12x+7<-11 or 5x-8>40

The corresponding composite function for (f∘g)(x) include the following: (f∘g)(x) = 4 - 15x.

In Mathematics and Geometry, a function composition is an operation (∘) that combines two functions f(x) and g(x), in order to produce a composite function h(x) = (g∘f)(x), such that h(x) = g.

In this exercise, we would determine the corresponding output values for the given composite function by using the substitution method as follows;

f(x) = 3x + 1

g(x) = 1 - 5x

(f∘g)(x) = 3(1 - 5x) + 1

(f∘g)(x) = 3 - 15x + 1

(f∘g)(x) = 4 - 15x.

Complete Question:

Let f(x)=3x+1 and g(x)=1-5x. Find (f∘g)(x).

Good morning ☕️

______

Answer:

She is 20 years old

____________________

Step-by-step explanation:

Let x be the age of the daughter.

Let y be the age of the mother.

then , we have to solve the system:

y=2x (1)

y+20=1.5(x+20) (2)

If we substitute y by 2x in the second equation we get :

(2) 2x+20=1.5(x+20) ⇔ 2x+20=1.5x+30 ⇔ 2x-1.5x=30-20

⇔ 0.5x=10 ⇔ x=20.

By the way the mother’s s age = 40 years.

:)

Answer:

21

Step-by-step explanation:

It might be 21/30 , hope it helps though :)

Answer:

21 is the un known value.

Step-by-step explanation:

10 times 3=30

7 times 3 = 21

so 21/30 is your answer.

Answer:

Step-by-step explanation:

41:2

41:43

This is because the question wants the number of burgers with onions to the total amount of burgers. The question already states 41 have onions. It also states the total amount of burgers is 43. Therefore, your answer is 41:43.

Answer:

C. 32 cm³

Step-by-step explanation:

[tex] {a}^{2}\frac{h}{3} = V[/tex]

[tex]({4})^{2}( \frac{6}{3}) = (16)(2) = 32[/tex]

a → length\base edge

I am joyous to assist you anytime.

Answer:

Step-by-step explanation: To find the area of the pyramid shown, we can first start by finding the area of the base. To find the area of the base, we can multiply the length by the width. Notice that both the length and the width of a square are equal so the area of a square will be equal to the length of a side multiplied by the length of a side.

Area = Length x Width = (side) (side)

Area = Side²

(4 cm²) = 16 cm².

Therefore, the area of the bases is 16 cm².

Now, let's finish the problem.

Image provided.

Answer:

  B) 116.88 inches

Step-by-step explanation:

we know that

To find out the length of 12 basketballs lined up next to each other, multiply the diameter of one basketball by 12

[tex]12(9.47)=113.64\ in[/tex]

therefore

The logical answer between the options is 116.88 inches, because the length cannot be less than 113.64 in

Answer:

-3.2x=-16

Step-by-step explanation:

Answer:

Step-by-step explanation:

[tex]\dfrac{4x+6}{2}=\dfrac{3x-15}{3}\qquad\text{cross multiply}\\\\3(4x+6)=2(3x-15)\qquad\text{use the distributive property}\\\\(3)(4x)+(3)(6)=(2)(3x)+(2)(-15)\\\\12x+18=6x-30\qquad\text{subtract 18 from both isdes}\\\\12x=6x-48\qquad\text{subtract}\ 6x\ \text{from both sides}\\\\6x=-48\qquad\text{divide both sides by 6}\\\\x=-8[/tex]

x=-8

Given equation is (4x+6)/2=(3x-15)/3, we need to find x

Multiply the numerator of one fraction to the denominator of other and denominator of the first term to the numerator of another term is called Cross Multiplication Method.

Given, (4x+6)/2=(3x-15)/3

Apply cross multiplication method

3(4x+6)=2(3x-15)

12x+18=6x-30

12x-6x=-30-18

6x=-48

Divide both sides by 6

x=-8

Therefore value of x in  (4x+6)/2=(3x-15)/3 is '-8'.

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Answer:

Yes, you are correct :)

Answer:

1/4

Step-by-step explanation:

Greatest revenue = Company D with 6.8 x 10^7

Least revenue = Company C with 9.0 x 10^4

Difference = 6.8 x 10^ 7 - 9.0 x 10^4

= 68000000 - 90000

= 6.79 x 10^7

Answer is D

The difference in revenue between the company with the greatest revenue and the one with the least revenue is  6.79 x [tex]10^7[/tex]

Option D is the correct answer.

We have,

From the table,

D has the greatest revenue.

C has the lowest revenue.

Now,

D revenue = 6.8 x [tex]10^7[/tex]

C revenue = 9 x [tex]10^4[/tex]

The difference in revenue between the company with the greatest revenue and the one with the least revenue.

= 6.8 x [tex]10^7[/tex] - 9 x [tex]10^4[/tex]

= 67910000

= 6791 x [tex]10^4[/tex]

= 6.79 x [tex]10^7[/tex]

Thus,

The difference in revenue between the company with the greatest revenue and the one with the least revenue is D. 6.79 x [tex]10^7[/tex]

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Answer:  7) vertex = ∠H       sides = HG and HI

                8) ∠H, ∠IHG, ∠GHI, ∠4

                9) ∠HVI, ∠HVJ, ∠IJV

NOTES:

1) The vertex is the point where the two segments, rays, or lines connect.

2) When naming an angle, the vertex is ALWAYS written in the middle with the sides on the left and right.

Answer:

Step-by-step explanation:

four hundred one thousand, three hundred seventy-eight

Answer:

The amount of money that should be invested at the rate of 5.25% is $12,000 and the amount money that should be invested at the rate of 4% is $13,000

Step-by-step explanation:

we know that

The simple interest formula is equal to

[tex]I=P(rt)[/tex]

where

I is the Final Interest Value

P is the Principal amount of money to be invested

r is the rate of interest  

t is Number of Time Periods

Let

x ------> the amount of money that should be invested at the rate of 5.25%

25,000-x -----> the amount money that should be invested at the rate of 4%

in this problem we have

[tex]t=1\ year\\ P_1=\$x\\P_2=\$(25,000-x)\\r_1=0.0525\\r_2=0.04\\I=\$1,150[/tex]

substitute in the formula above

[tex]I=P_1(r_1t)+P_2(r_2t)[/tex]

[tex]1,150=x(0.0525*1)+(25,000-x)(0.04*1)[/tex]

Solve for x

[tex]1,150=0.0525x+1,000-0.04x[/tex]

[tex]0.0525x-0.04x=1,150-1,000[/tex]

[tex]0.0125x=150[/tex]

[tex]x=\$12,000[/tex]

[tex]|$25,000-x=\$13,000[/tex]

therefore

The amount of money that should be invested at the rate of 5.25% is $12,000 and the amount money that should be invested at the rate of 4% is $13,000

Answer:

Step-by-step explanation:

Let x be the investment at 5.25% and y at 4%

Then we have

[tex]x+y =25000\\5.25x+4y = 115000[/tex]

We have to solve this system to get x and y

Multiply I equation by 4

[tex]100000=4x+4y\\115000=5.25x+4y\\-----------------------------\\15000 = 1.25x\\x = 12000\\y =25000-12000 = 13000[/tex]

12000 should be invested in 5.25% and 13000 in 4% interest.

Answer:

it's associatively property of addition

(a+b)+c= a+(b+c)

The coefficient of determination for this data set​ would be 0.91

A correlation coefficient is a number between -1 and 1 that tells you the strength and direction of a relationship between variables. In other words, it reflects how similar the measurements of two or more variables are across a dataset.

The correlation coefficient for this data set will be positive, since the dependent variable increases as the independent variable decreases.

Since the data appears to be fairly linear, the correlation coefficient will be close to 1 which means 0.91 is our best choice.

Hence, The coefficient of determination for this data set​ would be 0.91

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4x^2 - 36 = 0

4x^2 = 36

x^2 = 36/4

x^2 = 9

sqrt{x^2} = sqrt{9}

x = - 3 and x = 3

Answer:

90 Years = 47,304,000 Minutes = 47304000 Minutes.

Step-by-step explanation:

Answer:

Answer to D: 3/5

Step-by-step explanation:

There are 5 songs.

And 3 of them have the word "Mama" in the title.

Make 5 the total amount of songs and 3 songs are how many times the word "Mama" appears once in each song.

Answer:

20%

Step-by-step explanation:

15= 100%

3/15 = 1/5

100% divided by 5 is 20%

proportion: 1/5

Mimi has 15 cousins, and after subtracting the 3 who do not live in Texas, 12 of her cousins live there. By setting up a proportion, we calculate that 80% of Mimi's cousins live in Texas.

Mimi has 15 cousins, and all but 3 live in Texas. To find the percentage of her cousins that live in Texas, we first need to calculate the number of cousins who live in Texas. We do this by subtracting the 3 that do not live in Texas from the total number of cousins, which is 15.

Number of cousins living in Texas = Total cousins - Cousins not living in Texas
Number of cousins living in Texas = 15 - 3 = 12

Next, we set up a proportion to find the percentage. The proportion is based on the number of cousins in Texas over the total number of cousins:

Proportion = (Number of cousins in Texas / Total number of cousins) ×100%
Percentage = (12 / 15)× 100%
Percentage = 0.80 × 100%
Percentage = 80%

Therefore, 80% of Mimi's cousins live in Texas.

Answer:

120 mins

or

2hrs

Step-by-step explanation:60 min=1 hr

60 min/5=12 min

12(4)=48 min

24 min=1/5 of room

24(5)=120 min

120 min=2 hrs

It would take 2 hours to paint one room.

Ratio basically compares quantities, that means it shows the value of one quantity with respect to the other quantity.

If a and b are two values, their ratio will be a:b,

Given that,

Time taken to paint 2/5 of the room = 4/5 hour

To find the time taken to paint one room,

Use ratio property,

2/5 room takes = 4/5 hour

1 room takes = 4/5 x 5/2 hours

                      = 4 / 2 hours

                      = 2 hours.

The one room takes 2 hours to paint.

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Answer:

6^6

Step-by-step explanation:

6^4 x 6^3 / 6^-1

exponent rule add exponents 4+3=7 so 6^7

exponent rule subtract exponents 7-(-1) so

Answer= 6^8

Answer:

1644624

At least that's what i got on my calculator

Answer:

$98

Step-by-step explanation:

x+6(120-x)=230

x+720-6x=230

-5x=-490

x-98

x represented how much money Hannah had.

Answer:

[tex]y=0.25x[/tex]

Step-by-step explanation:

We are given that a graph which shows the relationship between the late fines the library charges and the number of days late.

From given graph we can see that

The graph passes through the points (2,0.5)  and (10,2.5).

We have to find the equation for the relationship.

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

By using the formula

Slope of graph=[tex]m=\frac{2.5-0.5}{10-2}[/tex]

Slope of graph=m=[tex]\frac{2}{8}=\frac{1}{4}[/tex]

Point slope- form:[tex]y-y_1=m(x-x_1)[/tex]

We have [tex]y_1=2.5,x_1=10[/tex]

Substitute the values then we get

The equation of for the relationship

[tex]y-2.5=\frac{1}{4}(x-10)[/tex]

[tex]y-2.5=0.25x-2.5[/tex]

[tex]y=0.25x-2.5+2.5=0.25x[/tex]

Hence, the equation for the relationship is given by

[tex]y=0.25x[/tex]

Answer:

The answer is B. 54 cm

Step-by-step explanation:

When you find the volume of a rectangle you have to multiply the length, width, and height. The length is 9, width 3, and height 2. When you multiply them together you'll get 54

Answer:8

Step-by-step explanation: trust me

The relationship between y and x, given that g is the midpoint of FH is y = (1/3)x + (1/3).

If g is the midpoint of FH, it means that FH is divided into two equal segments, FG and GH, such that FG = GH.

Given that FH = 6y - 2, set up an equation to represent this:

FH = FG + GH

Substituting the values we know:

6y - 2 = FG + GH

Since FG = GH then

6y - 2 = x + x

Now, combine like terms:

6y - 2 = 2x

To find the value of y, isolate it on one side of the equation:

6y = 2x + 2

Now, divide both sides by 6 to solve for y:

y = (2x + 2) / 6

y = (2/6)x + (2/6)

y = (1/3)x + (1/3)

So, y is equal to (1/3)x + (1/3).

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Answer:

√3 is greater than 1/3:

√3 = about 1.7

1/3 = about .3

The square root of 3 is greater than 1/3.

To determine which of the two real numbers is greater, we can compare their values directly. The square root of 3 is a well-known irrational number, and its approximate value is 1.732. On the other hand, 1/3 is a rational number with a value of approximately 0.333.

Let's compare the two:

- The square root of 3: [tex]\sqrt(3)[/tex]  = 1.732

- One third: 1/3 = 0.333

It is clear that 1.732 (the approximate value of √3) is greater than 0.333 (the approximate value of 1/3). Therefore, the square root of 3 is greater than 1/3.