mitchell has two rectangular prisms. prism B has a height that is twice the height of a prism A. The length and width of prism B are the same as the length and width of Prism A. The volume of prism B is

Answer:

EQUATION: X - 12 = 7X. SOLUTION: X = - 2.

Step-by-step explanation:

First, we do not know the number. When the number is unknown, it is a variable. I chose the variable, "X."

12 less than signals that we subtract 12. So that would be X - 12.

A product of 7 AND that number means we multiply 7 by X. That can be notated as 7X.

12 less than X is EQUAL to the product of 7 and X. So X - 12 = 7X.

To find the solution, we want to know the value of X. Move X to one side of the equation.

X - 12 = 7X

-X           -X

_________

-12     =   6X

Divide both sides by 6 to get X by itself.

X = - 2.

Answer:

length=(3x-2)

Step-by-step explanation:

area of rectangle=length*breadth

3x^2 + 7x - 6=length * (x+3)

3x^2 +(9-2)x -6=length *(x+3)

3x^2+9x-2x-6=length*(x+3)

3x(x+3)-2(x+3)=length*(x+3)

(x+3)(3x-2)=length*(x+3)

(x+3)(3x-2)/(x+3)=length

(3x-2)=length

Answer:

(3x - 2)

Step-by-step explanation:

Given that the area A = length × width

A = 3x² + 7x - 6 ← factor to obtain length

Consider the factors of the product of the coefficient of the x² term and the constant term which sum to give the coefficient of the x- term

product = 3 × - 6 = - 18 and sum = + 7

The factors are + 9 and - 2

Use these factors to split the x- term

3x² + 9x - 2x - 6 ( factor the first/second and third/fourth terms )

= 3x(x + 3) - 2(x + 3) ← factor out (x + 3) from each term

= (x + 3)(3x - 2)

We know (x + 3) is the width , then (3x - 2) is the length

Answer:

64

Step-by-step explanation:13+51=64

Given the expression below:

[tex] \large{ \frac{ {7}^{ \frac{3}{2} } }{ {7}^{ \frac{1}{2} } } }[/tex]

Use the following property:

[tex] \large \boxed{ {a}^{ \frac{m}{n} } = \sqrt[n]{ {a}^{m} } }[/tex]

Therefore:

[tex] \large{ \frac{ {7}^{ \frac{3}{2} } }{ {7}^{ \frac{1}{2} } } = \frac{ \sqrt{ {7}^{3} } }{ \sqrt{7} } } \\ \large{ \frac{ \sqrt{ {7}^{3} } }{ \sqrt{7} } = \frac{ \sqrt{7 \times 7 \times 7} }{ \sqrt{7} } \longrightarrow \frac{7 \sqrt{7} }{ \sqrt{7} } } \\ \large{ \frac{7 \cancel{ \sqrt{7} }}{ \cancel{ \sqrt{7} }} = 7}[/tex]

Note that a¹ = a. Therefore, 7¹ = 7.

Answer

Answer:

[tex]\sqrt{x+6}[/tex]

Step-by-step explanation:

So, there are a few things we need to go over to graph a function,

When a number is outside of a root, it changes the y value. For example:

y=[tex]\sqrt{x}+6[/tex]

With the +6, y will always be 6 higher than normal.

If it was -6, then y will always be 6 lower than normal.

What if the number is inside the root? Well, it works a little differently.

Instead of changing the y value, it changes the x value. For example:

y=[tex]\sqrt{x+6}[/tex]

So if you put a number in for x, lets say -6, wht would you get?

You would get -6+6=0

The square root of 0 is 0, so when x=-6, y=0

Normally, x would have to equal 0 for the y value to be 0.

So basically, when we see the number isnide of the root, we can think the our x coordinate being subtracted by that number.

This makes since, because if we subtract the +6 from x:

x-(+6)= x-6, and -6 is our x coordinate.

If it was -6 at the start, this would also work:

x-(-6)= x+6. So our x coordinate would start at 6.

Now, lets look at our graph.

As we can see, the x values start at -6, and the y values starts at 0.

This eliminates A and D, since the +6 would change the y value, not the x.

Remember that x-6 would make x a postive 6.

x+6 however, would make x a negative 6.

So we need x+6 in a square root.

This eliminates B, since it has a x-6, making the x coordinate postive 6, not negative 6.

So c is our answer.

Hope this helps!

Step-by-step explanation:

the value of x is 18 degree and the value of Y is 15 degree

Answer:

the answer for your question is b

Answer: 15

Step-by-step explanation: 5+9+11+12+13+14+17=81

Make an equation based on this and solve for the variable (x)

81+x/8=12

12*8=96

81+x=96

96-81=15

x=15

The area of the shaded region is (area of the circle) - (area of the square) - (area of the triangle)

Option A is the correct answer

A triangle is a 2-D figure with three sides and three angles.

The sum of the angles is 180 degrees.

We can have an obtuse triangle, an acute triangle, or a right triangle.

We have,

The shaded region consists of the area inside the circle but outside the square, as well as the area inside the equilateral triangle but outside the square.

Now,

The area of the circle is πr²

Since the square is inscribed in the circle, the diameter of the circle is equal to the diagonal of the square.

Let's say the side length of the square is s.

By the Pythagorean theorem,

s² + s² = (diameter)²

2s² = (2r)²

s² = r²

The area of the square is s² = r².

The area of an equilateral triangle with side length s is √(3)/4 x s².

Since the side length of the square is equal to the height of the equilateral triangle, the side length of the equilateral triangle is also equal to s.

The area of the shaded region.

= (area of the circle) - (area of the square) - (area of the triangle)

Thus,

The area of the shaded region is (area of the circle) - (area of the square) - (area of the triangle)

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Answer:

CE = 20

Step-by-step explanation:

Given a line parallel to a side of a triangle and intersecting the other 2 sides then it divides those sides proportionally, that is

[tex]\frac{6}{8}[/tex] = [tex]\frac{15}{CE}[/tex] ( cross- multiply )

6 CE = 120 ( divide both sides by 6 )

CE = 20

Answer:

C/3rd one. (y=2x+4)

Step-by-step explanation:

In the equation y=mx+b, m=slope of the line and b=y-intercept. From the graph, we know the y-intercept is 4 so we can write y=mx+4. To find the slope: (0-4)/(-2-0) = (-4)/(-2) = 2. We can replace the m with 2 to get the final equation of y=2x+4 which is also the third answer.

Answer:

k = 11

Step-by-step explanation:

Given the points are collinear then the slopes between consecutive points are equal.

Using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (5, 1) and (x₂, y₂ ) = (1, - 1)

m = [tex]\frac{-1-1}{1-5}[/tex] = [tex]\frac{-2}{-4}[/tex] = [tex]\frac{1}{2}[/tex]

Repeat with another 2 points and equate to [tex]\frac{1}{2}[/tex]

with (x₁, y₁ ) = (1, - 1) and (x₂, y₂ ) = (k, 4)

m = [tex]\frac{4+1}{k-1}[/tex] , then

[tex]\frac{5}{k-1}[/tex] = [tex]\frac{1}{2}[/tex] ( cross- multiply )

k - 1 = 10 ( add 1 to both sides )

k = 11

Answer:

y = 1sin(3x)

Step-by-step explanation:

y = A sin( (2π/ω)x )

A is amplitude = 1

ω is period = 2π/3

------------------------------

y = 1sin( 2π / (2π/3) x)

y = 1sin(3x)

The equation for the graph with a sinusoidal wave, given an amplitude of 1, a period of 2π/3, and a phase shift of 0, is y = sin((2π/3)x).

The equation for a sinusoidal wave can be written as:

y = A * sin(ωx + φ)

In this case, we are given the values of amplitude (A = 1), period (ω = 2π/3), and phase shift (φ = 0).

The amplitude (A) represents the maximum displacement or height of the wave from the center line. In this case, it is 1.

The period (ω) represents the length of one complete cycle of the wave. The period is the reciprocal of the frequency, and in this case, it is 2π/3.

The phase shift (φ) represents any horizontal displacement of the wave. In this case, the phase shift is 0, indicating that the wave starts at its equilibrium position.

Using these values, the equation for the given graph would be:

y = 1 * sin((2π/3)x + 0)

Simplifying it further:

y = sin((2π/3)x)

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Answer:

105mm

Step-by-step explanation:

To find the rainfall during the month of April simply multiply the number of days in April times the average daily rainfall

Number of days in April: 30

Average daily rainfall: 3.5mm

Rainfall during the month = 30 * 3.5 = 105mm

Answer:

11b^3+14b^2+b+9

---------------------------

         b2

Step-by-step explanation:

Answer:

1 centimeter

Step-by-step explanation:

nope

Answer:

Rate = 10.4%

Step-by-step explanation:

Given :

P = $30000

A = $42520

Interest earned = 42520 - 30000 = $12520

Time = 4years

Find R

     [tex]Interest = \frac{PRT}{100}[/tex]

        [tex]12520 = \frac{30000 \times R \times 4}{100}\\\\12520 = 300 \times 4 \times R\\\\12520 = 1200 \times R\\\\R = \frac{12520}{1200}\\\\R = 10.43 \%[/tex]

Round to 1 decimal place, Rate = 10.4%

[tex]R_2[/tex]  is 3 ohms

In a circuit containing two resistors [tex]R_1[/tex] and [tex]R_2[/tex] connected together in parallel, the total resistance [tex]R_T[/tex] is given by;

[tex]\frac{1}{R_T} = \frac{1}{R_1} + \frac{1}{R_2}[/tex]              ---------(i)

Make [tex]R_2[/tex] subject of the formula;

=> [tex]\frac{1}{R_2} = \frac{1}{R_T} - \frac{1}{R_1}[/tex]  

=> [tex]\frac{1}{R_2} = \frac{R_1 - R_T}{R_TR_1}[/tex]

=>   [tex]{R_2} = \frac{R_TR_1}{R_1 - R_T}[/tex]       ---------------(ii)

From the question,

[tex]R_1[/tex] = 6Ω

[tex]R_T[/tex] = 2Ω

Substitute these values into equation (ii) as follows;

=> [tex]{R_2} = \frac{2*6}{6 - 2}[/tex]

[tex]{R_2} = \frac{12}{4}[/tex]

[tex]R_2[/tex] = 3Ω

Therefore, the value of [tex]R_2[/tex] = 3 ohms or [tex]R_2[/tex] = 3Ω

Answer: is 3 ohms.

Explanation: edmentum/plato :)

Given:

Two brothers are sharing a certain sum of money in the ratio [tex]\dfrac{2}{3}:\dfrac{3}{5}[/tex].

The largest share was Gh¢500.00.

To find:

The total amount shared between them.

Solution:

It is given that, two brothers are sharing a certain sum of money in the ratio [tex]\dfrac{2}{3}:\dfrac{3}{5}[/tex].

First we need to make the denominators common.

[tex]Ratio=\dfrac{2\times 5}{3\times 5}:\dfrac{3\times 3}{5\times 3}[/tex]

[tex]Ratio=\dfrac{10}{15}:\dfrac{9}{15}[/tex]

[tex]Ratio=10:9[/tex]

So, the two brothers are sharing a certain sum of money in the ratio 10:9.

Let the shares of two brothers are 10x and 9x respectively. So, the larger share is 10x.

It is given that the largest share was Gh¢500.00.

[tex]10x=500[/tex]

[tex]x=\dfrac{500}{10}[/tex]

[tex]x=50[/tex]

Now, the total amount shared between them is:

[tex]Total=10x+9x[/tex]

[tex]Total=19x[/tex]

[tex]Total=19(50)[/tex]

[tex]Total=950[/tex]

Therefore, the total amount shared between them is Gh¢950.00.

Answer:

(0,4)

Step-by-step explanation:

Here, we want to find the y-intercept of the quadratic function

g(x) = 5x^2 + 9x + 4

Mathematically, we know that the y-intercept is the position on the graph where we have x = 0

so, to find the y-intercept value, we have to find g(0)

simply put, we have to substitute the value of 0 for x

Mathematically, we have this as;

g(0) = 5(0)^2 + 9(0) + 4

g(0) = 0 + 0 + 4

g(0) = 4

thus, we have the y-intercept point as (0,4)

[tex]\implies {\blue {\boxed {\boxed {\purple {\sf {21}}}}}}[/tex]

[tex]\large\mathfrak{{\pmb{\underline{\orange{Step-by-step\:explanation}}{\orange{:}}}}}[/tex]

[tex]3 \: ( \: x + 2 \: )[/tex]

Plugging in the value [tex]x = 5[/tex] in the above expression, we have

[tex] = 3\:( \: 5 + 2 \: )[/tex]

[tex] = 3 \: ( \: 7 \: )[/tex]

[tex] = 3 \times 7[/tex]

[tex] = 21[/tex]

[tex]\sf\pink{PEMDAS\: rule.}[/tex]

P = Parentheses

E = Exponents

M = Multiplication

D = Division

A = Addition

S = Subtraction

[tex]\red{\large\qquad \qquad \underline{ \pmb{{ \mathbb{ \maltese \: \: Mystique35☂}}}}}[/tex]

Answer:

116

Step-by-step explanation:

116 is parallel to y so that are the same its called corresponding angles

When a transversal cuts two parallel lines, the corresponding angles are equal.

In the given figure, the corresponding angles are 116° and y

So, they are equal

⇒   y = 116°

Answer:

OA . -6

Step-by-step explanation:

correct me if I'm wrong

Answer:

Step-by-step explanation:

Area of rectangle:

Given:

The area is:

A = (2x - 7)(3x² + 4x) =

   2x(3x² + 4x) - 7(3x² + 4x) =

   6x³ + 8x² - 21x² - 28x =

   6x³ - 13x² - 28x

Answer:

Area of rectangle = 6 x ³ - 13 x ² + 28

step by step explanation

Given That :-

To Find :-

Area of rectangle = Length × Width

Using Formula

Area of rectangle = Length × Width

substitute the values.

Area of rectangle = ( 2 x - 7 ) × ( 3 x ² + 4 )

= 2 x ( 3 x ² + 4 ) - 7 ( 3 x ² + 4 )

= 6 x ³ + 8 x - 21 x ² + 28

= 6 x ³ - 13 x ² + 28

Answer:

What is your question for probabilities?

Answer:

X=2, y=-1

Step-by-step explanation:

-4x +8y=-16 equation 1

4x +3y=5 equation 2

     11y=-11 add two equations to eliminate x

y=-1

solve for x by inputting y value into either equation

4x+3y=5

4x+3(-1)=5

4x-3=5

4x=8

x=2