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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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[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]
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[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]
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[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]
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[tex]\textbf{Answer:}\\\\\boxed{y = -\frac{1}{5}x-1}[/tex]
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[tex]\textbf{Additional Info:}\\\\\text{You can learn more about \textbf{slope-intercept form} below:}[/tex]
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For the circular cover we have:

A) The area is 379.94 ft²

B) The length of the rope must be 68.2 ft

Remember that the area of a circle of radius R is given by the formula:

[tex]A = pi*R^2[/tex]

Where pi = 3.14

In this case, the diameter of the pool is 20ft, then the radius is:

R = 20ft/2 = 10ft

And it must extend 12 inches beyond, then the radius of the cover must be:

R = 10ft + 12in

Now, we know that 1ft = 12 in, then we can rewrite the radius as:

R = 10ft +1ft = 11ft

Then the area of the cover is:

[tex]A = 3.14*(11ft)^2 = 379.94 ft^2[/tex]

B) now we want to get the length of the rope, we know that the rope runs along the cover, then the length of the rope must be equal to the circumference of the cover.

Remember that the circumference of a circle of radius R is:

[tex]C = 2*pi*R[/tex]

Then the length of the rope will be:

[tex]C = 2*3.14*11ft = 68.2ft[/tex]

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Answer:

C

Step-by-step explanation:

For lines l and m and the transversal line that creates angles 6 and 18, angles 6 and 18 are corresponding angles of lines l and m. If they are congruent, lines l and m are parallel.

Answer: Choice C

Answer:

12.5 inches

Step-by-step explanation:

We use proportion to calculate the scale drawing

27 feet = 5 inches, so

67.5 feet = more inches (we know that it would be bigger than 5 inches)

We then put the bigger number on top and crossmultiply by saying:

67.5 over 27 × 5

Your answer should come out as 12.5 inches.

Answer:

they are the same line

Step-by-step explanation:

if you divide the first line by 2 you'll get:

2(3x)+2y=2(23)===> 3x+y=23

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

Using translation concepts, function g(x) is given as follows:

g(x) = x² - 3.

A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.

Researching this problem on the internet, g(x) is a shift down of 3 units of f(x) = x², hence:

g(x) = x² - 3.

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[tex] \qquad \qquad \bf \huge\star \: \: \large{ \underline{Answer} } \huge \: \: \star[/tex]

There is one angle and an adjacent side of the triangle given equal to corresponding angle and side of the other triangle and if we observe the figure we can see that there's also a adjacent side XY common in both the Triangles.

Hence, the two triangles are congruent by SAS congruency criteria.

[tex] \qquad \large \sf {Conclusion} : [/tex]

Answer: m > -16

Step-by-step explanation:

[tex]\frac{3}{4}m > -12\\\\m > -\frac{4}{3}(12)=-16[/tex]

Answer:

Inequality Form: x > 17

Interval Notation: (17, ∞)

[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]

Step-by-step explanation:

8.√128/√2

ans √64

10.3√81

3√3*3*3*3(find factor)

3 √3(this is cube root therefore we kept one out of three then we kept remaining inside of root.this is surds because one factor is inside the surds if factor is not remaining inside the surds then this is not surds)

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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Considering the given proportion, the value of [tex]\frac{a}{a - b}[/tex] is:

C) 2

A proportion is a fraction of a total amount, and the measures are related using a rule of three.

The proportion between a and b is given by:

a/b = 2.

Then:

a = 2b.

The expression is:

[tex]\frac{a}{a - b} = \frac{2b}{2b - b} = \frac{2b}{b} = 2[/tex]

Hence option C is correct.

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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 :)

The equivalent of the expression [ (z−3)4z−6 ] is 4z² - 12z - 6.

Given the expression; (z−3)4z−6

First, we apply distributive property.

(z−3)4z−6

(z−3)4z−6

z(4z) - 3(4z) - 6

We remove the parentheses

4z² - 12z - 6

Therefore, the equivalent of the expression [ (z−3)4z−6 ] is 4z² - 12z - 6.

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Answer:

A = -5

B = 1

Step-by-step explanation:

Hello!

You simply plug in the given x-value into the equation to find the missing y-value.

Plug in -1 for x into y = 2x - 3.

Plug in 2 for x into y = 2x - 3.

Answer:

2nd option

Step-by-step explanation:

to find f(h(x)) substitute x = h(x) into f(x) , that is

f(h(x))

= f(2x + 3)

= 2x + 3 - 7

= 2x - 4

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

Answer:

angles of the triangle are equal 180

so 42+82=124

180-124=56

so the answer is 56

Step-by-step explanation:

Given the money invested and the interest rate, the value of the interest earned after 8 months is $82.50.

From the equation of simple interest; I = PRT

Given that;

I = PRT

I = $4,500 × 0.0275 × 8/12

I = $82.50

Given the money invested and the interest rate, the value of the interest earned after 8 months is $82.50.

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Answer:

Step-by-step explanation:

hello :

x² +5x+3=0

delta = b²-4ac   when :  a =1  and b=5    c=3

delta =5²-4(1)(3) =13

X1 =(-b-sqrt(delta))/2a

X2 =(-b+sqrt(delta))/2a

continu.....

Answer:

Part A

1. A third degree polynomial has exactly three zeros. This is because its highest power (or degree) is 3. Ray would only be correct in saying that a polynomial can have 4 zeros if it is a 4th degree polynomial. Since in this case, a 4rd degree polynomial is being discussed, Kelsey is correct.

2. Function chosen: g(x) = (x + 2)(x - 1)(x - 2)

End behaviour: x —> ∞, g(x) —> ∞

                         x —> - ∞, g(x) —> -∞

Zeros/x intercepts of the function: -2, 1, 2

y intercept: g(x) = (x + 2)(x - 1)(x - 2)

                   g(x) = (0 + 2)(0 - 1)(0 - 2)

                   g(x) = (2)(-1)(-2)

                   g(x) = 4

3. See Graph 1

Part B

4. f(x) = (x + 5)(x + 3)

Direction: opens upward

Zeros/x intercepts: -5, -3

y intercept: 15

5. See graph 2

Part C

You can draw the roller coaster yourself using the graphs below

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.

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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 :

g(x) = (x+5)²

Answer:

(0,3)

(-1,1)

Step-by-step explanation:

Hello!

Since both equations are equal to y, we can set the right-hand side of the equations equal to each other.

X can either be 0 or -1. Remember, a solution to a system is not complete without a y-value. Plug in 0 and -1 for x in the first equation, and find the corresponding y-values.

[tex]y = 2(0) + 3\\y = 3[/tex]

And

[tex]y = 2(-1) + 3\\y = -2 + 3\\y = 1[/tex]

So the solutions to the system are (0,3) and (-1,1)

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:

I think its 19.75