Which expression is equivalent to the following complex fraction?

1 minus StartFraction 1 Over x EndFraction divided by 2

[tex]\large\displaystyle\text{$\begin{gathered}\sf 9|x-8| < 36 \end{gathered}$}[/tex]

[tex]\large\displaystyle\text{$\begin{gathered}\sf Divide \ both \ sides \ by \ 9. \end{gathered}$}[/tex]

[tex]\large\displaystyle\text{$\begin{gathered}\sf Solve \ Absolute \ Value. \end{gathered}$}[/tex]

[tex]\large\displaystyle\text{$\begin{gathered}\sf We \ know \ x-8 < 4 \ and \ x-8 > -4 \end{gathered}$}[/tex]

         [tex]\large\displaystyle\text{$\begin{gathered}\sf x-8 < 4 \ (Condition \ 1) \end{gathered}$}\\\large\displaystyle\text{$\begin{gathered}\sf x-8+8 < 4+8 \ (Add \ 8 \ to \ both \ sides) \end{gathered}$}\\\large\displaystyle\text{$\begin{gathered}\sf x < 12 \end{gathered}$}[/tex]

           [tex]\large\displaystyle\text{$\begin{gathered}\sf x-8 > -4 \ (Condition \ 2) \end{gathered}$}\\\large\displaystyle\text{$\begin{gathered}\sf x-8+8 > -4+8 \ (Add \ 8 \ to \ both \ \ sides) \end{gathered}$}\\\large\displaystyle\text{$\begin{gathered}\sf x > 4 \end{gathered}$}[/tex]

[tex]\underline{\boldsymbol{\sf{Answer}}}[/tex]

[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf x < 12 \ and \ x > 4 \end{gathered}$} }[/tex]

[tex]\large\displaystyle\text{$\begin{gathered}\sf Therefore,\bf{\underline{the \ correct \ option}} \ \end{gathered}$}\large\displaystyle\text{$\begin{gathered}\sf is \ \bf{\underline{"A"}}. \end{gathered}$}[/tex]

Answer:

x=20

Step-by-step explanation:

x-15=5

x=5+15

x=20

There does not appear to be a linear relationship between the high school girls' height and their IQ scores.

The complete question is added as an attachment

To plot the scatter plot, we make use of the following representations:

Next, we enter the values in a graphing calculator.

From the summary on the graphing calculator, we can conclude that the scatter plot is (c)

To determine the sample correlation coefficient, we make use of the following representations:

Next, we enter the values in a graphing calculator.

From the graphing calculator, we have the following summary:

X Values

Y Values

X and Y Combined

R Calculation

r = ∑((X - My)(Y - Mx)) / √((SSx)(SSy))

r = -19.25 / √((107.875)(813.5))

r = -0.065

Hence, the sample correlation coefficient is -0.065

In (b), we have:

r = -0.065

This means that there is a negative correlation

i.e. There does not appear to be a linear relationship between the high school girls' height and their IQ scores.

To do this, we have:

Number of pairs, n = 8

Significance level =0.01

Using a graphing calculator;

At 0.01 significance level, the critical correlation coefficient is 0.7887

0.7887 is greater than 0.01

This means that we accept the null hypothesis.

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The volumes of the right prisms are listed below:

In this problem we have six cases of right prisms with rectangular bases, the volume of right prisms (V), in cubic length units, is equal to the product of the area of the base (A), in square length units, and the height (h), in length units. The equation of the volume of the right prism is shown below:

V = w · l · h     (1)

Where:

Now we proceed to calculate each volume:

Prism 1 (w = 2 / 3 ft, l = 1 / 3 ft, h = 1 / 2 ft)

V = (2 / 3 ft) · (1 / 3 ft) · (1 / 2 ft)

V = 1 / 9 ft³

Prism 2 (w = 1 / 8 in, l = 3 / 4 in, h = 13 / 16 in)

V = (1 / 8 in) · (3 / 4 in) · (13 / 16 in)

V = 39 / 512 in ³

Prism 3 (w = 7 / 8 cm, l = 1 / 4 cm, h = 1 / 12 cm)

V = (7 / 8 cm) · (1 / 4 cm) · (1 / 12 cm)

V = 7 / 384 cm³

Prism 4 (w = 1 / 7 cm, l = 7 / 8 cm, h = 2 / 3 cm)

V = (1 / 7 cm) · (7 / 8 cm) · (2 / 3 cm)

V = 1 / 12 cm³

Prism 5 (w = 9 / 10 m, l = 2 / 3 m, h = 1 / 5 m)

V = (9 / 10 m) · (2 / 3 m) · (1 / 5 m)

V = 3 / 25 m³

Prism 6 (w = 7 / 8 yd, l = 6 / 7 yd, h = 1 / 2 yd)

V = (7 / 8 yd) · (6 / 7 yd) · (1 / 2 yd)

V = 3 / 8 yd³

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The choice which is equivalent is  [tex]6x^2\sqrt{3}[/tex] option B

We have that;

[tex]\sqrt{6x^2} * \sqrt{18x^2}[/tex] where [tex]x\geq 0[/tex]

First, we factorize the square root

= [tex]\sqrt{2 * 3 * x^2 } . \sqrt{3 * 3 * 2 * x^2}[/tex]

Find the common factors

= [tex]2 * 3 x^2\sqrt{3}[/tex]

= [tex]6x^2\sqrt{3}[/tex]

Thus, the choice which is equivalent is  [tex]6x^2\sqrt{3}[/tex] option B

The complete question is;

Which choice is equivalent to the product below for acceptable values of X? sqrt 6x² * sqrt 18x²

a. [tex]6\sqrt{3x}[/tex]

b. [tex]6x^2\sqrt{3}[/tex]

c. [tex]6\sqrt{18x}[/tex]

d. [tex]\sqrt{108x^2}[/tex]

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Answer:

24

Step-by-step explanation:

1) according to the additional (see the attached picture) f(6)= -6 and g(5)= -5. Then

2) the given experssion can be written:

f(6)-6*g(5)=-6-6*(-5)=-6+30=24.

Answer:

I think its 19.75

Answer:

y = x - 2

Step-by-step explanation:

The general structure of an equation in slope-intercept form is:

y = mx + b

In this formula, "m" represents the slope and "b" represents the y-intercept. Before writing our equation in this form, we first need to find the slope. The slope can be found using the point-slope formula:

y₁ - y₂ = m(x₁ - x₂)

In this formula, "m" represents the slope, "x₁" and "y₁" represent the values from Point One, and "x₂" and "y₂" represent the values from Point Two. You can find the slope by plugging the values from the points into the equation and then simplifying.

x₁ = 0                 x₂ = -3

y₁ = -2                y₂ = -5

y₁ - y₂ = m(x₁ - x₂)

(-5 - (-2)) = m(-3 - 0)

-3 = m(-3)

1 = m

Now that we have a value for the slope, we can use the values from either one of the points to solve for the y-intercept (from the slope-intercept form equation).

m = 1

x = 0

y = -2

y = mx + b

-2 = (1)(0) + b

-2 = 0 + b

-2 = b

Therefore, the equation of the line in slope-intercept form is:

y = x - 2

Answer:

Step-by-step explanation:

for horizontal line slope m=0

eq. of horizontal line at (0,7) with slope 0 is

y-7=0(x-0)

y-7=0

or

y=7

slope of vertical line=∝

eq of vertical line through (0,7) is

y-7=∝(x-0)

or

x-0=0(y-7)

x-0=0

or

x=0

The value of the sum of the angles x + y of the given triangle is; 220°

We know that the sum of angles in a straight line is equal to 180°. Thus;

∠CFE + ∠OFE = 180

140 + ∠OFE = 180

∠OFE = 180 - 140

∠OFE = 40°

Similarly, we can use the same principle to get;

∠OEF + ∠BEF = 180°

∠OEF + y = 180°

∠OEF = 180 - y

Similarly,

∠AOF + ∠EOF = 180°

x + ∠EOF = 180°

∠EOF = 180 - x

Sum of angles in a triangle is equal to 180°. Thus;

40 + 180 - y + 180 - x = 180

Rearranging gives;

x + y = 180 + 180 + 40 - 180

x + y = 220°

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Answer: B

Step-by-step explanation: Since x is less than 7, the graph would be all real numbers that are less than 7, so the arrow would be on the left.

Also, since x is not 7 itself (not less than or equal to), the dot cannot be a full dot. Thus, the dot must be open (or curved in some textbooks) to indicate x is not apart of 7 but less than 7.

Hope this helped!

The first day when he would do these activities on the same day is December 7, 2023.

In order to determine which day Mr. Carson would wash his car, check his oils and check the tire pressure, the multiple of 8, 7, and 9 have to be determined.

A multiple of a number is the product of an integer and that number. A common multiple is a number that is common to all three numbers. The lowest common multiple of 8, 7 and 9 is 504. So, in 504 days he would do all three activities on the same day.

In order to convert 504 days, take note of the following:

365 days = 1 year

12 month = 1 year

1 month = 4 weeks

30 days = 1 month

504 / 365 = 1 year 139 days

139 days / 30 days  = 4 months 19 days

504 days = 1 year, 4 months and 19 days

1 year, 4 months and 19 days + July 18, 2022 = December 7, 2023

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Answer:

6

Step-by-step explanation:

Absolute value is a number's distance from 0, another way to think of it is that it makes any number positive, so |-6|, the absolute value of -6 would be 6.

Answer:

6

Step-by-step explanation:

The absolute value is always positive, since it's the number's distance from zero.

Thus, the absolute value of -6 is 6.

Done !!

Answer:

Inequality Form: x > 17

Interval Notation: (17, ∞)

__________________________________________________________

[tex]\text{\textbf{Hello!} In this question, we are trying to find the equation of a line}\\\text{that is \underline{perpendicular} to our given equation}[/tex]
__________________________________________________________

[tex]\textbf{Explanation:}\\\\\text{To help us answer our question, we need to note some of our given info:}\\\\\text{Equation: y = 5x + 1}\\\\\text{Point passed through: (5, -2)}\\\\\text{We can use the above information to help us find our perpendicular equation.}\\\\\text{We will be using the slope-intercept form equation to help get us our answer:}\\\\\text{y = mx + b}[/tex]

[tex]\text{When a line is perpendicular to an equation, it means that its slope is }\\\text{\textbf{opposite} which results in the lines to meet at a \underline{90-degree} angle.}[/tex]
__________________________________________________________

[tex]\textbf{Solve:}\\\\\text{To get our perpendicular slope, we will use the formula:}\\\\\text{m1 = }-\frac{1}{m2}\\\\\text{m1 will be our given slope (5) and m2 will be our already provided slope. }\\\\\text{This is also known as a \underline{negative reciprocal}. }\\\\\text{Therefore: m1 = }-\frac{1}{5}\\\\\text{Since we now know our slope, we can plug it into our "m" variable in the}\\\text{slope intercept equation:}\\\\\text{y = }-\frac{1}{5}x+b\\[/tex]

[tex]\text{To find where the point is on the y-intercept, we will plug in our point}\\\text{(5, -2) to it's corresponding spots in our new equation above.}\\\\\text{Plug "5" to x and "-2" to y and solve:}\\\\\text{-2 = }-\frac{1}{5}(5)+b\\\\\text{-2 = }-1+b\\\\\text{Add 1 to both sides.}\\\\\text{-1 = }b\\\\\text{Therefore, our y-intercept is -1.}[/tex]
[tex]\text{When we plug -1 into our new equation, we get:}\\\\\text{y = }-\frac{1}{5}x-1\\\\\text{Therefore, our perpendicular equation is: }\boxed{y = -\frac{1}{5}x-1}[/tex]
__________________________________________________________

[tex]\textbf{Answer:}\\\\\boxed{y = -\frac{1}{5}x-1}[/tex]
__________________________________________________________

[tex]\textbf{Additional Info:}\\\\\text{You can learn more about \textbf{slope-intercept form} below:}[/tex]
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__________________________________________________________

Answer:

2.92

Step-by-step explanation:

[tex]V=\frac{4}{3}\pi r^3 \\ \\ 105=\frac{4}{3}\pi r^3 \\ \\ r^3=\frac{105}{\frac{4}{3}\pi} \\ \\ r=\sqrt[3]{\frac{105}{\frac{4}{3}\pi}} \\ \\ r \approx 2.92[/tex]

Answer:

x=30,y=165,z=5

Step-by-step explanation:

check it bro

Answer:

A card balance is the total amount of money that you currently owe on your credit card. The balance increases when purchases are made and decreases when payments are made. Purchases, balance transfers, foreign exchange, fees, and interest all factor into your credit card balance.

please brainlest and like

The graph whuch best represents the solution to the system of equations is; A coordinate grid is shown from negative 10 to positive 10 on the x axis and also on the y axis. Two lines are shown intersecting on the ordered pair 3, 8.

As an alternative, solving the system of equations algebraically, we have;

-2x +14 = 2x +2

x = 3 and by substitution;

y = 8.

On this note, the point (3,8) is a solution of the graph and hence, the answer choice with two lines intersecting at (3,8) is correct.

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Answer:

Step-by-step explanation:

hello :

g(x) = (x+5)²

The derivative of the function [tex]f(x)=5^{2x}[/tex] is [tex]\frac{df}{dx} =2ln5(5^{2x})[/tex]

The derivative of a function f(x) is the ratio of the change in f(x) to the change in x

The given function is:

[tex]f(x)=5^{2x}[/tex]

Let u = 2x

Find the derivative of u. That is, du/dx

du/dx = 2

f(x) = 5^u

[tex]\frac{df}{du} =5^ulnu[/tex]

Using the chain rule of derivative

[tex]\frac{df}{dx}=\frac{df}{du} \times\frac{du}{dx}[/tex]

[tex]\frac{df}{dx} =5^uln5 \times 2\\\\\frac{df}{dx} =2ln5(5^{2x})[/tex]

The derivative of the function [tex]f(x)=5^{2x}[/tex] is [tex]\frac{df}{dx} =2ln5(5^{2x})[/tex]

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Answer:

(2,-3)

Step-by-step explanation:

I am not sure if you meant the first equation to be y or -y.  I solved it as y.

y = x-5                       -x -3y =7

I am going to take the second equation and write it as x =

-x - 3y = 7  Give equation

-x = 3y +7   Add 3y to both sides

x = -3y-7  Multiplied each term in the equation by -1 so that x could be positive

I am going to substitute -3y-7 for x in the first equation up above

y = x - 5

y = -3y -7 - 5  Substitute -3y-7 for x

y = -3y -12  Combined -7-5

4y = -12  Added 3y to both sides

y = -3  Divided both sides by 4.

I now know that y is -3, I will plug that into x = -3y-7 to solve for x

x = -3(-3) -7

x = 9-7   A negative times a negative is a positive

x = 2

The graph would be affected by horizontally stretching the curve of f(x) = x^2 when the coefficient is changed

The function is given as:

f(x) = x^2

When the coefficient of x^2 changes to 1/3, we have:

f(x) = 1/3x^2

The above represents a stretch of the function

This means that the graph would be affected by horizontally stretching the curve of f(x) = x^2 when the coefficient is changed

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Answer:

Step-by-step explanation:

hello :

Solut i on :

1) A line that passes through A(0, -6 ) andB (8 ,- -8)

Hello : let A(0,-6) B(8,-8)

the slope is : (YB - YA)/(XB -XA)

(-8+6)/(8-0) = -2/8=-1/4

an equation is : y=ax+b a is a slope

y = (-1/4)x +b

the line through point A (0;-6) : -6 = (-1/4)(0)+b

b = -6            the equation is : y =(-1/)4x-6

g(x) is just a translation of 10 units downwards, this means that the equation for g(x) is:

[tex]g(x) = f(x) - 10 = 5^x - 10[/tex]

Here we know that:

[tex]f(x) = 5^x[/tex]

And we want to find the equation for g(x), which is a translation of f(x).

If you look at the graph of f(x), you can see that it passes through:

(0, 1), (1, 5), (2, 25), etc.

And the graph of g(x) passes through:

(0, -9), (1, -5), (2, 15)

So in each point, the y-component is 10 units smaller than the correspondent for f(x).

Then g(x) is just a translation of 10 units downwards, this means that the equation for g(x) is:

[tex]g(x) = f(x) - 10 = 5^x - 10[/tex]

So the correct option is the last one.

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Using limits, the polynomial that has an even degree and a negative leading coefficient is:

Polynomial going down from the left and passing through the point negative 7 comma 0 and going to a local minimum and then going up through the point negative 3 comma 0 and 0 comma 8 to a local maximum and then down to the right through the point 4 comma 0.

A limit is given by the value of function f(x) as x tends to a value.

In this problem, to find the polynomial, we have to find the limits as x goes to infinity, hence:

[tex]\lim_{x \rightarrow -\infty} f(x) = [tex]\lim_{x \rightarrow -\infty} -a x^n[/tex]

Since n is even, we have that:

Since it goes down to the left and down to the right, hence the function is:

Polynomial going down from the left and passing through the point negative 7 comma 0 and going to a local minimum and then going up through the point negative 3 comma 0 and 0 comma 8 to a local maximum and then down to the right through the point 4 comma 0.

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Approximately 5 number of trays must be sold to cover all costs including labor.

The profit on each tray that was sold excluding labor cost is;

Profit = $35-$14

Profit = $21

Total labor cost for making party tray for a day is;

Total Labor Cost = Total labor hours * wages per hour * No. of labors

Total Labor cost = $7 * $8*2

Total Labor Cost = $112

Number of trays that must be sold to cover cost  is;

Total labor cost/ Profit per tray

Number of trays = $112/$21

= 5.33

Approximately 5 trays must be sold to cover all costs including labor.

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Answer: 19 and 14

Step-by-step explanation:

19^2+14^2= 557

What I did to start it is I tried 20 and 15 because I know the square roots of those and once I added them I saw that their sum was too big, so then I tried 19 and 14 because 19-14 is 5. It was really just guess and check :)

Answer:

[tex]\boxed {(f-g)(x) = x^{2}+3}[/tex]

Step-by-step explanation:

Given :

Now, this problem can be used using a simple formula.

[tex]\fbox {(f - g)(x) = f(x) - g(x)}[/tex]

Let's solve.

∴ The answer will be x² + 3.

Answer:

dependent

Step-by-step explanation:

because when x decreases y has to also decrease, so they are dependent on eachother