!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!QHELP

The correct answer is D. f(x) = 11x - 4 and g(x) = (x + 4)/11

To determine which pair of functions are inverses of each other, we need to check if the composition of the functions results in the identity function, which is f(g(x)) = x and g(f(x)) = x.

Let's test each option:

Option A:

f(x) = x/2 + 15

g(x) = 12x - 15

f(g(x)) = (12x - 15)/2 + 15 = 6x - 7.5 + 15 = 6x + 7.5 ≠ x

g(f(x)) = 12(x/2 + 15) - 15 = 6x + 180 - 15 = 6x + 165 ≠ x

Option B:

f(x) = ∛3x

g(x) = (x/3)^3 = x^3/27

f(g(x)) = ∛3(x^3/27) = ∛(x^3/9) = x/∛9 ≠ x

g(f(x)) = (∛3x/3)^3 = (x/3)^3 = x^3/27 = x/27 ≠ x

Option C:

f(x) = 3/x - 10

g(x) = (x + 10)/3

f(g(x)) = 3/((x + 10)/3) - 10 = 9/(x + 10) - 10 = 9/(x + 10) - 10(x + 10)/(x + 10) = (9 - 10(x + 10))/(x + 10) ≠ x

g(f(x)) = (3/x - 10 + 10)/3 = 3/x ≠ x

Option D:

f(x) = 11x - 4

g(x) = (x + 4)/11

f(g(x)) = 11((x + 4)/11) - 4 = x + 4 - 4 = x ≠ x

g(f(x)) = ((11x - 4) + 4)/11 = 11x/11 = x

Based on the calculations, only Option D, where f(x) = 11x - 4 and g(x) = (x + 4)/11, satisfies the condition for being inverses of each other. Therefore, the correct answer is:

D. f(x) = 11x - 4 and g(x) = (x + 4)/11

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Answer:

x=2;  y=2

Step-by-step explanation:

3x+2y=10

y=3x-4

We can substitute y from the first equation with the second equation:

3x+2(3x-4)=10

3x+6x-8=10

9x=18

x=2

Now plug this in to any of the equations (i used second equation):

y=3(2)-4

y=6-4

y=2

Check your answers:

y=3x-4

2=3(2)-4

2=6-4

2=2

Based on the scores in the final exam, the five number summary of the class is:

The minimum is the smallest score of 60. The maximum will be the largest score of 98.

The lower quartile can be found by the formula:

= (Second score + Third score) / 2

= (65 + 78) / 2

= 71.5.

The upper quartile is:

= (Third to last score + Second to last score) / 2

= (93 + 95) / 2

= 94

The median is:

= (5th score + 6th score) / 2

= (82 + 88) / 2

= 85

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Answer:

Step-by-step explanation:

Since RQTS is a parallelogram

\(\angle Q +\angle T=180^{o}\)

\(3x+5+9x-17=180^o\)

\(12x-12=180^o\)

\(12x-12+12=180+12\)

\(12x=192\)

\(\cfrac{12x}{12}=\cfrac{192}{12}\)

\(x=16\)

Hope it helps!

Another representation of the given algebraic expression 52s + 30b as required is; 2 (26s + 15b).

As evident in the task content; it follows that the equivalent expression to 52s + 30b is to be determined.

Given; 52s + 30b

Since 2 is a common factor to both terms of the equation; we have that;

2 (26s + 15b)

Ultimately, the equivalent expression is; 2 (26s + 15b).

Complete question:

What is 52s+30b in a factorized form.

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The bearing of D from C is equal to the angle measure 315°.

Bearing is usually measured in degrees, with 0° indicating the reference direction (usually North), and increasing clockwise to 360°. It refers to the direction or angle between a reference direction and a point or object.

By observation, the angle between the north line CN and the line CD is equal to 45°, the bearing of D from C is the angle formed beginning from the north line clockwise to the line CD calculated as:

360° - 45° = 315°

Therefore, the bearing of D from C is equal to angle measure 315°

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*see attachment for the diagram of the wall

Answer:

6 cans

Step-by-step explanation:

First, let's calculate the area of the wall to be painted = area of a rectangle

Area of the rectangle = length*width

From the diagram,

Length = 13 ft

Width = 10 ft

Area = 13*10 = 130 ft²

Given that 1 can of paint covers 25 ft²,

Number of can of paints that will cover 130 ft² = 130/25 = 5.2

This means we will need more than 5 cans. So Joan will need to get roughly 6 cams of blackboard paint.

The chance of the event B is 0.4 when using the probability for the two independent two event formula.

In the given question, if a and b are independent events with p(a) = 0.65 and p(a ∩ b) = 0.26, then we have to find the value of p(b).

Events classified as independent do not depend on other events for their occurrence.

Event A's likelihood of happening is P(A)=0.65.

The likelihood of the two events A and B intersecting is P(A∩B)=0.26.

Given that the likelihood of the two independent events is:

P(A∩B) = P(A)⋅P(B)

Then the probability of the event B will be,

P(B) = P(A)/P(A∩B)

P(B) = 0.65/0.26

P(B) =0.4

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The expression equivalent to\(-4x^2 + 2x - 5(1 + x)\)  is \(4x^2 + 8x + 5.\)

This expression matches the form \(x^2 + x + c,\) where c = 5.

To simplify the given expression \(-4x^2 + 2x - 5(1 + x)\) and make it equivalent to the expression \(x^2 + x + c,\) where c is a constant term, we need to perform some algebraic operations.

First, let's distribute the -5 to the terms inside the parentheses:

\(-4x^2 + 2x - 5 - 5x\)

Next, we can combine like terms:

\(-4x^2 + (2x - 5x) - 5 - 5x\)

Simplifying further:

\(-4x^2 - 3x - 5 - 5x\)

Now, let's rearrange the terms to match the form \(x^2 + x + c:\)

\(-4x^2 - 3x - 5x - 5\)

To make the leading coefficient positive, we can multiply the entire expression by -1:

\(4x^2 + 3x + 5x + 5\)

Now, we can combine the x-terms:

\(4x^2 + 8x + 5\)

So, the expression equivalent to \(-4x^2 + 2x - 5(1 + x)\) is \(4x^2 + 8x + 5.\)This expression matches the form \(x^2 + x + c,\) where c = 5.

It's important to note that the original expression and the equivalent expression have different coefficients and constants, but they represent the same mathematical relationship.

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so basically we just us do this

tan(26)=33/FE

Multiply to get rid of fraction

tan(26)FE=33

divide to get FE alone

FE = tan(26) * 33

FE=16.0951m

so it should be 16.0951m

Answer:

(1, 3, -2) is the answer

Answer:

a) AE and BC are parallel (as shown by the markings)

b) ED and CD are equal in length (as shown by the markings)

c) 3: AE is perpendicular AB, AB is perpendicular to AE/AC, AC is perpendicular to AB

Answer:

A

Step-by-step explanation:

Answer: A

Step-by-step explanation:

Answer: You need more information to solve this.

Step-by-step explanation:

a= how many cards you have overall

B= how many blue cards there are

C= how many blue cards you have after you took one out

D= how many cards you have overall after you took one out

B/a*C/D= your answer

Answer:

9/49

Step-by-step explanation:

4 purple beads and 3 green beads= 7 beads

P( green) = green = total = 3/7

Replace the bead

4 purple beads and 3 green beads= 7 beads

P( green) = green = total = 3/7

P( green , replace, green) = 3/7 * 3/7 = 9/49

The given is the Emotional Intelligence Quotient (EQ) score of a grade 8 class is normally distributed with a mean of 80 and a standard deviation of 20, and a random sample of 36 grade 8 learners is selected. The value of x is to be determined such that P(x << 80) = 0.4918.

The population mean is given by μ = 80.The standard deviation of the sample is given by:σ/√n = 20/√36 = 20/6.∴ Standard Error = σ/√n = 20/6 ≈ 3.33.Now, we have to find the z-score associated with a tail probability of 0.4918/2 = 0.2459.Using the standard normal distribution table, we get that the z-value associated with a tail probability of 0.2459 is approximately 0.67.

Now, using the formula for z-score: z = (x - μ) / Standard Error 0.67 = (x - 80) / 3.33 0.67 x 3.33 = x - 80 2.2301 + 80 = x 82.2301 = xThus, the value of x is 82.2301. Therefore, the option (a) 84 and the solution is provided above.

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Answer:

Point I is on line segment HJ; which means HI and IJ are equal.

HJ = 15

IJ = 10

Finding the length of HI, given the above statements:

Length of HI = 10 (reason: HI and IJ are congruent)

Answer:

8/2

Step-by-step explanation:

Answer:

The solution is:

Step-by-step explanation:

First, we'll calculate the function's average rate of change over [-1,1] as following:

Now, we make f'(x) = 3 and solve for x, as following:

Therefore, we can conlcude that the solution is:

Answer:

D) \(1 < x\leq 4\)

Step-by-step explanation:

1 is not included, but 4 is included, so we can say \(1 < x\leq 4\)

Answer:

1. 286

2. 588

3.300

The equation that would help the mathematician model the surface area of a square piece of paper as it was repeatedly cut is \(y = 36 \times \frac{1}{2}^x\)

Option D is the correct answer.

We have,

In this equation, the variable x represents the number of times the square is cut in half, and y represents the surface area of the square.

As x increases, the exponent of 1/2 decreases, causing the value of y to decrease.

This exponential decay accurately represents the idea that the surface area becomes less and less but never reaches zero units²

Thus,

The equation that would help the mathematician model the surface area of a square piece of paper as it was repeatedly cut is \(y = 36 \times \frac{1}{2}^x\).

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The correct equation that would help model the surface area of a square piece of paper as it is repeatedly cut in half is:  \(\(y=36(\frac{1}{2})^x\)\)

As the square is cut in half, the side length of the square is divided by 2, resulting in the area being divided by \(\(2^2 = 4\)\).

Therefore, the equation \(y=36(\frac{1}{2})^x\)\)accurately represents the decreasing surface area of the square as it is repeatedly cut in half.

and, \(\(y=x^2+4x-16\)\)is a quadratic equation that does not represent the decreasing nature of the surface area.

and, \(\(y=-25x^2\)\) is a quadratic equation with a negative coefficient.

and, \(\(y=9(2)^x\)\)represents exponential growth rather than the decreasing nature of the surface area when the square is cut in half.

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Answer: f(4)=17

Step-by-step explanation:

Plug 4 into 5x-3, as this includes 4 in the domain.

5(4)-3=17

===================================================

Explanation:

Since AE = BE, we know that triangle ABE is isosceles with A = B as the congruent base angles (it might help to rotate the triangle 90 degrees clockwise). The congruent base angles are always opposite the congruent sides of an isosceles triangle.

Focus on triangle ABE. Let's find the missing angle E.

A+B+E = 180

55+55+E = 180

110+E = 180

E = 180-110

E = 70

So angle BEA = 70 degrees

This means angle DEC is also 70 degrees. Angles BEA and DEC are congruent vertical angles.

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

Now focus on triangle DEC. We just found E = 70. The diagram shows D = 34. Use these items to find C

D+E+C = 180

34+70+C = 180

104+C = 180

C = 180-104

C = 76

Angle C is 76 degrees

Answer:

hey

Step-by-step explanation:

The value of 11p10 is 39,916,800.If "p" represents the                  permutation function, typically denoted as "P(n, r)" or "nPr," it signifies the number of ways to arrange "r" objects taken from a set of "n" distinct objects without repetition.

The value of 11p10 can be determined by applying the concept of permutations. In mathematics, permutations represent the number of ways to arrange a set of objects in a particular order.

In the expression 11p10, the number before "p" (11) represents the total number of objects, while the number after "p" (10) represents the number of objects to be arranged.

Using the formula for permutations, the value of 11p10 can be calculated as:

11p10 = 11! / (11 - 10)!

= 11! / 1!

Here, the exclamation mark denotes the factorial function, which means multiplying a number by all positive integers less than itself down to 1.

Simplifying further:

11! / 1! = 11 * 10 * 9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1 / 1 = 39,916,800.

In this case, 11p10 would represent the number of permutations of 10 objects taken from a set of 11 objects. However, without more details or the specific values of "n" and "r," the numerical value cannot be determined.

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Answer:

Will you help me plz I will follow you

Answer:

5/24 of a bag I just had this question an thought I'd help you

Answer:

Samee

Step-by-step explanation:

Answer:

TIAGZ

and Billie Eilish

DABABY

Step-by-step explanation:

Angela bought 16 gummy bears. It is Based on the data and money angela has.

Candice bought 8 gummy bears and Bernice bought 8 more gummy bears than Candice. Together the three girls spent £3.42 on gummy bears. This means that the cost of one gummy bear is £0.17.

To find the number of gummy bears Angela bought, we can set up a system of equations to represent the given information.

To work out how many gummy bears Angela bought, we can use the equation

where x is the number of gummy bears Angela bought. Solving this equation gives us x = 16. This means that Angela bought 16 gummy bears.

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We have proved that the intersection of any two distinct eigenspaces of a matrix A is {0}.

Let A be a square matrix and let v and w be two distinct eigenvectors of A associated with distinct eigenvalues λ and μ, respectively, such that Av = λv and Aw = μw. We need to show that the intersection of the eigenspaces of v and w, denoted by E(λ) and E(μ), respectively, is {0}.

Suppose there exists a nonzero vector u in the intersection of E(λ) and E(μ), i.e., u ∈ E(λ) ∩ E(μ). Then, by definition, Au = λu and Au = μu. Thus, we have λu = μu, which implies (λ - μ)u = 0. Since λ and μ are distinct, we have (λ - μ) ≠ 0. Therefore, we must have u = 0, which contradicts the assumption that u is nonzero. Thus, the intersection of E(λ) and E(μ) must be {0}.

Therefore, we have proved that the intersection of any two distinct eigenspaces of a matrix A is {0}.

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Let A be an n x n matrix and let λ1 and λ2 be distinct eigenvalues of A with corresponding eigenvectors v1 and v2, respectively. We want to show that the intersection of the eigenspaces E1 and E2 is {0}, where E1 and E2 are the eigenspaces corresponding to λ1 and λ2, respectively.

Since λ1 and λ2 are distinct eigenvalues, their difference λ1 - λ2 is nonzero. Therefore, we have u = 0, which contradicts the assumption that u is non-zero. Hence, the intersection of any two distinct eigenspaces of A is {0}.

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