What composition forms the equation p(x) when given the functions for h(x), f(x), k(x), and g(x)? PLEASE HELP!!!!! thank you!!!!! *will ofc give brainliest*
Answers
Answer: Choice B. k(h(g(f(x))))
For choice B, the functions are k, h, g, f going from left to right.
===========================================================
Explanation:
We have 4x involved, so we'll need f(x)
This 4x term is inside a cubic, so we'll need g(x) as well.
So far we have
g(x) = x^3
g( f(x) ) = ( f(x) )^3
g( f(x) ) = ( 4x )^3
Then note how we are dividing that result by 2. That's the same as applying the h(x) function
[tex]h(x) = \frac{x}{2}\\\\h(g(f(x))) = \frac{g(f(x))}{2}\\\\h(g(f(x))) = \frac{(4x)^3}{2}\\\\[/tex]
And finally, we subtract 1 from this, but that's the same as using k(x)
[tex]k(x) = x-1\\\\k(h(g(f(x)))) = h(g(f(x)))-1\\\\k(h(g(f(x)))) = \frac{(4x)^3}{2}-1\\\\[/tex]
This leads to the answer choice B.
To be honest, this notation is a mess considering how many function compositions are going on. It's very easy to get lost. I recommend carefully stepping through the problem and building it up in the way I've done above, or in a similar fashion. The idea is to start from the inside and work your way out. Keep in mind that PEMDAS plays a role.
Related Questions
Starting from the origin , explain how to plot the following three points accurately :
(-1,1) (1,-15) (2,1/4)
Answers
Answer:
Do you have a graph so that I can answer ?
What is the slope of the line represented by 3x - 7y = 28?
Answers
Why?
Reorganize the equation 3x-7y=28 you get
Y=3/7x-4
Because y=mx+b and m=the slope this shows that the slope is 3/7
Hope this helps :D
The toy factory at the North Pole uses 350 feet of wood to make 200 toys. At this rate,
how many feet of wood re needed to make 1 toy?
Answers
Answer:
1.75 feet of wood
Step-by-step explanation:
350/200 = 1.75
x/1 = 1.75
Multiply both sides by 1 to isolate x.
x = 1.75
At a baseball training camp, a computer system plots the paths of balls hit during sessions at the batting cage and generates equations for those paths. The path of a ball hit by David is described the equation h(t)=-9-6t+3t^2 .Find how long it would take the ball to hit the ground in an open field. Solve by completing the square.
Your answer:
Answers
Which of the following expressions are undefined? CHOOSE ALL THAT APPLY
A. 6/0
B. 5/0
C. 6/5-5
Answers
Answer:
6/0, 5/0, 6/5-5
Step-by-step explanation:
You cannot divide a number by 0:
6/0 is dividing by 05/0 is dividing by 06/5-5=6/0 which is dividing by 0Savannah is going to invest $220 and leave it in an account for 12 years. Assuming
the interest is compounded continuously, what interest rate, to the nearest tenth of a
percent, would be required in order for Savannah to end up
with $430
Answers
Answer:
5.7%
Step-by-step explanation:
The formla for calculating compound interest is expressed as;
A = P(1+r)^t
A is the amount = $430
P is the principal = $220
r is the rate
t is the time = 12 years
Substitute and get r;
430 = 220(1+r)^12
430/220 = (1+r)^12
1.955 = (1+r)^12
1.057 = 1+r
r = 1-1.057
r = 0.057
r = 5.7%
The interest rate is 5.7%
Bill is going for a run. He runs for 19.2 miles at a speed of 6 miles per hour. For how many hours does he run
Answers
Answer:
3.2miles per hour
Step-by-step explanation:
19.2 / 6 = 3.2
What is 10and 1 half divided by 7 eights
Answers
Answer:
12
Step-by-step explanation:
Answer:
12
Step-by-step explanation:
10 1/2 / 7/8= 12
I can't figure out d - 11
Answers
Answer: d = 17
Step-by-step explanation:
d - 11 = 6
So, by adding 11 to each side you'd get rid of the -11 on the left and isolate the variable
d = 17
Can anyone help me please??? Almost done Thank you!!
Answers
Answer:
you might’ve already answered this but it’s 65
Step-by-step explanation:
the two sides in a triangle have to be congruent so if one angle is 65, the other has to be 65 too :)
Answer:
65
Step-by-step explanation:
the given triangle is an isoceles triangle and opposite angles of opposite equal sides of isosceles triangle are equal
4. Tell if the measures 6, 14, and 13 can be side lengths of a triangle. If so, classify the triangle as acute,
right, or obtuse.
a. Yes; acute triangle
c. Yes; right triangle
b. Yes; obtuse triangle
Answers
Answer:
A. Yes; acute triangle
Step-by-step explanation:
a=6
b=14
c=13
Using Pythagorean theorem-
c^2 = a^2 + b^2
13^2 = 6^2 + 14^2
169 = 36 + 196
169 = 232
169 < 232
Therefore, (a) the triangle is acute.
If 169 =169 there would be a right triangle.
If c were greater than a + b there would be an obtuse triangle.
if U={natural number less than 10}, M={multiples of 2}, N={factors of 8} and O={even number} then can we write M intersection (N intersection O) = (M intersection N) intersection O? verify
Answers
Answer:
yes
Step-by-step explanation:
u={1,2,3,4,5,6,7,8,9}
m={2,4,6,8}
N={1,2,4,8}
O={2,4,6,8}
Now
M intersection (N intersection O) = (M intersection N) intersection O
or , {2,4,6,8} intersection {2,4,8} ={2,4,8}
intersection {2,4,6,8 }
:. {2,4,8} ={2,4,8}
Let fx) = x + 11 + 2 and g(x) - 2 x + 11. When does f(x) = g(x)?
Answers
Answer:when x= -2/3
That means, when the common product of f(x) & g(x) is x+2/3
Step-by-step explanation:
I’ll mark u as brainlist (all that apply)
Answers
Answer:
use some brain cells
Step-by-step explanation:
PLSSS HELP WILL GIVE BRAINLIEST FOR FIRST CORRECT ANSWER!!!!!!!!!
If a fair die is rolled once, what is the probability of one
An odd number
A number greater than 2
A square number?
Answers
Answer:
A fair die has 6 sides.
There are 3 odd numbers on a fair die so the probability would be 3/6
There are 4 numbers greater than 2 on a fair die o the probability of that would be 4/6
There is only one number that will make it square and that is 4. So the probability would be 1/6
What is the diameter of the circle shown above?
A) 1 inch
B) 3.14 inches
C) 8 inches
D) 16 inches
HURRY PLEASE DUE IN A FEW MINUTES!!! WILL MARK THANKS, 5 STARTS AND BRANLIEST IF RIGHT!!!!!!
Answers
Answer:
D. 16 in.
Step-by-step explanation:
The radius of the circle is 8 in. The diameter of any circle is twice the radius.
2 x 8 = 16
The diameter is 16 in. long.
I hope this helped :)
Tickets for a family of 6 to go skiing cost $48. whats the unit price ?
Answers
48/6 = 8
Solve.
The perimeter of a college athletic field is 100 meters and the length is 18 m more than the width
Find the length, width and area.
Answers
take the breadth as x and accordingly length as (x+18)
the formula for finding the perimeter of a rectangle is 2(l+b) now put the correct values as shown in the picture and form an equation this way you will be able to find x which is the breadth and length Is 18 morethan breadth ,now as u have found both length and breadth go ahead and find the area whose formula is length×breadth
HOPE IT HELPS
Select all of the fractions that are equivalent to -2/3
o 2/-3
o -3/-2
o -2/-3
o - 2/3
o -3/2
o -2/2
Please helppp
Answers
Answer:
Step-by-step explanation:
⇒o 2/-3 Doesn't matter where the minus is as long as there an odd numbere of them.
o -3/-2
o -2/-3
⇒o - 2/3 This is given. Is it really listed.
o -3/2
o -2/2
There really are only 2 of them. 3/2 in any form is not equal to 2/3.
-2/2 = - 1 not -2/3
-2/-3 There are an even number of - signs. The answer is 2/3
Solve for x x^2-2x+1=0
Answers
Answer:
x=1
Step-by-step explanation:
By factoring, you'll compress the equation to (x-1)^2=0
Next take out the square: x-1=0
Now subtract one to the other side to get x! x=1
Hope this helps! :)
13
A local business is calculating the total profit made f(x) after selling
x cupcakes. The business would like to predict their profit by creating an equation for the function.
Write an equation that models the total profit for the business below.
Drag and drop the numbers into the boxes to create the function's equation. Not all numbers listed will be used.
x | f(x)
_____
3 | -5
7 | -2
11 | 1
15 |4
(it won’t allow me to send another pic with the chart so i hope this helps. & the picture i did attach are the things you have to use to create the problem it has to be in the form f(x) = _ x + _
Answers
Answer:
The required equation is: [tex]\mathbf{f(x)=\frac{3}{4}x-\frac{29}{4}}[/tex]
Step-by-step explanation:
We need to find equation from the table given
x f(x)
3 -5
7 -2
11 1
15 4
We can write equation in the form of [tex]y=mx+b[/tex]
where m is slope and b is y-intercept.
Finding Slope
We can used the slope formula to find slope: [tex]Slope=\frac{y_2-y_1}{x_2-x_1}[/tex]
From the table we have: [tex]x_1=3, y_1=-5, x_2=7, y_2=-2[/tex]
Putting values and finding slope
[tex]Slope=\frac{y_2-y_1}{x_2-x_1}\\Slope=\frac{-2-(-5)}{7-3} \\Slope=\frac{-2+5}{7-3}\\Slope=\frac{3}{4}[/tex]
So, we get slope [tex]m=\frac{3}{4}[/tex]
Now, finding y-intercept
Using the slope [tex]m=\frac{3}{4}[/tex] and point (3,-5) we can find y-intercept
[tex]y=mx+b\\-5=\frac{3}{4}(3)+b\\-5=\frac{9}{4}+b\\b=-5-\frac{9}{4}\\b=\frac{-5*4-9}{4}\\b=\frac{-20-9}{4}\\b=\frac{-29}{4}[/tex]
The y-intercept is [tex]b=\frac{-29}{4}[/tex]
So, the equation having slope [tex]m=\frac{3}{4}[/tex] and y-intercept [tex]b=\frac{-29}{4}[/tex] will be:
[tex]y=mx+b\\y=\frac{3}{4}x-\frac{29}{4}[/tex]
The required equation is: [tex]\mathbf{f(x)=\frac{3}{4}x-\frac{29}{4}}[/tex]
rationalise the denoninator of 1 ÷ 5 - square root of 2
Answers
Answer:
Square root2 /3
Step-by-step explanation:
1. Multiply both numerator and denominator by square root of 2.
2. Square root 2 times itself is just 2 that so denominator is 5-2
3. 1 times Square root 2 is just Square root 2. So numerator is Square root 2
4. 5-2=3 so final answer is Square root 2 over 3
convert 18 1/10 into a decimal.
Answers
Answer:
the answer is 18.1 1/10 is the same thing as .1
If f(x) = x4 – 5, then what is the remainder when f(x) is divided by x + 1?
Answers
Answer:
The remainder is: f(-1) = -4
Step-by-step explanation:
We know that when a polynomial function f(x) is divided by x-c, then the remainder is f(c)
Given the function
[tex]f\left(x\right)\:=\:x^4\:-\:5[/tex]
It is stated that the function f(x) is divided by x + 1.
Thus, substituting x = -1 in the function to find the remainder f(-1)
i.e
f(-1) = (-1)⁴ - 5
f(-1) = 1 - 5
f(-1) = -4
Therefore,
The remainder is: f(-1) = -4
Answer:
9
Step-by-step explanation:
284 + 0 = 284 is an example of which property?
Answers
PLEASE HELP I WILL MARK BRAINLIEST
The measure of the supplement of an angle is 12 greater than twice the measure of its complement.
a. Measure of the angle = __________°
b. Measure of the supplement = __________°
Answers
a. 12 deg, b. 168 deg
We can create a systems of equations using this information, since supplement angles add up to 180 deg and complementary angles add up to 90 deg, when angle = x deg and supplement = y deg,
x + y = 180
y = 2(90 - x ) + 12
Solving:
x + 2(90 - x) + 12 = 180
-x + 180 + 12 = 180
x = 12
12 + y = 180
y = 168
Help brainliest for correct answer
Answers
Answer:
14 degrees.
Step-by-step explanation:
I am assuming that the 56 degree angle is at the centre of the circle.
The angle at the top in the circle = 1/2 * 56 = 28 degrees.
The reflex angle = 360 - 56 = 304 degrees.
If we draw a line from the vertex of the 56 degrees angle to the vertex of 28 degree angle we bisect the reflex angle and the 28 degree angle. Also the 2 triangles formed are congruent ( by SSS).
So x = 180 - 1/2 * 28 - 1/2 * 304
= 180 - 14 - 152
= 180 - 166
= 14 degrees.
1. Find the slope between (-1, -3) and (4, 0)
a. 5/3
b. -3
c. - 3/5
d. 3/5
2. Given the equation: 3y = 15x + 9, find slope.
a. 5
b. 2/3
d. -2/3
c. Undefined
3. Given a point and a slope, write the equation in slope-intercept form; (1, 2) and m= -3
a. y = -3x + 1
b. y = -3x – 5
c. y = -3x + 5
d. y = -3x – 1
4. Write the equation of the line in slope-intercept form: y-int = (0,3) , m = 2
a. y = 2x + 3
b. y = -2x + 3
c. y = 2x
d. y = 3x +2
5. Given two points, write the equation in point-slope form: (1, 3) and (-2, 12)
a. y – 1 = -3(x – 3)
b. y – 3 = 5(x – 1)
c. y – 3 = -3(x – 1)
d. y + 12 = -3(x – 1)
6. Write the equation of the function graphed below.
a. y= x - 1
b. y= -x - 4
c. y = x - 4
d. y = x +1
7. The table below represents a linear function. What is the slope of this function?
a. 1/3
b. -1/3
c. 3
d. -3
Answers
Answer:
Step-by-step explanation:
1. Slope = (y2-y1) / (x2-x1) = -3-0/ -1-4= -3/-5= 3/5 (d)
2.
Compare to the equation y= mx+b, where m is the slope
3y = 15x+9 divide by 3 each term
y = 15x/3 +9/3
y= 5x + 3 so slope is 5 ( a)
3.
use first the equation point- slope y-y1 =m (x-x1) and rearange it to be in slope-intercept form y=mx +b
y-y1 =m (x-x1)
y-2 = -3( x-1)
y = 2-3x+3
y= -3x +5 ( c)
4.
if the point y- intercept is at (0, 3) then the y-intercept is b=3
y= mx+b
y = 2x +3 (a)
5.
the equation point- slope y-y1 =m (x-x1), find the slope m= (y2-y1) / (x2-x1)
m= 3-12/ 1+2 = -9/3 = -3
y-1 = -3(x-3) is (a)
6.
y-intercept is at -4 ( yet the graph is off a bit -tell your teacher)
slope m = 1
so the equation is y=mx+b and here is y=x -4 (c)
7.
the slope is m= (y2-y1) / (x2-x1) si pich any two points from the table and calculate the slope
for example (0, 3) and (1, 0)
m = (3-0)/ (0-1) = 3/-1 = -3 (d)
1. Slope = (y2-y1) / (x2-x1) = -3-0/ -1-4= -3/-5= 3/5 (d)
2.
Compare to the equation y= mx+b, where m is the slope
3y = 15x+9 divide by 3 each term
y = 15x/3 +9/3
y= 5x + 3 so slope is 5 ( a)
3.
use first the equation point- slope y-y1 =m (x-x1) and rearange it to be in slope-intercept form y=mx +b
y-y1 =m (x-x1)
y-2 = -3( x-1)
y = 2-3x+3
y= -3x +5 ( c)
4.
if the point y- intercept is at (0, 3) then the y-intercept is b=3
y= mx+b
y = 2x +3 (a)
5.
the equation point- slope y-y1 =m (x-x1), find the slope m= (y2-y1) / (x2-x1)
m= 3-12/ 1+2 = -9/3 = -3
y-1 = -3(x-3) is (a)
6.
y-intercept is at -4 ( yet the graph is off a bit -tell your teacher)
slope m = 1
so the equation is y=mx+b and here is y=x -4 (c)
7.
the slope is m= (y2-y1) / (x2-x1) si pich any two points from the table and calculate the slope
for example (0, 3) and (1, 0)
m = (3-0)/ (0-1) = 3/-1 = -3 (d)
I WILL GIVE YOU THE BRAINIEST!!!
In a company, 60% of the workers are Men. If 2,320 people work for the company who aren't men, how many workers are there in all?
If Right.
Answers
Answer: 1392 people who work for the company are men.
I did this by multiplying 2320 by 0.6, which got me my answer.
Have a great day!
Stay safe and healthy!
Happy holiday seasons!
May I please have brainliest?
HELP ASAP PLS Which table represents the same equation as
y= -1/2x+5
Answers
Go to desmos graphing calculator and plug it in