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3 years ago

Find the exact solution(s) of the equation 1/3x^2 = 16

Mathematics

1 answer:

nordsb [41]3 years ago

3 0

Let's solve your equation step-by-step.

1/3x^2=16

Step 1: Divide both sides by 1/3.

1/3x^2 ÷ 1/3 = 16 ÷ 1/3

x^2=48

Step 2: Take square root.

x=±√48

x=4√3 or x=−4√3

Answer: x=4√3 or x=−4√3

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I don't have a question but I was wondering if you could check my work

cestrela7 [59]

The mean of a data sample can be found by adding all the terms in the data sample and dividing the result by the number of terms. In the first case we have the following data sample:

$12,8,15,11,9$

The mean of this sample is:

$\operatorname{mean}=\frac{12+8+15+11+9}{5}=\frac{55}{5}=11$

The mean absolute deviation is the sum of the differences between each data value and the mean, divided by the number of data values, the formula is:

$MAD=\frac{\sum ^{}_{}\mleft|x_i-\bar{x}\mright|}{n}$

Therefore, we must calculate the positive difference between each value and the mean, add them up, and divide the result by the number of data points in the sample. In the case of the first sample we get:

$\text{MAD}=\frac{(12-11)+(11-8)+(15-11)+(11-9)}{5}$

Solving the operation:

$\text{MAD}=\frac{10}{5}=2$

If done this way, all the results for each data set must be correct.

8 0

1 year ago

Form a quadratic polynomial whose zeroes are 3-√3/5 and 3+√3/5?

barxatty [35]

Answer:

x^2 -6x + 222/25

Step-by-step explanation:

If the zeros are as above, then ;

x = 3-√3/5 or x = 3 + √3/5

Firstly, let’s represent √3/5 by b

Thus;

The two roots are ;

x = 3-b or x = 3 + b

so;

x+ b -3 and x -3-b

The quadratic equation is the product of the two

(x + b-3)(x - b -3)

x(x - b-3) + b(x -b -3) -3(x - b -3)

= x^2 -bx -3x + bx -b^2 -3b -3x + 3b + 9

Collect like terms and we are left with;

x^2 -6x -b^2 + 9

So let’s put back b = √3/5

x^2 -6x -(√3/5)^2 + 9

x^2 -6x -3/25 + 9

x^2 -6x + 222/25

3 0

3 years ago

Paul purchased a used vehicle that depreciates under a straight-line method.

netineya [11]

Answer:

Option B. $900

Step-by-step explanation:

Let

y ----> the value of the car

x ----> the time in years

we know that

The linear function in slope intercept form is equal to

$y=mx+b$

where

m is the slope or the depreciation rate

b is the y-intercept or initial value of the car

we have

The y-intercept or initial value is equal to

$b=\$5,000$

$y=mx+5,000$

we have the ordered pair (5,500)

substitute the value of x and the value of y of the ordered pair in the linear equation and solve for m

$500=m(5)+5,000$

$5m=500-5,000\\5m=-4,500\\m=-\$900\ per\ year$

Is negative because is a decreasing function

The linear equation is equal to

$y=-900x+5,000$

therefore

It would depreciate $900 each year.

4 0

3 years ago

9. What is the likelihood that a randomly selected couple's relationship survived between 90 and 150 days

andrew-mc [135]

Answer:

0.5818

Step-by-step explanation:

Suppose the average teenage romantic relationship is normally distributed with a mean number of 100 days with a standard deviation of 30 days.

Answer:

The z score is used to determine how many standard deviations that the raw score is above or below the mean. If the z score is positive then the raw score is above the mean and if it is negative then it is below the mean. It is given by:

$z=\frac{x-\mu}{\sigma}\\ \\where\ \mu=mean,\sigma=standard\ deviation, x=raw\ score$

Given that:

$\mu=100\ days,\sigma=30\ days\\\\For\ x=90\\\\z=\frac{90-100}{30} =-0.33\\\\For\ x=150\\\\z=\frac{150-100}{30} =1.67$

Therefore, from the normal distribution table, P(90 < x < 150) = P(-0.33 < z < 1.67) = P(z < 1.67) - P(z < -0.33) = 0.9525 - 0.3707 = 0.5818

7 0

3 years ago

What is the midpoint of (8,7) and (4,3)

Sergeu [11.5K]

Hello! The midpoint of (8,7) and (4,3) Is (7.5, 3.5)

Hope this helps! And have a great day!

6 0

3 years ago