find (f•g) when f(x)=x^2-7x+12 and g(x)=3/x^2-16

Answers

Answer 1
Based on:

1) g(x) = 3 / (x^2 - 16),

2) f(x) = x^2 - 7x + 12, and

3) (f•g)(x) = the product of the two functions f(x) * g(x)

The solution is found by factoring the two polynomilas f(x) and g(x):

f(x) = x^2 - 7x + 12 = (x - 4) (x -3)
g(x) = x^2 - 16 = (x - 4) (x + 4)

=> (f•g) (x)  = (x - 4) (x - 3) / [ (x - 4)(x + 4) ] = (x - 3) / (x + 4)

Answer: (x - 3) / (x + 4)

Related Questions

Please help me on this question

Answers

Our goal is to isolate r. First add s to both sides
5r= K+s

Divide both sides by 5
r= (K+s)/5

Final answer: r= (K+s)/5
The answer is R=K/5+S

Solve for b 2(b-2)=2b+9

Answers

2(b-2)=2b+9
Distribute. 
2b-4=2b+9
Subtract 9 on both sides.
2b-13=2b
Subtract 2b on both sides.
-13=0
Because -13 is not equal to 0, there are no values of b that satisfy the equation.

What is the value of x?

Answers

all angle = 60 degrees

 so 2x-4 =60

2x=64

x = 64/2 = 32

x = 32

Consider the following system of equations.

Which statement describes why the system has two solutions?
A. Each graph has one y-intercept, which is a solution.
B. Each graph has one vertex, which is a solution.
C. The graphs of the equations intersect the x-axis at two places.
D. The graphs of the equations intersect each other at two places.

Answers

If you plot them you will see that the intersect each other in two different points.
The solution of a system of equations is the set of points of intersection of the graphs of the equations.
The answer is D.

Answer:

D. Each has a slope of –3, but one has a y-intercept of 3 and the other has a y-intercept of –1, which makes the lines equivalent.

Step-by-step explanation:

If you look at the graph (Firstly), you can see that both lines look similar, which is one big hint to this question. But (secondly), like the other person said, both have equivalent y-intercepts in each problem. I saw an open spot for me to answer this so I took it UuU!

Also Just Realized This Is A Totally Diff Question On My Quiz, So The Question That Goes With This Answer Is "Consider the equations and graph below.

y = negative 3 (x minus 1). Y = negative 3 x minus 1

On a coordinate plane, 2 lines are parallel to each other.

Which explains why this system has no solution?"

What is the length of BC

Answers

I'm pretty sure your answer is 17
Very sorry it doesn't let me see the attachment.

The table shows the outputs, y, for different inputs, x:

Input (x) 2 5 9 12
Output (y) 20 15 12 8



Part A: Do the data in this table represent a function? Justify your answer. (3 points)

Part B: Compare the data in the table with the relation f(x) = 5x + 14. Which relation has a greater value when x = 9? (2 points)

Part C: Using the relation in Part B, what is the value of x if f(x) = 64? (5 points)

Answers

a)

[tex]\bf \begin{array}{l|lllll} x&2&5&9&12\\ y&20&15&12&8 \end{array} \begin{array}{llll} \impliedby \textit{notice the x-values do not re} peat\\ \qquad \textit{therefore is a function} \end{array}[/tex]

b)

[tex]\bf \begin{array}{l|lllll} x&2&5&\stackrel{\downarrow }{9}&12\\ y&20&15&\boxed{12}&8 \end{array}\qquad \qquad \begin{array}{llll} f(x)=5x+14\\\\ x=9\\\\ 5(9)+14\implies 45+14\implies \boxed{59} \end{array}[/tex]

well, notice, which is larger?

c)

[tex]\bf \stackrel{f(x)}{64}=5x+14\implies 50=5x\implies \cfrac{50}{5}=x\implies 10=x[/tex]

Wall posters are usually sold curled up in cylindrical cardboard tubes. if the length of the tube is 84.5 cm, and the diameter of the tube is 2.40 cm, what is the area of the poster, in cm2? (assume the poster doesn't overlap itself.)
a. 637 cm2
b. 203 cm2
c. 382 cm2
d. 1529 cm2
e. 605 cm2

Answers

Length of the cylinder = 84.5 cm
Diameter of the cylinder = 2.40 cm

The circumference is
π(2.40 cm) = 2.4π cm.
The area is
A = (2.4π cm)*(84.5 cm) = 637.1 cm²

Answer: a. 637 cm²

someone please help me! thank you so much

Answers

Hello,

I believe the answer would be 5. Let me explain.

For the equation f(x) = -2x +3, I plugged in "-1" from the ordered pair into the equation as "x".

f(x) = -2 (-1) +3, and that would simplify to f(x) = 5,

so then y = 5.

Hope this helps!

May

Bob bought a bike for $250 and repaired it . He can now sell the bike for $300. What is the percent increase in the value bike ?

Answers

Answer:20%

Step-by-step explanation:

250*20%=50

50+250=300

Answer:

20%

Step-by-step explanation:

BRAINLIESTTTT aSAP!
i only need part b :)

Answers

For School A, the box plot is not symmetric since it is skewed to the left, however, for School B, the box plot is mostly symmetric since the information is fairly the same on both sides. 

Match the following unit volumes with the most appropriate converted unit volume:

1.    2.64 gallons ......             3 liters
2.   0.14 cubic meters .....     5 cubic feet
3.   5.35 cubic meters .......   7 cubic yards
4.   6.34 pints......                   10 liters

Answers

2.64 gal-10 liters
0.14 cubic meters -5 cubic feet
5.35 cubic meters- 7 cubic yards
6.34 pints=3 liters

The correct match is given below:-

2.64 gal-10 liters

0.14 cubic meters -5 cubic feet

5.35 cubic meters- 7 cubic yards

6.34 pints=3 liters

What is unit conversion?

Multiplication or division by a numerical factor, selection of the correct number of significant figures, and unit conversion are all steps in a multi-step procedure. Unit conversion is the process of changing a quantity's measurement between different units, frequently using multiplicative conversion factors.

Volume is a measurement of three-dimensional space that is occupied. It is frequently expressed mathematically using imperial or SI-derived units.

The correct match is given below:-

2.64 gal                      ⇒         10 liters

0.14 cubic meters      ⇒          5 cubic feet

5.35 cubic meters     ⇒         7 cubic yards

6.34 pints                   ⇒         3 liters

Hence, the unit conversion is all steps in a multi-step procedure.

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The only solution of the equation x2 + bx + 16 = 0 is x = 4. What is the value of b?

b = –16
b = –8
b = 8
b = 16

Answers

b equals negative 8. becasue 16 is too large

Answer:

Option B is correct.

value of b = -8

Step-by-step explanation:

Given the equation: [tex]x^2+bx+16= 0[/tex]

As per the condition: The only solution for the given equation is, x = 4.

Substitute this value of x =4 in given equation, to solve for b;

[tex](4)^2+b(4)+16= 0[/tex]

Simplify:

[tex]16+4b+16= 0[/tex]

or

[tex]32 + 4b= 0[/tex]  

Subtract 32 on both sides, we get;

32 + 4b -32 = 0-32

Simplify:

4b = -32

Divide both sides by 4 we get;

b = -8

therefore, the value of b = -8

A rectangle has perimeter 84 cm and length 35 cm. What is its width?

Answers

P = 2(L + W)
84 = 2(35 + W)
84/2 = 35 + W
42 = 35 + W
W = 42 - 35
W = 7

answer
its width 7 cm

Answer:  The required width of the rectangle is 7 cm.

Step-by-step explanation:  Given that a rectangle has perimeter 84 cm and length 35 cm.

We are to find the width of the rectangle.

Let w represents the width of the rectangle.

According to the given information,

length, l = 35 cm and perimeter, P = 84 cm.

Therefore, we get

[tex]P=2(l+b)\\\\\Rightarrow 84=2(35+w)\\\\\Rightarrow 42=35+w\\\\\Rightarrow w=42-35\\\\\Rightarrow w=7.[/tex]

Thus, the required width of the rectangle is 7 cm.

Suppose that you work part-time as a sales representative at a car dealership. You earn a base salary of $125 per week plus a 18% commission on all sales that you make. Your best friend has exactly the same job at another car dealership but earning a base salary of 85$ per week plus a 21% commission on all sales. How much do you and your friend need to sell in order to earn the same amount in any given week?

Answers

Define the two friends as person A and person B.

Let x =  the sales in a week.

Person A:
$125 per week plus 18% commission on sales.
Earnings in a week on x sales is
125 + 0.18x

Person B:
$85 per week plus 21% commission on sales.
Earnings in a week on x sales is
85 + 0.21x

For the two earnings to be equal,
85 + 0.21x = 125 + 0.18x
0.03x = 40
x = 40/0.03 = $1333.33

Answer: $1,333.33

Decide which of the two points lies on the graph of the line
3x+y=10
A.3,1
B. 1,3

Answers

3(x) + y = 10

3(3) + 1 = 10

9 + 1 = 10

10 = 10 (true)

A. 3, 1

hope this helps

The width of a rectangle is 3 less than twice its length. if the area of the rectangle is 193 cm 2 cm2, what is the length of the diagonal

Answers

W=2L-3
W*L=193
replace W with 2L-3: (2L-3)L=193
2L^2-3L-193=0
Cannot factor
are you sure the numbers are correct?
If it cannot be factored, use the quadratic formula to find out L, then you can find out W
use the Pythagorean theorem to find the diagonal. I don't see an easier way. 

Which value of a would make the following expression completely factored?

x2 – a
a 12
b 36
c 49
d 81

Answers

Answer:

The correct answer is twelve.

Step-by-step explanation:

The values of a would make the expression 36, 49 and 81.

The correct options are b, c, and d.

What is a quadratic equation?

For variable x : ax² + bx + c = 0, where a≠0 is a standard quadratic equation, which is a second-order polynomial equation in a single variable. It has at least one solution since it is a second-order polynomial equation, which is guaranteed by the algebraic basic theorem.

To factor the expression x² - a completely, we need to write it as a product of two binomials.

This can be done using the difference of squares formula, which states that a² - b² = (a + b)(a - b).

If we apply this formula to x² - a, we get:

x² - a = (x + sqrt(a))(x - sqrt(a))

This is a factorization of x² - a into two binomials, where the constant term a is represented by the square root of a.

For the expression x² - a to be completely factored, both factors must be irreducible (meaning they cannot be factored any further). This requires that a be a perfect square.

Out of the given options, 36, 49, and 81 are perfect squares.

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At a local store, hot dogs come in packages of 8, and hot dog buns come in packages of 12. For her party, Arpitha purchased the minimum number of hot dog packages and bun packages that she could while making sure to have the same number of hot dogs and buns. How many hot dogs can Arpitha serve at her party?

Answers

Let's first analyze the word problem we have here.

It is stating that she, Arpitha, bought the MINIMUM packs of hotdogs AND minimum packs of buns to get an equal number of buns to hotdogs.

We can find the multiples they have in common. 

8, 16, 24, 32, 40

12, 24, 36, 48, 60

They both have 24 in common, She bought 3 packs of hotdogs and two packs of hotdog buns.

Hope this helped!

They both have 24 in common, She bought 3 packs of hotdogs and two packs of hotdog buns.

We have given that,

At a local store, hot dogs come in packages of 8, and hot dog buns come in packages of 12.

Let's first analyze the word problem we have here.

It is stating that she, Arpitha, bought the minimum packs of hotdogs and minimum packs of buns to get an equal number of buns to hotdogs.

We can find the multiples they have in common.

8, 16, 24, 32, 40

12, 24, 36, 48, 60

They both have 24 in common, She bought 3 packs of hotdogs and two packs of hotdog buns.

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Kim, Laura and Molly share £385
The ratio of the amount of money Kim gets to the amount of money Mollley gets is 2:5
Kim gets £105 less than Molly gets

What percentage of the £385 does Laura get ?

With working out

Answers

Set x equal to the amount of money Kim gets, and y for Molly's money.

 x = 2/5y, since the ratio is 2:5.
y = 105 + x, since Molly has 105 more pounds than Kim.

Substitute x into this equation, so that y = 105 + 2/5y. Subtract 2/5y from both sides to get 3/5y = 105. Divide each side by 0.6 (equivalent to 3/5) and you get y = 175, which is how much Molly has. Kim gets 2/5 of Molly's share (or 105 fewer pounds), so she has 70.

70 + 175 (Kim and Molly's shares) is equal to 245. Therefore, Laura receives the remaining 140 pounds.

140/385 = a/100
Cross multiply so that 385a is 14000. Divide by 385 to get 36.4 (rounded).

Thus, Laura receives about 36.4% of the total money. Hope this helps (:

The Earth's circumference measured at the equator is approximately 1.3148 × 108 feet. What is the number written in standard form?

Answers

Answer:

The number written in standard form is [tex]131,480,000[/tex]

Step-by-step explanation:

we have

[tex]1.3148*10^8[/tex]

we know that

[tex]10^8=100,000,000[/tex]

substitute

[tex]1.3148*10^8=1.3148(100,000,000)[/tex]

Remember that

When multiplying decimals by 10, move the decimal point one space to the right

In this case move the decimal point eight spaces to the right

[tex]1.3148(100,000,000)=131,480,000[/tex]

therefore

The number written in standard form is [tex]131,480,000[/tex]

PLEASE HELP ME!!!!!! 20pts
Given: Circle P with a point O outside of the circle. How many tangent lines can be drawn from point O to the Circle P?

0
1
2
Infinite

Answers

The best way to determine how many tangent lines can be created is to actually draw the circle and point itself. Given circle and a point outside, extend lines going from the point to the circle where the line is tangent to the circle. From this, we can get only 2 tangent lines, nothing more. (See attached)

 

Answer:

2

Answer:

I think its 2

Step-by-step explanation:

What is (5,9) reflectes across the Y and X axis

Answers

(5, 9) reflected across the y axis is (5, -9)

(5, 9) reflected across the x axis is (-5, 9)

I hope this helps. (:

The reflection of points across Y and X axis will be equal to (-5, 9), (5, -9).

What is reflection of points?

A reflection is referred to as a flip in geometry. A reflection is the shape's mirror image.

A line, called the line of reflection, will allow an image to reflect through it. Every element inside a figure is thought to reflect another figure when they are all equally spaced apart from one another.

As per the mentioned data in the question,

The given point is (5, 9).

Under the reflection in the y-axis, points are converted as,

(x, y) ⇒ (-x, y)

So,

(5, 9) ⇒ (-5, 9)

Under the reflection in the x-axis, points are converted as,

(x, y) ⇒ (x, -y)

So,

(5, 9) ⇒ (5, -9)

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A life insurance policy costs $11.61 for every $1,000 of insurance. At this rate, what is the cost of $75,000 of insurance?

Answers

The cost is $870.75 for the life insurance.

What is the area of a parallelogram whose vertices are A(−4, 9) , B(11, 9) , C(5, −1) , and D(−10, −1) ?

Answers

Did you get the answer?

120 is the answer to this problem

You live near a bridge that goes over a river. The underneath side of the bridge is an arch that can be modeled with the function y= -0.000475x^2 + 0.851x, where x and y in feet. How high above is the river bridge (the top of the arch)? How long is section of bridge above the arch?

A)The bridge is about 1,791.58 ft. above the river, and the length of the bridge above the arch is about 381.16 ft.

B)The bridge is about 1,791.58 ft. above the river, and the length of the bridge above the arch is about 895.79 ft.

C)The bridge is about 381.16 ft. above the river, and the length of the bridge above the arch is about 895.79 ft.

D)The bridge is about 381.16 ft. above the river, and the length of the bridge above the arch is about 1,791.58 ft

Answers

y= -0.000475x^2 + 0.851x

How high above is the river bridge (the top of the arch)?

You have to find the vertex of of the parabole: the y-coordinate is the highest point.

Remember that the x-coordinate of the vertex of a parabole is at - b / 2a.

That is  x = - 0.851 / [ 2(-0.000475) = 895.79

The corresponden y is y = -0.000475(895.79)^2 + 0.851(895.79) = 381.16 feet above the river.

How long is section of bridge above the arch?

The section of the brige is equal to the difference of the two roots

Roots: y= -0.000475x^2 + 0.851x = 0

=> x( - 0.000475x + 0.851) = 0

=> x = 0 and x = 0.851 / 0.000475 = 1791.58

Then the section is 1791.58 feet long.

Therefore, the answer is the option D)The bridge is about 381.16 ft. above the river, and the length of the bridge above the arch is about 1,791.58 ft

Find the constant of variation k for the direct variation. 3x+5y=0

Answers

Direct variations take the form y=kx. We need to solve for y in order to find k. 

3x+5y=0 
5y=-3x 
y=(-3/5)*x 
k=-3/5.

Answer:

The constant of variation is

-3/5

your welcome XD


Solve for N.
-n/5 = -5


N = -25
N = -1
N = 25

Answers

Multiply both sides by 5.

-n = -25

Divide -1 on both sides,

n = 25

Hope this helps!
-n = -5 * 5
-n = -25
n = 25

Answer: C) or the third option.

For the given functions f and g, find the requested composite function value. (15 pts!!!)

f(x) = √x+3, g(x) = 5x; Find (f ×g)(3).
a. 3√2
b. 5√30
c. √30
d. 5√6

Answers

it would be b or d i hope that help

PLEASE ANSWER THIS

Classify each expression as a polynomial or not. If the expression is a polynomial, name it according to its degree and its number of terms.

f(x)=x^2sqrt3+x-5

I already know it is a polynomial because the highest variable is 2. Please help me with the rest. The question itself confuses me

Answers

The degree is 2 becasuse of the x^2  and there are 3 terms so it is a trinomial.

A website-hosting service charges businesses a onetime setup fee of $275 plus d dollars for each month. If a business owner paid $1,091 for the first 12 months, including the setup fee, what is the value of d? a. Create an equation to represent this situation.

b.Solve your equation above to find the value of d. Show all work to receive full credit

Answers

(a) The total amount that is to be paid by the company is equal to the setup fee and the total fee collected for each month. The equation that can be used in order to determine the answer is,
      S = 275 + dx

where S is the total amount paid, d is the monthly fee and x is the number of months. Substituting the known values from the given,
    1091 = 275 + d(12)

or,   1091 = 12d + 275

(b) To determine the value of d, follow the steps given below,
    Substract 275 in each side of the equation,
    1091 - 275 = 12d + 275 - 275

Simplifying,
     816 = 12d 

    Divide both sides of the equation by 12,
      816/12 = 12d/12

Simplifying,
   68 = d
  
  or d = 68

Hence, d = 68
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