Show your work F(x)=5x^2-4x+1 G(x)=3x-2 H(x)=x+1 K(x)= 4x What is (g*h)(x)= What is g(k(x))= What is k(g(0)) =

Answers

Answer 1

Answer:

What is (g × h)(x)?

The answer is 3x²+x-2

What is g(k(x))?

The answer is 12x - 2 or 2(6x-1)

What is k(g(0))

The answer is -8

Explanation:

Given these functions —

[tex]f(x) = 5 {x}^{2} - 4x + 1 \\ g(x) = 3x - 2 \\ h(x) = x + 1 \\ k(x) = 4x[/tex]

Find (g × h)(x)

[tex](g \times h)(x) = g(x) \times h(x)[/tex]

Substitute g(x) = 3x - 2 and h(x) = x + 1

[tex](3x - 2) \times (x + 1) \\ (3x - 2)(x + 1)[/tex]

Multiply the polynomial.

[tex]3 {x}^{2} + 3x - 2x - 2[/tex]

Subtract - 2x out of 3x —

[tex]3 {x}^{2} + x - 2[/tex]

Thus, the answer is —

[tex](g \times h)(x) = 3 {x}^{2} + x - 2[/tex]

Find (g(k(x))

Substitute k(x) = 4x in g(x).

[tex]g(x) = 3x - 2 \\ k(x) = 4x[/tex]

[tex]g(k(x)) = g(4x)[/tex]

[tex]g(4x) = 3(4x) - 2[/tex]

Distribute 3 in 4x —

[tex]g(4x) = 12x - 2[/tex]

Thus the answer is —

[tex]g(k(x)) = 12x - 2[/tex]

Alternative Solution

[tex]g(k(x)) = 2(6x - 1)[/tex]

Find k(g(0))

Given two functions — k(x) and g(x)

[tex]k(x) = 4x \\ g(x) = 3x - 2[/tex]

Evaluate the value of g(0) as we substitute x = 0 in g(x)

[tex]g(0 ) = 3(0) - 2 \\ g(0) = 0 - 2 \\ g(0) = - 2[/tex]

Since we need to find k(g(0)), our currently input is g(0).

From k(x) and g(0) —

[tex]k(x) = 4x \\ g(0) = - 2[/tex]

Substitute g(0) = -2 in k(x)

[tex]k(g(0)) = 4(g(0)) \\ k( - 2) = 4( - 2) \\ k( - 2) = - 8[/tex]

Thus, the answer is —

[tex]k(g(0)) = - 8[/tex]


Related Questions

Rewrite
barrel
as a unit rate
hour
A barrel/hour
B. barrels/hour
c. 10 barrels/hour
barrel/hour

Answers

Answer:

C

Step-by-step explanation:

vmlstjtndgydcyedhdhdh

Can anyone tell me theorem of Parallelogram*#​

Answers

Answer:

Theorem 1: In a parallelogram, the opposite sides are of equal length. Theorem 2: If the opposite sides in a quadrilateral are the same length, then the figure is a parallelogram. Theorem 3: A quadrilateral is a parallelogram if and only if the diagonals bisect each other.

Step-by-step explanation:

Hope this helps!!!

i suck at math sadly i wish i could

Segments DE, EF, and DF are midsegments of ABC. Find the length of the indicated segment


AE= ​

Answers

Answer: 2

Step-by-step explanation:

I think that is the answer :)

(1 + 2) x (3 + 4) whats the answer?

Answers

Answer: 21

Step-by-step explanation: 3 x 7 = 21

Answer:

21

Step-by-step explanation:

so 1 plus 2 which is 3 then do 3 plus 4 which is 7 so 3 times 7 is 21

Solve the system of linear equations.

−x+2y=7
x−2y=7

Answers

The answer is no solution.
hope that helps!
the answer is infinity *no solution*
have a good day!

please help! asap! xoxo

Answers

Answer: the answer is 6

Step-by-step explanation:

The answer is c I’m right

what is 1696 divided by 43

Answers

Answer:

39.44

Step-by-step explanation:

Answer:

39.4418605

Step-by-step explanation:

8 cans of corn cost $16. What is the cost per can?

Answers

Answer:

Step-by-step explanation:

$16 / 8 cans = $2 per can

Pay $0.24 for each banana OR pay $1.99 per pound of bananas ​

Answers

Answer:

0.24 for each banana, it seems cheaper.

Step-by-step explanation:

depends on how many bananas you get for a pound

Show that the cosine law simplifies to the Pythagorean theorem when the contained angle between the two known sides is 90°.

Answers

Answer:

See Below.

Step-by-step explanation:

We want to show that the Law of Cosines simplifies to the Pythagorean Theorem when the contained angle between the two known sides is 90°.

The Law of Cosines is given by:

[tex]c^2=a^2+b^2-2ab\cos(C)[/tex]

Where a and b are the two known sides, and C is the angle between them.

If C is 90° then we will have:

[tex]c^2=a^2+b^2-2ab\cos(90 ^\circ)[/tex]

Recall that the cos(90°)=0. Hence:

[tex]c^2=a^2+b^2-2ab(0)[/tex]

Simplify:

[tex]c^2=a^2+b^2[/tex]

So, we acquire the Pythagorean Theorem as desired.

Complete the solution of the equation. Find the value of y when x equals 7. x - 4y = 19 Enter the correct answer.​

Answers

The correct answer is -3. You just plug 7 into the equation and solve for y

Answer: the correct answer is to teacha don’t like you assigning this bullish!+ when will you ever in your life use this feel bad for y’all I dropped out

Step-by-step explanation:

Plz help its due tomorrow

Answers

Answer:

I think D

Step-by-step explanation:

because all the information seems important

Enter the number in two equivalent froms

Answers

The decimal equivalent is 0.60, and the percent is 60%. If you do 3/5, you get 0.60, and to get the percentage, you move the decimal two to the right, and add the percent sign. I hope you understand. :)

Decimal equivalent: 0.6 (all u had to do is divide)
Percent equivalent:60%

Roger grew 42 plants with 14 seed packets. With 16 seed packets, how many total plants can Roger have in his backyard?

Answers

Answer:

48 plants

Step-by-step explanation:

can anyone help me pls will mark branliest

Answers

Answer:

rock climb costs $7

Step-by-step explanation:

2 laser tags +3 rock climb = $31   ( 1 )

4 laser tags + 1 rock climb = $27   (2)

multipy (1) by -2 and add the equations

-4 laser tags -6 rock climb = $ -62  

4 laser tags + 1 rock climb = $27

-6 rock climb +1 rock climb = -62+27

-5 rock climb = -35 divide both sides by -5

1 rock climb = $7

The point (-3, 15) undergoes a translation of 9 units right and 10 units down. What are the coordinates of the new
point?
(-12,10)
® (-12,5)
(6,10)
D (6,5)

Answers

Answer:

This would be D. (6, 5)

Step-by-step explanation:

When moving 9 to the right, you take -3 and add 9 to it, which gives you 6.

Do the same thing with 15, but subtract 10 from it, since you are going to the left. This gives you 5.

Therefore, your answer should be (6, 5)

-3 + 9 = 6

15 + 10 = 5

Brainliest to correct answer. Please help!!! Last year, Trevor gave $5,462 to his local charity, which he calculated as 22.5% of his yearly salary. How much money does Trevor make in a year?

Answers

Answer:

6 690.95 US$

Step-by-step explanation:

Please help me with the answer!! There is the picture of the problem^

Answers

Answer:

6

Step-by-step explanation:

Answer:

6

Step-by-step explanation:

f(x) = √2x-4

f(20) = √2(20)-4

f(20) = √40-4

f(20) = √36

f(20) = 6

Solve step by step! Please answer correctly !!!!!!! Will mark brainliest !!!!!!!!!!!!!!

Answers

Let x be a and b
Now,
a=30[alternate angles]
b=40 [same reason as above]
So,
a+b=x
40+30=70
Hope it helps
Pls mark brainliest

What is the slope of the line?

Answers

Answer:

[tex]m=\frac{1}{3}[/tex]

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to Right

Algebra I

Slope Formula: [tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

Step-by-step explanation:

Step 1: Define

Find points from graph.

Point (2, -1)

Point (-4, -3)

Step 2: Find slope m

Simply plug in the 2 coordinates into the slope formula to find slope m

Substitute [SF]:                     [tex]m=\frac{-3+1}{-4-2}[/tex]Add/Subtract:                       [tex]m=\frac{-2}{-6}[/tex]Simplify:                                [tex]m=\frac{1}{3}[/tex]

Brenton’s weekly pay, P(h) , in dollars, is a function of the number of hours he works, h. He gets paid $20 per hour for the first 40 hours he works in a week. For any hours above that, he is paid overtime at $30 per hour. He is not permitted to work more than 60 hours in a week.

Answers

No se cual es esa respuesta porque no

Please help ! !!!!!!!!

Answers

Answer:

c, 50

Step-by-step explanation:

120-24= 96

Since we are measuring the size of one of the halves, you have to split that number in half, so 96 ÷ 2= 48.

48 rounds up to 50, so 50 is the answer

Need help asap please!!

Answers

Answer:

A) 40 + d

B) 45 days

Step-by-step explanation:

A)

total cost = (cost of the air conditioner itself) + (money charged per day)*(days)

cost of air conditioner itself = $40

money charged per day = $1

days = d

40 + 1*d

= 40 + d

B)

total cost = 40 + d

total cost = $85

85 = 40 + d

45 = d

Time used the air conditioner for 45 days.

4. When simplified, what is the value of 175, if i2 = – 1.

Answers

Answer:

5i[tex]\sqrt{7}[/tex]

Step-by-step explanation:

Using the rule of radicals

[tex]\sqrt{a}[/tex] × [tex]\sqrt{b}[/tex] ⇔ [tex]\sqrt{ab}[/tex]

i² = - 1 ⇒ i = [tex]\sqrt{-1}[/tex]

Given

[tex]\sqrt{-175}[/tex]

= [tex]\sqrt{25(7)(-1)}[/tex]

= [tex]\sqrt{25}[/tex] × [tex]\sqrt{7}[/tex] × [tex]\sqrt{-1}[/tex]

= 5i[tex]\sqrt{7}[/tex]

Answer:

[tex]5i\sqrt{7}[/tex]

Step-by-step explanation:

In order to solve this question we need to know how to multiply roots. You will need to understand that when we multiply [tex]\sqrt{a}[/tex] by [tex]\sqrt{b}[/tex], the following is true.

[tex](\sqrt{a})(\sqrt{b}) = \sqrt{ab}[/tex]                       (1)

From the question it self we know that [tex]\sqrt{ab}[/tex] is equal to [tex]\sqrt{-175}[/tex]. We also know that [tex]i^{2} = -1[/tex] or in other words [tex]i = \sqrt{-1}[/tex].

Now we will need to factors [tex]\sqrt{-175}[/tex] so that at the end we will end up representing [tex]\sqrt{-175}[/tex] as a product of [tex]\sqrt{-1}[/tex] and some other number. In order to determine the unknown number we will just have to divide [tex]\sqrt{-175}[/tex] by [tex]\sqrt{-1}[/tex]. From the equation (1) that I mention at the start we can figure out that......

[tex]\sqrt{a} = \frac{\sqrt{-175} }{\sqrt{-1} } = \sqrt{175}[/tex]   (in our case [tex]\sqrt{a}[/tex] is the unknown number we are trying to find)

Now we can rewrite [tex]\sqrt{-175}[/tex] as the following.....

[tex]\sqrt{-175} = (\sqrt{175})(\sqrt{-1})[/tex]

From here we substitute [tex]\sqrt{-1}[/tex] with [tex]i[/tex] and simplify [tex]\sqrt{175}[/tex]. In order to simplify [tex]\sqrt{175}[/tex] we will have to factor [tex]\sqrt{175}[/tex] in a way that we will see [tex]\sqrt{175}[/tex] as a multiple of a perfect square root. An so we get the following

[tex]\sqrt{-175} = (\sqrt{175})(i) = (\sqrt{7})(\sqrt{25} )(i) = (\sqrt{7})(5)(i) = 5i\sqrt{7}[/tex]

It is possible to construct an equilateral triangle using only a straightedge and a compass.

Answers

Answer:

yes it is possible

Step-by-step explanation:

Answer:

Yes

Step-by-step explanation:

NEED HELP ASAP‼️‼️‼️‼️‼️‼️ IL CASH APP 20$ IF CORRECT ‼️‼️‼️‼️What is the solution to this system?

{2x + y = 8
{y = 2x + 4

Answers

Answer:

x = 1 and y = 6

Step-by-step explanation:

Add these equations

-2x+y=4

2x+y=8

2y=12

    2

y = 6

Plug in 12 for y.

-2x+(6) = 4

     -6    -6

-2x = -2

     -2

x = 1

Need help once again
Question is in the screenshot
No spam and no useless answers for the points

Please show your work

It means a lot to me :)

Answers

Hi there!

[tex]\large\boxed{\text{ She is incorrect.}}[/tex]

The format of a logarithmic equation is:

[tex]a^{b} = c\\\\log_{a}c = b[/tex]

In this instance:

a = e

b = 3x

c = 7

Rewrite as the logarithmic equation:

[tex]log_{e}7 = 3x[/tex]

Solve. Evaluate [tex]log_{e}7[/tex] and use algebra to find x:

[tex]1.946 = 3x\\\\x = 0.649[/tex]

Conversion Measurement *
(10 Points)
Mario drew a line on the wall to measure his
height, but the measuring tape he used was
marked only in metric units. If he measured his
height to be 127.5 centimeters, how tall is
Mario in feet and inches?
(1 centimeter = 0.4 inch)
51 feet
5 feet 1 inch

Answers

Answer:

The answer is 4 feet and 3 inches.

Step-by-step explanation:

I got nut in my but just finished giving head locked up with the feds took a lot of meds I gotta go to bed before i cut my dreads met up with my hommie his name Fred give me a pinciple I think I need some led

Answers

Answer:

what are you talking about???

Step-by-step explanation:

brainliest and chill bro


The first side of a triangle is scm long.
The second side is twice as long as the first.
The third side is 5 cm longer than the second side.
a The perimeter of the triangle is 1 metre.
Write an equation to show this.
b Solve the equation.
c Find the length of the longest side of the triangle.​

Answers

Answer:

First side is 19, second side is 38 and third side, the longest is 43.

Step-by-step explanation:

Let's call the first side a.  

The second side, being twice as long as the first, is 2a.

The third side is 2a+5.

The equation is:

a+2a+2a+5=100, since 1 metre is 100 centimetre.

5a+5=100

5a=95

a=19

First side is 19, second side is 38 and third side, the longest is 43.

An equation is formed of two equal expressions. The length of the longest side of the triangle is 43 cm.

What is an equation?

An equation is formed when two equal expressions are equated together with the help of an equal sign '='.

Given to us that the first side of a triangle is x cm long, The second side is twice as long as the first, The third side is 5 cm longer than the second side and The perimeter of the triangle is 1 metre. Therefore,

The length of the first side will be x cms.The length of the second side will be twice x, 2x.The third side is 5 cm longer than the second side, 2x+5.

Since the perimeter of the triangle is 1 meter which is equal to 100 cm. And the perimeter is the sum of all the sides of a triangle. The perimeter can be written as,

[tex]x+(2x)+(2x+5) = 100\\\\x+2x+2x+5=100\\\\5x+5=100\\\\5x=95\\\\x=19[/tex]

Thus, the value of x is 19.

A.)  The equation that represents this condition is x+2x+2x+5=100.

B.) The length of the longest side of the triangle is 2x+5, where the value of x is 19. Therefore, the length of the longest side can be written as,

[tex]\text{Length of the third side} =2x+5 =2(19)+5=38+5=43\rm\ cms[/tex]

Thus, the length of the longest side of the triangle is 43 cm.

Learn more about Equation:

https://brainly.com/question/2263981

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