Four functions are given below. Perform the indicated compositions to determine which functions are inverse to each other. Be sure to simplify the results.
f(x)=16x+19
(x)=16x−19
h(x)=16x−1619
j(x)=16x+304

We are given that the quadratic function has the equation:

y = a(x + 6)(x - 2)

To find the value of a, we can use the fact that the function passes through the point (3, 36). This means that when x = 3, y = 36. Substituting these values into the equation, we get:

36 = a(3 + 6)(3 - 2)

36 = 9a

a = 4

Therefore, the value of a is 4.

Answer:

The answer is "180".

Step-by-step explanation:

Please find the complete question in the attached file.

Let's

x = ounces solution of A

y = ounces solution of B

\(x + y = 180 \\\\y = 180 - x\\\\0.60x + 0.85y = 0.75(180)\\\\0.60x + 0.85y = 135\\\\\)

Multiply both sides of the equation by 100 to remove the decimal points.

\(60x + 85y = 13500\\\\60x + 85(180 - x) = 13500\\\\60x + 15300 - 85x = 13500\\\\-25x = -1800\\\\x = 72\ \ ounces\\\\y = 180 - 72 \\\\y = 108 \ \ ounces\\\\\)

A matrix consisting entirely of zeros is called a zero matrix, or an all-zero matrix.

It is denoted with the symbol O and can be written in a matrix form, such as O = [0 0 0 0] where the number of columns and rows depends on the size of the matrix. A zero matrix is a matrix which has all its elements equal to zero. It has a number of special properties that make it useful in linear algebra. For instance, the sum of any two zero matrices is a zero matrix, and any scalar multiple of a zero matrix is a zero matrix. Additionally, the product of two zero matrices is a zero matrix, and the product of a zero matrix and an identity matrix is a zero matrix. These properties make it useful in solving systems of linear equations where all the coefficients are zero. Finally, the inverse of a zero matrix does not exist since its determinant is zero.

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Answer:

if you where to flip CBE on top of ABD they will fit perfect

Step-by-step explanation:

its not rlly that hard if you can see point AD = CE so is AB=CB both triangles end at B they both have a right angle at the end of ABD and CBE and both have an acute angle at the end at point B from AD and CE

Answer:

By AA postulate

Step-by-step explanation:

\( In\: \triangle ABD \: \&\: \triangle CBE\)

\( \angle BAD\cong\angle BCE... (given) \)

\( \angle ABD\cong\angle CBE... (given) \)

\( \therefore \triangle ABD\sim\triangle CBE\) (By AA postulate)

Answer: 33.81<=w<=33.91

Step-by-step explanation:

w=weight in ounces

33.86-0.05<=w<=33.86+0.05 ==> 0.05 weight difference form 33.86, the ideal weight.

33.81<=w<=33.91

Answer:

BC = 30.73

Here,

\(\sf \frac{AB}{BQ} = \frac{CD}{DQ}\)

so first solve for QD

\(\sf \hookrightarrow \frac{32}{15} = \frac{19.2}{DQ}\)

\(\sf \hookrightarrow 32(DQ)} =19.2(15)\)

\(\sf \hookrightarrow 32(DQ)} =288\)

\(\sf \hookrightarrow DQ =9\)

Now! using Pythagoras theorem,

Answer:

BC = 30.7 units (nearest tenth)

Step-by-step explanation:

As ∠AQR = ∠CQR  then ∠AQB = ∠CQD

This means that ΔABQ ~ ΔCDQ

Therefore, the side lengths of two similar triangles are proportional.

\(\begin{aligned} \sf \dfrac{AB}{CD} & =\sf \dfrac{BQ}{QD}\\\sf \implies \dfrac{32}{19.2} & =\sf \dfrac{15.0}{QD}\\\sf \implies QD & = \sf 9 \end{aligned}\)

Pythagoras' Theorem:  \(\sf a^2+b^2=c^2\)

(where a and b are the legs, and c is the hypotenuse, of a right triangle)

Given:

Substituting values into the formula:

\(\begin{aligned}\sf 24^2+19.2^2 & = \sf BC^2\\\sf BC^2 & = \sf 944.64\\\sf BC & = \sf \pm\sqrt{944.64}\\\sf BC & = \sf 30.7 \ (nearest \ tenth)\end{aligned}\)

(since distance is positive only)

Answer:

The maximum value of a function is the place where a function reaches its highest point, or vertex, on a graph.

I hope it helps.

a)   The blood pressure after 15 seconds is 102.5.

b) The maximum blood pressure is 115 and the minimum blood pressure is 65.

a. To find the blood pressure after 15 seconds, we can substitute t = 15 into the equation P = 25 sin(2nt) + 90:

P = 25 sin(2n(15)) + 90

P = 25 sin(30n) + 90

Since sin 30° = 1/2, we have:

P = 25 (1/2) + 90

P = 12.5 + 90

P = 102.5

Therefore, the blood pressure after 15 seconds is 102.5.

b. The maximum and minimum blood pressures occur at the points where sin(2nt) takes its maximum and minimum values, respectively. Since the range of sin function is [-1, 1], the maximum value of sin(2nt) occurs when 2nt = π/2 + kπ for some integer k, and the minimum value occurs when 2nt = -π/2 + kπ for some integer k.

Solving for t in each case, we get:

2nt = π/2 + kπ

t = (π/4n) + (kπ/2n)

and

2nt = -π/2 + kπ

t = (-π/4n) + (kπ/2n)

The first equation gives us the times when the maximum blood pressure occurs, and the second equation gives us the times when the minimum blood pressure occurs. Since the period of sin(2nt) is π/n, the first two times are:

t₁ = π/(8n), t₂ = (3π)/(8n)

At these times, sin(2nt) takes its maximum value of 1, so the maximum blood pressure is:

Pmax = 25(1) + 90 = 115

The next two times are:

t₃ = (5π)/(8n), t₄ = (7π)/(8n)

At these times, sin(2nt) takes its minimum value of -1, so the minimum blood pressure is:

Pmin = 25(-1) + 90 = 65

Therefore, the maximum blood pressure is 115 and the minimum blood pressure is 65.

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Answer:

$6,900

Step-by-step explanation:

To calculate the potential amount of credit available on the home equity loan, first you have to calculate 75% of the appraised value:

$127,000*75%= $95,250

Then, as Evelynn has an existing mortgage, you have to subtract this amount from $95,250:

$95,250-$88,350= $6,900

According to this, the answer is that the potential amount of credit available on a home equity loan is $6,900.

To find the standard form of the equation of an ellipse, we need to know the coordinates of the center, the lengths of the major and minor axes, and the orientation of the ellipse. In this case, we know that the center is at the origin, and the vertices are (±7,0), which means that the major axis is the x-axis and has a length of 14.

The foci are (±5,0), so we can calculate the distance between them as 2c = 10, where c is the distance from the center to each focus.
Using the formula for the distance between the foci and the center of an ellipse, we can find the value of b, the length of the minor axis: c^2 = a^2 - b^2, where a is half the length of the major axis. Substituting the values we have, we get:
5^2 = 7^2 - b^2
b^2 = 7^2 - 5^2
b^2 = 24
So the length of the minor axis is 2b = 2sqrt(24) = 8sqrt(3).
Now we can write the equation of the ellipse in standard form:
x^2/a^2 + y^2/b^2 = 1
Substituting the values we have, we get:
x^2/7^2 + y^2/(8sqrt(3))^2 = 1
Simplifying, we get:
x^2/49 + y^2/192 = 1
Therefore, the standard form of the equation of the ellipse with the given characteristics and center at the origin is x^2/49 + y^2/192 = 1.

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uhm wait cz I think I had made a mistake and I need to fix it

The first term on the left-hand side represents the flux of the quantity D(pu δ) across the cell boundaries, and the second term represents the change of this flux within the cell.

To integrate the 1D steady-state convection-diffusion equation over a typical cell, we can start with the given equation:

D/dx(pu δ) = d/dx (rd δ/dx)

Here, D is the diffusion coefficient, p is the velocity, r is the reaction term, u is the concentration, and δ represents the Dirac delta function.

To integrate this equation over a typical cell, we need to define the limits of the cell. Let's assume the cell extends from x_i to x_i+1, where x_i and x_i+1 are the boundaries of the cell.

Integrating the left-hand side of the equation over the cell, we have:

∫[x_i to x_i+1] D/dx(pu δ) dx = D∫[x_i to x_i+1] d(pu δ)/dx dx

Using the integration by parts technique, the integral can be written as:

= [D(pu δ)]_[x_i to x_i+1] - ∫[x_i to x_i+1] d(D(pu δ))/dx dx

Similarly, integrating the right-hand side of the equation over the cell, we have:

∫[x_i to x_i+1] d/dx (rd δ/dx) dx = [rd δ/dx]_[x_i to x_i+1]

Combining the integrals, we get:

[D(pu δ)][x_i to x_i+1] - ∫[x_i to x_i+1] d(D(pu δ))/dx dx = [rd δ/dx][x_i to x_i+1]

This equation can be further simplified and manipulated using appropriate boundary conditions and assumptions based on the specific problem at hand.

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a)The radius of convergence is R = |-2 - (-πi)| = |-2 + πi| = √(2^2 + π^2) ≈ 3.146.b)The radius of convergence is R = |1 + i - i| = |1| = 1. c)The radius of convergence is R = |1 + i - i| = |1| = 1.

The radius of convergence of a Taylor series centered at a point z0 is the distance from z0 to the nearest singularity of the function.

(a) The function sinz/e^z has singularities at z = kπi for any integer k, and the nearest singularity to z0 = -2 is at z = -πi. Therefore, the radius of convergence is R = |-2 - (-πi)| = |-2 + πi| = √(2^2 + π^2) ≈ 3.146.

(b) The function 1/cosz' has singularities at z = (k + 1/2)π for any integer k, which are equidistant from z0 = 0. Therefore, the radius of convergence is R = π/2.

(c) The function z^2+1/(z−i) has a singularity at z = i, which is the nearest singularity to z0 = 1 + i. Therefore, the radius of convergence is R = |1 + i - i| = |1| = 1.

Note that these radii of convergence only guarantee convergence within the radius; the series may converge or diverge at the boundary.

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Answer:

8°

Step-by-step explanation:

For exterior angle QRS, angles RPQ and PQR are its remote interior angles.

m<QRS = m<RPQ + m<PQR

4x - 15 = x + 1 + x - 2

2x = 14

x = 7

m<RPQ = x + 1 = 7 + 1 = 8

At Game 7, the attendance for the basketball team had declined by 5% x 6 games = 30% and This means that the attendance at Game 7 was 23,500 x (1 - 0.3) = 16,450 people.

The attendance for a basketball team declined at a rate of 5% per game throughout a losing season. This means that for every game, the attendance dropped by 5% in comparison to the attendance of the game before it.

15 games were played in the season and 23,500 people were at the first game. To calculate the attendance at Game 7, we first need to calculate the total amount that the attendance had declined by by the 7th game.

This can be done by multiplying the rate of decline (5%) by the number of games that had passed (6 games). This gives us a total decline of 30%. We then need to calculate the attendance at Game 7 by subtracting the total decline from the initial attendance.

This can be done by multiplying the initial attendance (23,500) by (1 - 0.3), which gives us 16,450 people. Therefore, the attendance at Game 7 was 16,450 people.

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Answer:

In order to have 9 coin he would have 4 quarters 5 nickels.

Answer:

b. To find the probability a customer who ordered pancakes came to thediner late, we need to look at the intersection of the "pancakes" row and the "late" column. This gives us a probability of 0.1, or 10%

c. To determine whether breakfast choice and meal time are independent, we need to see if the probability of one event changes based on the occurrence of the other event. In this case, it seems that breakfast choice and meal time are not independent, as the probability of being late seems to differ based on what breakfast item the customer chose. For example, the probability of being late is higher for customers who ordered pancakes compared to those who ordered cereal. Therefore, the choice of breakfast item appears to be related to the probability of being late, and so breakfast choice and meal time are not independent.

Step-by-step explanation:

Answer:

Step-by-step explanation:

.4s-500=.3s-300

.1s=200

s=$2000

The vertex of the equation g(x) = I x ₊ 6 I is (₋6 , 0).

Given the equation is g(x) =  I x ₊ 6 I

The equation of the absolute value function  is:

y = I x ₋ h I ₊ k where (h , k) is the vertex.

When the input is 0, the vertical axis will be intersected by the graph of an absolute value function. The horizontal axis is not usually where they cross. Depending on how the graph has been moved and reflected, it may or may not cross the horizontal axis.

compare the given equation to the above form.

y = I x ₊ 6 I ₊ 0

y = I x ₋ (₋6) I ₊ 0

hence we (h,k) as (₋6 , 0)

Therefore the coordinates of the vertex are (₋6 , 0)

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2 ----› 10% of 20 = 10/100 × 20 = 200/100 = 2/1 = 2

52.5 ----› 35% of 150 = 35/100 × 150 = 0.35 × 150 = 52.5

4.5 ----› 30% of 15 = 30/100 × 15 = 0.3 × 15 = 4.5

10 -----› 20% of 50 = 20/100 × 50 = 0.2 × 50 = 10

Answer:

D. 280miles

*Step by step explanation*

miles= 160miles × 7gallons / 4 gallons

miles = 280 miles

Step-by-step explanation:

Total letters = 11

Probability of letter M = 2/11

Probability of second M = 1/10

Answer:

24 mg find the whole area then subtract 16 boom!

Answer:

Cement = 20

Step-by-step explanation:

2x6=12

2x4=8

12+8=20

Answer:

adults 2

children 3

Step-by-step explanation:

x + y = 5

12x + 9y = 51

x = 5 - y

12(5 - y) + 9y = 51

60 - 12y + 9y = 51

-3y + 60 = 51

-3y = 51 - 60

-3y = -9

y = -9/-3

y = 3

x = 5 - y

x = 5 - 3

x = 2

First determine how much dirt is "cut"

V = l*w*h

V = 35 ft * 67 ft * 4 ft

V =9380 ft^3

Now determine how much dirt is used

V = l* w * h

V = 27 ft* 24ft * 6ft

V =3888 ft ^3

Subtract to determine how much is left

9380 - 3888

5492 ft^3

But the question asks for yd^3

5492 ft^3 * 1yd/ 3 ft * 1 yd / 3ft * 1 yd / 3 ft

5492 / 27 yd ^3

203.407407 yd^3

203.4 yd^3

The formula you have given (SS₁ + SS₂) / (n₁+ n₂) is actually the formula for the unweighted average of the variances, which is not appropriate when the sample sizes and variances are different between the two samples.

The formula for pooled variance is:

pooled variance = (SS₁+ SS₂) / (df₁ + df₂)

where SS₁ and SS₂ are the sum of squares for the two samples, df₁ and df₂ are the corresponding degrees of freedom, and the pooled variance is the weighted average of the variances of the two samples, where the weights are proportional to their degrees of freedom.

Note that the denominator is df₁ + df₂ not n₁+ n₂. The degrees of freedom take into account the sample sizes as well as the number of parameters estimated in

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Answer:

66.25 fluid ounces Step-by-step explanation:25% additional of 53 is 53 x 25% = 13.2513.25 + 53 = 66.25

Step-by-step explanation:

The matching is given below.

Let a be the initial value and x be the power of the exponent function and b be the increasing factor. The exponent is given as

y = a(b)ˣ

You are asked to write exponential equations from word problems.

We know that factor 2 represents doubling, factor 4 represents quadrupling, factor 3 represents tripling, and factor 1/2 represents halving.

Then the matching is given below.

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