If f(x) is a linear function, f(- 3) = - 3 , and f(5) = 4 , find an equation for f(x)

Answers

Answer 1

[tex]f(x)=mx+b[/tex]

[tex]f(-3)=-3[/tex] meaning that (-3,-3)

[tex]f(5)=4[/tex] meaning that (5,4)

(1 ) Find slope.

[tex]m=\frac{y_2-y_1}{x_2-x_1}\\m=\frac{4+3}{5+3}\\m=\frac{7}{8}[/tex]

The slope is 7/8

(2) Substitute any ordered pairs in the equation.

I'll use (5,4)

[tex]f(x) = \frac{7}{8}x+b\\4=\frac{7}{8}(5)+b\\4=\frac{35}{8}+b\\32=35+8b\\32-35=8b\\-3=8b\\-\frac{3}{8}=b\\b=-\frac{3}{8}[/tex]

Therefore the equation for f(x) is [tex]f(x)=\frac{7}{8}x-\frac{3}{8}[/tex]


Related Questions

Solve for x: 5x + 15 = 28​

Answers

Answer:

x= 2 [tex]\frac{3}{5}[/tex]

Step-by-step explanation:

5x + 15 = 28

5x + 15 (-15) = 28 (-15)

5x = 13

5/5x = 13/5

x= 2 [tex]\frac{3}{5}[/tex]

Answer:

x=2.6

Step-by-step explanation:

1)write equation

2)put line through equal sign(if on paper, its way easier to put a line through.)

3)subtract 15 from 15

4)subtract 15 from 28(13)

If it were to be a negative 15 youd add 15. Never add or subtract to a number with a letter!

5)what's left over is 5×=28 divide 5 on both sides.

6)13÷5=2.6

Let V=ℝ2 and let H be the subset of V of all points on the line 4x+3y=12. Is H a subspace of the vector space V?

Answers

Answer:

No, it isn't.

Step-by-step explanation:

We have [tex]V=IR^{2}[/tex] and let [tex]H[/tex] be the subset of [tex]V[/tex] of all points on the line

[tex]4x+3y=12[/tex]

We need to find if [tex]H[/tex] is a subspace of the vector space [tex]V[/tex].

In [tex]IR^{2}[/tex] all the possibilities for own subspace of the vector space [tex]IR^{2}[/tex] are :

[tex]IR^{2}[/tex] itself.The vector [tex]0_{IR^{2}}=\left[\begin{array}{c}0&0\end{array}\right][/tex]All lines in [tex]IR^{2}[/tex] that passes through the origin  (  [tex]0_{IR^{2}}=\left[\begin{array}{c}0&0\end{array}\right][/tex]  )

We know that [tex]H[/tex] is the subset of [tex]IR^{2}[/tex] of all points on the line [tex]4x+3y=12[/tex]

If we look at the equation, the point [tex]\left[\begin{array}{c}0&0\end{array}\right][/tex] doesn't verify it because :

[tex]4x+3y=12\\4(0)+3(0)=12\\0=12[/tex]

Which is an absurd. Therefore, [tex]H[/tex] doesn't contain the origin (and [tex]H[/tex] is a line in [tex]IR^{2}[/tex]). Finally, it can't be a vector space of [tex]V=IR^{2}[/tex]

What is the exact value of sin(75°)?

Answers

Step-by-step explanation:

sin 75°: Now using the formula for the sine of the sum of 2 angles, sin(A + B) = sin A cos B + cos A sin B, we can find the sine of (45° + 30°) to give sine of 75 degrees.

Answer:

D.)

Step-by-step explanation:

Edge

The expression 63 × 42 is equivalent to which of the following numerical expressions?

18 x 8


B.

(6 x 4) 5


C.

246


D.

216 x 16

please answer

Answers

Answer:

2646

Step-by-step explanation:

is the correct answer for This question

The required equivalent expression is (216 x 16).

The correct is D.

What is Expression?

In mathematics, an expression is a phrase that has at least two numbers or variables and at least one maths operation. Addition, subtraction, multiplication, or division are all examples of maths operations. An expression's structure is as follows:

(Number/variable, Math Operator, Number/variable) is an expression.

We have the Expression as,

6³ x 4²

Now, expand the exponents as

= 6 x 6 x 6

= 216

and, 4² = 4 x 4 = 16

Thus, the required equivalent expression is (216 x 16).

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In the model for exponential growth or decay, the amount, or size, at t=0 is represented by __ the amount, or size, at time t is represented by __

Answers

1. A0 (small 0)
2.A0^ekt

In the model for exponential growth or decay, the amount, or size, at t=0 is represented by  [tex]N=N_{0}[/tex]. and at time t is represented by [tex]N=N_{0}e^{kt}[/tex]

Let us consider that [tex]N_{0}[/tex]  is the initial amount and N is represent that amount after growth or decay in time t .

Model for exponential growth or decay is,

                                 [tex]N=N_{0}e^{kt}[/tex]

Amount at t=0 is,

                             [tex]N=N_{0}e^{k*0}=N_{0}[/tex]

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Please help me solve this! x^2-4x-21 as a product of binomial factors

Answers

Answer:

( x-7) (x+3)

Step-by-step explanation:multiply to -21 and add to -4

-7 * 3 = -21

-7+3 = -4

( x-7) (x+3)

whats the area of a circle if the diameter 6

Answers

Answer:

28.27

Step-by-step explanation:

Answer:

18.84

Step-by-step explanation:

6x3.14 = 18.84. multiply by pi

8 less than the length L

Answers

Answer:

L-8=?

Step-by-step explanation:

Mario paid $30 to activate his cellular phone plus $50 per month. Type an equation:_

Answers

Answer:

50x + 30

Step-by-step explanation:

50 is the amount per month and x is how many months he's paying. If he's paying for 5 months then you replace x with 5 so on and so forth. the + 30 is the amount he paid to active his phone

Answer:

pa rompa pero no poden con mi pom pom con pom pom con pom pom

Step-by-step explanation:

A Ferris wheel can accommodate 55 people in 30 minutes. How many people could ride the Ferris wheel in 5 hours? What was that rate per hour?

Answers

Answer:

i believe your answer is 550 people, which would be 110/hr

Step-by-step explanation:

Hope that helps!

Select the correct answer.

The surface area of a cube is 600 square inches. What is the area of one of its faces?

A 6 square inches

B. 36 square inches

C. 75 square inches

D. 100 square inches​

Answers

Answer:

D=100 square inches

Step-by-step explanation:

Area of a square=side^2

Area of a cube=6xside^2

let the side be a

6a^2=600

a^2=600/6

a^2=100

Answer:

im on it its d

Step-by-step explanation:

Help me with this please

Answers

Answer:

The First Table

Step-by-step explanation:

The y-values increase inconsistently, while the other tables are constant.

Can someone help me plz

Answers

Answer:

i think the answer is 7

The answer should be 7

how do u find the third side

Answers

Answer:

Square root of 49

The missing side is 7

Step-by-step explanation:

With the Pythagorean theorem.

25^2= 625

24^2= 576

Square root of 49=7

The missing side is 7

Graph the greatest integer, f(x) = [x]

Answers

Answer:

Step-by-step explanation:

help me answer this question please​

Answers

Answer:

f'(2) = 8

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Calculus

The definition of a derivative is "the slope of the tangent line".

Derivatives of constants are 0.

Basic Power Rule:

f(x) = cxⁿ f’(x) = c·nxⁿ⁻¹

Step-by-step explanation:

Step 1: Define

f(x) = 3x² - 4x + 2

Step 2: Find 1st Derivative

Basic Power Rule:                    f'(x) = 2·3x²⁻¹ - 1·4x¹⁻¹Simplify:                                    f'(x) = 6x - 4

Step 3: Find tangent slope

Define:                    f'(x) = 6x - 4, x = 2Substitute:              f'(2) = 6(2) - 4Multiply:                  f'(2) = 12 - 4Subtract:                 f'(2) = 8

Step 4: Identify

f'(2) = 8 tells us that at x = 2, the slope of the tangent line is 8.

Help no troll answer plz

Answers

Answer:

Step-by-step explanation:

Q 4. (25m + 25m) ÷ 25 sec. = 2 m/sec.

Q 5. This question belongs to Physics and not Mathematics!!!

Wavelength (lambda) = Velocity (v) ÷ Frequency ( [tex]sec^{-1}[/tex] or Hz )

f = v / (lambda)

f = 3 / 2 = 1.5 (Hz)

Q 6. 0.060 ÷ 2 = 0.030 m

Solve for f: (-1/8)f - (3/4) -
(1/4)f = 11

Answers

Answer: The answer is f= –31 1/3.

Step-by-step explanation: To solve for f, you’ll need to simplify the both sides of the equation, and then isolating the variable. Use online advanced calculators to calculate the equation to view all the steps.

LMC given numbers 60 and 80​

Answers

Question:LCM of 60 and 80

240 is answer

LCM : least common factor
The least common multiple is 240.

How many kilometers are in 60 miles? Note: There are 1.609kms in 1mi.

Answers

Answer:

Your answer is 96.5606 Kilometers.

Step-by-step explanation:

1.609 x 60 = 96.5606

Mark as brainliest if it's correct!

Answer:

96.5606kms

Step-by-step explanation:

Given a test that is normally distributed with a mean of 100 and a standard deviation of 12, find:

(a) the probability that a single score drawn at random will be greater than 110

(b) the probability that a sample of 25 scores will have a mean greater than 105

(c) the probability that a sample of 64 scores will have a mean greater than 105

(d) the probability that the mean of a sample of 16 scores will be either less than 95 or greater than 105

Answers

Answer:

(a)  0.2033

(b)  0.0188

(c)  0.0004

(d)  0.095

Step-by-step explanation:

(a) the probability that a score at random is greater than 110 is obtained with a normal distribution of mean 100 and standard deviation 12 can be estimated using the z-table for Z = (110 -  100)/12 = 0.83

So P (X > 110) = P (Z > 0.83) = 0.2033

(b) Probability that a sample of 25 scores will have a mean greater than 105:

we use a standard distribution with the same mean (100) but the standard distribution reduced by a factor of [tex]\sqrt{25} = 5[/tex]. That is a standard deviation of 12/5 = 2.4. which gives a Z-value of (105-100) / 2.4 = 2.08

P (X> 105) = P (Z > 2.08) = 0.0188

(c) Probability that a sample of 64 scores will have a mean greater than 105:

we use a standard distribution with the same mean (100) but the standard deviation reduced by a factor of [tex]\sqrt{64} = 8[/tex]. That is a standard deviation of 12/8 = 1.5. which gives a Z-value of (105-100) / 1.5 = 3.33

P (X> 105) = P (Z > 3.33) = 0.0004

(d) the probability that the mean of a sample of 16 scores will be either less than 95 or greater than 105

This will be the addition of the two probabilities. We use a standard distribution with the same mean (100) but the standard distribution reduced by a factor of [tex]\sqrt{16} = 4[/tex]. That is a standard deviation of 12/4 = 3. which gives us two different Z values to study:

(105-100) / 3 = 1.67

and for X= 95 ==> Z = (95 - 100)/3 = - 1.67

P (X > 105) = P (Z > 1.67) = 0.0475

P (X < 95) = P (Z < -1.67) = 0.0475

which add up to: 0.095.

Using the normal distribution and the central limit theorem, it is found that there is a:

a) 0.2033 = 20.33% probability that a single score drawn at random will be greater than 110.

b) 0.0188 = 1.88% probability that a sample of 25 scores will have a mean greater than 105.

c) 0.0004 = 0.04% probability that a sample of 64 scores will have a mean greater than 105.

d) 0.095 = 9.5% probability that the mean of a sample of 16 scores will be either less than 95 or greater than 105.

In a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

It measures how many standard deviations the measure is from the mean.  After finding the z-score, we look at the z-score table and find the p-value associated with this z-score, which is the percentile of X. By the Central Limit Theorem, the sampling distribution of sample means of size n has standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

In this problem:

Mean of 100, hence [tex]\mu = 100[/tex].Standard deviation of 12, hence [tex]\sigma = 12[/tex].

Item a:

This probability is 1 subtracted by the p-value of Z when X = 110, hence:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{110 - 100}{12}[/tex]

[tex]Z = 0.83[/tex]

[tex]Z = 0.83[/tex] has a p-value of 0.7967.

1 - 0.7967 = 0.2033

0.2033 = 20.33% probability that a single score drawn at random will be greater than 110.

Item b:

Sample of 25, hence [tex]n = 25, s = \frac{12}{\sqrt{25}} = 2.4[/tex].

This probability is 1 subtracted by the p-value of Z when X = 105, hence:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{105 - 100}{2.4}[/tex]

[tex]Z = 2.08[/tex]

[tex]Z = 2.08[/tex] has a p-value of 0.9812.

1 - 0.9812 = 0.0188

0.0188 = 1.88% probability that a sample of 25 scores will have a mean greater than 105.

Item c:

Sample of 64, hence [tex]n = 64, s = \frac{12}{\sqrt{64}} = 1.5[/tex].

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{105 - 100}{1.5}[/tex]

[tex]Z = 3.33[/tex]

[tex]Z = 3.33[/tex] has a p-value of 0.9996.

1 - 0.9996 = 0.0004

0.0004 = 0.04% probability that a sample of 64 scores will have a mean greater than 105.

Item d:

Sample of 16, hence [tex]n = 16, s = \frac{12}{\sqrt{16}} = 3[/tex].

Both 105 and 95 are the same distance of the mean, so we find one probability, and multiply by 2.

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{105 - 100}{3}[/tex]

[tex]Z = 1.67[/tex]

[tex]Z = 1.67[/tex] has a p-value of 0.9525.

1 - 0.9525 = 0.0475.

2 x 0.0475 = 0.095

0.095 = 9.5% probability that the mean of a sample of 16 scores will be either less than 95 or greater than 105.

A similar problem is given at https://brainly.com/question/24663213

Please help me as soon as possible! :)

1 1/8 + b ≥ 7/16

Answers

Answer: 42

Step-by-step explanation:

Example:

Solve x + 7 < 15

Solution:

x + 7 < 15

x + 7 – 7 < 15 – 7

x < 8

Inequalities Of The Form “x – a < b” or “x – a > b”

Please mark me brainliest if this helped you ! (by clicking the little crown on my answer) it helps a lot thnx! (*≧∀≦*)

The solution of the inequality 1 1/8 + b ≥ 7/16 will be;

⇒ - 11/16 ≤ b

What is Inequality?

A relation by which we can compare two or more mathematical expression is called an inequality.

Given that;

The inequality is,

⇒ 1 1/8 + b ≥ 7/16

Now,

Solve the inequality as;

The inequality is,

⇒ 1 1/8 + b ≥ 7/16

Solve for b as;

⇒ 9/8 + b ≥ 7/16

Subtract 9/8 as,

⇒ 9/8 + b - 9/8  ≥ 7/16 - 9/8

⇒ b ≥ (7 - 18) / 16

⇒ b ≥ - 11/16

⇒ - 11/16 ≤ b

Thus, The solution of the inequality 1 1/8 + b ≥ 7/16 will be;

⇒ - 11/16 ≤ b

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how many eights are there in three and a quater​

Answers

6 .. hope that answers ur question :)

The snow is now 52 inches deep. If this was a 77%
decrease, what was the initial depth

Answers

Answer:

29.3785310734 is the exact answer but you can estimate

Step-by-step explanation:

Let’s say the initial depth was 100%.

A 77% decrease would mean that 77% of the 100% was added to the hole so then it final result would be 177% of the initial hole which is also 52 as given. 177% is the same as 1.77 so we would divide 52 by 1.77 to get that x = 29.3785310734. Still confusing? Just look here:

PLZ HELP!!!this is due in 5mins
WILL GIVE BRAINLIEST...
Francine has a picture with a length 5/3 its width. She wants to enlarge the picture to have an area of 240 in2. What will the dimensions of the enlarged picture be?

w = 20 in, h = 12 in
w = 24 in, h = 10 in
w = 12 in, h = 20 in

Answers

w = 12 in, h = 20 in
The width would be 12 inches, and the height would be 20 inches.

I hope this helps with your test! Please mark Brainliest! :))

Explain why 3( + 4) = 3( − 5) has no solution. Choose the best response below. I NEED THIS ASAP!!!
a. The coefficients of are the same, but the constant terms are different.
b. The coefficients of are the same, and the constant terms are same.
c. The coefficients of are different, but the constant terms are the same.
d. The coefficients of are different, and the constant terms are different.

Answers

Answer:

a. The coefficients of are the same, but the constant terms are different.

Step-by-step explanation:

it makes the most sence to me, but appoligise if I'm wrong

A car travels 2,347 feet in 10 seconds. At that speed, how far can this car travel in 50 seconds?

Answers

Answer: 11,735

Step-by-step explanation:

2,347 x 5 = 11,735

Answer:

play car games and find out

Step-by-step explanation:

Is (2, 2) a solution of the inequality y < 3x - 5?

Answers

Answer: it’s not a solution or C

Step-by-step explanation:

the given point is (2,2) there is a x value and a y value

so 2 < 3(2)-5 *we know 3*2 is 6 and 6-5 is 1*

2 does NOT equal to 1

Answer:

Third option, It is not a solution.

Step-by-step explanation:

En un molino azucarero cada trabajador recibe un bono mensual de $100.00 el trabajadorbtiene la opcion de gtar dicho bono comorando azucar de ingenio a un precio preferencial de 9.75 el kilogramo
suponiendo que dispone de $100 pesos extras para comprar
¿a partir de cuantoa kilogramos el trabajos empieza a pener de su dienero?
¿cual es la expresion algebraica que representa la situacion del trabajador?

Answers

Ummmmm I’m sorry hold on

What is the chance of rolling two dice and the dice add up to six?

Answers

around 13% chance

Step-by-step explanation:

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