For f(x) =1/x^2-3

find:

(a) f(3) (3 points)

(b) f(2+h) (3 points)

Answers

Answer 1

Answer:

[tex]f(3) = \frac{-26}{9}[/tex]

[tex]f(2 + h) = \frac{- 11 - 12h - 12^2}{4 + 4h + h^2}[/tex]

Step-by-step explanation:

Given

[tex]f(x) = \frac{1}{x^2} - 3[/tex]

Required

Find f(3) and f(2 + h)

Solving f(3)

Substitute 3 for x in [tex]f(x) = \frac{1}{x^2} - 3[/tex]

[tex]f(3) = \frac{1}{3^2} - 3[/tex]

[tex]f(3) = \frac{1}{9} - 3[/tex]

Take LCM

[tex]f(3) = \frac{1 - 27}{9}[/tex]

[tex]f(3) = \frac{-26}{9}[/tex]

Solving f(2 + h)

Substitute 2 + h for x in [tex]f(x) = \frac{1}{x^2} - 3[/tex]

[tex]f(2 + h) = \frac{1}{(2 + h)^2} - 3[/tex]

[tex]f(2 + h) = \frac{1}{(2 + h)(2 + h)} - 3[/tex]

[tex]f(2 + h) = \frac{1}{4 + 2h + 2h + h^2} - 3[/tex]

[tex]f(2 + h) = \frac{1}{4 + 4h + h^2} - 3[/tex]

Take LCM

[tex]f(2 + h) = \frac{1- 3(4 + 4h + h^2)}{4 + 4h + h^2}[/tex]

[tex]f(2 + h) = \frac{1- 12 - 12h - 12^2}{4 + 4h + h^2}[/tex]

[tex]f(2 + h) = \frac{- 11 - 12h - 12^2}{4 + 4h + h^2}[/tex]


Related Questions

In Oscar's grade, 70 students are enrolled in health and 30 students are not. What
percentage of the students in the school are enrolled in health?
Write your answer using a percent sign (%).

Answers

Answer:

70%

Step-by-step explanation:

Step 1:

70 + 30 = 100          Add

Step 2:

Total of 100 Students

Step 3:

70/100             Divide

Answer:

70%

Hope This Helps :)

Answer:

70% of the students are enrolled in health class.

Step-by-step explanation:

We are given that there are 70 students enrolled in health and that 30 are not. Therefore, we need to determine the total number of students in Oscar's grade.

[tex]70 + 30 = 100[/tex]

Oscar has 100 students in his grade. If 70 of those students are enrolled in health, we can divide those students by the total number of students and convert our fraction to a decimal and then a percentage.

[tex]\displaystyle\frac{70}{100} = \frac{7}{10} = 0.7\\\\0.7 \times 100 = 70\%[/tex]

Therefore, 70% of the students are enrolled in health class.

Type the correct answer in each box Functions h and k are inverse functions, and both are defined for all real number Using this relationship, what is the value of each function composition? (h*k)(3) ​

Answers

The value of the given composite functions would be,

1) (h o k)(3) = 3

2) (k o h)(-4b) = -4b

How to interpret Inverse Functions?

When two functions are inverses, then each will reverse the effect of the other.

For the functions f and g, we can say that;

(f o g)(x) = x and (g o f)(x) = x

For the given example,

The functions h and k are inverse functions.

Thus, for any real input value 'x',

(h o k)(x) = x and (k o h)(x) = x

So, the value of the given composite functions would be,

1) (h o k)(3) = 3

2) (k o h)(-4b) = -4b

Read more about Inverse of Function at; https://brainly.com/question/11735394

#SPJ1

7+5(x−3)=227, plus, 5, left parenthesis, x, minus, 3, right parenthesis, equals, 22 a true statement?

Answers

Answer:

x = 47

Step-by-step explanation:

Given the equation :

7+5(x−3)=227

Expand the equation :

7 + 5x - 15 = 227

5x = 227 + 15 - 7

5x = 235

x = 235 /5

x = 47

Statement is true at x = 47

3p- 2c^3- 3c^3p +2 Write as a product

Answers

Answer:

[tex] (3p + 2) (1 - c)(1 + c + {c}^{2} )[/tex]

Step-by-step explanation:

[tex]3p- 2c^3- 3c^3p +2 \\ \\ = (3p - 3 {c}^{3} p) +( 2 - 2c^3) \\ \\ = 3p(1 - c^3) + 2(1 - c^3) \\ \\ = (1 - c^3)(3p + 2) \\ \\ = (1 - c)(1 + c + {c}^{2} )(3p + 2) \\ \\ = \bold{ \red{(3p + 2) (1 - c)(1 + c + {c}^{2} )}}[/tex]

4. A county clerk has a given amount of money to budget for cultural events. Cultural Events
based on the scattplot, what does the point(0,18)represent?
A.the total amount of the budget givin to the country
B.
the total amount of the budget spent after 18months
C.the average amount spend out of the budget each month
D.the predicted amount of time after which the entire budget will be spent​

Answers

Step-by-step explanation:

fjmfplfpefpı6j6jefkıbnkfeknkefekfekffn

Parallel to the line y=-3x + 5 passes through (-4,5)

Answers

Answer:

The equation of line that is Parallel to the line y=-3x + 5 passes through (-4,5) is: y = -3x-7

Step-by-step explanation:

Given equation of line is:

[tex]y = -3x+5[/tex]

General form of slope-intercept equation of line is:

[tex]y=mx+b[/tex]

Comparing both we get

m = -3

The slope of two parallel line sis equal.

Let m1 be the slope of line parallel to given line, then

m1 = -3

Putting in general form

[tex]y = -3x+b[/tex]

Putting (-4,5) in equation

[tex]5 = -3(-4) +b\\5 = 12+b\\b = 5-12\\b = -7[/tex]

Putting in the general form, we get

[tex]y = -3x-7[/tex]

Hence,

The equation of line that is Parallel to the line y=-3x + 5 passes through (-4,5) is: y = -3x-7

Determine the remaining sides and angles of the triangle ABC

what is the measure of angle B

what is the length of side a

what is the length of side b​

Answers

Answer:

The measure of angle B is 41.5°

The length of side a is 30.6 feet ⇒ to the nearest tenth

The length of side b is 32.9 feet ⇒ to the nearest tenth

Step-by-step explanation:

The sum of the measures of the interior angles in a triangle is 180°

In the given Δ ABC

∵ m∠A = 38.1°

∵ m∠C = 100.4°

→ By using the fact above

∵ m∠A + m∠B + m∠C = 180°

∴ 38.1 + m∠B + 100.4 = 180

→ Add the like terms in the left side

∴ 138.5 + m∠B = 180

→ Subtract 138.5 from both sides

∴ m∠B = 41.5°

The measure of angle B is 41.5°

∵ a is the opposite side of ∠A

∵ b is the opposite side of ∠B

∵ c is the opposite side of ∠C

→ By using the sine rule

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

∵ c = 48.4 ft, m∠A = 38.1°, m∠B = 41.5°, and m∠C = 100.4

→ Substitute them in the sine rule above

∴ [tex]\frac{a}{sin38.1}[/tex] = [tex]\frac{b}{sin41.5}[/tex] = [tex]\frac{48.4}{sin100.4}[/tex]

→ By using cross multiplication between the 1st and the 3rd fractions

∴ a × sin 100.4 = 48.8 × sin 38.1

→ Divide both sides by sin 100.4

∴ a = 30.61429861

The length of side a is 30.6 feet ⇒ to the nearest tenth

→ By using cross multiplication between the 2nd and the 3rd fractions

∴ b × sin 100.4 = 48.8 × sin 41.5

→ Divide both sides by sin 100.4

∴ b = 32.87596206

The length of side b is 32.9 feet ⇒ to the nearest tenth

15*PLEASE ANSWER FAST VERY URGENT!!!!!

Answers

Answer:

25/15 - 12/15

Step-by-step explanation:

turn the mixed number to an improper fraction, then multiply the denominator and numerator by 5 to reach 15 and then 5 x 3 and 4 x 3 to get 12/15. I hope this helps

if a(2x-3)=bx+5 then the solution for x in terms of a and b is

Answers

Answer:

x=(3a+5)/(2a-b)

Step-by-step explanation:

first we distribute the a to the 2x and -3

2ax -3a=bx+5

we move the -3a over by adding 3a

2ax=bx+5+3a

then we move the bx over

2ax-bx=5+3a

we can now group the left side like this

x(2a-b)=5+3a)

to find x all we must do is divide both sides by (2a-b)

x=(3a+5)/(2a-b)

May u please help me ill give out the brainly

Answers

Answer:

sorry type it out

Step-by-step explanation:

The ratio of pizza to nachos sold during A-lunch is 4 to 3. There was 48 nachos sold. What number of pizzas sold during A-lunch?

Answers

Answer:

64 pizzas

Step-by-step explanation:

4:3 * x:48

x resembles the amount of pizzas sold,

what times 3 = 48?

x=16

4 * 16 is 64

64 pizzas were sold

* Let me know if you have any questions*

A board measures 15 meters in length and is cut into two pieces. One-piece measures 7 meters. Write an equation to find the length of the other piece?
Pls help

Answers

Answer:  7.2 + L= 19.5


A submarine started at the
surface of the water and was moving underwater at
22 feet per minute toward the ocean floor. The submarine traveled at this rate
for 75 minutes before coming to rest on the ocean floor. Which of the following
integers represent the depth of the ocean floor in feet?

Answers

Answer:

1650

Step-by-step explanation:

75x22+1650

Someone please help me with my whole quiz! I am on question 5. I am doing a lot of points for this!

Answers

Answer:

For any equation X€R But here is Nothing like it.

Step-by-step explanation:

0 = -x^-4 is wrong to say.


What is a proportional relationship?

Answers

Answer:

Proportional relationships are relationships between two variables where their ratios are equivalent. Another way to think about them is that, in a proportional relationship, one variable is always a constant value times the other. That constant is know as the "constant of proportionality

Step-by-step explanation:

which statements are true select all that apply. Extra points!!! ​

Answers

1 is false
2 is true
3. is false
4. is true


1 & 3 are false
2 & 4 are true

Write these following fractions in order from greatest to least

1/9
1/2
1/8

Answers

♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️

[tex] \frac{1}{9} = \frac{1 \times 8}{9 \times 8} = \frac{8}{72} \\ [/tex]

[tex] \frac{1}{2} = \frac{1 \times 36}{2 \times 36} = \frac{36}{72} \\ [/tex]

[tex] \frac{1}{8} = \frac{1 \times 9}{8 \times 9} = \frac{9}{72} \\ [/tex]

_________________________________

[tex] \frac{8}{72} < \frac{9}{72} < \frac{36}{72} \\ [/tex]

[tex] \frac{1}{9} < \frac{1}{8} < \frac{1}{2} \\ [/tex]

♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️

Thus the order from greatest to least is :

[tex] \frac{1}{2} \: , \: \frac{1}{8} \: , \: \frac{1}{9} \\ [/tex]

♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️

Translate this sentence into an equation.
17 less than Vidya's savings is 64

Answers

Answer:

S - 17=64

Step-by-step explanation:

The opera theater manager believes that 23#% of the opera tickets for tonight's show have been sold. If the manager is accurate, what is the probability that the proportion of tickets sold in a sample of 869869 tickets would differ from the population proportion by less than 3%3%

Answers

Answer:

0.9642

Step-by-step explanation:

Sample proportion p follows a Normal distribution with mean = p0 = 0.23 and Standard deviation = √P0(1 - P0) / n = √0.23(1-0.23) / 869 = 0.0143

Then Z = p - mean / Standard deviation = X - 0.23 / 0.01343

P(0.2<p<0.26) = P(p<0.26) - P(p<0.2)

= P(p-023/0.0143 < 0.26-0.23/0.0143) - P(p-0.23/0.0143 < 0.2-0.23/0.0143)

= P(Z < 2.1) - P(Z < -2.1)

= 0.9821 - 0.0179

= 0.9642

Elijah builds model airplanes at a constant rate. He can build 5 model airplanes in 150 minutes, and 10 model airplanes in 300 minutes. How long would it take him to build 15 model airplanes.

Answers

Answer:

450 minutes

Step-by-step explanation:

Since Elijah can build 5 model airplanes in 150 minutes. He can build 1 model airplane in 30 minutes. To find this you divide 150 by 5. The question asks for how many minutes it would take Elijah to build 15 model airplanes. Since 1 x 15 = 15 model airplanes, you use proportions and also multiple the time by 15, so 30 x 15 = 450 minutes.

Answer:

450 Minutes or 7 hours 30 minutes

Step-by-step explanation:

Because the rate of Sets to minutes is 1:30 for every 1 he builds it take 30 minutes so 30 x 15 = 450 or 150 x 3 because every 5 sets there 150 minutes

Hope this helped :)

how do I know how many extraneous solutions there is

Answers

Answer:

how do u know how many extraneous solutions there is?

Step-by-step explanation:

To find whether your solutions are extraneous or not, you need to plug each of them back in to your given equation and see if they work. It's a very annoying process sometimes, but if employed properly can save you much grief on tests or quizzes.

Answer: To find whether your solutions are extraneous or not, you need to plug each of them back in to your given equation and see if they work. It's a very annoying process sometimes, but if employed properly can save you much grief on tests or quizzes

Step-by-step explanation:

Please can I have brainliest I need one more to rank up

8/180.0 i really need this anwser kid version for my kid pls and i would help but i also dont know

Answers

Hi, is this a fraction and are you asking for it to be simplified?

If so 8/180 simplifies to 2/45. If you're asking for 8 divided by 180, the answer is 0.04444444 or simply 0.0444... and rounded to the 100th place is 0.04

Please help ASAP! Mathematics!

Answers

Answer:

B.) See attachment below

Step-by-step explanation:

Answer:

Personally, I would say the answer is B.

But don't quote me.

Sorry if i'm wrong. Let me know if I am.

Have a great day hon.

Helppppo!!!!
Jzjsjsjssjskksksksksksksk
Jsjsjsjss
Jajajaj
Jajajaj
Pleaseee

Answers

Answer:A: yes, f and g are both concave down

B: yes, f and g are both concave up

C: no, f is concave up and g is concave down

D : no, f is concave down and g is concave up

Step-by-step explanation:

what is order of operations for 20-5x2+6

Answers

Answer:

multiply, add, then subtract so your answer should be 4

Step-by-step explanation:

Parenthesis

Exponents

Multiplication

Division

Addition

Subtraction

(please excuse my dear aunt sally)

HELP THIS IS URGENT FIND THE AREA OF THE SHAPE SHOWN BELOW

Answers

Answer:

uuhh sorry

Step-by-step explanation:

what is the value of 4/5(8+7)-2/3(8+7)​

Answers

Answer:

The answer is 2.

Hope this helps and if you could mark this as brainliest. Thanks!

How much simple interest would x dollars earn in 13 months at a rate of r percent?​

Answers

16 im adding this for yes reasons

00:0
A toy shop purchases 125 identical stuffiedi animals for a total cost of $312.50 and sells them for $7 each
What is the percent markup?
%

Answers

Answer:

They marked it up 30 cents

Step-by-step explanation:

you do 312.50 divided by 125. Then you get 2.50. Then you multiply 7 times 125 then you get 2.80. Finally you do 2.80 minus 2.50 which equals 30 cents.

answer choices

AAS
ASA
SSS
HL
SSA
AAA
SAS

Answers

Where is the question?
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