Make a the subject of the formula s=ut + 1/2at^2

If y is directly proportional to x square and y equal 1/8 when x = 1/2 what is the positive value of x when y it was 9/2?

mojhsa [17]

Answer:

d

Step-by-step explanation:

Given y is directly proportional to x² then the equation relating them is

y = kx² ← k is the constant of proportion

To find k use the condition y = $\frac{1}{8}$ when x = $\frac{1}{2}$ , then

$\frac{1}{8}$ = k( $\frac{1}{2}$ )² = $\frac{1}{4}$ k ( multiply both sides by 8 )

1 = 2k ( divide both sides by 2 )

k = $\frac{1}{2}$

y = $\frac{1}{2}$ x² ← equation of proportion

When y = $\frac{9}{2}$ , then

$\frac{9}{2}$ = $\frac{1}{2}$ x² ( multiply both sides by 2 )

9 = x² ( take the square root of both sides )

x = ± $\sqrt{9}$ = ± 3

with positive value x = 3 → d

8 0

4 years ago

A store is having a 20% off sale on all merchandise If Mai buys one item and save $13 what was the original price of her purchas

katrin [286]

Answer:

Step-by-step explanation:

20% off...and she saves $13

so 20% of what number is 13

0.20x = 13

x = 13/0.20

x = 65 <== original price

7 0

3 years ago

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Consider a data set containing the following values: 70 65 71 78 89 68 50 75 The mean of the preceding values is 70.75. The devi

Leokris [45]

Answer:

If this is the sample data, the sample variance is 125.07 and the sample standard deviation is 11.18

If this is a population data, the population variance is 109.44 and the population standard deviation is 10.46

Step-by-step explanation:

We are given the following data-set:

70, 65, 71, 78, 89, 68, 50, 75

Deviations from the mean

–0.75, –5.75 , 0.25, 7.25, 18.25, –2.75, –20.75, 4.2

Sample size, n = 8

Sample:

$\text{Standard Deviation} = \sqrt{\displaystyle\frac{\sum (x_i -\bar{x})^2}{n-1}}$

where $x_i$ are data points, $\bar{x}$ is the mean and n is the number of observations.

Sum of squares of differences =

0.5625 + 33.0625 + 0.0625 + 52.5625 + 333.0625 + 7.5625 + 430.5625 + 18.0625 = 875.5

$s = \sqrt{\dfrac{875.5}{7}} = 11.18$

$\text{ Sample variance} = s^2 = 125.07$

Population:

$\text{Standard Deviation} = \sqrt{\displaystyle\frac{\sum (x_i -\bar{x})^2}{n}$

where $x_i$ are data points, $\bar{x}$ is the mean and n is the number of observations.

Sum of squares of differences =

0.5625 + 33.0625 + 0.0625 + 52.5625 + 333.0625 + 7.5625 + 430.5625 + 18.0625 = 875.5

$\sigma = \sqrt{\dfrac{875.5}{8}} = 10.46$

$\text{ Population variance} = \sigma^2 = 109.44$

7 0

3 years ago

Mike jogged a total distance of 5 1/3 miles during the months of October and November. If Mike only jogger 1/6 mile every day, W

Bumek [7]

Answer:

D

Step-by-step explanation:

If he jogged $x$ miles every day, and he jogged a total distance of $y$ miles, then he runs for $y/x$ days. This is an extension of the $d=rt$ or distance equals rate times time.

We plug in for y and x to get that he runs for $5~1/3~~/~~1/6$ .

So, the answer is $\boxed{D}$ and we're done!

7 0

3 years ago

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Please help <br> The diagram shows a 5ft student standing near a tree

Novosadov [1.4K]

Answer:

25 ft

Step-by-step explanation:

The diagram shows two triangles that are similar. Similar triangles have equal angles and sides that are proportional to each other. Since the base of each triangle is given, we can find the proportion of the sides:

$\frac{smaller}{larger}=\frac{8}{40}=\frac{1}{5}$

Given the ratio of the smaller to larger triangle, we can set up a proportion to find the missing height of the larger triangle:

$\frac{1}{5}=\frac{5}{x}$ , where 'x' represent the height of the tree

cross-multiply: x = (5)(5) or 25 ft

8 0

3 years ago