The table shows a baseball player's batting average at home and away during the day and at night.

How do you find the volume, in cubic inches of a prism?

Margaret [11]

Answer: V= Area of the base x the height

Step-by-step explanation:

Assuming the measurements of the sides are already in inches, say the area of the base ends up being 14in and the height of the prism is 5in, multiply those numbers and your answer would be 70 inches cubed.

5 0

3 years ago

Find the equation of the line that passes through the points (-5,7) and (2,3)

Olegator [25]

Answer:

$y=-\frac{4}{7}x+4\frac{1}{7}$

Step-by-step explanation:

So, in order to solve this problem, I started off by drawing it out. On my graph that I have attached below, I first started out by locating the points (-5,7) and (2,3). Now, this is an optional step, but I highly encourage practicing your graphing skills by solving this problem on graph paper as well. Next, I connected the two points that I just graphed. This is the line that passes through (-5,7) and (2,3).

Now, here is where the actual solving starts. If you haven't already been taught this yet, I will introduce it to you now. I am going to find the equation of this line by filling in what I know in the equation y=mx+b, where m= the slope of the line, and b= y intercept.

Slope of the line: m= $\frac{y_{1} - y_{2} }{x_{1} - x_{2} } = \frac{7-3}{-5-2} = \frac{4}{-7}= -\frac{4}{7}$

If you haven't been taught how to find the slope of a line I recommend you find out.

Substitute the slope into the equation.

$y=-\frac{4}{7} x+b\\$

Now, we will solve for the 'b,' or y intercept.

We already have x and y values to use: (-5,7) or (2,3). I'll use x=2 and y=3 to solve for the y intercept.

$y=-\frac{4}{7} x+b\\\\3=-\frac{4}{7} *2+b\\\\3=-\frac{8}{7} +b\\b=3+\frac{8}{7} \\b=\frac{21}{7}+\frac{8}{7}=\frac{29}{7} =4\frac{1}{7} \\b=4\frac{1}{7}$

Last step: substitute the slope and y intercept into y=mx+b.

$y=mx+b\\y=-\frac{4}{7}x+4\frac{1}{7}$

That is the answer to this problem.

I hope this helps.

3 0

4 years ago

Please hurry find the measure of S

Andrews [41]

Answer:

m∠S = 29.5

Explanation:

Q

S $\huge\boxed {\sf \triangle}$ R

In this triangle, QR = SQ, which means its an isosceles triangle, angle S and R is similar.

Thus solve:

m∠S = (180° - 121°)/2

m∠S = 29.5°

3 0

2 years ago

Read 2 more answers

Use the Midpoint Rule and the given data to estimate the value of the integral I. (Give the answer to two decimal places.)

svlad2 [7]

Answer:

a) integral = 24.72

b) |Error| ≤ 0.4267

Step-by-step explanation:

a)

The integral:

$\int_{0}^{3.2} f(x) dx$

can be approximated with the midpoint rule, as follows:

6.7*(0.8 - 0.0) + 8.9*(1.6 - 0.8) + 6.9*(2.4-1.6) + 8.4*(3.2 - 2.4) = 24.72

(that is, all the intervals are 0.8 units length and f(x) is evaluated in the midpoint of the interval)

b)The error bound for the midpoint rule with n points is:

|Error| ≤ K*(b - a)^3/(24*n^2)

where b and are the limits of integration of the integral and K = max |f''(x)|

Given that -5 ≤ f''(x) ≤ 1, then K = 5. Replacing into the equation:

|Error| ≤ 5*(3.2 - 0)^3/(24*4^2) = 0.4267

5 0

3 years ago

a rectangle prism has a volume of 3x^2 + 18x+ 24. its base has a length of x + 2 and width of 3, what expression represents the

OlgaM077 [116]

$\bf \textit{volume of a rectangular prism}\\\\
V=lwh\qquad 
\begin{cases}
l=x+2\\
w=3\\
V=3x^2 + 18x+ 24
\end{cases}\implies \cfrac{V}{lw}=h
\\\\\\
\cfrac{3x^2 + 18x+ 24}{3(x+2)}=h\implies \cfrac{\underline{3}(x^2 + 6x+ 8)}{\underline{3}(x+2)}=h
\\\\\\
\cfrac{(x+4)\underline{(x+2)}}{\underline{(x+2)}}=h\implies x+4=h$

6 0

3 years ago