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2 years ago

8

five eights of the people on a hike were children. there are 20 children on the hike. how many people total

1 answer:

Lelu [443]2 years ago

5 0

Answer:

There were a total of 32 people on the hike.

Step-by-step explanation:

Represent the number of people total by p. Then:

(5/8)p = c = the number of children

Since there are 20 children on the hike, (5/8)p must equal 20:

(5/8)p = 20

Solve for p by multiplying both sides by (8/5):

(8/5)(5/8)p = 20(8/5), or

p = 32

There were a total of 32 people on the hike.

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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

If JKLM is a rhombus, MK = 30, NL = 13, and mZMKL = 41°, find each measure.

oksian1 [2.3K]

Answer:

$NK = 15$

$JL = 26$

$KL = 19.85$

$\angle JKM =49$

$\angle JML =41$

$\angle MLK = 90$

$\angle MNL =90$

$\angle KJL =41$

Step-by-step explanation:

Given

$MK = 30$

$NL = 13$

$\angle MKL = 41$

Solving (a): NK

MK is a diagonal and NK is half of the diagonal. So:

$NK = \frac{1}{2} * MK$

$NK = \frac{1}{2} * 30$

$NK = 15$

Solving (b): JL

JL is a diagonal, and it is twice of NL.

$JL = 2 * NL$

$JL = 2 * 13$

$JL = 26$

Solving (c): KL

To solve for KL, we consider triangle KNL where:

$\angle KNL = 90$

and

$KL^2 = NL^2 + NK^2$

$KL^2 = 13^2 + 15^2$

$KL^2 = 394$

$KL = \sqrt{394$

$KL = 19.85$

Solving (d - h):

To do this, we consider triangle JKN

$\angle KNL = \angle LNM = \angle MNJ = \angle JNK = 90$ -- diagonals bisect one another at right angle

Alternate interior angles are equal. So:

$\angle MKL = \angle KMJ = \angle KJL = \angle JLM = 41$

Similarly:

$\angle MKJ = \angle KML = \angle MJL = \angle JLK = 90 - 41$

$\angle MKJ = \angle KML = \angle MJL = \angle JLK = 49$

So:

$\angle JKM =49$

$\angle JML =41$

$\angle MLK = \angle MLJ + \angle JLK$

$\angle MLK = 49 + 41$

$\angle MLK = 90$

$\angle MNL =90$

$\angle KJL =41$

5 0

2 years ago

Which equation has the same solutions as 4x + x - 5 = 0 ?

Lyrx [107]

5x-5=0
You simplify the left side

4 0

1 year ago

Read 2 more answers

The volume of a cylinder can is 1.54 litre and area of base is 77cm^2 Find its height

goblinko [34]

Answer:

The height is 20 cm.

Step-by-step explanation:

First, we have to know that the volume formula is V = πr²h and the base area of cylinder is a circle. So we can let πr² be 77 cm² . Then we have to substitute the following values into the formula :

$v = 1.54 \: l$

$v = 1540 \: {cm}^{3}$

$v = \pi \times {r}^{2} \times h$

Let πr² be 77,

Let v be 1540,

$1540 = 77 \times h$

$77h = 1540$

$h = 1540 \div 77$

$h = 20 \: cm$

5 0

3 years ago

Find the circumference and area of the circle. Round to the nearest tenth.<br> 2 m

Fed [463]

Radius=2m

Circumference:-

$\\ \bull\sf\dashrightarrow 2\pi r$

$\\ \bull\sf\dashrightarrow 4(3.14)$

$\\ \bull\sf\dashrightarrow 12.56m$

Area.

$\\ \bull\sf\dashrightarrow \pi r^2$

$\\ \bull\sf\dashrightarrow 3.14(2)^2$

$\\ \bull\sf\dashrightarrow 3.14(4)$

$\\ \bull\sf\dashrightarrow 12.56m^2$

8 0

2 years ago

Read 2 more answers