Jaclyn has $160 saved and earns $40 each month in allowance. Pedro has $980 saved and writes a check for $20 a month to pay his cable bill and he writes a check for $42.50 each month to pay his phone bill. If they both save their entire allowances, how long will it take before Jaclyn and Pedro have saved the same amount of money?

Answer:

y = (4/5)x + 16

Point-slope form:

y - 12 = (4/5)(x + 5)

Step-by-step explanation:

slope = m; (-5, 12)

m = (4/5)    (x₁, y₁)

y - y₁ = m(x - x₁)

y - 12 = (4/5)(x - (-5))

y - 12 = (4/5)(x + 5)

y - 12 = (4/5)x + 4

  +12                +12

--------------------------

y = (4/5)x + 16

I hope this helps!

The scale factor of the dilation is the ratio of the lengths of the corresponding sides of the two triangles. Since triangle ABC and triangle A'B'C' both have side lengths of AB, BC, and CA, the scale factor is 1.

1. Calculate the length of the sides of triangle ABC:

AB = length of side AB of triangle ABC

BC = length of side BC of triangle ABC

CA = length of side CA of triangle ABC

2. Calculate the length of the sides of triangle A'B'C':

A'B' = length of side A'B' of triangle A'B'C'

B'C' = length of side B'C' of triangle A'B'C'

C'A' = length of side C'A' of triangle A'B'C'

3. Calculate the scale factor of the dilation:

Scale factor = (AB/A'B') x (BC/B'C') x (CA/C'A')

= (length of side AB of triangle ABC / length of side A'B' of triangle A'B'C')

x (length of side BC of triangle ABC / length of side B'C' of triangle A'B'C')

x (length of side CA of triangle ABC / length of side C'A' of triangle A'B'C')

= 1 x 1 x 1

= 1

Therefore, the scale factor of the dilation is 1.

Learn more about triangle here

https://brainly.com/question/2773823

#SPJ4

Answer:

(5,1)

Step-by-step explanation:

to fins the midpoint add both x points and divide by 2. then, both y points and divide by 2.

8+2/2 , 3-1/2

10/2 , 2/2

5 , 1

hope this helps! brainliest please?

Answer:

The length of the diagonal, d is approximately 24.49 cm

Step-by-step explanation:

The question asks to find the length of the interior diagonal of a rectangular prism, also known as a cuboid;

The parameters of the prism are;

The height of the prism = 10 cm

The width of the prism = 10 cm

The length of the prim = 20 cm

The length of the given diagonal of the cuboid is found by Pythagoras's theorem from the height, 'h', of the cuboid and the diagonal of the base of the cuboid

Let 'l' represent the diagonal of the base of the cuboid, we have, by Pythagoras's theorem;

l² = ((20 cm)² + (10 cm)²) = 500 cm²

The length of the diagonal, 'd', by Pythagoras's theorem is given as follows;

d = √(l² + (²10 cm))

By plugging in the known value for 'l² = 500 cm²', we get;

d = √(500 cm² + (²10 cm)) = √(600 cm²) = 10·√6 cm

The length of the diagonal, d = 10·√6 cm ≈ 24.49 cm (by rounding to the nearest hundredth cm)

The inverse of a biconditional statement is not equivalent to the original statement. The inverse statement may have a different meaning or convey a different condition.

The inverse of a biconditional statement involves negating both the "if" and the "only if" parts of the statement. In this case, the inverse of the biconditional statement would be:Inverse of Statement 1: A figure is not a polygon if and only if not all of its sides are line segments.

Now, let's analyze the relationship between Statement 2 and its inverse.

Statement 2: A figure is not a polygon if and only if not all of its sides are line segments.

Inverse of Statement 2: A figure is not a polygon if and only if all of its sides are line segments.

The inverse of Statement 2 is not equivalent to Statement 1. In fact, the inverse of Statement 2 is a different statement altogether. It states that a figure is not a polygon if and only if all of its sides are line segments. This means that if all of the sides of a figure are line segments, then it is not considered a polygon.

In contrast, Statement 1 states that a figure is a polygon if and only if all of its sides are line segments. It affirms the condition for a figure to be considered a polygon, stating that if all of its sides are line segments, then it is indeed a polygon.

For more such question son inverse visit:

https://brainly.com/question/3831584

#SPJ8

(a) The firm is operating in the long run, and its supply function is determined by the profit maximization condition.

(b) The firm's input demand functions can be derived from the profit function, and their degree of homogeneity is 1/2. Changes in input prices will impact the firm's input demand.

(c) The market supply function can be derived by aggregating the supply functions of all 40 firms operating in the market.

(d) Given the market conditions and demand function, the total market supply can be calculated.

(a) The firm is operating in the long run because it has the flexibility to adjust its inputs and make decisions based on market conditions. The firm's supply function is determined by maximizing its profit, which is achieved by setting the marginal cost equal to the market price. In this case, the supply function for each firm can be derived by taking the derivative of the profit function with respect to the price of output (p).

(b) The input demand functions for the firm can be derived by maximizing the profit function with respect to each input price. The degree of homogeneity of the input demand functions can be determined by examining the exponents of the input prices. In this case, the degree of homogeneity is 1/2. Changes in the input prices will affect the firm's input demand as it adjusts its input quantities to maximize profit.

(c) The market supply function can be derived by aggregating the individual supply functions of all firms in the market. Since there are 40 identical firms, the market supply function can be obtained by multiplying the supply function of a single firm by the total number of firms (40).

(d) To determine the total market supply, we substitute the given market conditions and demand function into the market supply function. By solving for the market quantity at a given market price, we can calculate the total market supply.

In conclusion, the firm is operating in the long run, and its supply function is determined by profit maximization. The input demand functions have a degree of homogeneity of 1/2, and changes in input prices impact the firm's input demand. The market supply function is derived by aggregating the individual firm supply functions, and the total market supply can be calculated using the given market conditions and demand function.

Learn more about market supply here:

https://brainly.com/question/13486321

#SPJ11

The coefficient of X₂ suggests that for every one-unit increase in X₂, Y is expected to increase by 16 units, assuming X₁ remains constant. The high value of R (0.98) indicates a strong linear relationship between the independent variables (X₁ and X₂) and the dependent variable (Y).

a. The estimated coefficient of X₂ (16) represents the change in the dependent variable (Y) associated with a one-unit increase in the independent variable X₂ while holding all other variables constant.

In this case, for every one-unit increase in X₂, the predicted value of Y is expected to increase by 16 units, assuming X₁ remains constant.

b. A Goodness of Fit Coefficient, also known as R², measures the proportion of the total variation in the dependent variable (Y) that can be explained by the independent variables (X₁ and X₂ ) in the multiple linear regression model.

An R² value of 0.98 indicates that approximately 98% of the variability in the dependent variable can be explained by the independent variables included in the model. This suggests that the chosen independent variables (X₁ and X₂ ) have a strong linear relationship with the dependent variable (Y).

In conclusion, the estimated coefficient of X₂  in the multiple linear regression equation indicates the expected change in the dependent variable (Y) associated with a one-unit increase in X₂, while keeping X₁ constant.

Additionally, the high R² value of 0.98 suggests that the independent variables in the model (X₁ and X₂ ) explain a significant portion of the variability in the dependent variable (Y). Therefore, the model provides a good fit to the data and demonstrates a strong relationship between the independent variables and the dependent variable.

To know more about linear refer here:

https://brainly.com/question/29066440#

#SPJ11

Complete Question:

For the following estimated multiple linear regression equation, Y = 8 + 45X₁ + 16X₂

a. what is the interpretation of the estimated coefficient of X₂

b. if R² (Goodness of Fit Coefficient) is 0.98 in this estimated regression equation, what does that tell you?

Answer:

The distance between the bird houses are 10.26 feet

Step-by-step explanation:

The distance between the birdhouses is 10.26 feet.

A mathematical expression gets simpler when it is transformed into an equivalent, frequently shorter statement. One strategy for promoting uniformity in job effort, cost, and time is procedure simplification. It lessens diversity and variation that is harmful, unwanted, or unneeded.

Given, Penelope has a birdhouse that is 4 and 9/10 feet above the roof of her garage. She has a second birdhouse that is 5.36 feet below the roof of her garage. thus,

Distance between garage roof and birdhouse = 4.9 feet

Distance between garage roof and second birdhouse  = 5.36 feet

Since these birdhouses are in the opposite directions of the garage roof

Hence the total distance between them = 4.9 + 5.36

the total distance between birdhouses is 10.26 feet

Therefore, the Two birdhouses are 10.26 feet apart from each other.

Learn more about simplification here:

brainly.com/question/24242989

#SPJ2

Answer:

400 - 120 - 220 -175 -60 +50 = -125

Step-by-step explanation:

Answer:

\(A = x^{2} + x\)

Step-by-step explanation:

Area of a triangle = bh/2

Your base is 2x and the height is x + 1

So, A = (2x)(x + 1)/2

        A = \(x^{2} + x\)

The explicit definition of the given geometric sequence is a(n) = 909 (4/3)ⁿ⁻¹.

Given is a geometric sequence,

a(n) = 909, if n = 1

a(n) = 4/3 a(n-1) if n > 1

The explicit formula for a geometric sequence is,

a(n) = a(1) rⁿ⁻¹

Here a(1) is the first term and r is the common ratio.

Here, a(1) = 909

r = a(2) / a(1) = 4/3 × 909 / 909 = 4/3

Explicit formula is,

a(n) = 909 (4/3)ⁿ⁻¹

Hence the required definition is a(n) = 909 (4/3)ⁿ⁻¹.

Learn more about Explicit Formulas here :

https://brainly.com/question/15174001

#SPJ1

(a) False: Just because a matrix is diagonalizable does not guarantee that it has an LU-decomposition. Diagonalizability relates to eigenvectors and eigenvalues, while LU-decomposition involves triangular matrices.

(b) True: If a real and symmetric matrix has distinct eigenvalues, then it is guaranteed to have an orthonormal basis of eigenvectors. This is a property of real symmetric matrices known as the Spectral Theorem.

(c) True: If a matrix is invertible, then it is also diagonalizable. In fact, any invertible matrix is diagonalizable.

(d) True: If a matrix is diagonalizable and the eigenvectors come from different eigenspaces, then they are mutually orthogonal. Eigenvectors corresponding to distinct eigenvalues are always orthogonal.

(e) False: The existence of an LU-decomposition does not imply diagonalizability. An LU-decomposition involves triangular matrices, while diagonalizability is related to eigenvectors and eigenvalues.

(f) True: If a matrix has distinct eigenvalues, then it is always diagonalizable. This is a property of matrices with distinct eigenvalues.

Learn more about Spectral Theorem here : brainly.com/question/31317199        

#SPJ11

Answer:

1/4x

Step-by-step explanation:

Answer: The answer for this is 9.45

Answer: (6, -31)

Explanation: See attachment

Answer: The appropriate hypotheses for this significance test are:

Null hypothesis (H0): The true mean travel time for all students who attend this school is equal to 20 minutes.

Alternative hypothesis (Ha): The true mean travel time for all students who attend this school is greater than 20 minutes.

The null hypothesis states that there is no difference between the claim (20 minutes) and the sample mean (22.4 minutes). The alternative hypothesis states that there is a difference and the sample mean is greater than the claim. The student will use the sample data and a chosen significance level (such as α = 0.05) to decide whether to reject or fail to reject the null hypothesis.

Step-by-step explanation:

From the given combination, there are 280 ways to select a three-course meal.

What is the combination?

Combinations are ways of choosing things from a collection when the order of the choices does not matter. The number of selections is denoted by \(^{n} C_{r}\) if you have to choose "r" items from "n" things.

Given, 7 appetizers, 10 entrees, and 4 desserts

To select a three-course meal, we will choose 1 item from each course.

i.e. 1 appetizer from 7 appetizers

AND

1 enter from 10 entrees

AND

1 dessert from 4 desserts

So, For appetizers, selections = \(^{7} C_{1}\)

For entrees, selections = \(^{10} C_{1}\)

For desserts, selections = \(^{4} C_{1}\)

Total possibilities =  \(^{7} C_{1}\) * \(^{10} C_{1}\)* \(^{4} C_{1}\) = 7*10*4 = 280

Hence, there are 280 ways to select a three-course meal.

To learn more about combination

https://brainly.com/question/28065038

#SPJ4

The correct answer is: All three functions have the same minimum.

To compare the functions and determine which one has the smallest minimum value, we need to evaluate the minimum points of each function.

Let's analyze each function:

1. f(x) = -5 sin(2x - π) + 2: This is a sinusoidal function with an amplitude of 5, a phase shift of π/2 to the right, and a vertical shift of 2 units upwards. The minimum value of this function occurs at the bottom of the sinusoidal curve.

2. g(x): This is a quadratic function that passes through the points (1, 2), (2, -2), and (3, 5). Since the function is a quadratic, it will have a vertex which represents the minimum or maximum point of the curve. To determine the vertex and the minimum value, we can use the vertex form of a quadratic function.

3. h(x): This function is given as a set of coordinates. Since the function is not explicitly defined, it's not possible to determine its exact behavior or minimum value without additional information.

Based on the information provided, we can compare f(x) and g(x) for their minimum values. To do so, we would need to find the vertex of the quadratic function g(x) using the given points. Without the specific quadratic equation, it is not possible to determine which function has the smallest minimum.

Therefore, the correct answer is: All three functions have the same minimum.

For more such questions on functions, click on:

https://brainly.com/question/11624077

#SPJ8

Answer:

Its 20

s

3

+

50

s

2

+

32

s

+

6

Step-by-step explanation:

Answer:

20\(s^{3}\) + 50\(s^{2}\) + 32s + 6

Step-by-step explanation:

(4s+2)(5s^2+10s+3)

=(4s+2)(5s^2+10s+3)

=(4s)(5s^2)+(4s)(10s)+(4s)(3)+(2)(5s^2)+(2)(10s)+(2)(3)

=20s^3+40s^2+12s+10s^2+20s+6

=20\(s^{3}\) + 50\(s^{2}\) + 32s + 6

The subgame perfect Nash equilibrium involves Player 1 receiving a piece that is no less than 1/4 of the original cake, Player 2 receiving a piece that is no less than 1/2 of the cake, and Player 3 receiving a piece that is no less than 1/4 of the cake. Player 2 obtains the largest piece at 1/2 of the cake, while Player 1 gets a share that is no less than 1/4 of the cake, which is larger than Player 3's share of the remaining cake.

The subgame perfect Nash equilibrium and complete strategies are as follows:

Learn more about Nash equilibrium:

brainly.com/question/29398344

#SPJ11

Answer:

20,000 is the length of the book with 20,000 pages.

Answer:

cool!!

Step-by-step explanation:

The question asks us to solve the following system of equations by elimination:

Solution

Answer

The solution to the system of equation is:

x = -8

y = 9

The measurement that is closest to the value of x, in centimeters, is given as follows:

14.3.

In this problem, we have a right triangle, in which the legs, which are the sides between the angle of 90º, are of 11.9 cm and 7.9 cm.

Then the hypotenuse x, which is the segment connecting both legs, is obtained using the Pythagorean Theorem.

The Pythagorean Theorem states that the measure of the hypotenuse squared is equals to the sum of the squares of the measures of each side.

Then the length of x is calculated as follows:

x² = 11.9² + 7.9²

x = square root of (11.9² + 7.9²)

x = 14.28.

Closest to 14.3, rounding to the nearest tenth, meaning that the third option is correct.  

We suppose that 11.9 cm and 7.9 cm are the measures of the legs.

More can be learned about the Pythagorean Theorem at https://brainly.com/question/28853425

#SPJ1

Answer:

(3,1)

Step-by-step explanation:

Answer:

Not Defined

Step-by-step explanation:

Anything divided by 0 is said to be infinity or not defined.

A function, C(x), to model the water used by the car wash on a shorter day will be (B) 3x³ + 4x² - 11x - 8.

To find a function, C(x), to model the water used by the car wash on a shorter day:

Given information -

Now the amount of water is cut from the total water usage so to find out the new model c(x) we need to subtract the decrease in water from the total water usage.

We are trying to find:

Therefore, a function, C(x), to model the water used by the car wash on a shorter day will be (B) 3x³ + 4x² - 11x - 8.

Know more about equations here:

https://brainly.com/question/2972832

#SPJ4

The correct question is given below:

The water usage at a car wash is modeled by the equation W(x) = 4x3 + 6x2 − 11x + 7, where W is the amount of water in cubic feet and x is the number of hours the car wash is open. The owners of the car wash want to cut back their water usage during a drought and decide to close the car wash early two days a week. The amount of decrease in water used is modeled by D(x) = x3 + 2x2 + 15, where D is the amount of water in cubic feet and x is time in hours.

Write a function, C(x), to model the water used by the car wash on a shorter day

Answer:

b. 64.2 ft^2

Step-by-step explanation:

area of parallelogram: A = bh = 10.7 x 6 = 64.2 ft^2

Answer: The answer should be 3 hours

Step-by-step explanation: 8+4=12, divide the sum by 36: 36÷12=3

She had worked 3 hours.