You are buying 3 shirts and 2 pairs of pants. You spend $300. Let x represent the price of the shirt and y represent the price of the pants. Write an equation that can be used to find the price of the shirts and pants. Directions: Write the equation in both slope-intercept and standard form for each of the scenarios below. a. Standard Form: b. Slope-Intercept Form: c. If the shirts cost $20 each how much were each of the pants? d. Using the Standard Form, identify the x-intercept of the graph and explain how the x-intercept relates to the price of the pants and shirts. e. Using the Standard Form, identify the y-intercept of the graph and explain how the y-intercept relates to the price of the pants and shirts

Answer:

D. y=3x+4

This is the correct answer

Answer:

This equation is equivalent to the formula for finding the perimeter of a rectangle

I don't understand, what's the question?

Answer:

13 feet

Step-by-step explanation:

All sides of a square are the same length.

If we call each side of the square 's', then the formula for the area of the square is A = s×s = s2.

The problem states the area is 169 square feet.

A = s2

169 = s2

Take the square root of both sides.

13 = s

Each side of the court is 13 feet!

Answer:

B. 1/8

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Algebra I

Step-by-step explanation:

Step 1: Define

\(\displaystyle f(x) = 2(4)^x\\f(-2) \ is \ x = -2\)

Step 2: Evaluate

The rate at which the depth of the liquid is increasing when the depth of the liquid reaches one-third of the height of the bowl is 1.25 cm s⁻¹.

The volume of the liquid in the bowl is given by the following integral:

\(V = \int\limitsx_{0}^{h} \, \pi r^{2}(y) dy\)

where r = radius of the bowl and y = height of the liquid.

The radius of the bowl is equal to the distance from the curve y = (4/(8-x)) - 1 to the y-axis. This can be found using the following equation:

r = √{(4/(8-x)) - 1}² + 1²

The height of the liquid is equal to the distance from the curve y = (4/(8-x)) - 1 to the x-axis. This can be found using the following equation:

h = (4/(8-x)) - 1

Substituting these equations into the volume integral:

\(V = \int\limitsx_{0}^{h } \, \pi {\sqrt{(4/(8-x)) - 1)^{2} + 1^{2} (4/(8-x))} - 1 dy\)

Evaluate this integral using the following steps:

Expand the parentheses in the integrand.

Separate the integral into two parts, one for the integral of the square root term and one for the integral of the linear term.

Integrate each part separately.

The integral of the square root term can be evaluated using the following formula:

\(\int\limits^{b} _{a} \, dx \sqrt{x} dx = 2/3 (x^{3/2}) |^{b}_{a}\)

The integral of the linear term can be evaluated using the following formula:

\(\int\limits^{b} _{a} \, {x} dx = (x^{2/2}) |^{b}_{a}\)

Substituting these formulas into the integral:

V = π { 2/3 (4/(8-x))³ - 1/2 (4/(8-x))² } |_0^h

Evaluating this integral:

V = π { 16/27 (8-h)³ - 16/18 (8-h)² }

The rate of change of the volume of the liquid is given by:

dV/dt = π { 48/27 (8-h)² - 32/9 (8-h) }

The rate of change of the volume of the liquid is 7π cm³ s⁻¹. Also the depth of the liquid is one-third of the height of the bowl. This means that h = 2/3.

Substituting these values into the equation for dV/dt:

dV/dt = π { 48/27 (8-2/3)² - 32/9 (8-2/3) } = 7π

Solving this equation for the rate of change of the depth of the liquid:

dh/dt = 7/(48/27 (8 - 2/3)² - 32/9 (8 - 2/3)) = 1.25 cm s⁻¹

Therefore, the rate at which the depth of the liquid is increasing when the depth of the liquid reaches one-third of the height of the bowl is 1.25 cm s⁻¹.

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Answer:

Step-by-step explanation:

This sequence is adding 5 so

17 22 27 32 37 42 47 52 57 62 67 72 77 82 87 92 97 102 107 112 117 122 127 132 137 = 1925

Answer: The sum of the first 25 terms of this arithmetic sequence is 1925.

Explanation: This sequence, beginning at 17, increases by 5 per term. By simply adding 5 to the preceding term in the sequence, you can find the next term. The first term is 17, and the last term is 137. This means the list of terms is 17, 22, 27, 32, 37, 42, 47, 52, 57, 62, 67, 72, 77, 82, 87, 92, 97, 102, 107, 112, 117, 122, 127, 132, and 137. The sum of these terms is 1925.

Answer:

one equal to 5

Step-by-step explanation:

5x x 66

Answer: 69 bozo LLLLLLLLLLLLLLLLLLLLLLLLLLL

Step-by-step explanation:

69

During the exponential phase, e.coli bacteria in a culture increase in number at a rate proportional to the current population. If growth rate is 1.9% per minute and the current population is 172.0 million, the population 7.2 minutes from now can be calculated using the following formula:

P(t) = P ₀e^(rt)where ,P₀ = initial population r = growth rate (as a decimal) andt = time (in minutes)Substituting the given values, P₀ = 172.0 million r = 1.9% per minute = 0.019 per minute (as a decimal)t = 7.2 minutes

The population after 7.2 minutes will be:P(7.2) = 172.0 million * e^(0.019*7.2)≈ 234.0 million (rounded to the nearest tenth)Therefore, the population of e.coli bacteria 7.2 minutes from now will be approximately 234.0 million.

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To show that the equations are the same, we need to rewrite one of the equations as an equivalent equation of the second

Damita's claim is true

The equations are given as:

0.8x - 0.8 = 1.6

4/5 ( x - 1 ) = 1 (3/5)

We need to rewrite one of the equations, as follows:

4/5 ( x - 1 ) = 1 (3/5)

Express as decimal

0.8 ( x - 1 ) = 1 + 0.6

Open the brackets

0.8x - 0.8 = 1.6

Now we have:

0.8x - 0.8 = 1.6 (the first equation) and 0.8x - 0.8 = 1.6 (the equivalent of the second equation)

The above shows that both equations are the same

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Answer:

Step-by-step explanation:

    A,  use  three_digite  rounding  arithmetic  to compute  13- 6 and determine  the absolute,relative ,and percentage errors.

tepeat part (b) using  three – digit chopping arithmetic.

Answer:

{-9,-8,-7,-6,-5}

Step-by-step explanation:

Set C is negative Integers greater than -10

{-9, -8, -7, -6, -5, -4, -3, -2, -1}

Elements less than or equal to -5

{-9, -8, -7, -6, -5}

Answer:

hshdjsjshsvdhjajsjdhbdbxnrndb

Step-by-step explanation:

ndncnxnsnbs

hshdhrhrhrj

gehrhrhhfhf

hshrjrjsnna

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

Explanation:

The graph of \(y \ge -\frac{1}{3}x+2\) has the boundary y = (-1/3)x+2 which is a solid line. This line goes through (0,2) and (3,1). We shade above the boundary because of the "greater than" sign.

The graph of y < 2x+3 has a dashed boundary line of y = 2x+3, and we shade below the boundary because of the "less than" sign.

The two regions overlap in the upper right corner where it's shaded in the darkest color. The points (2,2), (3,1) and (4,2) are in this upper right corner region. If we plug the coordinates of each point into each inequality, then we'll get true statements.

For instance, let's try (x,y) = (2,2) into the first inequality

\(y \ge -\frac{1}{3}x+2\\\\2 \ge -\frac{1}{3}(2)+2\\\\2 \ge -\frac{2}{3}+2\\\\2 \ge -\frac{2}{3}+\frac{6}{3}\\\\2 \ge \frac{-2+6}{3}\\\\2 \ge \frac{4}{3}\\\\2 \ge 1.33\\\\\)

Which is true since 2 is indeed larger than 1.33, so that confirms (2,2) is in the shaded region for \(y \ge -\frac{1}{3}x+2\\\\\)

Let's check the other inequality as well

\(y < 2x+3\\\\2 < 2(2)+3\\\\2 < 4+3\\\\2 < 7\\\\\)

That works too. So (2,2) is in BOTH shaded regions at the same time; hence, it's a solution to the system. You should find that (3,1) and (4,2) work for both inequalities also. This will confirm choice A is the answer.

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

Extra info (optional section)

A point like (3,-1) does not work for the first inequality as shown below

\(y \ge -\frac{1}{3}x+2\\\\-1 \ge -\frac{1}{3}(3)+2\\\\-1 \ge -1+2\\\\-1 \ge 1\\\\\)

Since -1 is neither equal to 1, nor is -1 larger than 1 either. The false statement at the end indicates (3,-1) is not a solution to that inequality.

Based on the graph, the point (3,-1) is not above the blue solid boundary line. All of this means we can rule out choice B.

You should find that (1,-2) is a similar story, so we can rule out choice C. Choice D can be ruled out because (2,0) is not a solution to the first inequality.

Answer:

-3/4 x + 1/2

Step-by-step explanation:

First, you're going to sort by like terms

-1/8 +5/8= 4/8=1/2

+2 1/4 x- 3x= -3/4x

then write out as

-3/4 x + 1/2

Answer:

-3/4x+1/2

Step-by-step explanation:

It’s not solving.  It’s combining like terms.

-3/4x+4/8

-3/4x+1/2

The law illustrated is Distributive Law

This question is under a topic called algebra laws.

The laws are;

- Commutative law; This implies that when we are to add or multiply numbers, the order of addition or multiplication doesn't matter as we will still get same result.

- Associative law; This implies that if we want to add more than 2 numbers, if we decide to add the first 2 before adding the third one, we will still get the same result as if we added the second one to the third one before adding to the first one. This law also applies to multiplication.

- Distributive law; This implies that when two numbers are multiplied to produce a result, both numbers are factors of the result.

We are told in the question that ; 5n x 1 = 5n

This means that 5n and 1 are factors of 5n and this corresponds to distributive law

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The reasoning presented lacks explicit explanations and logical connections between the steps, making it difficult to fully understand the intended proof strategy.

The given proof aims to show that the Separation Axioms can be derived from the Replacement Schema using a particular construction involving a formula p(x, y). Let's analyze the proof step by step:

Define the formula p(x, y) as x = yo(x).

This formula states that for each x, y pair, x is equal to the unique object y such that y is obtained by applying the operation o to x.

Define the set F as {(x, x) (x)}.

This set F contains pairs (x, x) where x is the unique object obtained by applying the operation (x) to x.

Claim: F(X) = {y (x = X)p(x, y)} = {y: (x = X)x = y^o(x)} = {x: (3x € X)o(x)} = {x X: (x)}.

This claim asserts that F(X) is equivalent to {y (x = X)p(x, y)}, which is further equivalent to {y: (x = X)x = y^o(x)}, and so on.

The proof states that since (x, y) satisfies the functional formula VaVyVz(p(x, y)^(x, z) y = z), it follows that (x, y) is a functional formula.This step emphasizes that the formula p(x, y) satisfies certain properties that make it a functional formula, which is relevant for the subsequent deductions.

Finally, the proof concludes that the Separation Axioms follow from the Replacement Schema, based on the previous steps.

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After answering the presented question, we can conclude that expressions Therefore, the population of the rural city in 2030 is approximately 11,014.18.

In mathematics, you can multiply, divide, add, or subtract. An expression is constructed as follows: Number, expression, and mathematical operator A mathematical expression is made up of numbers, variables, and functions (such as addition, subtraction, multiplication or division etc.) It is possible to contrast expressions and phrases. An expression or algebraic expression is any mathematical statement that has variables, integers, and an arithmetic operation between them. For example, the expression 4m + 5 has the terms 4m and 5, as well as the provided expression's variable m, all separated by the arithmetic sign +.

To approximate the population in 2030, we need to find the value of P(t) when t = 44, since 2030 is 44 years after 1986.

Using the given exponential growth model, we have:

\(P(t) = 3400^(0.0371t)\\P(44) = 3400^(0.0371*44)\\P(44) = 3400^1.6334\\P(44) = 11014.18\\\)

Therefore, the population of the rural city in 2030 is approximately 11,014.18.

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Answer:

506

Step-by-step explanation:

8 to the power of 3 is equal to 512

and then 9 times 2 divided by 3 is equal to 6 so you just subtract 6 from 512

Answer:

506

Step-by-step explanation:

\(8^{3}\) - 9 * 2 ÷ 3

Simplify using the order of operations (exponents first)

\(8^{3}\) = 512

512 - 9 * 2 ÷ 3

Multiply

512 - 18 ÷ 3

Divide

512 - 6

Subtract

506

Hope this helps :)

Answer:

The answer is 161.5

Step-by-step explanation:

Step-by-step explanation: The top half of the kite is 6 in times 17 in because 8.5 + 8.5 = 17 so its 102. Half of 102 is 51 so 51 is the area of the top half. The bottom half is 13 in times 17 in which equals 221. Half of 221 is  110.5. Then 110.5 + 51 = 161.5... So your answer is 161.5 square inches.

Answer:

113° = y

Step-by-step explanation:

y = 180 - 67

y = 113°

Hope this helps!

Answer:

M=7

Step-by-step explanation:

Answer:

7

Step-by-step explanation:

Subtract 9 from 9 and 65. Then divide 8 from 8m and 56. Then the answer is 7

The functions f and g are:

a. f(x) = 1/x

b. g(x) = x + 2

a) To find two functions f and g such that (fog)(x) = 1/(x + 2), we need to determine how the composition of the two functions f and g produces the given expression.

Let's start by assuming g(x) = x + a, where a is a constant. This means that g(x) adds the constant a to the input x.

Next, let's determine the function f(x) such that (fog)(x) results in the desired expression. We have:

(fog)(x) = f(g(x)) = f(x + a)

b) To simplify the expression 1/(x + 2) and make it match f(g(x)), we can consider f(x) = 1/x.

Substituting the expressions for f(x) and g(x) into (fog)(x), we have:

(fog)(x) = f(g(x)) = f(x + a) = 1/(x + a)

Comparing this with the desired expression 1/(x + 2), we see that a = 2. Therefore, the functions f and g are:

a. f(x) = 1/x

b. g(x) = x + 2

Using these functions, we can verify the composition (fog)(x):

(fog)(x) = f(g(x)) = f(x + 2) = 1/(x + 2)

Thus, (fog)(x) = 1/(x + 2), which matches the desired expression.

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The expression −(4b)(4b)(4b) using positive exponents is -(4b)³

From the question, we have the following parameters that can be used in our computation:

−(4b)(4b)(4b)

Express properly

So, we have

−(4b) * (4b) * (4b)

5⁻¹² * 32⁻³ * 9⁻¹⁵

By using the definition of positive exponents, we have

−(4b) * (4b) * (4b) = -(4b)³

So, the solution is -(4b)³

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Answer:

-63 ft

Step-by-step explanation:

15.75 x 4 = 63 (since you are diving downward it would be the same as going negative, so the altitude is going down)

Answer:

See below

Step-by-step explanation:

For the second step, \(\angle T\cong\angle R\) by Alternate Interior Angles. The rest of the steps appear to be correct.

9514 1404 393

Answer:

  5880 J

Step-by-step explanation:

PE = mgh = (60 kg)(9.8 m/s²)(10 m) = 5880 J