Find f o g if f(x) = 3x^2 - 12 and g(x) = 5x + 3. f(g(x)) = Choices: a. 35x2 - 70 b. 15x2 - 30x + 9 c. 75x2 + 45x - 10 d. 75x2 + 90x + 15

Answer:

Step-by-step explanation:

If  x and y be real numbers satisfying 2/x=y/3=x/y, then any two of the equation are equated as shown;

2/x = y/3 ... 1 and;

y/3 = x/y... 2

From equation 1, 2y = 3x ... 3

and from equation 2; y² = 3x ... 4

Equating the left hand side of equation 3 and 4 since their right hand sides are equal, we will have;

2y = y²

2 = y

y = 2

Substituting y = 2 into equation 3 to get the value of x;

2y = 3x

2(2) = 3x

4 = 3x

x = 4/3

The value of x³ will be expressed as (4/3)³ = 4*4*4/3*3*3 = 64/27

Answer:

0

Step-by-step explanation:

The t-intercept here is what's khown as the x-intercept wich is given by C(t)=0

● C(t) = 2t^4-8t^3+6t^2

● 0 = 2t^4-8t^3+6t^2

Factor using t

● t(2t^3-8t^2+6t^1) = 0

Wich means that t=0

Answer:

second option

Step-by-step explanation:

Parallel lines have the same slope, and since the slope of the given line is 1/2, we know the slope of the answer will be 1/2, which eliminates the first and last options. We know the slope and a point that belongs to the line, (-2, 1), so we can use point-slope formula to derive the equation of the line.

y - 1 = 1/2(x + 2)

y - 1 = 1/2x + 1

y = 1/2x + 2

Answer:

here,

A=2×22÷7×17/2×21

A=22×17×3

A=1122 sq.cm

Answer: hundredths place

Step-by-step explanation:

Answer:

the answer is 1.00

Step-by-step explanation:

pls mark me as the brainliest and tell me thanks

Answer:

Hey there!

The circumference of a circle is [tex]\pi(d)[/tex], where d is the diameter, and [tex]\\\pi[/tex] is a constant roughly equal to 3.14.

The diameter is 16, so plugging this into the equation, we get 3.14(16)=50.24.

The circumference of the circle is 50.24 yards.

Hope this helps :)

Answer:

9 years = 12 grams

Step-by-step explanation:

0 years = 96 grams

After 3 years , the amount left is 1/2 of what you started with

3 years = 1/2 *96 = 48 grams

After 3 years , the amount left is 1/2

6 years = 1/2 (48) = 24 grams

After 3 years , the amount left is 1/2

9 years = 1/2 ( 24) = 12 grams

Assuming angle A is opposite to side a, B is the opposite to side b, and angle C is the opposite to side c.

Answer:

The right triangle has the following angles:

A = 48.31º, B = 41.69º and C = 90º.

The sides are:

[tex] \\ a = 37.26[/tex], [tex] \\ b = 33.12[/tex] and c = 49.9.

Step-by-step explanation:

The inner sum of a triangle = 180º.

A=48.31º,

C=90º

A + B + C = 180º

48.31º+ B + 90º = 180º

B = 180º - 90º - 48.31º

B = 41.69º

We can apply the Law of Sines to solve for unknown sides:

[tex] \\ \frac{a}{sinA} = \frac{b}{sinB} = \frac{c}{sinC}[/tex]

We know that sin(90º) = 1.

[tex] \\ \frac{a}{sin(48.31)} = \frac{b}{sin(41.69)} = \frac{49.9}{1}[/tex]

Then, a is:

[tex] \\ \frac{a}{sin(48.31)} = \frac{49.9}{1}[/tex]

[tex] \\ a = 49.9*sin(48.31)[/tex]

[tex] \\ a = 49.9*0.7467[/tex]

[tex] \\ a = 37.26[/tex]

Thus, b is:

[tex] \\ \frac{b}{sin(41.69)} = \frac{49.9}{1}[/tex]

[tex] \\ b = 49.9*sin(41.69)[/tex]

[tex] \\ b = 33.12[/tex]

Answer:

1,880.82

Step-by-step explanation:

Answers:

sin a=12/15=4/5

step by step explanation:

AB=9, and BC=12

find c: hyp.=√12²+9²=c²

c=15

sin a=opp/hyp.=12/15=4/5 ( convert to degrees)

a=41.10

Answer:

3

Step-by-step explanation:

Use this equation

[tex]\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex] substitute

-6-3/0-3 subtract

-9/-3 simplify

-3/-1 two negitives cansle out

3/1=3

Hope this helpes, if it did, please consider giving me brainliest, it will help me a lot. If you have any questions, feel free to ask.

Have a good day! :)

Answer:

3

Step-by-step explanation:

To find the slope, we use the slope formula

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

   = ( -6 -3)/(0 -3)

    = -9/-3

    = 3

Answer:

  growth rate = 0.1733 per day, or 17.33% per day

Step-by-step explanation:

Since the doubling time is 4 days, the growth factor over a period of t days is ...

  2^(t/4)

Then the growth factor for 1 day is

  2^(1/4) ≈ 1.189207

The instantaneous growth rate is the natural log of this:

  ln(1.189207) ≈ 0.1733 . . . per day

Answer:

Step-by-step explanation:

-8*3= -24+14=-10

Answer:

-12 and 2.

Step-by-step explanation:

-12*2= -24,

-12+2=-10

Answer:

5 games

Step-by-step explanation:

To find how many games the team scored at least 70 points, we need to look at the 7 on the stem side. The 7 means 70, and we add the digits on the leaf side. For example, 7 | 2 is 72. The numbers on the leaf side are: 1, 1, 2, and 3.

There are no points for the 8 on the stem side, but on 90, there is one digit on the leaf side: 1. So, the points they scored over 70 are 71, 71, 72, 73, and 91, which equals to five games.

Answer:

[tex]\boxed{\mathrm{5 \ games}}[/tex]

Step-by-step explanation:

At least 70 points makes it 70 and more. It should be at least 70 and at most anything above then 70.

So, In 5 games, the team scored at least 70. (71,71,72,73 and 91)

Answer:

h = 7.1 cm

Step-by-step explanation:

To find the height of the triangle, we can first find the area of the triangle using the Heron's formula:

[tex]S = \sqrt{p(p-a)(p-b)(p-c)}[/tex]

Where a, b and c are the sides of the triangle and p is the semi perimeter of the triangle:

[tex]p = \frac{a+b+c}{2} = \frac{15 + 8 + 17 }{2} = 20\ cm[/tex]

So the area of the triangle is:

[tex]S = \sqrt{20(20-15)(20-8)(20-17)}[/tex]

[tex]S = 60\ cm^2[/tex]

Now, to find the height, we can use the following equation for the area of the triangle:

[tex]S = base * height/2[/tex]

The height draw in the figure is relative to the side of 17 cm, so this side is the value of base used in the formula. So we have that:

[tex]60 = 17 * h/2[/tex]

[tex]h = 120/17[/tex]

[tex]h = 7.06\ cm[/tex]

Rounding to the nearest tenth, we have h = 7.1 cm

Answer:

7.1 cm

Step-by-step explanation:

:D

The complete question is;

The Customer Service Center in a large New York department store has determined that the amount of time spent with a customer about a complaint is normally distributed, with a mean of 8.9 minutes and a standard deviation of 2.5 minutes. What is the probability that for a randomly chosen customer with a complaint, the amount of time spent resolving the complaint will be as follows. (Round your answers to four decimal places.)

(a) less than 10 minutes

(b) longer than 5 minutes

(c) between 8 and 15 minutes

Answer:

A) P (x < 10) = 0.6700

B) P (x > 5 ) = 0.9406

C) P (8.0000 < x < 15.0000) = 0.6332

Step-by-step explanation:

A) we are given;

Mean;μ = 8.9 minutes

Standard deviation;σ = 2.5 minutes

Normal random variable;x = 10

So to find;P(x < 10) we will use the Z-score formula;

z = (x - μ)/σ

z = (10 - 8.9)/2.5 = 0.44

From z-distribution table and Z-score calculator as attached, we have;

P (x < 10) = P (z < 0.44) = 0.6700

B) similarly;

z = (x - μ)/σ =

z = (5 - 8.9)/2.5

z = -1.56

From z-distribution table and Z-score calculator as attached, we have;

P (x > 5 ) = P (z > -1.56) = 0.9406

C)between 8 and 15 minutes

For 8 minutes;

z = (8 - 8.9)/2.5 = -0.36

For 15 minutes;

z = (15 - 8.9)/2.5 = 2.44

From z-distribution table and Z-score calculator as attached, we have;

P (8.0000 < x < 15.0000) = P (-0.36 < z < 2.44) = 0.6332

Answer:

Yes

Step-by-step explanation:

Let s be the price of snickers, g the price of galaxy and k the price of kitkat.

●For Mariam the equation will be:

8 s + 3 g + 3k = 8

●For Zainab the equation will be:

4 s + 9 g + 4 k = 10.9

Take the first equation and divide both sides by 4 to make it easier.

You get:

● 2s + 0.75 g + 0.75k = 2

Take the second equation and divide both sides by 2 to make easier.

You get:

● 2s + 4.5g + 2k = 5.45

The new system of equation is:

● 2s +0.75g + 0.75k = 2

● 2s + 4.5g + 2k = 5.45

Express s in the first equation using the other variables.

● 2s +0.75g +0.75k = 2

● 2s + 0.75(g+k) = 2

● 2s = 2-0.75(g+k)

● s = 1- 0.325 (g+k)

Replace s by the new expression in the second equation:

●2 [1-0.325(g+k)] +4.5 g +2k = 5.45

●2-0.75(g+k) +4.5g + 2k = 5.45

●2- 0.75g -0.75k +4.5 g +2k = 5.45

●2+ 3.75g + 1.25k = 5.45

● 3.75g +1.25k = 3.45

We have eliminated one variable (s)

We will keep (3.75g+1.25k=3.45) and use it.

Now that we eliminated in the second equation do it again in the first one.

You will get a system of equations with two variables.

Solve it and replace g and k with the solutions.

Finally solve the equation and find s.

Answer:

[tex]\sqrt{x-4} +5[/tex]

Step-by-step explanation:

the conjugate of [tex]\sqrt{x-4} -5[/tex]  is the term that completes a²-b² when multiplied by each other

a²-b² = (a+b)(a-b)

Answer:

see below

Step-by-step explanation:

Using the Pythagorean Theorem:

a^2+ b^2 = c^2

5^2+ 9^2 = 13^2

25+81 = 169

106 = 169

This is not true so it is not a right triangle

Answer:

[tex]\boxed{\sf Not \ a \ right \ triangle}[/tex]

Step-by-step explanation:

Apply Pythagorean theorem to check if the triangle is a right triangle.

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

[tex]5^2+ 9^2 = 13^2[/tex]

[tex]25+81=169[/tex]

[tex]106=109[/tex]

False statement.

The triangle is not a right triangle.

Answer:

Hey there!

A=1/2bh

14=1/2(28)h

14=14h

h=1

Hope this helps :)

Answer:

Step-by-step explanation:

Area of a triangle is

[tex] \frac{1}{2} \times b \times h[/tex]

where b is the base

h is the height

From the question

Area = 14in²

b = 14 inches

So we have

[tex]14 = \frac{1}{2} \times 28 \times h[/tex]

which is

[tex]14 = 14h[/tex]

Divide both sides by 14

That's

[tex] \frac{14}{14} = \frac{14h}{14} [/tex]

We have the final answer as

h = 1

Therefore the height is 1 inch

Hope this helps you

Answer:

6[tex]\frac{2}{3}[/tex]

Step-by-step explanation:

y + 1[tex]\frac{1}{6}[/tex] = 7[tex]\frac{5}{6}[/tex]

y + [tex]\frac{7}{6}[/tex] = [tex]\frac{47}{6}[/tex]

y = 40/6 = 20/3 = 6[tex]\frac{2}{3}[/tex]

Answer:

Max area is 16

Step-by-step explanation:

If A² + B² = C², then A² + B² = 64. The largest triangle area is when both A² and B² are equal to 32, so 32 + 32 = 64.

So equal side of the triangle is √32 or about 5.6568. The area of the triangle is then 1/2(5.6568 × 5.6568) or 16.

The maximal area of a right triangle is 90.496

Derivative of a function of a real variable measures the sensitivity to change of the function value with respect to a change in its argument. Derivatives are a fundamental tool of calculus.

Given:

let the perpendicular be 'x'

and base be 'y'

Using Pythagoras theorem

x² + y² = 8²

x² + y² = 64

y²= 64- x²

y = √64-x²

Now, Area of triangle

= 1/2* base* height

=xy/2

=x *√64-x²*1/2

On differentiating both side

A' = 64-2x²/√64-x²*1/2

Setting derivative function equal to zero,

64= 2x²

32=x²

x=5.656

So, Area of triangle = x *√64-x²*1/2

= 90.496

Learn more about differentiation here:

https://brainly.com/question/24898810

#SPJ2

Answer:

angle C = 38 degrees

Step-by-step explanation:

Refer to attached figure (sorry, forgot to attach earlier)

Given

AIB = 109

Let

CAX = XAB = x

CBY = YBA = y

XIB = YIA = x+y    ........exterior angles

XIB = YIA = 180-109 = 71   ............ sum of angles on a line

=>

x+y = 71

ACB = 180 - 2x -2y  ................. sum of angles of a triangle

= 180 - 2(x+y)

= 180 - 2(71)

= 180 - 142

= 38

Answer:

0.40

Step-by-step explanation:

The computation of the probability for the second student be sophomore and the first is a freshman is shown below:

Let us assume

Sophomore = S

Freshman = F

Based on this assumption, the probability is as follows

So,

[tex]= \frac{P(S\cap F)}{P(F)} \\\\ = \frac{P(S) \times P(F)}{P(F)} \\\\ = \frac{16}{40}[/tex]

= 0.40

Hence, the probability for the second student be sophomore and the first student be freshman is 0.40

Answer:

[tex]\boxed{y\leq 6}[/tex]

Step-by-step explanation:

[tex]y-8 \leq -2[/tex]

Adding 2 to both sides

[tex]y \leq -2+8[/tex]

[tex]y \leq 6[/tex]

Answer:

[tex] f(x) = 6x^2 +2 , -6 <x<9[/tex]

[tex] f(x) = 12 , 9 \leq x <13[/tex]

And we want to evaluate f(x=9)

And for this case the answer would be:

[tex] f(9)= 12[/tex]

Best answer:

O 12

Step-by-step explanation:

For this problem we have the following function given:

[tex] f(x) = 6x^2 +2 , -6 <x<9[/tex]

[tex] f(x) = 12 , 9 \leq x <13[/tex]

And we want to evaluate f(x=9)

And for this case the answer would be:

[tex] f(9)= 12[/tex]

Best answer:

O 12

Question:

Diners frequently add a​ 15% tip when charging a meal to a credit card. What is the price of the meal without the tip if the amount charged is ​$20.70? How much was the​ tip?

Answer:

Price of meal = $18

Tip price = $2.70

Step-by-step explanation:

Let the price of the meal be y;

Let the tip be t

From the question;

15% of y is the tip charge (t). i.e

t = 15%y

=> t = 0.15y          --------(i)

The total amount charged is $20.70  (This means that the sum of the price of the meal and the tip is $20.70)

=> y + t = 20.70            [substitute the value of t=0.15y from equation (i)]

=> y + 0.15y = 20.70

=> 1.15y = 20.70

=> y = [tex]\frac{20.70}{1.15}[/tex]

=> y = $18

Therefore the price of the meal, y, is $18.

From equation (i),

t = 0.15y           [substitute the value of y = $18]

t = 0.15(18)

t = $2.70

Therefore the tip was $2.70

Answer:

Step-by-step explanation:

This is a permutation problem. Given the 10 cards with numbers 2, 3, 4,5,5,7,7,7,7,7 on it, if Salvador is going to make a row call, the number of ways he can order a row is as shown below;

Total number of cards = 10!

number of times the digit 5 was repeated = 2times

number of times the digit 7 was repeated = 5times

The number of ways he can make a row call = 10!/2!5!

= 10*9*8*7*6*5!/2*5!

=  10*9*8*7*6/2

=  10*9*8*7*3

= 15,120 different ways

Hence, the number of ways he can order the row is 15,120 number of ways.