PLEASE HELP ME ASAP?!?<br> Find the length of the missing side. Simplify all radicals.

Jen Butler has been pricing Speed-Pass train fares for a group trip to New York. Three adults and four children must pay $ 132.

laiz [17]

Let a=price of adult ticket
let c=price of a child's ticket
start out by writing the following system of equations:
3a+4c=132
2a+3c=94
then, multiply the first equation by 2, and the second equation by 3 to get the following system of equations:
6a+8c=264
6a+9c=282
subtract the like terms to get the following equation:
-c=-18
divide both sides by -1 to get rid of the negative to get the price of a child's ticket to be $18. to find the price of an adult ticket, pick one of the original equations to substitute the 18 in for c to find a. for example:
2a+3c=94
2a+3(18)=94
2a+54=94
-54 -54
2a=40
2 2
a=20

or if you decide to use the other equation:
3a+4c=132
3a+4(18)=132
3a+72=132
-72 -72
3a=60
3 3
a=20
either way, you still get an adults ticket to be $20 and a child's ticket to be $18.

8 0

3 years ago

What is the volume of the prism?

mezya [45]

Answer:

40 $\frac{5}{8}$ $cm^{3}$

Step-by-step explanation:

The figure is a rectangular prism, so the formula would be Volume = length x width x height.

length = 6 $\frac{1}{2}$ cm

width = 2 $\frac{1}{2}$ cm

height = 2 $\frac{1}{2}$ cm

If you plug everything you have in the problem into the volume equation, you would get : Volume = 6 $\frac{1}{2}$ cm x 2 $\frac{1}{2}$ cm x 2 $\frac{1}{2}$ cm.

Without a calculator, I would first turn the mixed numbers into improper fractions.

6 $\frac{1}{2}$ = $\frac{13}{2}$

2 $\frac{1}{2}$ = $\frac{5}{2}$

Volume = $\frac{13}{2}$ x $\frac{5}{2}$ x $\frac{5}{2}$

When you multiply everything together you should get $\frac{325}{8}$ .

As a mixed number, that would be 40 $\frac{5}{8}$ $cm^{3}$ .

7 0

3 years ago

A company is manufacturing an open-top rectangular box. They have 30 cm by 16 cm sheets of material. The bins are made by cuttin

Natalija [7]

Answer:

a. (30 - 2x)(16 - 2x)x. b. length 21.2 cm , width = 7.2 cm and height x = 4.4 cm

Step-by-step explanation:

a. Let x be the side of the squares to be cut from each corner. Since we have two corners on each side, the length of the resulting box from the 30 cm by 16 cm sheet is L = 30 - 2x. Its breadth is B = 16 - 2x. The height of the resulting box is x. So its volume V = LBx = (30 - 2x)(16 - 2x)x.

b. To find the maximum value of V, we differentiate V with respect to x and equate it to zero.

So, dV/dx = 0

d(30 - 2x)(16 - 2x)x/dx = 0

-2(16 - 2x)x + (-2)(30 - 2x)x + (30 - 2x)(16 - 2x) = 0

32x + 4x² - 60x - 4x² + 480 - 60x - 32x + 4x² = 0

4x²- 120x + 450 = 0

x²- 30x + 112.5 = 0

Using the quadratic formula, we find x. So, with a = 1, b = - 15 and c = 112.5,

$x = \frac{-(-30)+/-\sqrt{(-30)^{2} - 4 X 1 X 112.5} }{2 X 1} \\= \frac{30+/-\sqrt{900 - 450} }{2}\\ = \frac{30+/-\sqrt{450} }{2}\\ = \frac{30+/-21.21 }{2}\\\\ = \frac{30+21.21 }{2} or \frac{30-21.21 }{2}\\ = \frac{51.21 }{2} or \frac{8.79}{2}\\ = 25.605 or 4.395$