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3 years ago

Find the number that completes each of the following proportions: a.8120=4c b.n0.5=0.71 c.8x=23 d. 7:6=k:120

Mathematics

1 answer:

egoroff_w [7]3 years ago

4 0

Answer:

a. c = 2030,

b. n = 1.42,

c. x = 2.875,

d. k = 140

Step-by-step explanation:

a ) 8120 = 4c,

c = 8120 / 4 = 2030

b ) 0.5n = 0.71,

n = 0.71 / 0.5 = 1.42

c ) 8x = 23,

x = 23 / 8 = 2.875

d ) 7 : 6 = k : 120

Here we want to convert this ratio into fraction form,

7 / 6 = k / 120

And now we can cross - multiply to determine the value of k,

6k = 7(120) = 840,

k = 840 / 6 = 140

We can check the value of k, by plugging it back into our ratio, and see if it reduces to 7 : 6,

140 : 120,

14 : 12,

7 : 6

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Q bisects PR, PQ=3y, and PR=42. Find y and QR.

Vedmedyk [2.9K]

|PR| = |PQ| + |QR|; |PQ| = |QR| conclusion |PR| = 2|PQ|

|PQ| = 3y; |PR| = 42; |QR|=?

subtitute

42 = 2(3y)
6y = 42 |divide both sides by 6
y = 7

|QR| = 3(7) = 21

3 0

3 years ago

Jim is trying to improve his speed on the track so he can qualify for the State Championships. As he is running, he goes from 70

kumpel [21]

Answer:

His acceleration is $\frac{1}{15}$ meters per seconds²

Step-by-step explanation:

Acceleration is the rate of change of the speed

The formula of acceleration is $a=\frac{v_{f}-v_{i}}{t}$ , where

$v_{f}$ is the final speed
$v_{i}$ is the initial speed
The unit of the acceleration is meters/second²

∵ Jim goes from 70 meters/minute (beginning speed) to

106 meters/minute (final speed) in 9 seconds

∴ His initial speed $v_{i}$ = 70 meters/minute

- Change it the meter per second

∵ 1 minute = 60 seconds

∴ $\frac{70}{(1)(60)}=\frac{70}{60}=\frac{7}{6}$ meters/second

∴ $v_{i}$ = $\frac{7}{6}$ meters/second

∵ His final speed $v_{f}$ = 106 meters/minute

- Change it the meter per second

∴ $\frac{106}{(1)(60)}=\frac{106}{60}=\frac{53}{30}$ meters/second

∴ $v_{f}$ = $\frac{53}{30}$ meters/second

∵ The time of the change of his speed is 9 seconds

∴ t = 9

∵ The formula of acceleration is $a=\frac{v_{f}-v_{i}}{t}$

- Substitute the values of t, $v_{i}$ and $v_{f}$ in the formula above

∴ $a=\frac{\frac{53}{30}-\frac{7}{6}}{9}=\frac{1}{15}$

∴ His acceleration is $\frac{1}{15}$ meters per seconds²

3 0

3 years ago

Y=x-5; domain = {4,6,8}

Lostsunrise [7]

Answer:

Range = {-1, 1, 3}

Step-by-step explanation:

<u><em>The question asks for the range.</em></u>

The function given is

$y=x-5$

The domain is the set of 3 numbers:

Domain = {4,6,8}

We need to find the range.

First, the range is the set of all y-values for which the function is defined.

When we will be given the domain with a set of numbers, the range would be the numbers that we get when we evaluate the the function at those numbers.

So, we evaluate the function (y-values) at x = 4,6, and 8.

At x = 4:

$y=x-5\\y=4-5\\y=-1$