Step-by-step explanation:
a= 16x+3-14x+15
combine like terms, 16x-14x= 2x
so,
2x+3+15,
15+3=18
18=2x, divide 18 by 2
x=9
b) *open the parenthesis* -1/6 *24x = -4x
-1/6*60 = -10
-4x- (-10)= -4x+10
-4x+10+2x= -4x+2x= -2x
-2x=10 = 2x=-10 = x=-5
Cheers!
Answer:
<h3>1) 5(7
- x + 8)</h3>
first box: 5 * 7 = 35
35 x^2
second box: 5 * -1 = -5
-5x
third box: 5 * 8 = 40
40
answer: 35 - 5x + 40
<h3>2) 2x(4x^2 + 3x + 6)</h3>
first box: 2x * 4x^2
2 * 4 = 8
x * x^2 = x^3
8x^3
second box: 2x * 3x
2 * 3 = 6
x * x = x^2
6x^2
third box: 2x * 6
2 * 6 = 12
12x
answer: 8x^3 + 6x^2 + 12x
<h3>
3) (tp + 5)(4p - 6)</h3>
top left box: tp * 4p
p * p = p^2
4t
top right box: tp * - 6
-6tp
bottom left box: 5 * 4p
5 * 4 = 20
20p
bottom right box: 5 * - 6
5 * -6 = -11
-11
answer: 4tp^2 - 6tp + 20p - 11
<h3>
4) (4a - 8)(8a - 1)</h3>
top left box: 4a * 8a
4 * 8 = 32
a * a = a^2
32a^2
top right box: 4a * -1
4 * -1 = -4
-4a
bottom left box: -8 * 8a
-8 * 8 = -64
-64a
bottom right box: -8 * - 1
-8 * - 1 = 8
8
32a^2 - 4a - 64a + 8
<em>combine like terms</em>
32a^2 - 68a + 8 = answer
Answer:
The student took 2.5 minutes to paint 1 square foot.
Step-by-step explanation:
In order to know how long the student took to paint each square foot we first need to know the total area of the bulletin board. Since it is a rectangle we can compute it's area by multiplying the width and the height. That is:
area = 2*3 = 6 square foot
Since the student took 15 minutes to paint the whole board the pace at which he was working can be calculated by dividing the total area of the board by the time he took to paint all of it. So we have:
pace = 6/15 = 0.4 foot/min
To find how long it took him to paint 1 square foot we can divide it by the pace he was painting. We have:
time = 1/0.4 = 2.5 minutes
The student took 2.5 minutes to paint 1 square foot.
see the attached figure to better understand the problem
we know that
The Area of the composite figure is equal to the sum of Area 1, Area 2 and Area 3
The Area 1 is a triangle
The Area 2 is a rectangle
The Area 3 is equal a semicircle
therefore
<u>the answer is the option</u>
a triangle, a rectangle, and a semicircle