Answer:
[tex]f(g(x)) = \frac{10x-9}{3 + 3x}[/tex]
Step-by-step explanation:
Given
[tex]f(x) = \frac{1}{x} - 3[/tex]
[tex]g(x) = \frac{3}{x} + 3[/tex]
Required
Find f(g(x))
If: [tex]f(x) = \frac{1}{x} - 3[/tex]
Then:
[tex]f(g(x)) = \frac{1}{3/x + 3} -3[/tex]
Solve the denominator (take LCM)
[tex]f(g(x)) = \frac{1}{\frac{3+3x}{x}} -3[/tex]
[tex]f(g(x)) = \frac{x}{3 + 3x} - 3[/tex]
It can be solved further as:
[tex]f(g(x)) = \frac{x-3(3 + 3x)}{3 + 3x}[/tex]
[tex]f(g(x)) = \frac{x-9 + 9x}{3 + 3x}[/tex]
[tex]f(g(x)) = \frac{10x-9}{3 + 3x}[/tex]
Jerome won the lottery! He donated 1/2 of the money to charity and gave his parents 1/6 of the winnings. The remaining 1/3 was divided equally among his 5 friends. The expression given represents the part of the lottery money for each friend received. "1/3 (divided by) 5" Which expression is equivalent to the amount of money each friend received? A: 1/5 (divided by) 1/3 B: 1/5 x 1/3 C: 1/3 (divided by) 1/5 D: 5/1 x 1/3
Answer:
B: 1/5 x 1/3
Step-by-step explanation:
a. [(-28)-(+42)] - (-13)
Answer:
= -57 is answer
Step-by-step explanation:
−28−42−(−13)
have a good day!
What is the slope of the line that passes through the points (2, -3) and (5, 1)
Answer:
Answer is (4) 4/3
Step-by-step explanation:
[tex]\frac{1- -3}{5-2}[/tex]
[tex]\frac{4}{3}[/tex]
Answer:
slope is 4/3
Step-by-step explanation:
1-(-3)/5-2
4/3
PleSee help!!! 10 points for it
2. What is an interest that is computed on the
principal and then added to it?
A. Simple Interest
B. Compound Interest
C. Interest
D. Principal
Answer:
Step-by-step explanation:
The time to complete a project varies inversely
with the number of employees. If 3 people can
complete the project in 7 days, how long will it
take 5 people?
O 4.2
O 21
O 11.7
O 2.1
Answer:
4.2
Step-by-step explanation:
T = K/N
K= TN
= 3×7
K= 21
Therefore the time required for 5 employees can be calculated as follows
T= 21/5
= 4.2
A box has 70 cookies . 10% are broken (a) What fraction is broken ?
(b) What fraction remained whole?
Answer:
Step-by-step explanation:
70(10/100)=7 broken cookies.
7/70=1/10 is the fraction broken
(70-7)/70=63/70 is the fraction remaining whole
Answer:
(a) 1/7 are broken
(b) 6/7 remain whole
Step-by-step explanation:
70 is a nice number to deal with in terms of percentages and fractions. If 10% of the cookies are broken, do 10/70. That fraction simplified gets you 1/7. To find the remaining whole cookies. Do 7/7 - 1/7 = 6/7 (or if you already know that in your head that works too)
The graph shows your elevation during a bike ride. Which statement is true about your bike ride?
Answer:
You were running downhill for the first 15 minutes.
help pleaseeeeeee!!!!!!
Answer:
5x + 100
Step-by-step explanation:
(2x + 6) x 2 = 4x + 12
14x + 8 - 4x + 12 =
10x + 20 / 2 =
5x + 100
Hope that helps!
It takes Naomi 4 minutes to run 5 laps. How long does it take her to run 30 laps? Use a table, double number line, tape diagram or another strategy to show your thinking.
(Please hurry I'm being timed)
Answer:
24 minutes
Step-by-step explanation:
5x6=30
4x6=24
What are two fractions equivalent to 2/8?
Hm, any two? 1/4 and 4/16 are equal to 2/8.
Hope this helps.
How many tens are in the number 639
Answer:
63 tens are in 639 are in that number
Answer:
There are 63 full tens in 639.
Step-by-step explanation:
639÷10=63.9
Hope this helps! :)
туре or Movie
Number or
Students
36
Horror
Drama
26
Comedy
30
Sci-Fi
28
Based on the data in the table, what is the probability that a random
Answer: 3/4, because the probability of renting a comedy is 1/4
================================================================
Explanation:
We have 36+26+30+28 = 120 students. 30 of which rented a comedy.
The probability of renting a comedy is 30/120 = (30*1)/(30*4) = 1/4
The probability of not renting a comedy is 1 - (1/4) = 4/4 - 1/4 = (4-1)/4 = 3/4.
Or you could say that 1/4 = 0.25, so 1-0.25 = 0.75 which converts to the fraction 3/4.
If you had 4 people and 1 of them rents a comedy, then the other 3 hasn't rented a comedy.
120g:5kg in simplest form
find the equation for the line that passes through the point (4,-3), and that is perpendicular to the line with the equation y= -3/4x-3
Answer:
hi
Step-by-step explanation:
Answer
Slope between two given points (1,3) and (2,7) is
m=
2−1
7−3
=4
Then perpendicular slope is m
1
=
4
−1
The line equation with this slope is given by
y=
4
−1
x+c.......(1)
Now, the above line passes through the point (−4,−3)
⇒−3=
4
−1
×(−4)+c
⇒c=−4
Therefore required line is 4y+x+16=0 (Substitute
′
c
′
in (1) and simplify)
Which answer is an equation in point-slope form for the given point and slope?
Point (1, 9), Slope: 5
(A) y - 9 = 5(x + 1)
(B) y+9 -5(x - 1)
(C) y-9=5(x - 1)
(D) y-1-5(x +9)
Answer:
Step-by-step explanation:
Point-slope equation for line of slope m that passes through (x₀,y₀):
y-y₀ = m(x-x₀)
In your case, m=5 and (x₀,y₀)=(1,9):
y-9 = 5(x-1)
how to find the interest for a 2% interest rate loan of $3000 for 1 year, BUT instead of the 2% in the example, switch it to 3% interest on a $3500 loan.
Answer: See Explanation
Step-by-step explanation:
Simple interest is calculated as:
= principal × rate × time.
The interest for a 2% interest rate loan of $3000 for 1 year will be:
= principal × rate × time.
= $3000 × 2% × 1
= $3000 × 2/100 × 1
= $3000 × 0.02 × 1
= $60
The interest for a 3% interest rate loan of $3500 for 1 year will be:
= principal × rate × time.
= $3500 × 3% × 1
= $3500 × 3/100 × 1
= $3500 × 0.03 × 1
= $105
1/3 1/4 3/8 7/24 5/12 which is the biggest
Answer: 5/12
Step-by-step explanation:
Answer:
Step-by-step explanation:
5/12 is the biggest
An angle measures 154º more than the measure of its supplementary angle. What is the
measure of each angle?
Answer:
167 & 13
Step-by-step explanation:
(180-154)/2=
26/2=13
154+13=167
1. The cost of a fish dinner for a restaurant is $7.95. If they sell it for $11.95, what is the percent markup?
Answer:
the answer will be
50.3144 %
Select the statement that describes this expression: 32 ÷ 4 + ( fraction 1 over 2 x 16) − 2
Answer:
Step-by-step explanation:
32 ÷ 4 + ([tex]\frac{1}{2}*16) - 2[/tex] = 8 + (1*8) - 2
= 8 + 8 - 2
= 16 - 2
= 14
Answer:
The quotient of 32 and 4 added to the product of fraction 1 over 2 and 16, then subtract 2
Step-by-step explanation:
0.4 divided by 2.3 plzz fast
Answer:
divided by 2.3 plzz fastdivided by 2.3 plzz fast
Step-by-step explanation:
divided by 2.3 plzz fast
divided by 2.3 plzz fastdivided by divided by 2.3 plzz fast plzz fast
In a triangle with all sides equal, what is the degree measure of any of the
angles? Write one number. *
answer:
the degree measure would be 60°
60 + 60 + 60 = 180
therefore, 60 is the answer.
5 times a number is 14 less than the square of that number. Find the negative solution.
Answer:
x=-2
Step-by-step explanation:
5x=x^2 - 14
x^2-5x-14=0
(x-7)(x+2)=0
x=7,-2
Question
A random sample of SAT scores has a sample mean ofă = 1060 and sample standard deviation of s = 195. Use the
Empirical Rule to estimate the approximate percentage of SAT scores that are less than 865.
Answer:
The approximate percentage of SAT scores that are less than 865 is 16%.
Step-by-step explanation:
The Empirical Rule states that, for a normally distributed random variable:
Approximately 68% of the measures are within 1 standard deviation of the mean.
Approximately 95% of the measures are within 2 standard deviations of the mean.
Approximately 99.7% of the measures are within 3 standard deviations of the mean.
In this problem, we have that:
Mean of 1060, standard deviation of 195.
Empirical Rule to estimate the approximate percentage of SAT scores that are less than 865.
865 = 1060 - 195
So 865 is one standard deviation below the mean.
Approximately 68% of the measures are within 1 standard deviation of the mean, so approximately 100 - 68 = 32% are more than 1 standard deviation from the mean. The normal distribution is symmetric, which means that approximately 32/2 = 16% are more than 1 standard deviation below the mean and approximately 16% are more than 1 standard deviation above the mean. So
The approximate percentage of SAT scores that are less than 865 is 16%.
help pls
Find the volume of the composite solid.
Answer:
80cm3
Step-by-step explanation:
volume of the composite solid=volume of the
pyramid+
volume of the
cuboid
volume of the pyramid=1/3* base area*height
=1/3*5*4*6
=40cm3
volume of the cuboid=base area *height
=5*4*2
=40cm3
volume of the composite solid=40cm3+40cm3
=80cm3
true or false. the cross section of a rectangular prism is a prism
Answer:
true
Step-by-step explanation:
7 cm
10.5 cm
13 cm
Your Turn!
3 m
15 m
11 m
5m
Answer: number 1 . 6688.5 then rounded is 6689.
Number 2. 2475
Step-by-step explanation:
A small theater head six rows of 26 chairs each an extra seven chairs have just been brought in how many chairs are in the theater now
Using only addition what is 20 - 9 + 8 -7
Answer:
12
Step-by-step explanation:
Answer: 12
Step-by-step explanation:
I don't know if you mean using the Complements Method but I really wouldn't recommend using this method for all problems unless your teacher asked you to specifically.
Here is how to:
1. take the "complement" of the number we are subtracting (The "complement" is the number to add to make 10 (or 100, 1000, etc, depending on how many digits we have)
2. add it to to the number we are subtracting from
3. discard the extra "1" on the left
If you mean to do it mentally, think about it like this:
20 + (-9) = 11 You are essentially adding negative nine to twenty, not subtracting nine. If you want to see this better, try using a number line. When you add a negative number, you move to the left on the number line.
Same thing with 8 + (-7) = 1
You are adding negative seven to eight.
All that is left to do is adding both of the results together, and you get twelve.
11 + 1 = 12