Can somebody help me with my math?

Suppose a radio station desires to estimate the proportion of the market

In-s [12.5K]

About 3.4% large according to the coordinates

6 0

3 years ago

One number is 4 times another number. The sum of their reciprocals is 5. What are the two numbers?

ivann1987 [24]

Answer:

The two number are:

$y=1,\:x=\frac{1}{4}$

Step-by-step explanation:

Let 'x' be the first number

let 'y' be the second number

Given that one number is 4 times another number, the first equation is

$y = 4x$

Next, the sum of their reciprocals is 5, so

$\frac{1}{x}+\frac{1}{y}=5$

Now, we have the system of equations

$\begin{bmatrix}y=4x\\ \frac{1}{x}+\frac{1}{y}=5\end{bmatrix}$

Let us solve the system of equations

$\begin{bmatrix}y=4x\\ \frac{1}{x}+\frac{1}{y}=5\end{bmatrix}$

substitute y = 4x in the equation $\frac{1}{x}+\frac{1}{y}=5$

$\frac{1}{x}+\frac{1}{4x}=5$

Least Common Multiple of x, 4x: 4x

Adjust fractions based on L.C.M

$\frac{4}{4x}+\frac{1}{4x}=5$

$\frac{4+1}{4x}=5$

$\:\frac{5}{4x}=5$

Multiply both sides by 4x

$\frac{5}{4x}\cdot \:4x=5\cdot \:4x$

Simplify

$5=20x$

switch sides

$20x=5$

Divide both sides by 20

$\frac{20x}{20}=\frac{5}{20}$

Simplify

$x=\frac{1}{4}$

For y = 4x, substitute $x=\frac{1}{4}$

$y = 4x$

$y=4\cdot \frac{1}{4}$

$y=1$

Therefore, the two number are:

$y=1,\:x=\frac{1}{4}$

<u>Verification:</u>

$\frac{1}{x}+\frac{1}{y}=5$

substituting $y=1,\:x=\frac{1}{4}$

$\:\frac{1}{\frac{1}{4}}+\frac{1}{1}=\:5\:\:$

$4+1=5$

$5 = 5$

L.H.S = R.H.S

and

$y = 4x$

substituting $y=1,\:x=\frac{1}{4}$

$y\:=\:4\left(\frac{1}{4}\right)$

$y=1$

8 0

3 years ago

Suppose rafiq went to the nursey and bought a tree priced at 49.99 and two packages of fertilizer priced at 13.99 each. The sale

Mashutka [201]

Answer:

$83.04

Step-by-step explanation:

1. Add up all the prices (49.99, 13,99, 13.99) = 77.97

2. Tax is 6.5% (.065 in decimal form)

3. Multiply 77.97 * .065 = 5.06805

4. 5.06805 rounds to 5.07

5. Add the total purchase (77.97) to the tax (5.07) = 83.04

5 0

3 years ago

You and your friend are paid $38.25 for doing yard work. You worked 2.5 hours and your friend worked 2 hours. You split the mone

Nina [5.8K]

Answer:

Your share of money is $21.25.

Step-by-step explanation:

You and a friend are paid $38.25 for doing yard work.

You worked 2.5 hours and your friend worked 2 hours.

Let there be x dollars per hour for both friends. As same work is completed, and friends are paid together, we can write the equation as:

$2.5x+2x=38.25\\4.5x=38.25$

x = 8.5 dollars

Hence, friend earned = 2x = 2 x 8.5 = 17 dollars

You earned 2.5x = 2.5 x 8.5= 21.25 dollars

Hence, your share of money is $21.25.

Please Mark As Brainliest If The Answer Helped You.

3 0

2 years ago

Read 2 more answers

If y=1/2x-2 determine the value of y when x=-12

vfiekz [6]

Answer:

y = -8

Step-by-step explanation:

y = 1/2x - 2

y = 1/2(-12) - 2

y = -6 - 2

y = -8

Answer: y = -8

4 0

3 years ago

Read 2 more answers