frequencies rule for chi-square had been violated by the data, which categories could be combined together in a meaningful way to increase the expected frequencies?
Answers
If the chi-square test's expected frequencies rule is broken, either the row or the column is combined to provide a higher frequency that can be used to run the independence test.
Generally speaking, if more than 20% of the anticipated frequencies have a value of less than 5, Chi-Square should not be used (it does not matter what the observed frequencies are).
Both the chi-square test and Fisher's exact test are inappropriate if the sampled values' independence is broken. This presumption will be broken if the same subject results in more than one observation in the contingency table.
There are distinct assumptions for each non-parametric test as well. The data in the cells should represent frequencies or counts of cases rather than percentages or other data transformations, according to the Chi-presumptions. square's The variables' levels are mutually exclusive.
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What is a degree of a monomial and how do you find it? Like for example, how do you find the degree of the monomial x^2?
Answers
The degree of a monomial is the power of the variable in the monomial
What is a degree of a monomial?
The degree of a monomial is defined as the highest power of the variable term in the monomial
How to find the degree of a monomial?As a general rule, a monomial has only one term
An instance of a monomial is
ax^n
Using the definition above, the degree of the monomial is n
Simlarly, the degree of x^2 is 2
This is because 2 is the power of the variable term
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The ice cream shop sells cones for two dollars and sundaes for three dollars. Rachel makes a table to compare the cost of the ice cream treats. Part A: complete the pattern on the table for the cost of 0, 1, 2, and 3 ice cream treats. Then write the ordered pair for each row.
Answers
Given:
The cost of the cone is $2.
The cost of sundaes is $3.
Required:
Cost of cone and sundaes for different values.
The table for the data is:
Cost of ice-cream cone cost of ice-cream sundaes ordered pair
0 0 (0,0)
2 3 (2,3)
4 6 (4,6)
6 9 (6,9)
Hence, the missing values of the table is obtained.
Nicholas was the lucky journalist assigned to cover the Best Beard Competition. He recorded the contestants' beard colors in his notepad. Nicholas also noted if the contestants were signed up for the mustache competition later in the day. Only in the beard competition Also in the mustache competition Red beard 2 5 Grey beard 2 06 2 What is the probability that a randomly selected contestant has a red beard or is only in the beard competition? Sm out Simplify any fractions
Answers
Sample space n(s)=2+2+5+7=16
Let P(E) be the probability of red beard or is only in the beard competition:
Total number of red beard=2+5=7
P(red beard)=2/7
Lee and Sandy work at the same factory. Lee earns $17 per hour, and Sandy earns $20 per hour. Factory manager announces that all the workers' wages will go up by $1.50 per hour, starting next month.What will be the percent increase in Lee's hourly wage, rounded to one decimal place?
Answers
Is the ordered pair a solution of the equation?
4x + 5y = -1; (1,-1)
a. yes
b. no
Answers
Answer:
a. Yes
Step-by-step explanation:
If you plug the numbers in, 1 is x and -1 is y. The equation would look something like this:
4-5=-1
Now, do 4-5
4-5=-1
-1=-1
The answer would be a, yes.
Hope this helps! :D
Identify the term that completes the equation.
Answers
Based on the right triangle altitude theorem, the term that completes the equation is: a. YZ.
What is the Right Triangle Altitude Theorem?The right triangle altitude theorem state that when an altitude is drawn to from the vertex of a right triangle to intersect the opposite side perpendicularly, the length of the altitude would be equal to the geometric mean of the line segments that are formed by the altitude on the right triangle's hypotenuse.
In other words, the square of the length of the altitude equals the product of the line segments formed, according to the right triangle altitude theorem.
XZ = altitude
WY = hypotenuse
WZ and YZ are the line segments formed.
Therefore, the equation would be:
XZ² = (WZ)(YZ) [right triangle altitude theorem]
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