Which expression is equivalent to 30(1/2x-2)+40(3/4y-4

Answer: 64π

Step-by-step explanation: A = (d)^2 π

64 x π

64π

Answer:

1. [tex]\frac{x^2+4x-7}{x-1}[/tex]

2. [tex]\frac{x^2-2x+7}{x-1}[/tex]

3. [tex]\frac{2x^2-x-7}{x-1}[/tex]

4. [tex]\frac{2x^2-3x+7}{x-1}[/tex]

Step-by-step explanation:

1. [tex](x+5) + \frac{-2}{x-1}[/tex]

Taking LCM

[tex]=\frac{(x-1)(x+5)+(-2)}{x-1}\\ Solving:\\=frac{x(x+5)-1(x+5)-2}{x-1} \\=frac{x^2+5x-1x-5-2}{x-1} \\Adding\,\,like\,\,terms:\\=\frac{x^2+4x-7}{x-1}[/tex]

2. [tex]x-1 +\frac{6}{x-1}[/tex]

Taking LCM and solving

[tex]=\frac{(x-1)(x-1)+6}{x-1}\\=\frac{(x(x-1)-1(x-1)+6}{x-1}\\=\frac{x^2-1x-1x+1+6}{x-1}\\Adding\,\,like\,\,terms:\\=\frac{x^2-2x+7}{x-1}[/tex]

3. [tex](2x+1)+\frac{-6}{x-1}[/tex]

Taking LCM and solving:

[tex]=\frac{(2x+1)(x-1)-6}{x-1} \\=\frac{2x(x-1)+1(x-1)-6}{x-1} \\=\frac{2x^2-2x+1x-1-6}{x-1}\\Adding\,\,like\,\,terms:\\=\frac{2x^2-x-7}{x-1}[/tex]

4. [tex](2x-1)+\frac{6}{x-1}[/tex]

Taking LCM and solving:

[tex]=\frac{(2x-1)(x-1)+6}{x-1} \\=\frac{2x(x-1)-1(x-1)-6}{x-1} \\=\frac{2x^2-2x-1x+1+6}{x-1}\\Adding\,\,like\,\,terms:\\=\frac{2x^2-3x+7}{x-1}[/tex]

Answer:

I'm pretty sure that is correct.

Step-by-step explanation:

Answer:

Distance = 3r

Step-by-step explanation:

We are to write an algebraic expression and then simplify it for the given situation:

The distance traveled by a train in three hours with a constant speed of r miles per hour.

We know the formula of distance linking the speed and the time.

Distance = speed × time

Substituting the given values to get:

Distance = r × 3

Distance = 3r

Answer:

Second option: (-2,-3) and (1,0)

Step-by-step explanation:

Given the system of equations [tex]\left \{ {{y = x^2 + 2x-3} \atop {y = x - 1}} \right.[/tex], you can rewrite them in this form:

[tex]x^2 + 2x-3= x - 1[/tex]

Simplify:

[tex]x^2 + 2x-3-x+1=0\\\\x^2+x-2=0[/tex]

Factor the quadratic equation. Choose two number whose sum be 1 and whose product be -2. These are: 2 and -1, then:

[tex](x+2)(x-1)=0\\\\x_1=-2\\\\x_2=1[/tex]

Substitute each value of "x"  into any of the original equation to find the values of "y":

[tex]y_1= (-2) - 1=-3\\\\y_2=(1)-1=0[/tex]

Then, the solutions are:

(-2,-3) and (1,0)

ANSWER

The solutions are (-2,-3) and (1,0).

EXPLANATION

The given system has equations:

[tex]y = {x}^{2} + 2x - 3[/tex]

and

[tex]y = x - 1[/tex]

We equate both equations:

[tex] {x}^{2} + 2x - 3 = x - 1[/tex]

[tex] {x}^{2} + 2x - x - 3 + 1 = 0[/tex]

[tex] {x}^{2} + x - 2 = 0[/tex]

[tex](x - 1)(x + 2) = 0[/tex]

This implies that,

[tex]x = - 2 \: or \: x = 1[/tex]

When x=-2 , y=-2-1=-3

When x=1, y=1-1=0

The solutions are (-2,-3) and (1,0)

Answer: -1 is the slope of the red line,

Step-by-step explanation: The slope of parallel lines are always the same. Hope this helps!

Answer:

the slope would be -1

Step-by-step explanation:

Answer:

The answer in the procedure

Step-by-step explanation:

we know that

The cross  section formed by the slice is a square with the same dimensions of the base of rectangular prism

The length side of the square is 6 cm

The area of the cross section is equal to

[tex]A=b^{2}[/tex]

[tex]b=6\ cm[/tex]

substitute

[tex]A=6^{2}[/tex]

[tex]A=36\ cm^{2}[/tex]

Answer:

square and 36

Step-by-step explanation:

I took the test

Answer:1/55

Step-by-step explanation:

Answer: The answer is 1/55

Step-by-step explanation: because i got it right on edge. Can you mark brainliest?

Answer:

Option C

Step-by-step explanation:

we know that

The altitude of a three-dimensional object is equal to the height of the object, is the perpendicular distance of the base to the other base or the perpendicular distance of the base to the apex of the object

therefore

A segment that is perpendicular to the planes containing the two bases

The statement which best describes an altitude of a three-dimensional object is: C. a segment that is perpendicular to the planes containing the two bases.

Altitude is also referred to as an elevation and it can be defined as the vertical distance (height) above the surface of a plane.

In Geometry, the altitude of a three-dimensional object is characterized by the following:

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Answer:

It's B

Step-by-step explanation:

B,     16x2-9y2

Answer:  The correct option is (B) [tex]16x^2-9y^2.[/tex]

Step-by-step explanation:  We are given to find the following product :

[tex]P=(4x+3y)(4x-3y)~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]

To find the given product, we will be using the following formula :

[tex](a+b)(a-b)=a^2-b^2.[/tex]

The product (i) can be calculated as follows :

[tex]P\\\\=(4x+3y)(4x-3y)\\\\=(4x)^2-(3y)^2\\\\=16x^2-9y^2.[/tex]

Thus, the required product is [tex]16x^2-9y^2.[/tex]

Option (B) is CORRECT.

Answer:

B

Step-by-step explanation:

translation means to transcribe or change from on language/definition/understanding to another.

Answer:

B) x +20 is greater than or less to 45

Step-by-step explanation:

Answer:

x + 20 ≥  45

Step-by-step explanation:

You currently have : $20

You will earn : $x

Tomorrow you will end up with (20 + x) dollars

the pair of jeans cost $45, in order to afford the jeans, the amount of money that you will need must be equal or more than $45

Hence,

Money you will have tomorrow ≥ 45

or

x + 20 ≥  45 (Answer)

Answer:

Option D. Alia gets 3³ - 4² = 11 jelly beans.

Step-by-step explanation:

Kathy gives Kelly 3³ jelly beans.

Kathy gives Alia 4² fewer jelly beans than Kelly. This means that Alia gets the number of jelly beans obtained by Kelly decreased by 4².

To summarize:

#Kelly = 3³ = 27

#Alia = #Kelly - 4² = 3³ - 4² = 27 - 16 = 11

Then, option D is correct.

[tex]\dfrac{3}{5x}+\dfrac{9}{5x}=\dfrac{12}{5x}[/tex]

The sum of the given expression will be equal to 12 / 5x.

Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication and division.

The given expression is:-

[tex]=\dfrac{3}{5x}+\dfrac{9}{5x}[/tex]

[tex]= \dfrac{3+9}{5x}[/tex]

[tex]=\dfrac{12}{5x}[/tex]

Therefore the sum of the given expression will be equal to 12 / 5x.

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[tex]\bf (\stackrel{x_1}{-3}~,~\stackrel{y_1}{2})\qquad (\stackrel{x_2}{1}~,~\stackrel{y_2}{5}) \\\\\\ slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{5-2}{1-(-3)}\implies \cfrac{3}{1+3}\implies \cfrac{3}{4}[/tex]

[tex]\bf \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-2=\cfrac{3}{4}[x-(-3)] \implies y-2=\cfrac{3}{4}(x+3) \\\\\\ y-2=\cfrac{3}{4}x+\cfrac{9}{4}\implies y=\cfrac{3}{4}x+\cfrac{9}{4}+2\implies y=\cfrac{3}{4}x+\cfrac{17}{4}[/tex]

For this case we have a function of the form [tex]y = f (x)[/tex]

They ask us to find the value of the function when[tex]x = 2[/tex], that is, [tex]f (2).[/tex]

If we look at the figure, and we mark x = 2 in the graph, we obtain a value of[tex]y = 4[/tex]

So, we have that the function has a value of 4 when[tex]x = 2[/tex]

Answer:

Option C

Answer:

After these reflections, the coordinates of P′ will be (4 , -4)

Step-by-step explanation:

* Lets revise some transformation

- If point (x , y) reflected across the x-axis

∴ Its image is (x , -y)

- If point (x , y) reflected across the y-axis

∴ Its image is (-x , y)

* Lets solve the problem

- The triangle PQR with coordinates P(-4, -4), Q(-1, -3), and R(-3, -1)

- The triangle is reflected across the x-axis

∵ Δ PQR is reflected across the x-axis

∴ All y-coordinates of the vertices P, Q , R reversed their signs

∴ The new points will be (-4 , 4) , (-1 , 3) , (-3 , 1)

- The new vertices will reflected across the y-axis

∴ All x-coordinates of the new vertices reversed their signs

∴ The new points will be (4 , 4) , (1 , 3) , (3 , 1)

- The new vertices will reflected across the x-axis to form Δ P'Q'R'

∴ All y-coordinates of the new vertices reversed their signs

∴ P' = (4 , -4) , Q' = (1 , -3) , R' = (3 , -1)

* After these reflections, the coordinates of P′ will be (4 , -4)

Final answer:

After reflecting triangle PQR across the x-axis, then the y-axis, and the x-axis again, point P' will have coordinates (4, -4).

Explanation:

Reflecting a triangle across an axis involves flipping the triangle over that axis. Each reflection inverses the corresponding coordinate (x or y) of each vertex of the triangle, while the other coordinate remains the same. Starting with the first reflection across the x-axis, the y-coordinate of each point negates, but the x-coordinate remains unchanged. The second reflection is across the y-axis, which negates the x-coordinate and keeps the y-coordinate (already negated from the first reflection) the same. The third reflection across the x-axis negates the y-coordinate again, effectively returning it to its original value before the first reflection. So for point P(-4, -4), after these reflections, the new coordinates for P' will be (4, -4).

The rectangular wall that is painted in 15 minute. 6.4 square feet area is painted per minute.

A rectangle is a part of a quadrilateral, whose sides are parallel to each other and equal.

Given that,

The length of the rectangular wall = 12 ft.

The width of the rectangular wall = 8 ft.

The area of rectangle = 12 x 8 = 96 square feet.

Since, in 15 minutes, the rectangular wall is painted.

To find the area that painted in one minute,

Use ratio property,

15 minutes = 96 square feet painted,

1 minute = 96 / 15 square feet painted.

1 minute = 6.4 square feet.

6.4 square feet painted in 1 minute.

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Answer:

D. |x − 78| ≤ 20

Step-by-step explanation:

Given,

The monthly charges for a basic cable plan = $ 78,

Also,  it could differ by as much as $20,

So, the maximum charges = $(78 + 20) ,

And, the minimum charges = $(78 - 20),

Let x represents the monthly charges ( in dollars ),

78 - 20 ≤ x ≤ 78 + 20

⇒ 78 - 20 ≤ x and x ≤ 78 + 20

⇒ -20 ≤ x -78 and x-78 ≤ 20

⇒ 20 ≥ -(x-78) and x-78 ≤ 20   ( ∵ a > b ⇒ -a < -b )

⇒ |x-78| ≤ 20

Which is the required absolute value inequality to determine the range of basic cable plan costs,

Option 'D' is correct.

Answer:

Each pizza costs for $9.

Step-by-step explanation:

We are given that Mr. Mori bought four equally-priced pizzas and a $3 bag of potato chips.

Given that he spent a total $39, we are to find the cost of each pizza.

This can be represented by an equation:

[tex]4x+3=39[/tex]

Solving it to find x.

[tex]4x=39-3[/tex]

[tex]4x=36[/tex]

[tex]x=\frac{36}{4}[/tex]

x = 9

Therefore, the cost of each pizza is $9.

Answer:

C.X=9

Step-by-step explanation:

The marginal relative frequency of the number of people who prefer to read books is 0.42

Answer:

.42

Step-by-step explanation:

Answer:

[tex]y=25,700(0.85)^{x}[/tex]

Step-by-step explanation:

we know that

In this problem we have a exponential function of the form

[tex]y=a(b)^{x}[/tex]

where

y ----> represent the pool’s loss of water

x ----> the number of days

a is the initial value

a=25,700 gal

b ----> is the base

r=15%=15/100=0.15

b=(1-r)=1-0.15=0.85

The function is equal to

[tex]y=25,700(0.85)^{x}[/tex]

Answer:

2 is not in the domain of f of g

Step-by-step explanation:

* Lets revise at first the meaning of f of g (composite function)

- A composite function is a function that depends on another function

- A composite function is created when one function is substituted into

 another function

- Example:

# f(g(x)) is the composite function that is formed when g(x) is

  substituted for x in f(x).

- In the composition (f ο g)(x), the domain of f becomes g(x)

* Now lets solve the problem

∵ f(x) = 4x + 3

∵ g(x) = √(x - 9)

- Lets find f(g(x)), by replacing x in f by g(x)

∴ f(g(x)) = f(√(x - 9)) = 4[√(x - 9)] + 3

∴ f(g(x)) = 4√(x - 9) + 3

∵ The domain of f is g(x)

- The domain of the function is the values of x which make the

  function defined

∵ There is no square root for negative values

∴ x - 9 must be greater than or equal zero

∵ x - 9 ≥ 0 ⇒ add 9 for both sides

∴ x ≥ 9

∴ The domain of f of g is all the real numbers greater than or equal 9

∴ The domain = {x I x ≥ 9}

∵ 2 is smaller than 9

∴ 2 is not in the domain of f of g

Answer:

y = -7

Step-by-step explanation:

The easisest way to find the slope of this line is to use slope-intercept form.

Slope-intercept form:

y = mx + b

Where m = slope and b = y -intercept

In this graph, the y-intercept is -7. However, the line doesn't have a slope since its a straight horizontal line.

So, the mx part of the equation isn't a part of this new equation.

So, your equation would just y = -7

Answer:

18,102,783

Step-by-step explanation:

Answer:

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

Step-by-step explanation:

[tex](f-g)(x)=f(x)-g(x)\\\\f(x)=3x-1,\ g(x)=x+2\\\\\text{substitute:}\\\\(f-g)(x)=(3x-1)-(x+2)\\\\=3x-1-x-2\qquad\text{combine like terms}\\\\=(3x-x)+(-1-2)\\\\=2x-3[/tex]

The explicit formula that can be used to find the account's balance at the beginning of year 6 is B = P(1 + r/n)^(nt), which  gives the value as [tex]300(1.04)^6[/tex]

The explicit formula that can be used to find the account's balance at the beginning of year 6 is:

[tex]B = P(1 + r/n)^(nt)[/tex]

Where:

In this case, Jonah's initial investment is $300, the annual interest rate is 4%, interest is compounded annually (n = 1), and the number of years is 6 (t = 6). Plugging these values into the formula:

[tex]B = 300(1 + 0.04/1)^(1*6)[/tex]

[tex]B = 300(1 + 0.04)^6[/tex]

[tex]B = 300(1.04)^6[/tex]

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Answer:  5 ft

Step-by-step explanation:

Step 1: Find the volume of the driveway (in cubic yds)

[tex]\$ 108.89\div\dfrac{\$98}{yds^3}=\$ 108.89\times\dfrac{yds^3}{\$98}=\boxed{\dfrac{10}{9}yds^3}[/tex]

Step 2: Use the Volume formula (V = length × width × heighth) to find w

(convert each measurement into yds)

[tex]V=l\times w\times h\\\\\dfrac{10}{9}yds^3=12ft\bigg(\dfrac{1yd}{3ft}\bigg)\times w\times 6in\bigg(\dfrac{1ft}{12in}\bigg)\bigg(\dfrac{1yd}{3ft}\bigg)\\\\\\\dfrac{10}{9}yds^3=4yds\times w\times \dfrac{1}{6}yds\\\\\\\dfrac{10}{9}yds^3=\dfrac{2}{3}yds^2\times w\\\\\\\dfrac{3}{2yds^2}\times \dfrac{10}{9}yds^3=w\\\\\\\dfrac{5}{3}yds=w\\\\\\\dfrac{5}{3}yds\times\dfrac{3ft}{1yd}=w\\\\\\\large\boxed{5 ft=w}[/tex]

Five solutions of  y = 20x  with integer values for  x  ranging from -2 to 2 are (-2, -40), (-1, -20), (0, 0), (1, 20), and (2, 40).

To find five solutions of the equation  y = 20x , we can choose integer values for  x  starting with -2 and ending with 2, and then calculate the corresponding values of  y  using the given equation.

Starting with  x = -2 :

y = 20(-2) = -40

So, the first solution is (-2, -40).

Moving to  x = -1:

y = 20(-1) = -20

So, the second solution is (-1, -20).

At  x = 0 :

y = 20(0) = 0

So, the third solution is (0, 0).

Proceeding to  x = 1 :

y = 20(1) = 20

So, the fourth solution is (1, 20).

Finally, for  x = 2 :

y = 20(2) = 40

So, the fifth solution is (2, 40).

Therefore, the five solutions of the equation  y = 20x  with integer values for  x  ranging from -2 to 2 are:

(-2, -40), (-1, -20), (0, 0), (1, 20), and (2, 40).

Answer:

C

Step-by-step explanation:

Use exponents property:

[tex]\dfrac{x^a}{x^b}=x^{a-b}[/tex]

1. Note that

[tex]\dfrac{x^7}{x^{11}}=x^{7-11}=x^{-4}=\dfrac{1}{x^4}[/tex]

and

[tex]\dfrac{y^6}{y^8}=y^{6-8}=y^{-2}=\dfrac{1}{y^2}[/tex]

2. Now

[tex]\sqrt{\dfrac{55x^7y^6}{11x^{11}y^8}}=\sqrt{\dfrac{5}{x^4y^2}}=\dfrac{\sqrt{5}}{\sqrt{x^4}\sqrt{y^2}}=\dfrac{\sqrt{5}}{x^2y}[/tex]

because [tex]x>0,\ y>0[/tex]