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3 years ago

Create the f(x) function based on the table. Your answer should be in function notation. X f(x) - 10 -6 -9 -5 1-8 -4 -7 1-3 5 9

Mathematics

1 answer:

Minchanka [31]3 years ago

6 0

Answer:

$f(x) = x + 4$

Step-by-step explanation:

First create an equation in slope-intercept form, y = mx + b. To do this, find the rate of change or slope (m), and the y-intercept (b).

Using two pairs, (-7, -3) and (-8, -4),

$slope (m) = \frac{y_2 - y_1}{x_2 - x_1} = \frac{-4 -(-3)}{-8 -(-7)} = \frac{-1}{-1} = 1$

m = 1

To find b, substitute m = 1, x = -7 and y = -3 into y = mx + b.

Thus:

-3 = (1)(-7) + b

-3 = -7 + b

-3 + 7 = b

4 = b

b = 4.

Replace y with f(x), m with 1 and b with 4 in y = mx + b.

The function would be:

$f(x) = x + 4$

You might be interested in

The operation manager at a tire manufacturing company believes that the mean mileage of a tire is 30,393 miles, with a standard

Pie

Answer:

52.84% probability that the sample mean would differ from the population mean by less than 339 miles in a sample of 37 tires if the manager is correct

Step-by-step explanation:

To solve this question, we have to understand the normal probability distribution and the central limit theorem:

Normal probability distribution:

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score 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. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Central limit theorem:

The Central Limit Theorem estabilishes that, for a random variable X, with mean $\mu$ and standard deviation $\sigma$ , a large sample size can be approximated to a normal distribution with mean $\mu$ and standard deviation $s = \frac{\sigma}{\sqrt{n}}$

In this problem, we have that:

$\mu = 30393, \sigma = 2876, n = 37, s = \frac{2876}{\sqrt{37}} = 472.81$

What is the probability that the sample mean would differ from the population mean by less than 339 miles in a sample of 37 tires if the manager is correct

This probability is the pvalue of Z when X = 30393 + 339 = 30732 subtracted by the pvalue of Z when X = 30393 - 339 = 30054. So

X = 30732

$Z = \frac{X - \mu}{\sigma}$

By the Central Limit Theorem

$Z = \frac{X - \mu}{s}$

$Z = \frac{30732 - 30393}{472.81}$

$Z = 0.72$

$Z = 0.72$ has a pvalue of 0.7642.

X = 30054

$Z = \frac{X - \mu}{s}$

$Z = \frac{30054 - 30393}{472.81}$

$Z = -0.72$

$Z = -0.72$ has a pvalue of 0.2358

0.7642 - 0.2358 = 0.5284

52.84% probability that the sample mean would differ from the population mean by less than 339 miles in a sample of 37 tires if the manager is correct

4 0

3 years ago

Pls help I will give brainliest

miss Akunina [59]

Answer:

Step-by-step explanation:

the distance around the figure--we need to find the perimeter

we have rectangle that has the side, 8 and 15

P(r)=2(8)+2(15)=16+30=46

we also have half of the circle with the diameter =8 and r=4

Circumference =2*3.14*r

C=2*3.14*4=25.12

we need just half of the circle 25.12/2=12.56

P figure=46+12.56=58.56

Area= rectangle=l*w=8*15=120

Area(circle)=3.14*r^2=3.14*16=50.24

half circle 50.24/2=25.12

Area figure=120+25.12=145.12

6 0

3 years ago

8x^2+5=22x Need help learning factoring please put work so I can understand

sp2606 [1]

Answer: (2x - 5) • (4x - 1)

STEP 1 : Equation at the end of step 1

(23x2 - 22x) + 5

STEP 2 : Trying to factor by splitting the middle term

2.1 Factoring 8x2-22x+5

The first term is, 8x2 its coefficient is 8 .

The middle term is, -22x its coefficient is -22 .

The last term, "the constant", is +5

Step-1 : Multiply the coefficient of the first term by the constant 8 • 5 = 40

Step-2 : Find two factors of 40 whose sum equals the coefficient of the middle term, which is -22 .

-40 + -1 = -41

-20 + -2 = -22 That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -20 and -2

8x2 - 20x - 2x - 5

Step-4 : Add up the first 2 terms, pulling out like factors :

4x • (2x-5)

Add up the last 2 terms, pulling out common factors :

1 • (2x-5)

Step-5 : Add up the four terms of step 4 :

(4x-1) • (2x-5)

Which is the desired factorization

Final result : (2x - 5) • (4x - 1)

5 0

3 years ago

Determine how many solutions each equation has and solve each equation using the quadratic formula.

Vikki [24]

Answer:

9 ± 3 i √ 7 / 2

Step-by-step explanation:

hope this helps

7 0

3 years ago

Find the area of the figure.

ipn [44]

Answer:

89m

Step-by-step explanation:

First, find the area of the rectangle (ignoring the missing triangle inside). The area of the rectangle is its base times its height, which is 8*13=104.

Next, find the area of the triangle. The area of the triangle is its base times height, divided by two.

The width of one side of the rectangle is 13, and the width of the side of the rectangle is 8 (4 + 4). Therefore, subtract 8 from 13 and the missing section in the side of the rectangle is 5. 5 is equal to the base of the triangle.

The height of the triangle is given, which is 6. As stated before, the area of a triangle is its base times height divided by two, which is 5*6/2 in this case. The area of the triangle is equal to 15.

Now, subtract the area of the triangle from the area of the rectangle. 104-15=89.

3 0

3 years ago

Create the f(x) function based on the table. Your answer should be in function notation. X f(x) - 10 -6 -9 -5 1-8 -4 -7 1-3 5 9​

Create the f(x) function based on the table. Your answer should be in function notation. X f(x) - 10 -6 -9 -5 1-8 -4 -7 1-3 5 9