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3 years ago

11

A museum has a wax sculpture of a historical village. The scale is 1.5:8. If the height of a hut in the sculpture is 5 feet, how

tall is the original hut to the nearest whole foot?

1 answer:

Oksi-84 [34.3K]3 years ago

4 0

Let us say that x is the real height of the original hut, therefore we can establish the equation:

5 : x = 1.5 : 8

5 / x = 1.5 / 8

Solving for x:

x = 5 * 8 / 1.5

x = 40 / 1.5

<span>x = 26.67 ft</span>

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-x=-y+2 and 3y+4=2x solve using matrices

MissTica

$\begin{cases}-x=-y+2\\3y+4=2x\end{cases}\implies\begin{cases}x-y=-2\\2x-3y=4\end{cases}$

In matrix form, this is

$\begin{bmatrix}1&-1\\2&-3\end{bmatrix}\begin{bmatrix}x\\y\end{bmatrix}=\begin{bmatrix}-2\\4\end{bmatrix}$

The coefficient matrix has determinant

$\begin{vmatrix}1&-1\\2&-3\end{vmatrix}=-3+2=-1\neq0$

so it has an inverse, which is

$\begin{bmatrix}1&-1\\2&-3\end{bmatrix}^{-1}=\begin{bmatrix}3&-1\\2&-1\end{bmatrix}$

Multiply both sides by the inverse matrix:

$\begin{bmatrix}3&-1\\2&-1\end{bmatrix}\begin{bmatrix}1&-1\\2&-3\end{bmatrix}\begin{bmatrix}x\\y\end{bmatrix}=\begin{bmatrix}3&-1\\2&-1\end{bmatrix}\begin{bmatrix}-2\\4\end{bmatrix}$

$\implies\begin{bmatrix}x\\y\end{bmatrix}=\begin{bmatrix}-10\\-8\end{bmatrix}$

so that $x=-10$ and $y=-8$ .

8 0

3 years ago

There are 36 people in a fitness studio. What fraction represents the number of people running? • 3 8 of the people lifted weigh

klio [65]

Answer:

7/24

Step-by-step explanation:

3/8 is changed to 9/24 people lifting weights

1/3 is changed to 8/24 people cross training

17/24 people are not running

7/24 people are running

7/24 cannot be reduced

5 0

3 years ago

MN0 with vertices M(4,-5), N(5,-8), O(8, -6) ; translate the new figure M'N'O' (-2,5)

Aleks04 [339]

If you are translating a graph (-2,5), the easiest way to find the new points is to subtract the x value of each coordinate (M, N, and O) by 2. This will give you the new x values for the translated coordinates. Then, to find the new y values, add 5 to the y values of each coordinate. Then put the new x value and new y value in the form of a coordinate, and that will be your answer.

5 0

3 years ago

Rosie washes clothes for two families the first family pays her $500 more per month than the second. Her total earning per month

disa [49]

Answer:

Family 1: $1.850
Family 2: $1.350

Step-by-step explanation:

We know that the total monthly payment is 3200, so if we call Pa (family A`s payment) and Pb (Family B's payment) the payments:

Pa+Pb=3200
also, Pa = Pb+500

So if we replace Pa in the first ecuation:

Pb+500+Pb=3200
2Pb= 3200-500
Pb=2700/2= $1.350

then Pa+Pb=3200 => Pa= 3200-1350= $1.850

Good Luck!

8 0

2 years ago

Help me on this . It’s important

bixtya [17]

Answer:

The answer is 16.

Step-by-step explanation:

6 x 3 = 18

18 - 2 =16

5 0

3 years ago

Read 2 more answers