Find the area of the figure. (Sides meet at right angles.)
7 in
2 in
5 in
8 in
4 in
5 in
2 in
7 in
Answer:
36
Step-by-step explanation:
A parabola has an axis of symmetry at x = 5/12. The distance between its roots is 13/6. What is the equation of the parabola?
Answer:
The axis of symmetry of a parabola is the line that divides the parabola into two mirror images. This line always passes through the vertex of the parabola. For a parabola with an axis of symmetry at x = 5/12, the vertex of the parabola is at the point (5/12, 0).
The distance between the roots of a parabola is the distance between the x-coordinates of the two points where the parabola crosses the x-axis. In this case, the distance between the roots is 13/6.
To find the equation of the parabola, we can use the vertex form of the equation, which is given by y = a(x - h)^2 + k, where (h, k) is the coordinates of the vertex and a is a constant. In this case, the coordinates of the vertex are (5/12, 0) and the constant a can be determined using the distance between the roots.
To find a, we can use the fact that the distance between the roots of a parabola is equal to the square root of the product of the coefficients of the quadratic terms in the equation. In the vertex form, the coefficient of the x^2 term is a, so we can set up the following equation to find a:
(13/6)^2 = a * (5/12)^2
Solving for a, we find that a = -1/3.
Therefore, the equation of the parabola is y = -1/3(x - 5/12)^2.
In two or more complete sentences, explain how to use ordered pairs of points in f(x) = 2x + 5 and g(x)= x-5/2 to determine if f(x) and g(x) are inverses of each other. PLEASE EXPLAIN WITH WORDS IN TWO SENTENCES I NEED HELP ASAP
Answer:
See below.
Step-by-step explanation:
The given functions f(x) and g(x) are linear functions. Therefore, their inverses are a reflection about the line y = x.
The mapping rule for reflecting a point about the line y = x is:
(x, y) → (y, x)To determine if f(x) and g(x) are inverses of each other:
Input the x-value of the ordered pair into one function.Input the y-value of the ordered pair as the x-value of the other function.If the y-value of one function equals the x-value of the other function (and the x-value of one function equals the y-value of the other function), the functions are inverses of each other.
Given functions:
[tex]\begin{cases}f(x) = 2x+5\\\\g(x)=\dfrac{x-5}{2} \end{cases}[/tex]
Ordered pair: (2, 9)
Substitute x = 2 into f(x):
[tex]\implies f(2)=2(2)+5=9[/tex]
Substitute x = 9 into g(x):
[tex]\implies g(9)=\dfrac{9-5}{2}=2[/tex]
Therefore, the functions are inverses of each other since the x-value of function f equals the y-value of function g, and the y-value of function f equals the x-value of function g.
Determine whether y = -2x² - 3 is a function.
Answer:yes
Step-by-step explanation:
Please give an answer, and thinking. Thank you.
Answer:
see explanation
Step-by-step explanation:
- 1x + 4y = 12 , that is
- x + 4y = 12 ( add x to both sides )
4y = 12 + x ( divide each term by 4 )
y = 3 + [tex]\frac{1}{4}[/tex] x
Sarah made a floral arrangement with 60% roses. If there were a total of 25 flowers in the arrangement, how many roses?
Answer:
Step-by-step explanation:
turn percentage into decimal :
60/100 = 0.6
Then times it by how many flowers there are :
0.6×25 = 15
And your answer should be 15.
Two tailors, Zoe and Wanda, sit down to do some embroidery. Zoe can embroider 2 shirts per hour, and Wanda can get through 6 shirts per hour. In addition, the tailors had previously finished some shirts. Zoe has already completed 14 shirts, and Wanda has completed 6 shirts. Zoe and Wanda decide to take a break when they have finished the same total number of shirts. How long will that take? How many shirts, in total, will each tailor have finished?
After 2 hours, Zoe and Wanda will complete the same total number of shirts.
Each tailor will finish 18 shirts.
What is linear equation?
An algebraic equation of the form y=mx+b is referred to as a linear equation. m is the slope, and b is the y-intercept, and all that is involved is a constant and a first-order (linear) term. The variables in the preceding equation are y and x, and it is occasionally referred to as a "linear equation of two variables."
Given that,
Zoe can embroider 2 shirts per hour, and Wanda can get through 6 shirts per hour. Zoe has already completed 14 shirts, and Wanda has completed 6 shirts.
Assume that after x hours they have finished the same total number of shirts.
The number of shirts that Zoe finished is
Z(x) = 14 + 2x ....(i)
The number of shirts that Wanda finished is
W(x) = 6 + 6x ...(ii)
When they make same number of shirts, then Z(x) = W(x)
14 + 2x = 6 + 6x
6 + 6x = 14 + 2x
Subtract 2x from both sides:
6x - 2x = 14 - 6
4x = 8
Divide both sides by 4
x = 8/4
x = 2.
Putting x = 2 in Z(x) = 14 + 2x:
Z(2) = 14 + (2×2)
Z(2) = 18
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A school is painting its logo in the shape of a triangle in the middle of its sports field. The school wants the height of the triangle to be feet. The area of the logo must be at most 14 square feet. (The school doesn't want to buy more paint.) Write an inequality that describes the possible base lengths (in feet) of the triangle.
Use b for the base length of the triangular logo.
The inequality that describes the base length of the triangle is b ≤ 28/h
How to determine the inequality that describes the base length of the triangle?From the question, we have the following parameters that can be used in our computation:
Base = bHeight = hArea = At most 14 square feetThe area of a triangle can be calculated using the following formula
Area = 1/2 * Base * Height
Substitute the known values in the above equation, so, we have the following representation
Area = 1/2 * b * h
Evaluate the products
Area = 1/2bh
Recall that
Area = At most 14 square feet
This means that
Area ≤ 14
So, we have
1/2bh ≤ 14
Multiply through by 2
bh ≤ 28
Divide both sides by h
b ≤ 28/h
Hence, the inequality is b ≤ 28/h
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Which number line models the expression 1/8-(-3/4) ?
Answer: 7/8
Step-by-step explanation:
kelsey is welding 3 metal rods to make a triangle. If the lengths of two rods are 15 in. and 22in., what are the possible lengths of a third rod?
The required length of the third side should be less than the sum of the other two sides or less than 37 in.
As mentioned, Kelsey is welding 3 metal rods to make a triangle. If the lengths of two rods are 15 in. and 22in.,
What is inequality?Inequality can be defined as the relation of the equation containing the symbol of ( ≤, ≥, <, >) instead of the equal sign in an equation.
Here,
Let the length of the third side,
The property of the triangle states that the sum of the two sides of a triangle is always greater than the length of the third side.
So
x < 15 + 22
x < 37
Thus, the required length of the third side should be less than the sum of the other two sides or less than 37.
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Use the normal distribution to the right to answer the questions. (a) What percent of the scores are less than 19? (b) Out of 1500 randomly selected scores, about how many would be expected to be greater than 21? Standardized Test Composite Scores 1921Score mu equals 19.6 sigma equals 5.3 mu x A graph titled "Standardized Test Composite Scores" has a horizontal x-axis labeled "Score" from about 1 to 38 with tick marks at 19 and 21. A normal curve labeled μ = 21.2 σ = 5.4 is centered above the x-axis at 21.2. A vertical line segment labeled μ extends from the normal curve to the x-axis at 21.2. (a) The percent of scores that are less than 19 is nothing %. (Round to two decimal places as needed.) (b) About nothing scores would be expected to be greater than 21. (Round to the nearest whole number as needed.)
a) The percentage of scores that are less than 19 is of: 34.09%.
b) The amount out of the 1500 scores that would be greater than 21 is of: 774.
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 of the scores in this problem are given as follows:
[tex]\mu = 21.2, \sigma = 5.4[/tex]
The proportion of scores that are less than 19 is the p-value of Z when X = 19, hence:
Z = (19 - 21.2)/5.4
Z = -0.41.
Z = -0.41 has a p-value of 0.3409.
Hence the percentage is of 34.09%.
The proportion of scores that are greater than 21 is one subtracted by the p-value of Z when X = 21, hence:
Z = (21 - 21.2)/5.4
Z = -0.04
Z = -0.04 has a p-value of 0.484.
1 - 0.484 = 0.516.
Hence the amount out of the 1500 scores is given as follows:
0.516 x 1500 = 774 scores.
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POSSIBLE POINTS: 25
Ashanti has two bank accounts. Account A has $800, and she withdraws $50 per month for food.
Account B has $100, and she adds $30 per month from babysitting. When does account A and B have
the same amount of money in it?
Matthew and some friends are going to a concert. They hire a car service for $75 to drive them to a
restaurant for dinner and then the concert. They divide the $60 cost of the dinner equally. However, since
Matthew's dad provided concert tickets for the group, the friends agree that Matthew doesn't have to help pay
for the car service. The friends divide this cost equally among themselves. If each friend spends a total of $25,
how many friends went to the concert with Matthew?
n represents the number of friends, there must have been 2 friends with Matthew at the concert.
What is the arithmetic operation?
Arithmetic operations is a branch of mathematics, that involves the study of numbers, operation of numbers that are useful in all the other branches of mathematics. It basically comprises operations such as Addition, Subtraction, Multiplication and Division.
Let's call the number of friends n. The cost of the car service for the friends is 75 - 25 = 50 dollars. Since this cost is divided equally among the friends, each friend pays 50/n dollars.
The total cost for each friend, including the cost of the car service and the cost of dinner, is 25 dollars. Therefore, the cost of dinner for each friend is 25 - 50/n dollars.
Since the cost of dinner was divided equally among the friends, each friend paid 60/n dollars for dinner. Therefore, 25 - 50/n = 60/n.
Solving this equation for n, we get:
25 - 50/n = 60/n
50/n - 60/n = -25
10/n = 25
n = 2.5
Hence, n represents the number of friends, there must have been 2 friends with Matthew at the concert.
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First person to answer gets a Brainilest!!!Solve this math questions of the picture.
Answer: S wanted points I
Step-by-step explanation:
Select the correct answer.
Which list orders the angles of triangle ABC from smallest to largest measure?
B
OA.
B.
O C.
OD.
130
180
ZA, ZC, ZB
ZC, ZA, ZB
ZB, ZC, ZA
ZA, 2B, 2C
120
Answer:
<B, <C, <A
Step-by-step explanation:
The order from smallest to largest angle is the same as the order from shortest to longest opposite side.
Sides from shortest to longest:
120, 130, 180
Angles from smallest to largest:
<B, <C, <A
Consider the two expressions 6x^3 + 9x^2 + 4x + 7 and 3x^2 + 2 + 6x^3 + 6x^2 + 4x + 5.
a) Show that the two expressions represent equal numbers when x=10.
b) Explain why these two expressions do not represent equal numbers when x = -3/2.
c) Show that these two expressions represent equal numbers for all x other than x = -3/2.
When x = 10 the equations are equal and when x gets any value the two equations are equal.
What is equation ?
An equation is a mathematical statement that proves two mathematical expressions are equal in algebra, and this is how it is most commonly used. In the equation 3x + 5 = 14, for instance, the two expressions 3x + 5 and 14 are separated by the symbol "equal."
The equals sign is a part of mathematical expressions known as equations. Often, algebra is used in equations. When a calculation requires an exact number but you don't know it, algebra is utilized.
When x = 10 the equation becomes
6x³ + 9x² + 4x + 7
6(10)³ + 9(10)² + 4(10) + 7
= 6000 + 900 + 40 + 7
= 6947
6x³ + 3x² + 6x² + 4x + 5 + 2
= 6x³ + 9x² + 4x + 7
= 6(10)³ + 9(10)² + 4(10) + 7
= 6000 + 900 + 40 + 7
= 6947
Both the equations are equal when x = 10
When x = -3/2 the equation becomes
6x³ + 9x² + 4x + 7
6(-3/2)³ + 9(-3/2)² + 4(-3/2) + 7
= -20.25 + 20.25 + 6 + 7
= 13
6x³ + 3x² + 6x² + 4x + 5 + 2
= 6x³ + 9x² + 4x + 7
= 6(-3/2)³ + 9(-3/2)² + 4(-3/2) + 7
= -20.25 + 20.25 + 6 + 7
= 13
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Find the value of x in this equation
Answer:
x = 4
Step-by-step explanation:
7x = 3x + 16
7x - 3x = 16
4x = 16
4/4 x = 16/4
x = 4
use implicit differeniation to find dy/dx x^2+xy+y^2+1=0
The differentiation of the given function x² + xy + y² + 1 = 0 will be 2x + y + dy/dx(x + 2y) = 0.
What is the rate of change?The rate of change is the change of a quantity over 1 unit of another quantity.
Most of the time the rate of change is the change with respect to time.
As per the given,
x² + xy + y² + 1 = 0
Take the first derivative on both sides with respect to x as,
d/dx(x² + xy + y² + 1) = d/dx(0)
2x + xdy/dx + ydx/dx + 2ydy/dx + 0 = 0
2x + x(dy/dx) + y + 2y (dy/dx) = 0
2x + y + dy/dx(x + 2y) = 0
Hence "The provided function x2 + xy + y2 + 1 = 0 will be differentiated as 2x + y + dy/dx(x + 2y) = 0.".
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What is the geometric mean of 7 and 12? 09.5
02/21
04√21
Answer:
9.16
Step-by-step explanation:
formula for Geometric mean is
b = √a × √c
a = 7 and c = 12
b = √ 7×12
b = √84
b = 9.16
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Consider the following regression model: yi = B0 +B 1xi + ui. If the first four Gauss-Markov assumptions hold true, and the error term contains heteroskedasticity, then _____.a. Var(ui|xi) = 0b. Var(ui|xi) = 1c. Var(ui|xi) = Θi2d. Var(ui|xi) = Θc. Var(ui|xi) = Θi2
If the first two Gauss-Markov assumptions are met and heteroskedasticity exists in the error term, Var(ui|xi) = i2.
What is an example of heteroscedasticity?Examples. When there is a significant disparity in the magnitude of the observations, heteroscedasticity frequently develops. An old-fashioned illustration of heteroscedasticity is the relationship between income and food expenses. The variability of eating habits will rise as income does as well.
Does heteroskedasticity make a difference?Because normal regression model (OLS) regression presumes that all royalties are taken from a population with constant variance, heteroscedasticity is a concern (homoscedasticity). The particles ought to have a standard deviation in order to meet the plugs and be capable of relying on the results.
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One number is two less than a second number. Twice the second number is nine less than three times the first find the two numbers.
Answer:
13 and 15
Step-by-step explanation:
We set up equations.
X=Y-2
2Y=3X-9
We change X=Y-2 into Y=X+2.
Substituting for Y, we get 2Y=2X+4=3X-9
We now solve for x.
2X+4=3X-9 |-2X
4=X-9 |+9
13=X.
X=13
Substituting for Y, we get that Y =15 from the equation Y=X+2.
So, X=13 and Y=15
1 Select the correct answer. A group of 8 friends (5 girls and 3 boys) plans to watch a movie, but they have only 5 tickets. How many different combinations of 5 friends could possibly receive the tickets? A. 13 B. 40 C. 56 D. 64 Reset Next
The different combinations of 5 friends could possibly receive the tickets are 56.
What is combination?
A combination is a choice made from a set of distinct items in mathematics where the order of the choices is irrelevant.
The definition of a combination is "An arrangement of objects where the order in which the objects are chosen does not matter." A combination is a "selection of things" where the importance of the order of the things is negligible.
Given:
A group of 8 friends (5 girls and 3 boys) plans to watch a movie.
We have to find the different combinations of 5 friends could possibly receive the tickets.
Here there are total 8 friends.
We have to select 5 from 8 in 8C5 ways.
[tex]8_C_5 = \frac{8!}{5!*(8-5)!} \\8_C_5 = \frac{8!}{5!*3!} \\8_C_5 = \frac{6*7*8}{1*2*3}\\ 8_C_5 = 56[/tex]
Hence, the different combinations of 5 friends could possibly receive the tickets are 56.
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Convert the quadratic function from vertex form to standard form: g(x)= 1/2 (x+2)^2-8
Answer:
y = 1/2x² - 2x - 6
One number is 5 more than twice another and their sum is 23. Find the numbers.
The value of the numbers 'x' and 'y' will be 6 and 17, respectively.
What is the solution to the equation?The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.
One number is 5 more than twice another and their sum is 23.
Let the two numbers be 'x' and 'y'. Then the equations are given as,
y = 2x + 5 ...1
x + y = 23 ...2
From equations 1 and 2, then we have
x + 2x + 5 = 23
3x + 5 = 23
3x = 23 - 5
3x = 18
x = 6
Then the value of the variable 'y' will be given as,
6 + y = 23
y = 23 - 6
y = 17
The value of the numbers 'x' and 'y' will be 6 and 17, respectively.
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Ron got a cell phone rate of C(a)=0.22+0.10a. Graph the cost per minute. How much will a five minute call cost?
The cost of the five-minute call will be equal to $0.72.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that Ron got a cell phone rate of C(a)=0.22+0.10a. The cost of a five-minute call will be calculated as,
Cost = 0.22+0.10a
Cost = 0.22 + ( 5 x 0.10 )
Cost = 0.22 + 0.50
Cost = $0.72
The five-minute call will cost $0.72.
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Find three integer or decimal solutions to the following equation, and then graph the solution set.
5x+4y=20
Answer:
To find three integer or decimal solutions to the equation 5x + 4y = 20, we can first divide both sides of the equation by the GCF of the coefficients, which is 1. This gives us the equation 5x + 4y = 20/1, which can be rewritten as 5x + 4y = 20. We can then use the substitution method to solve for x in terms of y, by setting 4y = 20 - 5x and solving for x. This gives us x = (20 - 4y) / 5. Substituting this expression for x into the original equation, we get 5((20 - 4y) / 5) + 4y = 20, which simplifies to 20 - 4y + 4y = 20, or 20 = 20. This means that any value of y that satisfies the equation will also satisfy the original equation.
For example, if we choose y = 3, then x = (20 - 4 * 3) / 5 = 2, and the solution (x, y) = (2, 3) satisfies the equation 5x + 4y = 20. Similarly, if we choose y = 0, then x = (20 - 4 * 0) / 5 = 4, and the solution (x, y) = (4, 0) satisfies the equation. Finally, if we choose y = -1, then x = (20 - 4 * -1) / 5 = 5, and the solution (x, y) = (5, -1) satisfies the equation.
The solution set for the equation 5x + 4y = 20 is the set of all ordered pairs (x, y) that satisfy the equation. The three solutions we found are (2, 3), (4, 0), and (5, -1), and these solutions can be plotted on a coordinate grid to show the solution set. The graph of the solution set is a line that passes through the points (2, 3), (4, 0), and (5, -1).
Step-by-step explanation:
what is the slope of the line
Answer:
a) 9/5
Step-by-step explanation:
Formula we use,
→ Slope (m) = (y2 - y1)/(x2 - x1)
Now required slope will be,
→ m = (y2 - y1)/(x2 - x1)
→ m = (-16 - 2)/(-10 - 0)
→ m = (-18)/(-10)
→ m = 18/10
→ [ m = 9/5 ]
Hence, the slope is 9/5.
Reagan created a model of a rectangular flag.
Her model is 13 inches long.
It is a model of a flag that is 39 inches long.
How many times wider is the actual flag than Reagan's model?
The actual flag is
times wider than Reagan's model.
Actual Flag
39 inches
Reagan's
Model
13 inches
CLEAR
CHECK
The number of times that the actual flag is wider than the Reagan's model would be = 3 times.
What is rectangle?A rectangle is defined as a type of quadrilateral that has opposite sides that are parallel and equal to each other and all four angles are right angles.
The actual length of the rectangular flag = 39 inches long.
The length of Reagan's model = 13 inches.
To find the number of times wider than the actual flag the model is, use the formula:
= Length of actual flag / Length of model
= 39/13 = 3.
Therefore, the number of times that the actual flag is wider than the Reagan's model is 3 times.
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A = {red, blue, green, yellow, orange} B = {pink, blue, purple, yellow, green} Find A ⋂ B.
According to the given sets, A ⋂ B = {blue, green, yellow}.
What are sets?A set contains elements or members that can be mathematical objects of any kind, including numbers, symbols, points in space, lines, other geometric shapes, variables, or even other sets.
A set is a mathematical model for a collection of various things.
A ⋂ B:
A set called an intersection B has components that are found in both sets A and B.
The intersection of sets A and B is shown by the symbol, which is interpreted as "An intersection B" and written as A⋂B.
The set of components shared by all sets is the intersection of two or more sets.
So, we have:
A = {red, blue, green, yellow, orange}
B = {pink, blue, purple, yellow, green}
A ⋂ B which means common elements:
A ⋂ B = {blue, green, yellow}
Therefore, according to the given sets, A ⋂ B = {blue, green, yellow}.
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Unit rate reasoning down
In the unit rate between two units, the denominator is always one.
What is a unit rate?It is the quantity of an amount of something at a rate of one of another quantity.
In 2 hours, a man can walk for 6 miles
In 1 hour, a man will walk for 3 miles.
We have,
Unit rate is written in a fraction form where the denominator is always one.
Example:
6 miles in 3 minutes.
This can be written as,
6 miles = 3 minutes
Dividing 3 on both sides.
2 miles = 1 minute
= 2 miles per minute
Thus,
In the unit rate between two units, the denominator is always one.
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