Simplify the expression. Write your answer as a power.
k^13/k^5 * k^17/k^11

The solution for w in terms of x equation is w = -x/2 + 3.

Let's solve the equation :

8w - 8 = -4x + 16

To solve for either variable,  start by isolating one of them. Let's isolate w:

8w = -4x + 16 + 8

8w = -4x + 24

Now, divide both sides of the equation by 8 to solve for w:

w = (-4x + 24) / 8

w = -x/2 + 3

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An equation for this statement "The sum of seven times a number and 16 is 163," is 7n + 16 = 163.

The solution is 21.

In order to solve this word problem, we would assign a variable to the unknown number, and then translate the word problem into an algebraic equation as follows:

Let the variable n represent the unknown number.

Based on the statement "The sum of seven times a number and 16 is 163," we can logically deduce the following algebraic equation;

7n + 16 = 163

7n = 163 - 16

7n = 147

n = 147/7

n = 21.

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In the above mentioned similar triangles the length of DE is 5.25 cm.

A triangle is a three-sided polygon with three vertices. The triangle's internal angle, which is 180 degrees, is constructed.

Since triangles ABC and ADE are similar, their corresponding sides are proportional. We can use this fact to set up a proportion:

AB / AD = BC / DE

Substituting the given values, we get:

8 / AD = 6 / DE

Multiplying both sides by DE, we get:

8DE / AD = 6

Dividing both sides by 8/AD, we get:

DE = (6/8)AD

We need to find AD to solve for DE. To do this, we can use the fact that BD is an altitude of triangle ABC and triangle ADE is similar to triangle ABC. Therefore, triangle ABD is also similar to triangle ABC, and we can set up another proportion:

BD / AB = AD / AC

Substituting the given values, we get:

4 / 8 = AD / (8 + 6)

Simplifying, we get:

1/2 = AD / 14

Multiplying both sides by 14, we get:

AD = 7

Substituting this value back into the first equation, we get:

DE = (6/8)AD = (6/8)7 = 21/4 = 5.25

Therefore, the length of DE is 5.25 cm.

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Let's simplify step-by-step.

−7x2−6x+9−7x2−6x+9

=−7x2+−6x+9+−7x2+−6x+9

Combine Like Terms:

=−7x2+−6x+9+−7x2+−6x+9

=(−7x2+−7x2)+(−6x+−6x)+(9+9)

=−14x2+−12x+18

Answer:

=−14x2−12x+18

Let's simplify step-by-step.

−3x2−x+7−3x2−x+7

=−3x2+−x+7+−3x2+−x+7

Combine Like Terms:

=−3x2+−x+7+−3x2+−x+7

=(−3x2+−3x2)+(−x+−x)+(7+7)

=−6x2+−2x+14

Answer:

=−6x2−2x+14

Answer: -10x^2-7x+16

Step-by-step explanation: (-7x^2-6x+9)+(-3x^2-x+7)  

-7x^2-6x+9-3x^2-x+7

Nothing to distribute.

Combine like terms:

Final Answer: -10x^2-7x+16

Answer:

cute ima just be bold and say that i like you your really pretty

Given that the square region has been partitioned into 5 identical rectangular regions, and the perimeter of each rectangular region is 30. We are to find the perimeter of the square region.

As we know that the perimeter of a rectangle is given by P= 2 (l + b)
Let's say the length of the rectangle is 'l' and the breadth of the rectangle is 'b'. Since the five rectangular regions are identical, all of them will have the same length and breadth. Let's take the length and breadth of each rectangular region as x and y respectively. So, the perimeter of each rectangular region is given by P = 2(x + y) = 30Given P = 30, we get2(x + y) = 302x + 2y = 30x + y = 15... equation (1)
We know that the square region is partitioned into 5 identical rectangular regions. Therefore, the length of the square region will be 5 times the length of the rectangular region and the breadth of the square region will be the same as the breadth of the rectangular region. So, length of the square region = 5x, and breadth of the square region = y.
The perimeter of the square region = 2(5x + y) = 10x + 2yAs we know that x + y = 15 (from equation 1)So, 10x + 2y = 10(x + y) + 8y= 10(15) + 8y= 150 + 8y. Therefore, the perimeter of the square region is 150 + 8y.

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We will have the following:

So, the point (2, -1) is one of the many solutions.

The area of the hexagonal planter is 10.32 m²

Regular hexagon are polygon with 6 sides and are equiangular. This means the angles are the same.

area of hexagon = 1 / 2 × apothem × perimeter of hexagon

apothem = 1.72 m

side length = 2 m

area of hexagon = 1 / 2 ×  1.72 × 6(2)

area of hexagon = 1 / 2 ×  1.72 × 12

area of hexagon = 20.64 / 2

area of hexagon = 10.32

area of hexagon = 10.32 m²

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Answer:

B, set up a fraction trust ong

Answer:

0 slope

Step-by-step explanation:

flat horizantal line

no increase in y-value

The probability that a college selected at random from the state are (a)  3/10, b- 2/5, c- 1/2  and d- 1/10.

Probability refers to a possibility that deals with the occurrence of random events. The probability of all the events occurring need to be 1.

The formula of probability is defined as the ratio of a number of favorable outcomes to the total number of outcomes.

Out of the 50 colleges in a certain state, 25 are private, 15 offer engineering majors and 5 are private colleges offering engineering majors.

The probability that a college selected at random from the state (a) offers an engineering major.

= 15 / 50

= 3/10

The probability that a college selected at random from the state (b) offers an engineering major, given that it is public.

= 20 /50

= 2/5

The probability that a college selected at random from the state (c) is private, given that it offers an engineering major.

= 25/50

= 1/2

The probability that a college selected at random from the state (d) is public, given that it offers an engineering major.

= 5/50

= 1/10

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Answer: 3x+12

Step-by-step explanation:

Using the distributive property we can distribute the 3 to each of the terms in the parenthesis.

Therefore, 3(x+4) -= 3x+ 3*4 = 3x +12

Answer:

Step-by-step explanation

3x + 12=0

3x= -12

x = -12/3

x= -4:

Answer:

8x^2 + 5y + 1

Step-by-step explanation:

1 + x^2 - 3 + 2y + 7x^2 + 3 + 3y

group like terms

= x^2 + 7x^2 + 2y + 3y + 1 - 3 + 3

add similar items

= 8x^2 + 2y + 3y + 1 - 3 + 3

add similar items

= 8x^2 + 5y + 1 - 3 + 3

= 8x^2 + 5y + 1

If we test the null hypothesis at the 5% level of significance, then the decision is (c)reject null hypothesis and conclude the means are different .

In the question ,

it is given that ,

the results of a mathematics placement exam for two different campuses of college ,

we have to test the hypothesis that the mean score on campus 1 is higher than on campus 2 .

sample size (n₁) is = 330

the sample size (n₂) is = 310

the sample mean (μ₁) = 33

the sample mean (μ₂) = 31

the standard deviation , σ₁ = 8

the standard deviation , σ₂ = 7

the test statistic test z can be calculated using the formula ,

z = (μ₁ - μ₂)/√(σ₁²/n₁ + σ₂²/n₂)

Substituting the values of the sample size , sample mean and standard deviation ,

we get ,

z = (33 - 31)/√(8²/330 + 7²/310)

Simplifying further ,

we get ,

Z = 3.37

the test is for the null hypothesis at the 5% level of significance .

that means ,

Z₀.₉₅ = 1.645 ;

So , the p value = P(Z > 3.37)

= 1 - P(Z < 3.37)

= 1 - 0.9996

= 0.0004

since the p-value is (0.0004) < the level of significance (0.05) .

we can reject the null hypothesis .

There is significant evidence to conclude that the mean score on campus 1 is higher than campus 2 .

Therefore , the correct option is (c) .

The given question is incomplete the complete question is

The results of a mathematics placement exam at two different campuses of mercy college follow: ( the table is given below)

The college wants to test the hypothesis that the mean score on campus 1 is higher than on campus 2. if we test the null hypothesis at the 5% level of significance, what is the decision ?

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Answer:

126 mi²

Step-by-step explanation:

Surface Area of a Rectangular Prism :

The value of R(x) term is 36.

We are given that;

The equation x³ + 2x² - 72x - 28

Now,

We divide the first term, 8x, by the first term of d(x), which is x. This gives us 8, which is the third term of Q(x). We write 8 above the division bar and multiply it by d(x), which gives us 8x - 64. We subtract this from the new dividend, which gives us 36.

Since we cannot divide 36 by x-8 any further, we stop here and write 36 as the remainder R(x).

   x² + 10x + 8

  _______________

x-8 | x³ + 2x² - 72x - 28

    - (x³ - 8x²)

    -------------

        10x² - 72x

      - (10x² -80x)

      -------------

             8x -28

           - (8x -64)

           ----------

                36

Q(x) = x² + 10x + 8 and R(x) = 36.

Therefore, by the equation the answer will be R(x) = 36.

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Answer:

x=3

Step-by-step explanation:

RS=23-2x

ST=9x-5

RT=39

RS=x

RS+ST=RT

23-2x+9x-5=39

9x-2x+23-5=39

7x+18=39

7x=39-18

7x=21

x=21/7=3

x=3

so RS=3

hope this is helps u

Answer:

I'm pretty sure it's 17 units

Step-by-step explanation:

I got u

Answer:

Step-by-step explanation:

Part A:

We have two lines: y = 2 - x and y = 4x + 3 . Given two equations that are both required to be true. The answer is the points where the lines cross, this means we have to make the equations equal to each other. It will look like this:

                                                       2 - x = 4x + 3

Part B:

In order to solve the equation we need to put the like terms together. So we will add x on each side.

                                                       2 - x = 4x + 3

                                                           +x   +x

So now we get:

                                                           2 = 5x + 3

Now that x is on one side and is positive we will move 3 on the left side by subtracting it from each side.

                                                           2 = 5x + 3

                                                           -3         -3

So now we get:

                                                           -1 = 5x

Now that the like terms have been combined we need to find out what x alone is so we divide 5 on each side:

                                                           \(\frac{-1}{5}\) = \(\frac{5x}{5}\)

No we see that:

                                                           x = \(-\frac{1}{5}\)

Two angles whose sum is 180° are called supplementary angles. If a straight line is intersected by a line, then there are two angles form on each of the sides of the considered straight line.

Two angles whose sum is 180° are called supplementary angles. If a straight line is intersected by a line, then there are two angles form on each of the sides of the considered straight line. Those two-two angles are two pairs of supplementary angles. That means, that if supplementary angles are aligned adjacent to each other, their exterior sides will make a straight line.

When two lines cross at a single point, a linear pair of angles is generated. If the angles are next to each other after the two lines intersect, they are considered to be linear pairs. The total of the angles of a linear pair is always 180°. These angles are also referred to as supplementary angles.

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Answer:

i could  be wrong but B

Step-by-step explanation:

I assume it's D

S shows a variable you need to find to find how many students are in Social Studies class.

We have 2 points in the graph (3,4) and (-3,0) so the slope is

so the answer is A) 2/3

Answer:

A. 10,000 combinations

B. 5,040 combinations

Step-by-step explanation:

A. four-digit code from 0-9 without restriction

1st digit - 10 options

2nd digit - 10 options

3rd digit - 10 options

4th digit - 10 options

Number of possible options = 10 * 10 * 10 * 10 = 10^4 = 10,000 combinations

b. No repetition of digits

1st digit = 10 options

2nd digit = 9 options

3rd digit = 8 options

4th digit = 7 options

Number of possible choices = 10 * 9 * 8 * 7 = 5,040 combinations

The correct answer is option a. $7,594.46.

To calculate the amount you would reduce the amount you owe in the first year, we can use the formula for the equal installment of a loan. The formula is:

Installment = Principal / Number of Installments + (Principal - Total Repaid) * Interest Rate

In this case, the principal is $45,000, the number of installments is 5, and the interest rate is 8.5%.

Let's calculate the amount you would reduce the amount you owe in the first year:

Installment = $45,000 / 5 + ($45,000 - $0) * 0.085Installment = $9,000 + $3,825

Installment = $12,825

Therefore, you would reduce the amount you owe by $12,825 in the first year.The correct answer is option a. $7,594.46.

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The solution is y(t) = 2ln(t).

To solve the initial value problem using Laplace transform, we first need to take the Laplace transform of both sides of the differential equation:

L[y' * y] = L[t]

where L denotes the Laplace transform. We can use the convolution theorem of Laplace transforms to simplify the left-hand side:

L[y' * y] = L[y'] * L[y] = sY(s) - y(0) * Y(s) = sY(s)

where Y(s) is the Laplace transform of y(t). We also take the Laplace transform of the right-hand side:

L[t] = 1/s²

Substituting these results into the original equation, we get:

sY(s) = 1/s²

Solving for Y(s), we get:

Y(s) = 1/s³

We can use partial fraction decomposition to find the inverse Laplace transform of Y(s):

Y(s) = 1/s³ = A/s + B/s²+ C/s³

Multiplying both sides by s³ and simplifying, we get:

1 = As² + Bs + C

Substituting s = 0, we get C = 1. Substituting s = 1, we get A + B + C = 1, or A + B = 0. Finally, substituting s = -1, we get A - B + C = 1, or A - B = 0.

Therefore, we have A = B = 0 and C = 1, and the inverse Laplace transform of Y(s) is:

y(t) = tv²/2

To find the solution to the initial value problem, we substitute y(t) into the equation y' * y = t and use the fact that y(0) = 0:

y' * y = t

y' * t²/2 = t

y' = 2/t

y = 2ln(t) + C

Using the initial condition y(0) = 0, we get C = 0. Therefore, the solution to the initial value problem is:

y(t) = 2ln(t)

Note that this solution is only valid for t > 0, since ln(t) is undefined for t <= 0.

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Both circle C and circle E are similar to each other but the radii are different.

It is the center of an equidistant point drawn from the center. The radius of a circle is the distance between the center and the circumference.

Circle C is shown with a center at (negative 3, 1) and a radius of 4.

Circle E is shown with a center of (4, 9) and a radius of 3.

There is only one parameter in the circle which is radius or diameter.

Then both circle C and circle E are similar to each other but the radii are different.

As shown in the graph.

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Answer:

The answer is below

Step-by-step explanation:

a) T=2.25h+1.75d

To rewrite the equation to find d, we have to make d the subject of the formula.

T=2.25h+1.75d

Subtract 2.25h from both sides:

T - 2.25h = 2.25h + 1.75d - 2.25h

1.75d = T - 2.25h

Divide both sides by 1.75

1.75d/1.75 = (T - 2.25h) / 1.75

d = (T - 2.25h) / 1.75

b) Additive property and law of division

c) The money spent (T) = $18.25 and the number of hot dogs (h) = 5. To get the number of drinks, substitute the value of h and T in the equation d = (T - 2.25h) / 1.75. Hence:

d = (T - 2.25h) / 1.75

d = (18.25 - 2.25(5)) / 1.75

d = (18.25 - 11.25) / 1.75 = 7 / 1.75

d = 4

The number of drinks that can be bought is 4

There are 4 integers between 20 and 30 that have a prime factorization with exactly 3 factors that are not necessarily unique.

To find the integers with a prime factorization having exactly 3 factors, we need to look for numbers that can be expressed as the product of two distinct prime numbers.

Step 1: Identify the prime numbers between 20 and 30. The prime numbers in this range are 23, 29.
Step 2: Determine all possible pairs of distinct prime numbers. In this case, we have only one pair: (23, 29).
Step 3: Calculate the products of these pairs. The products of (23, 29) are 667 and 667.
Step 4: Count the integers between 20 and 30 that match these products. We have two integers that match, which are 21 and 27.
Step 5: Check if these integers have exactly 3 factors. The factors of 21 are 1, 3, 7, and 21 (a total of 4 factors), so it does not meet the criteria. The factors of 27 are 1, 3, 9, and 27 (a total of 4 factors), so it also does not meet the criteria.

Therefore, there are no integers between 20 and 30 with a prime factorization having exactly 3 factors that are not necessarily unique.

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