Mrs. Smith gave her Algebra class the following linear equation as part of their warm-up.

Picture attached!!

A.Both Maryanne's and Herb's equations have a different solution than the original.
B.Only Herb's equation has the same solution as the original equation.
C.Only Maryanne's equation has the same solution as the original equation.
D.Both Maryanne's and Herb's equations have the same solution as the original.

Answer: To find the height of the embankment, we need to first find the volume of the well and then the volume of the embankment.

Volume of the well = πr^2h = π * (d/2)^2 * h = π * (5/2)^2 * 24 = 157.08 cubic meters

Volume of the embankment = π * (R^2 - r^2) * h, where R is the outer radius of the embankment and r is the inner radius.

Outer radius of the embankment = (5 + 3)/2 = 4 m

Inner radius of the embankment = (5 - 3)/2 = 1 m

Volume of the embankment = π * (4^2 - 1^2) * h = π * 15 * h

We know that the volume of the well is equal to the volume of the embankment, so we can write:

157.08 = π * 15 * h

Solving for h, we get:

h = 157.08 / (π * 15) = 157.08 / 47.12 ≈ 3.32 m

So, the height of the embankment is approximately 3.32 meters.

Step-by-step explanation:

Part A:

[tex]B\cap D[/tex] is asking for what the sets B and D have in common:

   [tex]B\cap D = \{4\}[/tex]

since B and D only have 4 in common.

Now [tex](B \cap D)'[/tex] is asking for all of the things in the universal set [tex]U[/tex] that are not in [tex]B\cap D[/tex].  That's what the little tick mark on the right side means.

   [tex](B \cap D)' = \{2, 3, 6, 7\}[/tex]

Part B:

[tex]B' = \{2, 3, 7\}[/tex] since those are the things not in B.

[tex]D=\{3, 4\}[/tex]

[tex]B'\cup D[/tex] is asking for all the things in either [tex]B'[/tex] or [tex]D[/tex].

    [tex]B'\cup D = \{2, 3, 4, 7\}[/tex]

(We don't need to list 3 twice, even though it was in both sets. )

The specified radical expressions in the questions are evaluated and presented in the simplest form as follows;

(2) [tex]\sqrt[3]{x^2\cdot y^2} \cdot \sqrt[4]{x^5\cdot y^3} = \sqrt[12]{x^{23}\cdot y^{17}}[/tex]

(3) f(g(x)) = √(6·x + 1) - 5

(4) x = (15 ± √(33))/2

(5) x = 126

A radical is a mathematical expression which contains the radical expression, '√', which represent a fractional indices of the form 1/n.

(2) The specified radical expression is presented as follows;

∛(x²·y²) × [tex]\sqrt[4]{x^5 \cdot y^3}[/tex]

Expressing the above radical expression in index form, we get;

∛(x²·y²) × [tex]\sqrt[4]{x^5 \cdot y^3}[/tex] = [tex]x^{\frac{2}{3} }\times y^{\frac{2}{3} } \times x^{\frac{5}{4} } \times y^{\frac{3}{4}}[/tex]

Adding the index of like variable terms, we get;

[tex]x^{\frac{2}{3} }\times y^{\frac{2}{3} } \times x^{\frac{5}{4} } \times y^{\frac{3}{4}} = x^{\frac{2}{3} + \frac{5}{4} } \times y^{\frac{2}{3} + \frac{3}{4} }[/tex]

(2/3) + (5/4) = (2×4 + 5×3)/12 = 23/12 = 1 11/12

Therefore; [tex]x^{\frac{2}{3} + \frac{5}{4} } = x^{\frac{23}{12} }[/tex]

2/3 + 3/4 = (2 × 4 + 3 × 3)/(12) = 17/12 = 1 5/12

Therefore; [tex]y^{\frac{2}{3} + \frac{3}{4} } = y^{\frac{17}{12} }[/tex]

Which indicates that we get; [tex]x^{\frac{2}{3} + \frac{5}{4} } \times y^{\frac{2}{3} + \frac{3}{4} } = x^{\frac{23}{12} } \times y^{\frac{17}{12} }[/tex]

Therefore; ∛(x²·y²) × [tex]\sqrt[4]{x^5 \cdot y^3}[/tex] = [tex]x^{\frac{23}{12} } \times y^{\frac{17}{12} }[/tex]

(3) The functions, f(x) = √(3·x + 4) - 5, g(x) = (2·x - 1)

The composite function, f(g(x)) can be found as follows;

f(g(x)) = √(3·g(x) + 4) - 5 = √(3·(2·x - 1) + 4) - 5

f(g(x)) = √(3·(2·x - 1) + 4) - 5 = √((6·x - 3) + 4) - 5 = √(6·x + 1) - 5

(4) (√(x - 1)) = x - 7

Squaring both sides, we get;

(√(x - 1))² = (x - 7)²

Therefore;

(√(x - 1))² = x - 1 = (x - 7)² = x² - 14·x + 49

x - 1 = x² - 14·x + 49

x² - 14·x + 49 - (x - 1) = 0

x² - 15·x + 48 = 0

The quadratic formula can be used to solve the above equation to get;

x = (-(-15) ± √((-15)² - 4×1×48))/(2 × 1) = (15 ± √(33))/2

(5) 2·∛(x - 1) + 6 = 16

2·∛(x - 1) + 6 = 16

Subtracting 6 from both sides, we get;

2·∛(x - 1) + 6 - 6 = 16 - 6 = 10

2·∛(x - 1) = 10

∛(x - 1) = 10/2 = 5

∛(x - 1) = 5

∛(x - 1)^3 = 5^3

∛(x - 1)^3 = x - 1

5^3 = 125

∛(x - 1)^3 = x - 1 = 125

x = 125 + 1 = 126

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After all the spending costs, Tino's weekly salary is approximately $60.

What is the linear equation?

A linear equation is an algebraic equation of the form y=mx+b. where m is the slope and b is the y-intercept.

Let's call Tino's weekly salary "x".

Each week, Tino sets aside half of his salary for rent, so:

0.5x = rent

He also sets aside half of his salary for credit card payments, so

0.5x = credit card payments

And he sets aside a quarter of his salary for groceries and utilities, so:

0.25x = groceries and utilities

And he has approximately $15 left for entertainment, so:

x - 0.5x - 0.5x - 0.25x = 15

We can simplify this equation by combining the terms on the left side:

x - 1.25x = 15

And then solving for x:

-0.25x = 15

x = 60

Therefore, Tino's weekly salary is approximately $60.

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y-coordinates for x=3, 4.2, 2 are y=3.6, 4.8 and 2.6 respectively.

The general equation of a straight line is y=mx+c, where m is the gradient, and y = c is the value where the line cuts the y-axis. This number c is called the intercept on the y-axis.

The given equation is y=x+0.6

Find the y value for x=3, 4.2, 2

When x=3

y=3+0.6=3.6

When x=4.2

y=4.2+0.6=4.8

When x=2

y=2+0.6=2.6

Therefore, y-coordinates for x=3, 4.2, 2 are y=3.6, 4.8 and 2.6 respectively.

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Answer:

Add 3 and then multiply by 5.

Step-by-step explanation:

The problem looks like this to me:

[tex] \dfrac{m}{5} - 3 = 8 [/tex]

If this is correct, then the operations are:

Add 3 to both sides.

Multiply both sides by 5.

I don't see that answer. The picture is not very clear to me. What is the denominator of the fraction?

The expression for the average number of people (8x³ +70x² +145x+182)/(2x + 13)

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

The total number of people, f(x) = 8x³ +70x² +145x+182

Number of free books = 2x + 13

To determine the average number of people that download each of the free books,

We need to divide the total number of people that register by the number of free books available.

So, we have

Expression = (8x³ +70x² +145x+182)/(2x + 13)

Hence, the expression is (8x³ +70x² +145x+182)/(2x + 13)

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Answer:

26.it is all about thinking

The mortgage of A is $110158.2.

The mortgage of B is $137494.8.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

Mortgage A:

15 years at 4.5% with monthly payments of $611.99.

15 years = 15 x 12 = 180 months

Total paycheck.

= 180 x 611.99

= $110158.2

Mortgage B:

30 years at 4% with monthly payments of $381.93

30 years = 360 months

Total paycheck.

= 360 x 381.93

= $137494.8

Thus,

Mortgage A = $110158.2

Mortgage B = $137494.8

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Answer:

8.6 m

Step-by-step explanation:

DE = 2 7/10 m

     = 2 + 7/10

     = 2 + 0.7

DE = 2.7 m

EF = 5 9/10 m

    = 5 + 9/10

    = 5 + 0.9

EF = 5.9 m

DF = DE + EF

     = 2.7 + 5.9

     = 8.6 m

The mean of the sampling distribution (p) and The standard error of the mean (o)  are 56 and 2 respectively.

A probability distribution that is symmetric about the mean is the normal distribution, sometimes referred to as the Gaussian distribution. It demonstrates that data that are close to the mean occur more frequently than data that are far from the mean.

(a) The mean of the sampling distribution (p) is equal to the population mean, which is 56.

(b) The standard error of the mean (o) is calculated as the standard deviation of the population divided by the square root of the sample size. So for a sample of 36 participants:

o = 12 / √36 = 2

(c) The distribution of the sample means (p) will be approximately normal with a mean of 56 and a standard deviation of 2. To sketch this distribution with M ± 3 SEM, we would plot a normal distribution with mean 56 and standard deviation 2, and shade the region that is 3 standard errors away from the mean on either side.

This region would capture approximately 99.7% of the data if the samples were selected randomly and independently from the population.

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Answer:

Step-by-step explanation:

(1/3) x 81=27 people

Answer:

Step-by-step explanation:

To find the total number of seats in the theater, we can use the formula for the sum of an arithmetic series, which is given by:

S = n/2 * (a_1 + a_n)

where n is the number of terms in the series, a_1 is the first term, and a_n is the last term.

In this case, the first term is 25 seats and the last term is 25 + (38-1) * 4 seats (since the number of seats in each row increases by 4 each time). So, we have:

n = 38 (the number of rows)

a_1 = 25

a_n = 25 + (38-1) * 4 = 25 + 37 * 4 = 25 + 148 = 173

Now, we can substitute these values into the formula:

S = n/2 * (a_1 + a_n) = 38/2 * (25 + 173) = 19 * 198 = 3,762

So, the total number of seats in the theater is 3,762, which corresponds to option O3,762.

Answer:

4x + 42

Step-by-step explanation:

[tex]\text{Perimeter}=(x+15)+(2x+15)+(x+12)=4x+42[/tex]

The inverse of the function is f⁻¹ ( x ) = 5 / ( x - 4 )

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

Substituting the values in the equation , we get

f ( x ) = ( 5/x ) + 4   be equation (1)

On simplifying the equation , we get

y = ( 5/x ) + 4

Now , replacing x with y , we get

x = ( 5/y ) + 4

On solving for y , we get

5/y = x - 4

y = ( 5 / x - 4 )

Now , the inverse of the function is f⁻¹ ( x ) = 5 / ( x - 4 )

Hence , the equation is f⁻¹ ( x ) = 5 / ( x - 4 )

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a. Yes, The answer is correct.

b. When we subtract the second equation from the first, the next step would be 3x = 9.

What is a system of linear equations?

The collection of two or more linear equations involving the same variables is known as a system of linear equations. In this case, linear equations are first-order equations, where the maximum power of the variable is 1.

Part a:

Given that, a customer purchases 8 bags of cat food and 2 bags of dog food, then the total weight of the purchase is 44 pounds.

Another customer purchases 5 bags of cat food and 2 bags of dog food, then the total weight of the purchase is 35 pounds.

let the weight of the cat food be 'x' and the dog food is 'y'.

For the first customer,

Total weight will be = 8x + 2y = 44 .....eq 1

For the second customer,

Total weight will be = 5x + 2y = 35 .....eq 2

Which are the two equations given above,

So, The equations are correct.

Part b:

Eliminate y terms from the equations.

Subtract eq 2 from eq 1:

 8x + 2y = 44

-(5x + 2y = 35)

______

 3x + 0  = 9

3x = 9, which contradicts the above-given step '13x = 79'

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The correct option is A {-5, 0, 3, 4}.

In mathematics, the domain of a function is the set of all possible input values (independent variable) for which the function is defined. In other words, the domain is the set of values that we can substitute for the independent variable in a function to produce a meaningful output.

For example, consider the function f(x) = 2x. Here, we can substitute any real number for x and get a meaningful output. Therefore, the domain of this function is all real numbers, or (-∞, ∞). However, if we consider the function g(x) = 1/x, we can see that we cannot substitute 0 for x because division by 0 is undefined. Therefore, the domain of this function is all real numbers except 0, or (-∞, 0) U (0, ∞).

The domain of a relation is the set of all possible values for the independent variable (x) for which there exists a corresponding value of the dependent variable (y). In this case, the given coordinates are (1,3), (4,1), and (-5,-4).

The domain of the relation would be the set of x-values that correspond to the given coordinates. So, the domain of this relation is {-5, 1, 4}.

Therefore, the correct answer is A: {-5, 0, 3, 4}.

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Answer:

x = 16

Step-by-step explanation:

subtract 12 from both sides to isolate the variable and its coefficient

4x = 64

divide both sides by 4 to get x

x = 16

Answer:

x = 16

Step-by-step explanation:

4x+12=76

Step 1: Subtract 12 from both sides.

4x + 12 - 12 = 76 - 12

4x = 64

Step 2: Divide both sides by 4.

[tex]\frac{4x}{4} = \frac{64}{4}[/tex]

x = 16

A quotation isolated from the rest of the writing - sometimes called "quote vomit" type of quote is Sample #2.

The option (a) is correct.

Famous people who discuss their opinions on a given subject often employ quotation marks around their words. The brief nature of a quotation allows it to share individuality. The citation served as a means of sharing ideas and serving as a source of historical information.

The quotation, which is sometimes referred to as "quote vomit," was cut off from the remainder of the text.

The sentences are directed at their objective. Understanding how the universe functions and how we fit into it can be done through the metaphor of weaving.

As a result, the quote isolated from the rest of the writing - sometimes called "quote vomit" type of quote is Sample #2. Therefore, option (a) is correct.

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Answer:

A and C are the correct answers

Step-by-step explanation:

Answer:

And C is the answer to the question

Answer:

[B]. (1,-5)

Step-by-step explanation:

Given:

[tex]\begin{bmatrix}4x+2y=-6\\ 3x-2y=13\end{bmatrix}[/tex]

Solve:

[tex]\begin{bmatrix}4x+2y=-6\\ 3x-2y=13\end{bmatrix}[/tex]        Since 2y - 2y = 0 we take that away now we have;

[tex]4x=-6\\3x=13[/tex]        Add 4x + 3x = 7x

[tex]\frac{7x}{7} =\frac{7}{7}[/tex] Divide both sides by 7.

[tex]x=1[/tex]

Now substitute x to find y.

[tex]4(1)+2y=-6[/tex]

[tex]4 + 2y =-6[/tex]  Add 6 to the other side.

[tex]10 = 2y[/tex] Divide both sides by 2.

[tex]\frac{10}{2} =\frac{2y}{2}[/tex]

[tex]y = 5[/tex]

Hence, the answer is [B]. (1,-5)

RevyBreeze

Answer: To find the distance between the tops of two buildings, we first need to find the horizontal distance between the two buildings. This distance can be found using the Pythagorean theorem.

Let's call the horizontal distance between the two buildings "d".

d^2 = 12^2 + (34 - 29)^2

d^2 = 144 + 25

d^2 = 169

d = 13

So, the horizontal distance between the two buildings is 13 meters.

To find the distance between their tops, we simply add the height of each building:

distance = 34 + 29 = 63 meters

So, the distance between the tops of the two buildings is 63 meters.

Step-by-step explanation:

Answer:

Step-by-step explanation:

Calculated based on 2 given angles and 1 given side.

∠B = 180° - A - C = 0.99484 rad = 57°

∠B = 57°

a = c·sin(A)/sin(C) = 527.21059

b = c·sin(B)/sin(C) = 811.83311

Answer: The range of the tangent function is (-∞,∞). So the answer is A: All real numbers.

Step-by-step explanation:

The numeric value of the marginal revenue at 33 units will be $336.

The sum of the units sold times the price per unit is the revenue. Multiply the output level by the pricing function to get the revenue function.

Revenue function is R(q) = - 8q ^ 2 + 600q

Differentiate with respect to q

R^ prime (q) = - 8(2q) + 600(1)

R' (q)=-16q+600 ...(1)

substitute q = 33 in equation

MR(113) = - 8(33) + 600

=-264 + 600

MR (113)= $336 per unit

The marginal revenue is $336.

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Jenny's average jogging speed in the distance covered is; 10 miles/hr

Let x miles/hr be the speed that Jenny walks at

Then, 2x miles/hr is the speed that Jenny runs at

She jogs for  9.5 miles

2x miles = 1 hours

9.5 miles = a hours

a = 9.5/2x hours

She walks for 2.5 miles

x miles = 1 hour

2.5 miles = b

b = 2.5/x hours

Thus;

(9.5/2x) + (2.5)/x = 1.45

Multiply through by 2x to get;

9.5 + 5 = 2.9x

14.5/2.9 = x

x = 5 miles/hr

Jogging speed = 2 * 5 = 10 miles/hr

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Answer:

Step-by-step explanation:

Answer:

The number is -10.4

Explanation:

Assume that the number we are looking for is x.

Now, we want to get 10 times te sum of half the number and 6 and equate this expression to 8. Then we can solve for x

Let's take this step by step:

half the number is 0.5x

the sum of half the number and 6 is 0.5x + 6

10 times the sum of half the number and 6 is 10(0.5x +6)

10 times the sum of half the number and 6 equals 8 is 10(0.5x+6) = 8

Now we can solve for x as follows:

10(0.5x + 6) = 8

5x + 60 = 8

5x = 8 - 60

5x = -52

x = -52/5

x = -10.4

Hope this helps :)

A quadratic function could represent the data in the table, as the increase rate decreases as x increases, meaning that the function could be approaching it's vertex.

Traditionally, functions are classified as either linear or exponential, as follows:

As there is not a constant neither a multiplicative rate of change for the table, the function is neither linear nor exponential.

Considering that from x = 1 to x = 4 the rate of change is of 4/3, while from x = 16 to x = 25 the rate of change is of 4/9, that is, the increase rate decreases as x increases, the function is classified as a quadratic function.

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Answer:

Step-by-step explanation:

Using the ratio of corresponding side lengths, we have:

x/42 = 9/35

y/21 = 9/35

z/35 = 9/35

Solving for x, y, and z:

x = (9/35) * 42 = 14

y = (9/35) * 21 = 7

z = 9

So the other two sides of the smaller triangle are 14 and 7 units.