2
Which of the following expressions is equivalent to
V162?
O
27.32
36
27.1/6
.
9

Answer:

\(\boxed{\textsf{16y + 2 is Equivalent to 8 (2y + 1/4).}}\)

Step-by-step explanation:

\(\textsf{We are asked to find an \underline{equivalent expression}.}\)

\(\textsf{This expression is set up to allow us to use the \underline{Distributive Property}.}\)

\(\Large\textsf{What is the Distributive Property?}\)

\(\textsf{The \underline{Distributive Property} is a property that allows us to distribute.}\)

\(\large\underline{\textsf{For this problem;}}\)

\(\textsf{We can use the Distributive Property to distribute the 8 into values in the Parentheses.}\)

\(\large\underline{\textsf{Distribute:}}\)

\(\mathtt{8(2y+\frac{1}{4} )}\)

\(\mathtt{(8 \times 2y) + (8 \times \frac{1}{4}) .}\)

\(\boxed{\textsf{16y + 2 is Equivalent to 8 (2y + 1/4).}}\)

Answer:

16y + 2

Step-by-step explanation:

Now we have to,

→ Find the equivalent expression.

The expression is,

→ 8(2y + (1/4))

Let's simplify the expression,

→ 8(2y + (1/4))

→ 8(2y) + 8(1/4)

→ 16y + (8/4)

→ 16y + 2

Hence, the answer is 16y + 2.

Answer:

11 and 33

Step-by-step explanation:

The greater of two numbers is 3 times the smaller.

Let the numbers be

n and 3n

sum is 44

n + 3n = 44

4n = 44

Divide both sides by 4

n = 11

3n = 3 * 11

3n = 33

Answer:

smaller number is 11

bigger number is 33.

Step-by-step explanation:

Lets make the smaller number be a, the bigger number 3a since its 3 times a's value

the sum of a and 3a is 44

so we write

a+3a = 44

combine like terms

a+3a = 4a

4a = 44

divide both sides by 4

a = 11.

Now we know the smaller number is equal to 11, but we are not done just yet.

We have to find the value of the bigger number by plugging in 11 into our equation

11+3*11 = 44

11 + 33 = 44

which means the bigger number is 33

the slope is the number that x is multiplied by so the answer is C)7

Answer: No solution

Step-by-step explanation: when you subtract 5p from 9p you get 4p. Now you have 4p on both sides. To even it out, you have to subtract 4p from 4p. Not you are only left with the 3 and 6. The final answer is 3>6 which isn't true because 3 is LESS than 6. That is why this question has no solution.

The function g(x) = 8√x * eˣ is given. To find the derivative g'(x), we can use the product rule. The derivative of g(x) = 8√x * eˣ is g'(x) = 4√x * eˣ + 8√x * eˣ.

The product rule states that if we have a function h(x) = f(x) * g(x), then the derivative of h(x), denoted as h'(x), is equal to f'(x) * g(x) + f(x) * g'(x).

In this case, f(x) = 8√x and g(x) = eˣ. We need to find the derivatives f'(x) and g'(x) separately.

To find f'(x), we can use the power rule and the chain rule. The power rule states that the derivative of xⁿ is n * \(x^(n-1)\). Applying the power rule, we have f'(x) = 8 * (1/2) * \(x^(1/2 - 1)\) = 4√x.

To find g'(x), we can use the derivative of the exponential function, which states that the derivative of eˣ is eˣ. Therefore, g'(x) = eˣ.

Now, we can apply the product rule to find the derivative of g(x).

g'(x) = f'(x) * g(x) + f(x) * g'(x)

= (4√x) * eˣ + 8√x * eˣ

= 4√x * eˣ + 8√x * eˣ.

So, the derivative of g(x) = 8√x * eˣ is g'(x) = 4√x * eˣ + 8√x * eˣ.

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Answer:

8

5

6

Step-by-step explanation:

16-8=8

3+27-25=5

x^4/x^3= x=6

Answer:

a) y square-x square

(4)2-(2)2

16-4

12

b)x1+x3-y2

3+ (3)3-(5)2

3+27-25

30-25

5

c) x4÷x3

(6)4÷(6)3

1296÷216

6

The solution of the equation 3z minus 2 is equal to 46 is 16.

The given equation '3z minus 2 is equal to 46' can be written as

    3z - 2  =   46

Now solving for z because the value of z will give the required solution of the given equation. So now finding the z from the equation:

   3z = 46  + 2

   3z =  48

   z = 48/3

   z = 16

The value of the z is 16 which represents the solution of the given equation i.e 3z minus 2 is equal to 46.

Therefore it is concluded that the solution of the equation 3z minus 2 is equal to 46 is 16.

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Answer:

The numbers in increasing order are:

-1.3, -0.33, 0.4, 0.55

Step-by-step explanation:

We have numbers:

-1.3,0.4,-1/3,5/9

We need to arrange in increasing order.

First convert fractions into decimals.

-1/3 = -0.33

5/9 = 0.55

We have numbers: -1.3, 0.4, -0.33, 0.55

Arranging numbers in increasing order we arrange them form smallest to largest.

The numbers in increasing order are:

-1.3, -0.33, 0.4, 0.55

The series f(x), f′(x), f′(x), and ∫f(x) dx all converge for the entire real number line, -∞ < x < ∞, including the endpoints.

The intervals of convergence are as follows: (a) f(x) converges for -∞ < x < ∞.

(b) f′(x) converges for -∞ < x < ∞.

(c) f′(x) converges for -∞ < x < ∞.

(d) ∫f(x) dx converges for -∞ < x < ∞.

The given series f(x) can be written as the sum of the terms (-x^3)^n. We need to find the intervals of x for which this series converges.

For any value of x, when (-x^3)^n is raised to a positive power n, it becomes positive. Therefore, the series will converge for any x value.

Hence, the intervals of convergence for f(x), f′(x), f′(x), and ∫f(x) dx are -∞ < x < ∞. To check for convergence at the endpoints of the interval, we need to evaluate the series for x = ±∞.

For both cases, the terms (-x^3)^n will approach zero as n approaches infinity. Therefore, the series will converge at the endpoints as well.

In summary, the series f(x), f′(x), f′(x), and ∫f(x) dx all converge for the entire real number line, -∞ < x < ∞, including the endpoints.

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When considering two nonnegative numbers p and q such that p+q=6, the difference between the maximum and minimum of the quantity (p^2q^2)/2 is 81 - 0 = 81.

To find the maximum and minimum of the quantity (p^2q^2)/2, we can use the AM-GM inequality.
AM-GM inequality states that for any nonnegative numbers a and b, (a+b)/2 ≥ √(ab).

So, in our case, we can write:
(p^2q^2)/2 = (p*q)^2/2

Let x = p*q, then we have:
(p^2q^2)/2 = x^2/2
Since p and q are nonnegative, we have x = p*q ≥ 0.

Using the AM-GM inequality, we have:
(x + x)/2 ≥ √(x*x)
2x/2 ≥ x
x ≥ 0
So, the minimum value of (p^2q^2)/2 is 0.
To find the maximum value, we need to use the fact that p+q=6.

We can rewrite p+q as:
(p+q)^2 = p^2 + 2pq + q^2
36 = p^2 + 2pq + q^2
p^2q^2 = (36 - p^2 - q^2)^2

Substituting this into the expression for (p^2q^2)/2, we get:
(p^2q^2)/2 = (36 - p^2 - q^2)^2/2
To find the maximum value of this expression, we need to maximize (36 - p^2 - q^2)^2.

Since p and q are nonnegative and p+q=6, we have:
0 ≤ p, q ≤ 6
So, the maximum value of (36 - p^2 - q^2) occurs when p=q=3.

Thus, the maximum value of (p^2q^2)/2 is:
(36 - 3^2 - 3^2)^2/2 = 81

Therefore, the difference between the maximum and minimum of (p^2q^2)/2 is:
81 - 0 = 81.

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The standard deviation of the sample mean differences is 4.854

The table of values is given as:

Sample      Standard deviation

Red box     3.868

Blue box   2.933

The standard deviation of the sample mean differences is calculated using:

\(\sigma = \sqrt{\sigma_1^2 + \sigma_2^2}\)

This gives

\(\sigma = \sqrt{3.868^2 + 2.933^2}\)

Evaluate the expression

\(\sigma = 4.854\)

Also, the table of value do not give any information regarding the sample size.

This means that the sample size of the session regarding the number of people would purchase the red box and the blue box are unknown

Hence, the standard deviation of the sample mean differences is 4.854

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a)

Average price charged :

\(P=\dfrac{1.25+0.90+0.75+1.10}{4}\\\\P=\$1\)

b)

Total income, T =$ 800×1.25 + 1600×0.90 + 2000×0.75 + 600×1.10

T = $4600 .

Total number of box, n = 800 + 1600 + 2000 + 600 = 5000.

Average price per box, \(A=\dfrac{4600}{5000}=\$0.92/box\) .

Hence, this is the required solution.

Answer:

1. 38, 80, 89 and 4. 14, 15, 29

I don't know if there is supposed to be only one, but both of those do not form right triangles.

Step-by-step explanation:

Evaluate all of them and see if they meet the requirements of the Pythagorean Theorem, a² + b² = c².

1. 38, 80, 89

a² + b² = c²

38² + 80² = 89²

1444 + 6400 = 7921

7844 ≠ 7921.

This is an answer because it doesn't satisfy the Pythagorean Theorem.

2. 16, 63, 65

a² + b² = c²

16² + 63² = 65²

256 + 3969 = 4225

4225 = 4225

This isn't the answer because it satisfies the Pythagorean Theorem.

3. 36, 77, 85

a² + b² = c²

36² + 77² = 85²

1296 + 5929 = 7225

7225 = 7225

This isn't the answer because it satisfies the Pythagorean Theorem.

4. 14, 15, 29

a² + b² = c²

14² + 15² = 29²

196 + 225 = 841

421 ≠ 841

This is an answer because it does not satisfy the Pythagorean Theorem.

Answer:

composite!!!!!! I hope this helpssd

Answer:

composite

Step-by-step explanation:

Answer:

The answer is "They are skew and will never intersect".

Step-by-step explanation:

Please find the graph file in the attachment.

In the given scenario, since the two lines are neither parallel nor intersect, these are skewed. Each line will be in a parallel plane, therefore prevents them from crossing each other. Parallel indicates traveling in the same direction, but not converging or diverging.

Answer:

A or ,They are skew and will never intersect.

Step-by-step explanation:

edge 2021

The length of the rectangle is 6x² - 7x + 5, and the width is 1.

We have,

To factor the expression 6x² - 7x + 5 and determine the expressions for the length and width of the rectangle, we need to find two binomial expressions that, when multiplied, give us the given expression.

The expression 6x² - 7x + 5 cannot be factored into two binomial expressions with integer coefficients.

Therefore, we'll represent the length and width of the rectangle using the given expression itself.

Length = 6x² - 7x + 5

Width = 1 (or any constant value)

Thus,

The length of the rectangle is 6x² - 7x + 5, and the width is 1.

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The given polygons are similar and the scale factor of dilation is 3 : 2

Given data ,

Let the scale factor of the dilation be represented as k

Now , the value of k is

The measure of the ratio of corresponding sides are given as

21 / 14 = 12 : 8

3 : 2 = 3 : 2

Therefore , the dilation factor is 3 : 2

And , the measure of x is given by

21 / 14 = x / 12

3 / 2 = x / 12

Multiply by 12 on both sides , we get

x = 18

Hence , the dilation of polygon is solved

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The complete question is attached below :

Solve for x given that the polygons are similar. Then find the scale factor of the smaller figure to the larger figure

Answer:

idrk

Step-by-step explanation:

Answer:

84 cups of chicken broth

Step-by-step explanation:

Ratio of chicken broth to flour = 12 cups : 1 1/4 cups

Mr. Clark used 8 3 /4 cups of flour for his gumbo.

How many cups of chicken broth did he use?

Let x = cups of chicken broth he used

Ratio of chicken broth to flour = x cups : 8 3/4 cups

Equate the ratios

12 cups : 1 1/4 cups = x cups : 8 3/4 cups

12 ÷ 5/4 = x ÷ 35 / 4

12 * 4/5 = x * 4/35

48 / 5 = 4x / 35

Cross product

48 * 35 = 5 * 4x

1,680 = 20x

x = 1,680 / 20

= 84

x = 84 cups

The  solution of the given system of equations is (8, -1). of the given system of equations is (8, -1).

One method to solve the given system of equations is substitution:

- Solve one of the equations for one of the variables (e.g., x = 9 + y from the second equation).

- Substitute the expression for the variable into the other equation.

- Solve the resulting equation for the remaining variable.

- Substitute the value for the remaining variable back into one of the original equations to find the value of the other variable

Using this method with the given equations

- x - y = 9 -> x = 9 + y

- 3x + 2y = 22 -> 3(9 + y) + 2y = 22

- Simplifying and solving for y: 27 + 5y = 22 -> 5y = -5 -> y = -1

- Substituting y = -1 into x = 9 + y: x = 8

To check this solution, we can substitute these values back into both original equations and confirm that they are true statements.

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Answer:

Step-by-step explanation:

b/c we know that these triangles both have equal sides... that is given that ab and be are the same length.   and that be and cd are parallel , we know that they both are isosceles triangles and that the base angles are the same.  The side on ad and ae  have equal angles.

so we can make the equation

2a +56 = 180  (b/c we know that around a triangle it's 180°

2 a = 124

a = 62

so ∠ BAE = 62°

:)

The relationship is proportional when John works for the hour allocated.

Relationships between two variables that are proportional occur when their ratios are equal. Another way to consider them is that in a proportional relationship, one variable is consistently equal to the other's constant value. The "constant of proportionality" is the name of that constant.

Because the rate of change in a proportional relationship is constant (and equal to the constant of proportionality), it is a linear relationship.

In this case, when John works for an hour, he is paid $15, when he works for 2 hours, he's paid $30.

The constant will be:

= 15 / 1 or 30/2

= $15 per hour.

Therefore, it's a proportional relationship.

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When John works for an hour, he is paid $15, when he works for 2 hours, he's paid $30. Is the relationship proportional?

Answer: 30$

Step-by-step explanation:

Equation

C=5h

c=5(6)

c=30

ANSWER

The short piece is 10 meters long and the long piece is 33 meters long

EXPLANATION

Let the length of the shorter piece be x.

Let the length of the longer piece be y.

We have that the total length of the banner is 43 meters. This means that:

x + y = 43 ___(1)

The short piece is 23 meters shorter than the long piece. This means that:

x = y - 23 _____(2)

Now, we have a system of two simultaneous equations:

x + y = 43

x = y - 23

We can solve this by substitution.

Substitute the second equation into the first equation.

That is:

y - 23 + y = 43

Collect like terms:

y + y = 43 + 23

2y = 66

Divide through by 2:

y = 66 / 2

y = 33 m

Recall that:

x = y - 23

Therefore:

x = 33 - 23

x = 10 m

Therefore, the short piece is 10 meters long and the long piece is 33 meters long.

The equation of the tangent line represents a straight line that passes through the point of tangency and has a slope of -16.

The slope of the tangent line to the graph of the function y = x^4 - 10x^2 + 9 at x = 1 can be found by taking the derivative of the function and evaluating it at x = 1. The equation of the tangent line can then be determined using the point-slope form.

Taking the derivative of the function y = x^4 - 10x^2 + 9 with respect to x, we get:

dy/dx = 4x^3 - 20x

To find the slope of the tangent line at x = 1, we substitute x = 1 into the derivative:

dy/dx (at x = 1) = 4(1)^3 - 20(1) = 4 - 20 = -16

Therefore, the slope of the tangent line is -16.

To find the equation of the tangent line, we use the point-slope form: y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope.

Given that the point of tangency is (1, y(1)), we substitute x1 = 1 and y1 = y(1) into the equation:

y - y(1) = -16(x - 1)

Expanding the equation and simplifying, we have:

y - y(1) = -16x + 16

Rearranging the equation, we obtain the equation of the tangent line:

y = -16x + (y(1) + 16)

To find the slope of the tangent line, we first need to find the derivative of the given function. The derivative represents the rate of change of the function at any point on its graph. By evaluating the derivative at the specific value of x, we can determine the slope of the tangent line at that point.

In this case, the given function is y = x^4 - 10x^2 + 9. Taking its derivative with respect to x gives us dy/dx = 4x^3 - 20x. To find the slope of the tangent line at x = 1, we substitute x = 1 into the derivative equation, resulting in dy/dx = -16.

The slope of the tangent line is -16. This indicates that for every unit increase in x, the corresponding y-value decreases by 16 units.

To determine the equation of the tangent line, we use the point-slope form of a linear equation, which is y - y1 = m(x - x1). We know the point of tangency is (1, y(1)), where x1 = 1 and y(1) is the value of the function at x = 1.

Substituting these values into the point-slope form, we get y - y(1) = -16(x - 1). Expanding the equation and rearranging it yields the equation of the tangent line, y = -16x + (y(1) + 16).

The equation of the tangent line represents a straight line that passes through the point of tangency and has a slope of -16.

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