The value of y varies directly with x. If x=3, then y=21. What is the value of x when y=105?

Which of the following is a point-slope equation of a line that passes through

Mademuasel [1]

Answer:

The Answer is: y = -2/3x + 10/3

Step-by-step explanation:

Given points (-1, 4) and (8, -2) first find the slope:

m = (y - y1)/(x - x1)

m = (4 - (-2)) / (-1 - 8)

m = 4 + 2 / -9

m = -6/9 = -2/3

Use the point slope form and point (8, -2) and slove for y:

y - y1 = m(x - x1)

y - (-2) = -2/3(x - 8)

y + 2 = -2/3x + 16/3

y = -2/3x + 16/3 - 2

y = -2/3x + 16/3 - 6/3

y = -2/3x + 10/3

Proof using the point (-1, 4):

f(-1) = -2/3(-1) + 10/3

= 2/3 + 10/3

= 12/3 = 4, giving point (-1, 4)

Hope this helps! Have an Awesome Day!! :-)

4 0

3 years ago

Joshua walked 14 feet down the hall of his house to get the door he continued in a straight line out the door and across the yar

AleksandrR [38]

Answer:

Joshua walked 48 feet in total.

Step-by-step explanation:

To find the total distance we need to sum every distance that he walked. We have:

- First: Joshua walked down the hall to the door = 14 feet

- Second: He continued in a straight line out the door and across the yard to the mailbox = 24 feet

- Third: He came straight back across the yard and stopped to pet his dog = 10 feet

Hence, the total distance is:

$d_{T} = d_{1} + d_{2} + d_{3} = 14 ft + 24 ft + 10 ft = 48 ft$

Therefore, Joshua walked 48 feet in total.

I hope it helps you!

8 0

3 years ago

simplify, 6+3-3-3-3-3-21-5-5234-534-5-4-4-3-43-3-443--4-4-4-4--4-4-4-4-4-4-4--44-4--4-4-4=5647765865886*556386588668*56586856853

Nataly [62]

Answer:

−6294≠Infinity

Step-by-step explanation:

−6294≠Infinity

5 0

3 years ago

What is the area occupied by the castle below Quadir built from wooden blocks?

Firlakuza [10]

Answer:

4x6x12x5x4x4x5=

115200

6 0

3 years ago

One year had the lowest ERA (earned-run average, mean number of runs yielded per nine innings pitched) of any male pitcher at

lord [1]

Answer:

Thomas had the better year relative to their peers.

Step-by-step explanation:

<u>The complete question is</u>: One year Thomas had the lowest ERA (earned-run average, mean number of runs yielded per nine innings pitched) of any male pitcher at his school, with an ERA of 3.31. Also, Karla had the lowest ERA of any female pitcher at the school with an ERA of 3.02. For the males, the mean ERA was 4.837 and the standard deviation was 0.541. For the females, the mean ERA was 4.533 and the standard deviation was 0.539. Find their respective z-scores. Which player had the better year relative to their peers, or ? (Note: In general, the lower the ERA, the better the pitcher.)

We are given that for the males, the mean ERA was 4.837 and the standard deviation was 0.541. For the females, the mean ERA was 4.533 and the standard deviation was 0.539.

As, we know that the z-score is calculated by the following formula;

Z = $\frac{X-\mu}{\sigma}$ ~ N(0,1)

where, $\mu$ = population mean

$\sigma$ = standard deviation

Now, firstly we will calculate the z score for Thomas;

z-score = $\frac{X-\mu}{\sigma}$

= $\frac{3.31-4.837}{0.541}$ = -2.823

{Here, the mean ERA for the males was 4.837 and the standard deviation was 0.541}

Similarly, we will calculate the z score for Karla;

z-score = $\frac{X-\mu}{\sigma}$

= $\frac{3.02-4.533}{0.539}$ = -2.807

{Here, the mean ERA for the females was 4.533 and the standard deviation was 0.539}

Now, it is stated in the question that the lower the ERA, the better the pitcher.

So, we can clearly see that Thomas had a lower ERA of z-score as -2.823 < -2.807. This means that Thomas had the better year relative to their peers.

5 0

3 years ago