On a piece of paper, graph this system of inequalities. Then determine which

Determine the equation of g(x) that results from translating the function f(x) = (x + 10)2 to the right 12 units.

N76 [4]

$f(x)=(x+10)^2\\\\\Downarrow T_{\vec{a}=[12; 0]-translation\ 12\ units\ to\ the\ right}\\\\g(x)=(x+10-12)^2=(x-2)^2$

8 0

3 years ago

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Calculate the volume of the composite solid.

Leokris [45]

Answer:

B.) 191.1 cubic cm.

Step-by-step explanation:

First find the area of the rectangular prism. Because the formula is l * w * h, this becomes $7 * 6 * 3.55$ = 149.1.

For the volume of a pyramid, the equation is $\frac{Base*height}{3}$ . We already know the height, and because it's sitting on top of the rectangular prism, the base should have the same area. In other words, if the prism has a base of 7*6, then the pyramid can be found through $\frac{3(7*6)}{3}$ . 7 Multiplied by 6 is 42, and since it's multiplied but also divided by 3, they cancel out, leaving only 42.

The sum of both of these shapes is 191.1 cm³.

7 0

3 years ago

g a club of 12 people would like to choose a person for each office of president, a vice president, and a secretary. How many di

-Dominant- [34]

Answer:

220 possible ways

Step-by-step explanation:

Given

$n = 12$ --- people

$r = 3$ -- posts $(President, Vice\ President\ and\ Secretary)$

Required

Determine the number of selection

Since there is no condition attached, the number of selection is:

$Selection = ^nC_r$

Substitute values for n and r

$Selection = ^{12}C_3$

Apply combination formula

$Selection = \frac{12!}{(12-3)!3!}$

$Selection = \frac{12!}{9!3!}$

$Selection = \frac{12*11*10*9!}{9!*3*2*1}$

$Selection = \frac{12*11*10}{6}$

$Selection = \frac{1320}{6}$

$Selection = 220$

<em>Hence, there are 220 possible ways</em>

5 0

3 years ago

Evaluate each expression if a=4, b=6 and c=3<br> 7c+8a-5b

tankabanditka [31]

Answer: 38

Step-by-step explanation:

To solve this problem, you are simply going to plug in the values for the numbers into the equation so it would look like this:

7(3)+8(4)-5(6)

3 0

4 years ago

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What is the length of x

Temka [501]

Immediate math help from PAID TUTORS. (paid link)Click here to see ALL problems on Triangles
Question 118094: Find the length x in the triangle. Side 1=8. Side 2=x. Side 3=12 (Scroll Down for Answer!)Did you know that Algebra.Com has hundreds of free volunteer tutors who help people with math homework? Anyone can ask a math question, and most questions get answers!Check it Out!OR get immediate PAID help on:
Type Your Question Go!!! Answer by jim_thompson5910(34119) About Me (Show Source):You can put this solution on YOUR website!I'm assuming that the triangle is a right triangle and that side 3 is the hypotenuse.

We basically have this triangle set up:
Since we can see that the triangle has legs of 8 and x with a hypotenuse of 12, we can use Pythagoreans theorem to find the unknown side.

Pythagoreans theorem:
a%5E2%2Bb%5E2=c%5E2 where a and b are the legs of the triangle and c is the hypotenuse

8%5E2%2Bx%5E2=12%5E2 Plug in a=8, b=x, and c=12. Now lets solve for x

6+4+%2B++x++%5E+2+=+1+4+4 Square each individual term

+x++%5E+2+=+1+4+4+-+6+4 Subtract 64 from both sides

+x++%5E+2+=+8+0 Combine like terms

s+q+r+t+%28++x++%5E+2+%29+=+s+q+r+t+%28+8+0+%29 Take the square root of both sides

x=4%2Asqrt%285%29 Simplify the square root

Which approximates to... x+=+8+.+9+4+4+2+7+1+9+0+9+9+9+9+1+6
So our answer is x+=+8+.+9+4+4+2+7+1+9+0+9+9+9+9+1+6....

3 0

4 years ago