What is the volume of the following rectangular prism

Step-by-step explanation:

i) answer =1

ii) 2 -3m + 6n -2 x 3 3-m

Answer:

( i ) [tex]\boxed{1}[/tex]

( ii ) [tex]\boxed{2^{6n - 3m - 2}\times 3^{3 - m}}[/tex]

.

Step-by-step explanation:

( Part i )

[tex]\left(\frac{1}{x^{a - b}} \right)^{a + b}\left(\frac{1}{x^{b + a}} \right)^{b - a}[/tex]

[tex]= \left(\frac{1}{x^{(a - b)(a + b)}} \right)\left(\frac{1}{x^{(b + a)(b - a)}} \right)[/tex]

[tex]= \left(\frac{1}{x^{a^2 - b^2}} \right)\left(\frac{1}{x^{b^2-a^2}} \right)[/tex]

[tex]= \frac{1}{x^{a^2 - b^2 + (b^2 - a^2)}}[/tex]

[tex]= \frac{1}{x^0}[/tex]

[tex]= \frac{1}{1}[/tex]

[tex]= \boxed{1}[/tex]

.

( Part ii )

[tex]\frac{2^{m + n}\times 3^{2m + 3} \times 4^{2n -1}}{6^{2m + n}\times 12^{m - n}}[/tex]

[tex]=\frac{2^{m + n}\times 3^{2m + 3} \times 2^{2(2n -1)}}{(2\times3)^{2m + n}\times (3\times 2^2)^{m - n}}[/tex]

[tex]=\frac{2^{m + n}\times 3^{2m + 3} \times 2^{4n -2}}{2^{2m + n}\times3^{2m + n}\times 3^{m - n}\times 2^{2(m - n)}}[/tex]

[tex]=\frac{2^{m + n + 4n - 2}\times 3^{2m + 3}}{2^{2m + n + 2m - 2n}\times3^{2m + n + m - n}}[/tex]

[tex]=\frac{2^{m + 5n - 2}\times 3^{2m + 3}}{2^{4m - n}\times3^{3m}}[/tex]

[tex]= 2^{m + 5n - 2 - (4m - n)}\times3^{2m + 3 - 3m}[/tex]

[tex]= \boxed{2^{6n - 3m - 2}\times 3^{3 - m}}[/tex]

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Happy to help :)

Answer:

She would get less chocolate donuts then the cream filled donuts

Step-by-step explanation:

so I have 6 glazed donuts I bought, I also bought 2 chocolate donuts, if you subtract that you'd have 18 chocolate donuts

Answer:

The width is - 4 the lengeth is - 7

Step-by-step explanation:

w*l = 28in²

w = ?

l = w+3

w=2

2+3 = 5

5*2 = 10

w = 3

3+3 = 6

6*3 = 18

w = 4

4+3 = 7

7*4 = 28

So,

W = 4 L = 7

Answer:

3,300

Step-by-step explanation:

Answer:

x = 1[tex]\frac{1}{6}[/tex], y = 3[tex]\frac{2}{3}[/tex]

Step-by-step explanation:

y = -2x + 6 --- Equation 1

y = 4x - 1 --- Equation 2

Since both (-2x + 6) and (4x - 1) have the same total, y, they are equal.

-2x + 6 = 4x - 1

Isolate the like terms.

6 + 1 = 4x + 2x

Evaluate like terms.

6x = 7

Find x.

x = [tex]\frac{7}{6}[/tex]

x = 1[tex]\frac{1}{6}[/tex]

Substitute x = [tex]\frac{7}{6}[/tex] into Equation 2:

y = 4x - 1

y = 4([tex]\frac{7}{6}[/tex]) - 1

  = 4[tex]\frac{2}{3}[/tex] - 1

y = 3[tex]\frac{2}{3}[/tex]

Answer:

[tex]\theta=24^\circ[/tex]

Step-by-step explanation:

Trigonometry and Right Triangles:

The ratios of the sides of a right triangle are called trigonometric ratios. Any angle or side length can be calculated using the appropriate trigonometric ratio.

Please refer to the image below. The balloon is 100 feet high and the rope has a length of 250 feet. The right triangle formed allows us to apply a trigonometric ratio that relates the two given side lengths: the hypotenuse and the opposite leg to angle θ.

The sine ratio is defined as:

[tex]\displaystyle \sin\theta=\frac{\text{opposite leg}}{\text{hypotenuse}}[/tex]

[tex]\displaystyle \sin\theta=\frac{100}{250}=0.4[/tex]

[tex]\displaystyle \sin\theta=0.4[/tex]

Calculating θ:

[tex]\theta=\arcsin 0.4[/tex]

[tex]\theta=23.6^\circ[/tex]

To the nearest degree:

[tex]\mathbf{\theta=24^\circ}[/tex]

Answer:

where is the question here n a graph ?????

Answer:

(a/b)^k=a^k/b^k

Step-by-step explanation:

Using the laws of exponents, we know that (a/b)^k=a^k/b^k.

I couldn't get it to format correctly so just know that the "/" are for the fraction signs and the "^" is for the exponent marking.

Answer:

a^k / b^k

Step-by-step explanation:

You have to use the properties of the powers.

Answer: Inverse variation

Answer:

green part is 4m²

pink part is 91m²-4m² = 87m²

Answer:

here u go

area of the shaded part is 87m^2

Hi there! :)

[tex]\large\boxed{\text{H. 2.19}}[/tex]

Let x = number of pounds of grapes and y = cost in dollars:

Find the constant of proportionality by finding the price per pound:

[tex]\frac{6.57}{3} = \frac{c}{1} \\\\2.19 = c[/tex]

Therefore, the constant of proportionality is H. 2.19

Answer:

Step-by-step explanation:

O A. y= -2x - 1

O B. y= -2x + 1

O C. y= 1/2x + 1

O D. y= 2x - 1

Answer:

C: (1, 2.5)

Step-by-step explanation:

The point is not exactly on 2 or 3 on the y axis. So it is at 2.5. and when you read a graph you need to look at it from x to y so it should be C: (1, 2.5).

Answer: x=8

Step-by-step explanation: Solve for the x by simplifying both sides of the equation, then isolate the variable.

I hope this help you out!

Answer:

D

Step-by-step explanation:

I hope this helps

Answer:

Two extraneous solutions

Step-by-step explanation:

Answer:

$112.50

Step-by-step explanation:

13.50 / 6 = 2.25; this is how much it cost per pound

2.25 * 50 = 112.50

Answer:

A right 4 down 5

Step-by-step explanation:

counting the grid spaces from any point for example R and going to the point R' (R prime) will give you the translation

Answer:

The answer is D, or the bottom one.

[tex]\left \{ {{5x^2+6y^2=50} \atop {7x^+2y^2=10}} \right.[/tex]  is equivalent to [tex]\left \{ {{35x^2+42y^2 = 350} \atop {-35x^2-10y^2=-50}} \right.[/tex].

An equivalent relation of [tex]\left \{ {{5x^2+6y^2=50} \atop {7x^+2y^2=10}} \right.[/tex]  is to determine.

Relation between two values is defined as the how the value associate with others.

Here,
⇒  [tex]\left \{ {{5x^2+6y^2=50} \atop {7x^+2y^2=10}} \right.[/tex]  
⇒ multiply by 7 in first equation and by -5 in second equation.

⇒ [tex]\left \{ {{35x^2+42y^2 = 350} \atop {-35x^2-10y^2=-50}} \right.[/tex]

Thus, [tex]\left \{ {{5x^2+6y^2=50} \atop {7x^+2y^2=10}} \right.[/tex]  is equivalent to [tex]\left \{ {{35x^2+42y^2 = 350} \atop {-35x^2-10y^2=-50}} \right.[/tex].

Learn more about relation here:
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9514 1404 393

Answer:

  no

Step-by-step explanation:

When the second equation is put in standard form like the first equation is, then you can see they are different. They do not define the same line.

  3x +2y = 7

  x + y = 7 . . . . . second equation in standard form

Answer:

25.12

Step-by-step explanation:

Answer:

subtract 9 then when u get the answer divide by 5

Step-by-step explanation:

The first step in solving 5v + 9 = -51 is to subtract 9 from both sides of the equation.

This will isolate the variable v on the left-hand side of the equation.

The equation is:

5v + 9 = -51

To isolate v, we need to get rid of the 9 on the right-hand side of the equation. We can do this by subtracting 9 from both sides of the equation. This will give us the following equation:

5v + 9 - 9 = -51 - 9

Simplifying both sides of the equation, we get:

5v = -60

Now that the variable v is isolated, we can solve for the value of v by dividing both sides of the equation by 5. This will give us the following equation:

v = -60 / 5

Simplifying both sides of the equation, we get:

v = -12

Therefore, the value of v is -12.

To learn more about equation here:

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Answer:

‍♀️ i think if its a positive make it a negative and a negative make it a positive

Answer: See explanation

Step-by-step explanation:

Let the cost of the boogie board be represented by x.

The surfboard cost six times the boogie board. Therefore, surfboard =6x

The wetsuit is $300 less than the surfboard. This means wetsuit = 6x - 300

Together a boogie board, surfboard, and wetsuit cost $1,312. Therefore,

x + 6x + 6x - 300 = 1312

13x = 1312 + 300

13x = 1612

x= 1612 / 13

x = 124

Boogie board cost $124

Surfboard = 6x

= 6 × $124

= $744

Wetsuit = 6x - 300

= $744 - $300

= $444

Answer:

X=56 Y=56

Step-by-step explanation:

Answer:

5/2

Step-by-step explanation:

Start from (-2,-2) and count up and over until you get to (0,3) because slope is rise/run.

5/2

If you want to check your answer, you can always use the slope formula which is: y2-y1/x2-x1

3--2/0--2 = 5/2

Answer: Y=-5

Step-by-step explanation:

The reason is because if you look down the y axis from the origin you can see the location where the line crosses over the y axis in this case it was at (0,-5)

Answer:

2/3

Step-by-step explanation:

im pretty sure that's the answer

Answer:

y=3x-6

Step-by-step explanation: