Answer:
x² + 6x + 9
x² + 4x + 3
x³ + 8x² + 21x + 18
x + 2
Step-by-step explanation:
Given in the question two functions,
f(x) = x² + 5x + 6
g(x) = x + 3
1) (f+g)(x)
(x² + 5x + 6) + (x + 3)
x² + 5x + x + 6 + 3
x² + 6x + 9
2) (f-g)(x)
(x² + 5x + 6) - (x + 3)
x² + 5x - x + 6 - 3
x² + 4x + 3
3) (f.g)(x)
(x² + 5x + 6) . (x + 3)
x³ + 5x² + 6x + 3x² + 15x + 18
x³ + 8x² + 21x + 18
4) (f/g)(x)
(x² + 5x + 6) / (x + 3)
(x + 2)
-------------------
(x + 3) | (x² + 5x + 6)
x² + 3x
--------------------
2x + 6
2x + 6
-----------------
0
Answer:
Find the ratio of hops to distance traveled (1: 1.5), then multiply 150 by 1.5.
Step-by-step explanation:
A child is hopping along a sidewalk. The ratio table below shows the comparison between the number of hops and the distance traveled. Hopping Number of hops Distance traveled (ft) 20 30 50 75 80 120 150 ?
Which statement correctly explains how to find the distance traveled after 150 hops? Subtract 120 – 75 to get 45, then add that number to 120. Add 30 + 75 + 120. Find the ratio of hops to distance traveled (1:1.5), then multiply 150 by 1.5. Find the ratio of hops to distance traveled (1:1.5), then divide 150 by 1.5.
Solution:
The table is:
No. of hops Distance traveled
20 30
50 75
80 120
150 ?
From the table, for every 30 increase in the number of hops, the distance travelled increase by 45 feet
Find the slope of the line:
m = (y2-y1) / (x2-x1)
m=slope of the line
y2-y1 = change in distance travelled
x-2 - x1 = Change in number of hops
m = (y2-y1) / (x2-x1)
m = (75-30) / (50-20)
=45 / 30
m = 1.5
Then, the line is:
y = 1.5x
We substitute x = 150
y = 1.5x
y = 1.5 × 150
y = 225
<h3>
Answer: 10.99</h3>
Work Shown:
Angle B = 20 is the reference angle
AC = 4 is the side opposite this reference angle
BC = x is the unknown adjacent side
tan(angle) = opposite/adjacent
tan(B) = AC/BC
tan(20) = 4/x
x*tan(20) = 4
x = 4/tan(20)
x = 10.9899 approximately (make sure your calc is in degree mode)
x = 10.99 rounding to two decimal places
BC = 10.99
Answer:
x =147
Step-by-step explanation:
The sum of the angles is = 360 -(2x+1) ( since it will make a full circle)
42+(-124+x) =360-(2x+1)
Combine like terms
x-82 =359-2x
Add 2x to each side
x-82+2x = 359
3x -82 = 359
Add 82 to each side
3x-82+82 = 359+82
3x = 441
Divide by 3
3x/3=441/3
x =441/3 or 147
Answer:
She went on the slide 8 times and on the roller coaster 4 times
Step-by-step explanation:
We convert each statements to a mathematical equation.
Firstly, let's represent the number of times she went on the coaster with R and the number of times on the slide with S. We know quite well she went on 12 rides. Hence the summation of both number of times yield 12.
Mathematically, R + S = 12. ........(i)
Now we also know her total wait time was 3hours. Since an hour equals 60 minutes, her total wait time would equal 180 minutes.
To get a mathematical representation for the wait time, we multiply the number of roller coaster rides by 25 and that of the slides by 10.
Mathematically, 25R + 10S = 180 .......(ii)
Here we now have two equations that we can solve simultaneously.
From equation 1 we can say R = 12 - S. We can then substitute this into equation 2 to yield the following:
25(12 - s) + 10s = 180
300 - 25s + 10s = 180
300 - 25s + 10s = 180
300 - 15s = 180
15s = 300 - 180
15s = 120
S = 120/15
S = 8
S = 8 , and R = 12 - S = 12 - 8 = 4