What is the vertex of the absolute value function below?

Given:

The two points on the graph.

To find:

The distance between the two points in simplest radical form.

Solution:

From the given graph, it is clear that the two points on the graph are (-9,3) and (-3,-2).

Distance formula:

[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

Using the distance formula, the distance between two points (-9,3) and (-3,-2) is:

[tex]d=\sqrt{(-3-(-9))^2+(-2-3)^2}[/tex]

[tex]d=\sqrt{(-3+9)^2+(-5)^2}[/tex]

[tex]d=\sqrt{(6)^2+(-5)^2}[/tex]

On further simplification, we get

[tex]d=\sqrt{36+25}[/tex]

[tex]d=\sqrt{61}[/tex]

Therefore, the distance between the given points is [tex]\sqrt{61}[/tex] units.

Answer:

x=42°

Step-by-step explanation:

take x degree as reference angle

using tan rule

tan x=opposite/adjacent

tan x=9/10

tan x=0.9

x=[tex]tan^{-1}[/tex]0.9

x=41.98

x=42 degree

Answer:

41.987° which rounds to 42 degrees

Step-by-step explanation:

Answer: 4374

Step-by-step explanation:

Answer: 3(2+x) or 3x+6

Step-by-step explanation:

Take this a step at a time

First is a sum of two and a number

set "a number" as x

sum of two and a number would be 2+x

triple it

3(2+x) or 3x+6

Answer:

3(x+2)

Step-by-step explanation:

Explanation:

The " sum of a number and 2

" means ADD them:

→ x+2

Triple that means multiply by

3

→ 3(x+2)

Answer:g(x) is flipped and 2 times as steep and shifted left 5

Step-by-step explanation:

Answer:

x = 1.50

Step-by-step explanation:

We can use a ratio to solve

2 papers      1 paper

-------------  = --------------

3 dollars        x dollars

Using cross products

2x = 3*1

2x=3

Divide by 2

2x/2 = 3/2

x = 1.50

Answer:

$1.50

Step-by-step explanation:

example;

2/3=1.50

Have a great day <3

Answer:The answer is 4.06

Step-by-step explanation:

Okay I am 98% sure my math could be wrong since I don’t know what the possible answers to the question are but this is what I got.

Answer:

32

Step-by-step explanation:

The base angles of the triangle are the same since the sides are the same

<C = 74

A+B+C = 180 since the sum of the angles of a triangle = 180

74+B+74=180

Combine like terms

148+B =180

B = 180-148

B = 32

Answer:

[tex]\text{A. }32^{\circ}[/tex]

Step-by-step explanation:

From the Isosceles Base Theorem, the two base angles of a isosceles triangle are equal. Therefore, [tex]\angle A=\angle C=74^{\circ}[/tex].

Since the sum of the interior angles of a triangle is always equal to 180 degrees, we can write the following equation:

[tex]\angle A+\angle B+\angle C=180[/tex]

Substitute [tex]\angle A=\angle C=74^{\circ}[/tex] into this equation to solve for [tex]\angle B[/tex]:

[tex]74+\angle B+74=180,\\\angle B=180-74-74=\boxed{32^{\circ}}[/tex]

Answer:

13

Step-by-step explanation:

Francis borrowed 20$ and gives his dad 8$ he owes 12$ I hope it helps :)

Answer:

90

Step-by-step explanation:

there is 6 sides of box

2 bigger and 4 smaller

area of bigger side is 5×5 = 25 this is the area of one side as we have 2 sides so are of both sides is 25 + 25 = 50

now come to the smaller sides ( we have 4 here)

are of one side is 2× 5 = 10

so are of all 4 sides is 10× 4 = 40

now we get area of 4 smaller sides and 2 bigger sides

total area of box is 40+ 50 = 90

hope you understand

Answer:

Y: 0, x:0

Y:1, x: 3

Y: 2, x: 6

Y: 3, x:9

Step-by-step explanation:

Plug in the x to get the y

Answer:

-x+y+6z=? You did not spcify so I just made it 0

x = -22/5, y = -4/5, z = -3/5

Step-by-step explanation:

Solve the following system:

{-x - 3 y - 2 z = 8 | (equation 1)

-x + y + 6 z = 0 | (equation 2)

x - 9 y - 2 z = 4 | (equation 3)

Subtract equation 1 from equation 2:

{-x - 3 y - 2 z = 8 | (equation 1)

0 x+4 y + 8 z = -8 | (equation 2)

x - 9 y - 2 z = 4 | (equation 3)

Divide equation 2 by 4:

{-x - 3 y - 2 z = 8 | (equation 1)

0 x+y + 2 z = -2 | (equation 2)

x - 9 y - 2 z = 4 | (equation 3)

Add equation 1 to equation 3:

{-x - 3 y - 2 z = 8 | (equation 1)

0 x+y + 2 z = -2 | (equation 2)

0 x - 12 y - 4 z = 12 | (equation 3)

Divide equation 3 by 4:

{-x - 3 y - 2 z = 8 | (equation 1)

0 x+y + 2 z = -2 | (equation 2)

0 x - 3 y - z = 3 | (equation 3)

Swap equation 2 with equation 3:

{-x - 3 y - 2 z = 8 | (equation 1)

0 x - 3 y - z = 3 | (equation 2)

0 x+y + 2 z = -2 | (equation 3)

Add 1/3 × (equation 2) to equation 3:

{-x - 3 y - 2 z = 8 | (equation 1)

0 x - 3 y - z = 3 | (equation 2)

0 x+0 y+(5 z)/3 = -1 | (equation 3)

Multiply equation 3 by 3:

{-x - 3 y - 2 z = 8 | (equation 1)

0 x - 3 y - z = 3 | (equation 2)

0 x+0 y+5 z = -3 | (equation 3)

Divide equation 3 by 5:

{-x - 3 y - 2 z = 8 | (equation 1)

0 x - 3 y - z = 3 | (equation 2)

0 x+0 y+z = -3/5 | (equation 3)

Add equation 3 to equation 2:

{-x - 3 y - 2 z = 8 | (equation 1)

0 x - 3 y+0 z = 12/5 | (equation 2)

0 x+0 y+z = -3/5 | (equation 3)

Divide equation 2 by -3:

{-x - 3 y - 2 z = 8 | (equation 1)

0 x+y+0 z = -4/5 | (equation 2)

0 x+0 y+z = -3/5 | (equation 3)

Add 3 × (equation 2) to equation 1:

{-x + 0 y - 2 z = 28/5 | (equation 1)

0 x+y+0 z = -4/5 | (equation 2)

0 x+0 y+z = -3/5 | (equation 3)

Add 2 × (equation 3) to equation 1:

{-x+0 y+0 z = 22/5 | (equation 1)

0 x+y+0 z = -4/5 | (equation 2)

0 x+0 y+z = -3/5 | (equation 3)

Multiply equation 1 by -1:

{x+0 y+0 z = -22/5 | (equation 1)

0 x+y+0 z = -4/5 | (equation 2)

0 x+0 y+z = -3/5 | (equation 3)

Collect results:

Answer: {x = -22/5, y = -4/5, z = -3/5

Answer:

The point estimate for p is of 0.12.

The 90% confidence interval for p is 0.0862 < p < 0.1538.

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which

z is the z-score that has a p-value of [tex]1 - \frac{\alpha}{2}[/tex].

The manager of the dairy section of a large supermarket chose a random sample of 250 egg cartons and found that 30 cartons had at least one broken egg.

This means that [tex]n = 250, \pi = \frac{30}{250} = 0.12[/tex]

The point estimate for p is of 0.12.

90% confidence level

So [tex]\alpha = 0.1[/tex], z is the value of Z that has a p-value of [tex]1 - \frac{0.1}{2} = 0.95[/tex], so [tex]Z = 1.645[/tex].

The lower limit of this interval is:

[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.12 - 1.645\sqrt{\frac{0.12*0.88}{250}} = 0.0862[/tex]

The upper limit of this interval is:

[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.12 + 1.645\sqrt{\frac{0.12*0.88}{250}} = 0.1538[/tex]

The 90% confidence interval for p is 0.0862 < p < 0.1538.

Answer:

Data B

Step-by-step explanation:

Given the data :

A: 20347, 20327, 22117, 21762, 20864, 20102, 21684, 20063, 21728, 21580, 21720, 20920, 21442, 20766

B: 3.38, 4.64, 4.09, 3.93, 4.25, 4.63, 4.78, 4.25

The spread of a data gives the variation in the data values of a given sample.

To obtain which data has the larger spread, we obtain the coefficient of variation. Which is the ratio of the standard deviation and the mean of the dataset.

(Standard deviation / mean) * 100%

Using calculator :

Data A :

Mean, x = 21101.5714

Standard deviation, s = 700.28925

Coefficient of Variation :

(700.28925 / 21101.5714) * 100% = 3.32%

Data B :

Mean, x = 4.24375

Standard deviation, s = 0.457006955

Coefficient of Variation :

(0.457006955 / 4.24375) * 100% = 10.77%

10.77% > 3.32%

Hence. Data B has a larger spread

Answer:

2day I think might not be right

The number of days it will take him to reach his goal is 6.5 days.

Given that, Marty decided he wants to run a 5 km race.

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

Let the number of days be x.

He is starting by running [tex]1\frac{3}{4} =\frac{7}{4}[/tex] km and adding 1/2km each day.

Now, 7/4 +1/2 x= 5

⇒ 1/2 x= 5-7/4

⇒ 1/2 x=13/4

⇒ x=6.5 days

Therefore, the number of days it will take him to reach his goal is 6.5 days.

To learn more about an equation visit:

https://brainly.com/question/14686792.

#SPJ2

Answer:

The answer is [tex]t\geq 20[/tex].

Step-by-step explanation:

To solve the inequality, start by solving for the variable [tex]t[/tex].

To solve for the variable [tex]t[/tex], subtract [tex]3.5t[/tex] from both sides. The inequality will look like [tex]6.5t\geq 130[/tex].

Then, divide both sides by 6.5 in order to get the variable [tex]t[/tex] by itself. The inequality answer will look like [tex]t\geq 20[/tex].

Answer:

-12

Step-by-step explanation:

f (x)=6x – 6

Let x= -1

f(-1) = 6(-1) -6

      = -6-6

     = -12

Answer:

48 ANS.

MAY IT HELPED U

Answer:

A

Step-by-step explanation:

First you simplify both sides to get -2.4x+14.4 > 52.8

then you need to subtract the 14.4 from both sides giving -2.4x> 38.4

then divide both sides by -2.4 giving an answer of

x is less than or equal to -16 meaning you point to the left with a closed circle

Answer:

so we have to use the formula 4/3PiR^3

which if we do we get the volume of

V≈97478.08

Answer:

V≈97478.08cm³

Step-by-step explanation:

Using the formulas

V=4/3πr3

d=2r

V=1/6πd3

D=1

1/6·πd3 1/6π ·57.13≈97478.07565cm³

I hope this helps. I worked hard on this one.

Answer:

12313685 is the answer............happy to help u

Answer:

View the graph for a visual

Step-by-step explanation:

Answer:

Step-by-step explanation:

[tex]f(x)=xe^{\frac{x}{2} } \\f'(x)=x*\frac{1}{2} e^{\frac{x}{2} } +e^{\frac{x}{2} } =e^{\frac{x}{2} } (\frac{x}{2} +1)\\[/tex]

f'(x)=0, gives x=-2

we find f(x) at x=-3,-2,1

f(-3)=-3e^(-3/2)≈-0.67

f(-2)=-2e^(-2/2)=-2e^{-1}=-2/e≈-0.74

f(1)=1 e^(1/2)=√e≈1.65

Answer:

x ≥ 40

Step-by-step explanation:

3x - 55 ≥ 65

combine like terms

3x  ≥ 65 + 55

3x  ≥120

divide both sides of the equation by 3

x  ≥ 40

Answer:

0

Step-by-step explanation:

3(x+6)=18

3x+18=18

3x=18-18

3x=0

3x/3=0/3

x =0

Answer:

y=-1/2x+7

Step-by-step explanation:

I think its that

Answer:

y = (1/2) x + 3

Step-by-step explanation:

The equation of linear functions is y = m x + b

In this case, we know m = 1/2 , and have point (4,5). We only need to find our y-intercept or b value.

What we can do is substitute what we know into our formula which will give us variable b, or the y-intercept. That will look like:

5 = (1/2) * 4 + b

5 = 2 + b

3 = b

So, the equation is y = (1/2) x + 3 :)

Answer:

the missing angle will be 140°

Answer: 140

Step-by-step explanation:

Answer:

- 9 + 9i

Step-by-step explanation:

(- 7 + 3i) - (2 - 6i)

- 7 + 3i - 2 + 6i

- 7 - 2 + 9i

- 9 + 9i