Answers
Answer:
B
Step-by-step explanation:
Recall that [tex](g \circ f)(x)=g(f(x))[/tex]. In other words, we need to find [tex]f(x)[/tex] first and then put that value into [tex]g(x)[/tex].
We need to find [tex](g \circ f)(4) =g(f(4))[/tex]
[tex]f(x)=4x-2\\[/tex]
[tex]f(4)=4(4)-2=14[/tex]
[tex](g \circ f)(4) =g(f(4))=g(14)[/tex]
[tex]g(x)=-6x^2-8x-8[/tex]
[tex]g(14)=-6(14)^2-8(14)-8[/tex]
[tex]g(14) = (g \circ f) (4) =-1296[/tex]
Related Questions
5196
A large rectangle is made by joining three identical small rectangles as shown.
The perimeter of one small rectangle is 21 cm.
The width of one small rectangle is x cm.
x cm
Work out the perimeter of the large rectangle.
The final line of your answer should be of the form,
Perimeter of large rectangle is ... cm
Answers
Answer:
35 cm
Step-by-step explanation:
As shown in the image attached, the A large rectangle is made by joining three identical small rectangles,
The width of one small rectangle is x cm and the length of one small rectangle is 2x cm. Therefore the perimeter of the small rectangle is given as:
2(length + width) = Perimeter
2(2x + x) = 21
2(3x) = 21
6x = 21
x = 21/6 = 3.5 cm
x = 3.5 cm
From the image attached, the width of the large rectangle is 2x (x + x) and the length is 3x (2x + x). Therefore, the perimeter of the large rectangle is:
2(length + width) = Perimeter
2(3x + 2x) = Perimeter
Perimeter = 2(5x)
Perimeter = 10x
Perimeter = 10(3.5)
Perimeter = 35 cm
The transformation from the function f(x)=3x to the function f(x) 3x-8
Answers
Answer:
It moves 8 to the right
Step-by-step explanation:
This is in the y axis so it will move 8 on the x axis
The population, P in thousands of a resort community is shown by
P(t)= 500t/2t^2+9'
where t is the time in months since city council raised property taxes.
Find the interval on which the population was 40,000 or greater
Answers
Answer:
t ≤ 4.24
Step-by-step explanation:
P(t) ≥ 40000 implies
500t/(2t²+9) ≥ 40000
Multiplying through by t², we have
500t ≥ 40000(2t²+9)
500t/40000 ≥ 2t²+9
Collecting like terms
0.0125t ≥ 2t²+9
0 ≥ 2t²+ 9 - 0.0125t
2t²+ 9 - 0.0125t ≤ 0
2t²- 0.0125t + 9 ≤ 0
Using the quadratic formula,
[tex]t = \frac{-(-0.0125) +/-\sqrt{(-.0125)^{2} - 4 X 2 X 9} }{2 X 2} \\= \frac{0.0125 +/-\sqrt{(0.00015625 - 288} }{4}\\= \frac{0.0125 +/-\sqrt{-287.9998} }{4}\\= \frac{0.0125 +/-16.97i }{4}\\=0.00313 + 4.24i or 0.00313 - 4.24i[/tex]
The factors of the equation are (t - 0.00313 -4.24i) and (t - 0.00313 + 4.24i)
So, (t - 0.00313 -4.24i)(t - 0.00313 + 4.24i) ≤ 0
(t - 0.00313)² - 4.24² ≤ 0
(t - 0.00313)² ≤ 4.24²
taking square-root of both sides,
√(t - 0.00313)² ≤ √4.24²
t - 0.00313 ≤ 4.24
t ≤ 4.24 + 0.00313
t ≤ 4.24313 ≅ 4.24
t ≤ 4.24
Work out the surface area of this cylinder
8.2 cm
17.5 cm
Answers
Answer: 1324.12 sq. cm.
Step-by-step explanation:
A=2πrh+2πr2
A = 2π x 8.2 x 17.5 + 2π x 8.2^2
A = 2π x 143.50 + 2π x 67.24
A= 1324.12
Answer:
SA = 1324.1 cm²
Step-by-step explanation:
Surface Area of Cylinder = [tex]2\pi rh+2\pi r^2[/tex]
Where r = 8.2 cm, h = 17.5 cm
=> SA = [tex]2(3.14)(8.2)(17.5)+2(3.14)(8.2)^2[/tex]
=> SA = [tex]901.6+2(3.14)(67.24)[/tex]
=> SA = 901.6 + 422.5
=> SA = 1324.1 cm²
Each term in the sequence below is 9 more than 1/3 the previous term. What is the value of y-x?
81, 36, x, y,...
Plz explain
Answers
Answer:
y - x = - 5
Step-by-step explanation:
Applying the rule gives
x = [tex]\frac{1}{3}[/tex] × 36 + 9 = 12 + 9 = 21
y = [tex]\frac{1}{3}[/tex] × 21 + 9 = 7 + 9 = 16
Thus
y - x = 16 - 21 = - 5
A company makes 140 bags.
47 of the bags have buttons but no zips.
48 of the bags have zips but no buttons.
22 of the bags have neither zips nor buttons.
A bag is selected at random.
What is the probability that the bag has buttons
Answers
Answer: 0.5
Step-by-step explanation:
Total bags (U) = 140
Number of bags with both button and zip:
(48 + 47 + x + 22) = 140
117 + x = 140
x = 140 - 117
x = 23
Therefore, probability that bag has button :
Total Number of bags with button:
(Bags with button alone + bags with both button and zip)
(47 + 23) = 70
Probability = (required outcome / Total possible outcomes)
P(bag has button) = (number of bags with button / total number of bags)
P(bag has button) = 70/140 = 0.5
P(bag has button) = 0.5
Find the 87th term of the arithmetic sequence –19, -13, -7,...
Answers
Answer:
87th term is 497
Step-by-step explanation:
first, you have to find the nth term:
figure out the difference between your set of numbers (in our case +6)
that means that is 6n. next, the nth term is basically the 0th term so you have to find the 0th term. all you have to do is do the inverse of 6n (-6n or -6), which gives us -25.
nth term= 6n-25
now replace n with 87.
final step:
87*6 (6n and n=87) and that gives you 522. then, you have to do 522-25, due to the equation. 522-25=497
497 is your 87th term.
Answer:
-535Step-by-step explanation:
[tex]a = -19\\d = T_{2} -T_{1} \\d = -19-(-13)\\d = -19+13\\d = -6\\T_{n}= a+(n-1)d \\\\T_{87} = -19+(87-1)-6\\T_{87} = -19+(86)*-6\\T_{87} = -19-516\\T_{87} = -535[/tex]
A large amount of peanuts was divided equally into 6 small bags. The total number of peanuts, p, was 342 which statement can be used to write an expression and then find the number of peanuts that ended up in each bag
Answers
Answer:
342/6 = 57
Step-by-step explanation:
Just basic division
342/6 = 57
just basic division
Can you help me with this question
Answers
Answer:
-1.67
Step-by-step explanation:
what is the graph of y > x2-9.
Answers
Answer:
The 1st graph
Step-by-step explanation:
When you graph the equation in a graphing calc, you should be able to see that the graph most similar would be the 1st one.
Which of the following represents the factorization of the polynomial below x^2+13x+42
Answers
Answer:
(x+7)(x+6)
Step-by-step explanation:
x²+13x+42
x²+6x+7x+42
x(x+6)+7(x+6)
(x+6)(x+7)
Answer:
a) (x+7) (x+6)
Step-by-step explanation:
That is the correct answer because you get it when you factor the current equation.
Hope it helps
Each of these figures is based on a rectangle whose centre is shown.
How many of the figures have rotational symmetry of order two?
Answers
The last 2 shapes.
When you rotate both of them 360 degrees only at 180 and back at 360 it looks same.
Use completing the square to solve for X in the equation (c+7)(x-9)=25
Answers
Answer:
x = 1 ± √89
Step-by-step explanation:
Step 1: Expand
x² - 2x - 63 = 25
Step 2: Isolate xs
x² - 2x = 88
Step 3: Complete the square
x² - 2x + 1 = 88 + 1
(x - 1)² = 89
Step 3: Square root both sides
√(x - 1)² = ±√89
x - 1 = ±√89
Step 4: Isolate x
x = 1 ± √89
Jacob is asked to simplify the expression-3a+4b+5a+(-7b) -3a+4b+5a+(-7b) = -3a+5a+4b+(-7b) which property is this ?
Answers
Answer:
B
Step-by-step explanation:Communative property.
Which of the following is the shape of a cross-section of the figure shown below?
Answers
Answer:
B. Pentagon
Step-by-step explanation:
A cross-section is basically the 2D figure created by slicing through a 3D shape.
Take a look at this figure: it's a pentagonal prism. One note to remember is that for all prisms, their cross-sectional shapes are the same shapes as the shape of their bases.
Here, the two bases are pentagons, so we know the cross-section will be a pentagon.
Thus, the answer is B.
~ an aesthetics lover
f(x) = x^2. What is g(x)?
Answers
Answer:
B
Step-by-step explanation:
The coordinates are (1, 9).
x = 1
y = 9
Put x as 1, and the output should be 9.
g(1) = ( 3 (1) )²
g(1) = (3)²
g(1) = 9
Answer:
b
Step-by-step explanation:
B is correct since you could use a graphing calculator to solve this by plugging each answer choice into the calc.
another way is to plug 1 or x into each of the equations and see which choice has 9 as y
Simply the expression (2x^2y)^3
Answers
Answer:
8 x^6 y^3
Step-by-step explanation:
(2x^2y)^3
(ab)^c = a^c * b^c
2^3 * x^2^3 * y^3
8 * x^2^3 * y^3
We know that a^b^c = a^(b*c)
8 * x^(2*3) * y^3
8 * x^(6) * y^3
8 x^6 y^3
Alexandra and her children went into a movie theater and will buy bags of popcorn
and drinks. She must buy at most 12 bags of popcorn and drinks altogether. Write an
inequality that would represent the possible values for the number of bags of popcorn
purchased, b, and the number of drinks purchased, d.
Answers
Answer:
let number of bags of popcorn = b
let number of drinks = d
at most = maximum
b + d ≤ 12
Resolve into factors:2p(p-1)-p+1
Answers
Answer:
Do it your self
Step-by-step explanation:
Hope this helps!!
if y= -6 when x= -2 find y when x= 5
Answers
Answer:
Y=15 when x=5
Step-by-step explanation:
if y= -6 when x= -2
So y=? When x=5
Y=15
Hope this helps
Good Luck
A. One player places 1 red, 5 green and 3 blue tiles in Bag A, and 6 red, 4 green, and 2 blue in Bag B. What is the probability that the second player draws 2 tiles of the same color?
Answers
Answer:
[tex]\frac{8}{27}[/tex] is the probability that a player draws out two tiles of the same color assuming they are drawing one tile from each bag.
Step-by-step explanation:
In each bag there are red, green, and blue tiles, meaning that no matter which color is pulled out first there is always some probability that the second tile will be the same color. So, we can set up three possible outcomes:
Red: The player pulls out a red tile first. This has a [tex]\frac{1}{9}[/tex] probability of happening. Then in order to succeed for the problem, the next tile also needs to be red which has a [tex]\frac{6}{12}[/tex] probability attached to it. [tex]\frac{1}{9}[/tex] × [tex]\frac{6}{12}[/tex]=[tex]\frac{1}{18}[/tex] probability of happening.
Green: There is a [tex]\frac{5}{9}[/tex] probability of the player pulling out a green tile first. In this case we want to calculate the probability of the second tile being green, which would be [tex]\frac{4}{12}[/tex]. [tex]\frac{5}{9}[/tex]×[tex]\frac{4}{12}[/tex]=[tex]\frac{5}{27}[/tex].
Blue: There is a [tex]\frac{3}{9}[/tex] probability of the first tile being blue in which case we are hoping for the second tile to be blue as well. The probability of the second tile being blue is [tex]\frac{2}{12}[/tex] on its own, and them both being blue is [tex]\frac{3}{9}[/tex]×[tex]\frac{2}{12}[/tex]=[tex]\frac{1}{18}[/tex]
Adding [tex]\frac{1}{18}[/tex]+[tex]\frac{1}{18}[/tex]+[tex]\frac{5}{27}[/tex] we get the answer [tex]\frac{8}{27}[/tex].
Jayden is running laps at track practice. The track is 25 kilometers around. Jayden runs 1 lap in 2 minutes. How many minutes does it take Jayden to run 1 kilometer?
Answers
Answer:
0.08 minutes for a kilometer.
Step-by-step explanation:
If the track is 25 kilometers, and he runs 25 kilometers in 2 minutes, he runs a kilometer in 2÷25 minutes or 0.08 minutes which is 4.8 seconds.
I'm pretty sure the track isn't 25 kilometer or he can't run a lap in 2 minutes. But if so, the answer is 0.08 minutes.
Write 14/√2 + √50 in the form b√2 where b is an integer.
Answers
Answer:
[tex]12 \sqrt{2} [/tex]
Step-by-step explanation:
Taking the terms one at a time,
[tex] \frac{14}{ \sqrt{2} } \\ \frac{14 * \sqrt{2} }{ \sqrt{2} * \sqrt{2} } \\ \frac{14 \sqrt{2} }{2} \\ 7 \sqrt{2} [/tex]
[tex] \sqrt{50} \\ \sqrt{25 * 2} \\ \sqrt{25}* \sqrt{2} \\ 5 * \sqrt{2} \\ 5 \sqrt{2} [/tex]
Adding the terms, you have;
[tex]7 \sqrt{2} + 5 \sqrt{2} =(7 + 5) \sqrt{2} = 12 \sqrt{2} [/tex]
Hope it helps!
I'm out!
Answer:
12
Step-by-step explanation:
14/√2 +√50= 14*√2/√2*√2+ √25*2= 7√2+5√2= 12√2
12√2= b√2
b=12
HOW DO U COMBINE LIKE TERMS I LITERALLY FORGOT LMK DO NOT LOOK IT UP OR ELSE CAUSE IMMA USE GRAMMARLY FOR UR ANSWERS AND SEE IF U DIDNT LOOK IT UP THANK YOU SMMMMM
Answers
Answer:
you combine like terms by adding them up
Step-by-step explanation:
A ball is thrown into the air with an upward velocity of 36 ft/s. Its height h in feet after t seconds is given by the function h = –16t^2 + 36t + 10. a. In how many seconds does the ball reach its maximum height? Round to the nearest hundredth if necessary. b. What is the ball’s maximum height?
Answers
Step-by-step explanation:
We have,
A ball is thrown into the air with an upward velocity of 36 ft/s. Its height h in feet after t seconds is given by the function :
[tex]h=-16t^2 + 36t + 10[/tex] ......(1)
Part (a) :
The maximum height reached by the ball is given by :
[tex]\dfrac{dh}{dt}=0\\\\\dfrac{d(-16t^2 + 36t + 10)}{dt}=0\\\\-32t+36=0\\\\t=\dfrac{36}{32}\\\\t=1.125\ s[/tex]
Part (b) :
The maximum height of the ball is calculated by putting t = 1.125 in equation (1) such that :
[tex]h=-16(1.125)^2 + 36(1.125)+ 10\\\\h=30.25\ m[/tex]
(8x - 4)(7y + 2) multiplying binomials
Answers
Step-by-step explanation:
8x(7y+2)-4(7y+2)
=56xy+16x-28y-8
Answer:
56xy+16x-28y-8
Step-by-step explanation:
you have to use the FOIL method to solve this is problem which is
F-First
O-Outer
I-Inner
F-Last
Please HELP!!!!!!!!!!!!!!!!!
Answers
Answer:
I think it might be the second one or maybe the first one
Step-by-step explanation:
Im not quite sure so dont blame me if its wrong
A boy carries a 2 kg bag and walks 8m on a level road to his house. How much work has he done by carrying the bag? a. 4 J b. 16 J c. zero
Answers
Answer:
160J
Step-by-step explanation:
I think this is the answer
Find the product of (x − 3)2
Answers
Answer:
x^2-6x+9
Step-by-step explanation:
(x-3)^2
(x-3)(x-3)
x^2-3x-3x+9
x^2-6x+9
how do you write 25 x 10^6 in standard form
Answers
Answer:
2.5*10^7
Step-by-step explanation:
Answer:
Brainliest!!!
Step-by-step explanation:
See picture