All categories

3 years ago

Phil is riding his bike. He rides 21 miles in 2 hours, 31.5 miles in 3 hours, and 42 miles in 4 hours. Find the

Mathematics

1 answer:

gavmur [86]3 years ago

7 0

Answer:

Step-by-step explanation:

You might be interested in

Express each ratio as a fraction in simplest form: <br><br> 0.3 km to 500 m

deff fn [24]

0.3km=300m
300m:500m
(/100)
3:5
3+5=8
0.3km= 3/8
500m= 5/8

5 0

3 years ago

Read 2 more answers

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

Engineering The equation for the cross section of a spotlight is y+5= 1/2x^2.

Marysya12 [62]

Answer:

$p=1/2\ or\ 0.5\ inches$

Step-by-step explanation:

From the question we are told that

Equation of cross section is $y+5= \frac{1}{2x^2}$

Generally the equation can be rewritten mathematically as

$y+5= \frac{1}{2}x^2$

$x^2=(y+5)2$

$(x-0)^2=(y-(-5))2$

Generally the equation of a parabola with vertical axis is mathematically given by

$(x - h)2 = 4p(y - k)$

Therefore comparing equations

$(x-0)^2=(y-(-5))2$

$4p=2$

$p=2/4$

The distance from the bulb to the vertex of the cross section is given by

$p=1/2\ or\ 0.5\ inches$

4 0

3 years ago

Bria drank an 8-ounce glass of water

Alik [6]

Answer:

3 8-ounce glasses of water were left

Step-by-step explanation:

If you divide 32 by 8, you get 4. And since she already drank a glass of water, you subtract 1 from 4, and you are left with 3.

4 0

3 years ago

Please help me and I need the work :<

nasty-shy [4]

Answer:

1/4 inch 1 inch

______ = _____

1 foot 4 feet

3 × 4 = 12

4 × 4 = 16

7 0

4 years ago