Using f(x) = 8x + 5 and g(x) = 7x - 2, find:g(f(6))

Answers

Answer 1

Answer:

369

Step-by-step explanation:

g(f(x)) simply means to put the whole expression of function f(x) into the place of "x" in g(x).

and to find the functional value for a specific x we just need to calculate functional value for f(x) and use that result as input for g(x).

f(6) = 8×6 + 5 = 48 + 5 = 53

and now

g(53) = 7×53 - 2 = 371 - 2 = 369

to check we do the general functional substitution :

g(f(x)) = 7×(8x+5) - 2 = 56x + 35 - 2 = 56x + 33

g(f(6)) = 56×6 + 33 = 336 + 33 = 369

correct


Related Questions

In the diagram below

Answers

Answer:

Step-by-step explanation:

Given RT bisects QTS, so

3x+9 = 5x-3

9+3 = 5x-3x

2x = 12

x = 6

Check:

3(6) + 9 = 27

5(6)-3 = 27

checks

What the car monthly payment?? Show work plz

Answers

Answer:

$656.25

p=35000

t=5

r=2.5

interest=ptr/100

=35000x5x2.5/100

=4375

amount=p+i

=35000+4375

=39375

now,

5 yr= 5x12months = 60 months

$39375/60=$656.25

i think so...

how many whole numbers starting with 1 and ending with 1000 are perfect squares?​

Answers

Answer:

There are 31 perfect squares between 1 and 1000

Hope it helps❤️

78.4 divided by 0.56

Answers

78.4 ÷ 0.56 = 140

I just used an online calculator like you could do. But, here you go.

78.4 divided by 0.56 = 140

Paul wants to buy a bicycle that costs $86.50. He has saved $60. He earns $5.30 an hour working after school and can save half of his total earnings. How many hours will he have to work to buy the bicycle?

Answers

He needs to work 10 hours

Answer:

10 hours

Step-by-step explanation:

86.50-60=26.50

5.30/2=2.65

2.65*10=25.50

so 10 hours of work to buy the bicycle

CAN ANYONE HELP ME WITH THIS QUICKKKKK!

Answers

Step-by-step explanation:

You can mention the main values like N = 50 , Efm= 2640 in the answer box and put the formula for calculating mean Efm/N and simply show the answer. Goodluck

What is the general equation for direct
variation?

Answers

Answer:

☆ y=kx

Example: if we have x= 3 and y= 15

Find y?

y= kx

*We know that y= 15 and x= 3

So,

15=k(3)

15=3k

*divide 3 from both sides

K=5

y=5x

y=5(5)=25

☆▪☆▪☆▪☆▪☆

Hope it helps..

Have a great day!!

The factors of x cube -10x square -53x-42

Answers

Answer:

[tex]x^3 - 10 x^2 -53x -42 = ( x + 1)(x + 3) (x - 14)[/tex]

Step-by-step explanation:

 [tex]x^3 - 10x^2 -53x - 42[/tex]

The factors of 42 : ±1 , ±2 , ±3 , ±6, ±7, ±14, ±21 , ±42

Using trial and error method we will find the first root of the polynomial.

1 : ( 1 )³ - 10 ( 1 )² - 53 ( 1 ) - 42

     1 - 10 - 53 - 42  ≠ 0

   Therefore 1 is not a root

-1 : ( -1 )³ - 10 (- 1 )² - 53 (- 1 ) - 42

      - 1 - 10 + 53 - 42

       53 - 53 = 0

Therefore - 1 is a root of the polynomial.

Therefore ( x + 1) is a factor.

Now by long division or by using synthetic division we can find other factors.

Synthetic Division :

                             -1 | 1      -10       -53      - 42

                                | 0     - 1          11          42

                                |______________________

                                  1      - 11       - 42        0

Therefore ,

[tex]x^3 - 10 x^2 -53x -42 = ( x + 1)(x^2 - 11x +42)[/tex]  ------ ( 1 )

Next further factorize x² - 11x - 42

   x² - 11x - 42

= x² -  14x + 3x - 42

=x(x - 14) + 3 (x - 14)

=(x + 3 )(x - 14)

Therefore ,

[tex]x^3 - 10 x^2 -53x -42 = ( x + 1)(x + 3) (x - 14)[/tex]

ABCD is a square. Square A B C D is shown. The length of A B is x + 6 and the length of B C is 2 x minus 1. What is the length of line segment DC? 5 units 7 units 11 units 13 units

Answers

Answer:

DC = 13units

Step-by-step explanation:

For a square, all the sides are equal, hence;

AB = BC

x+6 = 2x-1

x-2x = -1-6

-x = -7

x =7

Also DC =AB

DC = x+6

DC = 7+6

DC = 13units

Hence the length of DC is 13units

Answer: 13 units

Step-by-step explanation:

DC = 13 units

Step-by-step explanation:

For a square, all the sides are equal, hence;

AB = BC

x+6 = 2x-1

x-2x = -1-6

-x = -7

x =7

Also DC =AB

DC = x+6

DC = 7+6

DC = 13 units

Hence the length of DC is 13 units

⚠️TEST QUESTION PLEASE HELP DUE IN 5 MINUTES⚠️

Answers

Answer:

Step-by-step explanation:

The letter c

Each pair of figures is similar find the missing sie

Answers

Answer:

x = 3

Step-by-step explanation:

since they are similar use these ratios

x/9 = 1/3

do cross multiplication

9*1 = 3*x

9/3 = x

3 = x

What is the value of g(3)

Answers

Answer:

f(3)=2 (from the right table). g(f(3))=g(2)=-3.

Step-by-step explanation:

lemme get Brainliest please

Correct option is
A
−2
Given,
g(x)=2x−3
In order to find g(2) and g(3) we have to put 2 and 3 in place of x
g(2)=2×2−3
g(2)=4−3=1

g(3)=(2×3)−3
g(3)=6−3=3
g(2)−g(3)=1−3
g(2)−g(3)=

2 consecutive postive nos are such that the sum of their squares is 113. Find the 2 numbers

Answers

Answer:

7,8

Step-by-step explanation:

n^2+(n+1)^2=113; this is the information we are provided in the question.

n^2+n^2+2n+1=113 ; just expanding the numbers

2n^2+2n-112=0 ; moving everything to the same side

n^2+n - 56= 0 ; divide everything by two

(n-7)(n+8)=0 : factor the polynomial

so answers for n are: 7 and -8. since the questions asks for positive numbers -8 cannot be correct.

so n=7

n+1 = 8

Laura and martin obtain a 25 year 120,000 conventional mortgage at 8.5% on a house selling for 140,000 their monthly mortgage payment including principal and interest is 966 dollars

Answers

Complete Question

Laura and martin obtain a 25 year 120,000 conventional mortgage at 8.5% on a house selling for 140,000 their monthly mortgage payment including principal and interest is 966 dollars

a) Determine the total amount they will pay for their house

b) How much of the cost will be interest?

c) How much of the first payment on the mortgage is applied to the principal?

Answer:

a)  [tex]X=\$289800[/tex]

b)  [tex]I=\$169800[/tex]

c)   [tex]Y=\$116[/tex]

Step-by-step explanation:

From the question we are told that:

Time [tex]T=25years =>300 months[/tex]

Initial Mortgage [tex]N=140,000[/tex]

Mortgage  [tex]N'=120,000[/tex]

Rate [tex]r=8.5\%=>0.085[/tex]

Monthly Mortgage payment P=\%966

a)

The total amount Payable X is mathematically given as

 [tex]X=Monthly\ Mortgage\ payment*Number\ of\ months[/tex]

 [tex]X=966*300[/tex]

 [tex]X=\$289800[/tex]

b)

Generally the equation for Interest I is mathematically given by

 [tex]Interest= Total\ amount\ Payable -Mortgage N'[/tex]

 [tex]I=289800-120000[/tex]

 [tex]I=\$169800[/tex]

c)

Generally the equation for Interest I is mathematically given by

 [tex]I=Ptr[/tex]

Where

 [tex]t= Month +.1month=>1/12[/tex]

Therefore

 [tex]I=120000*1/12*0.085[/tex]

 [tex]I=850[/tex]

Therefore the first payment on the mortgage is applied to the principal is

 [tex]Y=\$966-850[/tex]

 [tex]Y=\$116[/tex]

help meeeeeeeeeeee (25 points)

Answers

Answer:

239 mm^2

Step-by-step explanation:

We will split the figure into 3 pieces

The bottom rectangle

A = l*w = 7*3 = 21 mm^2

The top rectangle

A = l*w = 5*10 = 50 mm^2

The right triangle

A = 1/2 b*h = 1/2 ( 16) * (16+5) = 8 * (21) = 168 mm^2

The total area is 21+50+168 =239

Pls help me I don’t understand how they got 6 on the first one let alone the rest of the questions. -due tomorrow- will give brainliest—thanks

Answers

Answer:

(x, y)

-2, 0

-1, -4

1, -6

2, -4

3, 0

Work:

x^2 - x - 6

(-3)^2 -(-3) - 6

9 + 3 - 6 = 9 - 3 = 6

Just substitute the x values, and solve for y

Answer:

Step-by-step explanation:

[tex]substitute x=-3\\ x^{2} -x-6=(-3)^{2} -(-3)-6=9+3-6=12-6=6[/tex]

(125^2 +25^2) (5^2-1) is divisible by 3

Answers

Answer:

See Below.

Step-by-step explanation:

We want to prove that the expression:

[tex](125^2+25^2)(5^2-1)[/tex]

Is divisible by three.

We can simplify the second factor:

[tex]=(125^2+25^2)(25-1)\\\\ = (125^2+25^2)(24) \\\\ = (125^2+25^2)(8\cdot 3)[/tex]

Since the second factor is being multiplied by three, we can conclude that the entire expression is divisible by three.

Answer:

It is divisible by 3.

Step-by-step explanation:

(125² + 25²)(5² - 1) ÷ 3

(15625 + 625)(25 - 1) ÷ 3

(16250)(24) ÷ 3

390000 ÷ 3

130000

What is the area of a circle with a radius of 3.5cm

Answers

Answer:

A≈38.48cm²

Step-by-step explanation:

Answer:

38.48 cm²

Step-by-step explanation:

Area of a circle goes by the formula πr²

Substitute in the value of r;

area = π(3.5)²

= 38.48451 cm²

~ 38.48 cm² (2 d.p.)

URGENT: Click on the graph to choose the correct answer to the equation.

x > 2
(Choose one of the pictures as the answer)

Answers

Answer:

The first graph.

Step-by-step explanation:

The equation is x is greater than 2. Therefore, the graph needs to shade anything greater than 2, but not 2.

Evaluate:
will give brainliest

Answers

Answer:

80

Step-by-step explanation:

S4 = 2(3°+3¹+3²+3³)

= 2(1+3+9+27)

= 2(40)

= 80

80 PTS PLS ANSWER WILL AWARD BRAINLIEST

Answers

Answer:

I think it’s A B B A and the last one is D is believe

Step-by-step explanation:

Answer:

2. A

3. A

4. D

5. A

6.

a) 180-n =  m

b) 180-40 = 140

7.  a) 161-(38+80)=a

b)38+80=118

b)161-118 = 43, a = 43

8. a) NMQ, and NQR

    b) NMR and NPR

Step-by-step explanation:

Remember, two vertical angles are always congruent or the same. Complimentary angles equal 90 degrees and supplementary angles equal 180 degrees.

please answer this !!!
You toss a coin 83 times. The coin lands 40 times on heads and 43 times on tails. If you define a fails as a success, what is the relative frequency of tails?​

Answers

Answer:

to do this we have to divide 43 by 83

0.51807228915

so the frequency is about 51.8%

what is (x+2)(x-2) equal ?

Answers

(x - 4)^2 , i hope this helps

Answer:

x^2 - 4

Step-by-step explanation:

since it is in the form of

a^2 - b^2 = (a + b)(a - b)

u can directly write x^2 - 2^2

=x^2 - 4

process :

(x + 2)(x - 2)

=x(x - 2) + 2(x - 2)

=x^2 - 2x + 2x - 4

=-2x and plus 2x gets cancel

=x^2 - 4

I wil Mark BRANLIEST!! HELP!!!! Consider the graphs of linear function f(x) = 3x, quadratic function g(x) = 3x2, and exponential function h(x) = 2x. Which statement about the functions f, g, and h is correct?
A. As x increases, the value of f(x) will eventually exceed the values of g(x) and h(x).
B. As x increases, the value of g(x) will eventually exceed the values of f(x) and h(x).
C. As x increases, the value of h(x) will eventually exceed the values of f(x) and g(x).
D. As x increases, the values of both f(x) and g(x) will eventually exceed the value of h(x).
Here the Graph: https://www.savvasrealize.com/community/proxy/assessment/68bd51a0599744be92849bd2e08be180/images/bdbcc6b2-8670-4ddc-95a2-a48b6d6da348

Answers

Answer:

option C

Step-by-step explanation:

Given :

[tex]f(x) = 3x \\\\g(x) = 3x^2\\\\h(x) = 2^x[/tex]

We will just put values for x and check the function :

Let x = 1

f(x) = 3

g(x) = 3

h(x) = 2

Let x = 10,

f(x) = 30

g(x) = 300

h(x) = 1024

Let x = 100

f(x) = 300

g(x) = 30000

h(x) = [tex]1.27 \times 10^{30}[/tex]

Clearly , as x increases value of h(x) exceeds the value of f(x) and g(x).

What is the gradient of the blue line

Answers

Answer:

1/4

Step-by-step explanation:

1) Find two points of the line

(4,2)  and (8,3)

Gradient = (y2 - y1)/(x2-x1)

(3-2)/(8-4) = 1/4

Expand and simplify (x - 1)(x + 2)(x - 1)

Answers

Answer:

[tex](x - 1)(x + 2)(x - 1)=(x-1)^{2}(x+2)[/tex]

Step-by-step explanation:

Use the product rule [tex]x^{a} x^{b}=x^{a+b}[/tex]

Answer:

x^3 -3x + 2

Step-by-step explanation:

(x - 1)(x - 1) =

x^2 -2x + 1 (x+2) =

x^3 + 2x^2

      -2x^ - 4x

                  x + 2

----------------------------

x^3 -3x + 2

Find the value of (2x-1) -(y+3) when x=3 and y=1

Answers

Answer:

1

Step-by-step explanation:

(2*3-1)-(1+3)

(6-1)-4

5-4

1

If this helps you mark as brainlist

Answer:

putting the Given values in equation

(3*3-1)-(1+3)

=8-4

=4

A car travels at a speed of s miles per hour. It covers 126 miles in 3 hours.
The equation that can be used to find the value of s is
× s = ??

The speed of the car is ??
miles per hour.

PLEASE HELP (also thanks for the answers on the last couple of questions yall)

Answers

Answer:

Step-by-step explanation:

This is a distance = rate times time problem where you are calling the rate "speed" instead. So our formula for distance then is distance = speed times time which is

d = st

The distance traveled in 126 miles and the time it took to do this was 3 hours. Filling in those values gives us

126 = s3 or

126 = 3s since multiplication is commutative. Solve for s by dividing both sides by 3 to get

s = 126/3 which is

s = 42 miles per hour

what is 65 divded by 487

Answers

Answer:

0.13347022587

Step-by-step explanation:

Answer:

7 R 32

Step-by-step explanation:

   0 0 7

6 5 4 8 7

 − 0    

   4 8  

 −   0  

   4 8 7

 − 4 5 5

     3 2

Please solve this equation. Thank you!

38x-12y = (6+2n)x + (4-n)y​​

Answers

Step-by-step explanation:

the answer is in the above image

Answer:

39x -12y = (6n+2n)X+(4-n)y

6+2n=38

2n=38-6

2n=32

n=32÷2

n= 16

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