What is the equation of the following graph in vertex form?
y = (x − 3)^2 − 1
y = (x + 3)^2 − 1
y = (x − 4)^2 − 2
y = (x − 4)^2 + 8

Answer (2 answers):

x = -2/5,  x = -14/5

Step-by-step explanation:

First step is to try and get the absolute value by itself on one side and everything else that's not inside the absolute value on the other side.

9|5x+8|=54

|5x+8| = 54/9

|5x+8| = 6

Remember how absolute values turn everything positive? For example

|-4|=4, but |4|=4 as well. So we must do the same to our problem by splitting up the absolute equation into two parts.

|5x+8| = 6     and     |-(5x+8)| = 6

now solve the first equation.

(Just remove the absolute value sign and solve it normally)

5x+8 = 6

5x = -2

x = -2/5

Now solve the other equation

-(5x+8) = 6

-5x - 8 = 6

-5x = 14

x = -14/5

Answer:

190 km an hour

Step-by-step explanation:

Answer:

24

Step-by-step explanation:

Answer: Domain = { -3 , 6 , 5 , -6}

Range = { 7 , 2 , -1 , -6 }

Step-by-step explanation:

considering the points given

[tex]x_{1}[/tex] = -3                                [tex]y_{1}[/tex] = 7

[tex]x_{2}[/tex] = 6                                [tex]y_{2}[/tex] = 2

[tex]x_{3}[/tex] = 5                                [tex]y_{3}[/tex] = -1

[tex]x_{4}[/tex] = -9                               [tex]y_{4}[/tex] = -6

This shows that that is relationship between the values of x and the values of y.

All the values of x represent the domain and all the values of y represent the range.

Therefore :

Domain = { -3 , 6 , 5 , -6}

Range = { 7 , 2 , -1 , -6 }

Option A: 1/3(3.14)(3cm)^2(18cm) is the correct answer

Step-by-step explanation:

Given

Diameter of Cone = d = 6 cm

Radius will be:

r = d/2 = 6/2 = 3 cm

Height of cone = h = 3d = 18 cm

The volume of cone is given by:

[tex]V = \frac{1}{3}\pi r^2h[/tex]

Putting the values

[tex]V = \frac{1}{3} (3.14)(3)^2(18)[/tex]

Hence,

Option A: 1/3(3.14)(3cm)^2(18cm) is the correct answer

Keywords: Volume, cone

Learn more about volume at:

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Answer:

45 degrees

Step-by-step explanation:

because 2 and 5 are vertical angles they are therefore congruent by definition, 5 is half of one and one is a right angle so measure angle 2 = 45 degrees

Answer:

50

Step-by-step explanation:

The total of all 6 angles make a circle, which equals 360°. Using the information below the figure,

2 * m∠5 = 90°, since 2 * m∠5 = m∠1 and ∠1 is a right angle.

Because ∠1, ∠5, and ∠6 are on one side of line L, they must equal 180°, and if ∠1 equals 90°,

m∠5 + m∠6=90°.

Since 2 * m∠5=m∠1 and m∠1=90°, m∠1 must be 45°. And by Transitive Property, m∠6 also equals 90°.

If the total measure of the angles is 360° and ∠1, ∠5, and ∠6 add up to 180°, ∠2, ∠3, and ∠4 must also add to 180°.

m∠6=m∠3 - 20°. We know that m∠6 is 45°, so we put that into an equation. I am going to use x as the measure of ∠3.

45=x-20  >>>  20+45=x-20+20  >>>  20+45=x  >>>  65=x  >>>  x=m∠3  >>>  m∠3=65

m∠3=m∠4, so m∠3+m∠4=65+65, or 130. And like I said above, ∠2, ∠3, and ∠4 must add to 180°. 180 minus 130 (the measure of ∠3 + ∠4) = 50, which has to be the measure of ∠2

Answer:

3/4

Step-by-step explanation:

2/2=1

1-1/4=4/4-1/4=3/4

Answer:

3/4

Step-by-step explanation:

1. Cancel 2.

1 - 1/4.

2. Get the same dominators.

1 X 1/4 X 4/4

3. Simplify.

4/4 - 1/4.

4-1/4

3/4

Answer:

4[tex]\sqrt{450}[/tex] = 4[tex]\sqrt{25 * 18}[/tex]    

                                  = 4 × 5 [tex]\sqrt{18}[/tex]

                                  =  20 [tex]\sqrt{18}[/tex]

                                  = 20 [tex]\sqrt{9 * 2}[/tex]

                                  = 20 × 3 [tex]\sqrt{2}[/tex]

                                  = 60 [tex]\sqrt{2}[/tex]

-5 [tex]\sqrt{0.6}[/tex] =  -5 [tex]\sqrt{0.6}[/tex]

                                   =  -  [tex]\sqrt{25 * 0.6}[/tex]

                                   =  - [tex]\sqrt{25 * \frac{3}{5}[/tex]

                                   = - [tex]\sqrt{15}[/tex]

Steps Explanation:

Answer:

[tex]5\frac{2}{3}[/tex] miles.

Step-by-step explanation:

Kevin recorded the distances he ran last week in the table attached to this question.

Now, the total number of miles he ran on Monday through Wednesday is the same as the total number of miles he ran on Thursday and Friday.

Hence, {x + (x + 9) + (x + 4)} = {2x + (4x - 2)}

⇒ 3x + 13 = 6x - 2

⇒ 9x = 15

⇒ [tex]x = \frac{15}{9} = \frac{5}{3}[/tex]  

Therefore, he ran on Wednesday = x + 4 = [tex]\frac{5}{3} + 4 = \frac{17}{3} = 5\frac{2}{3}[/tex] miles. (Answer)

Answer: 9 miles

Step-by-step explanation:

x + x + 9 + x +4 = 2x + 4x-2

Collecting like terms

x + x + x +9 + 4 = 2x + 4x -2

Collect like terms

3x +13 = 6x -2

3x - 6x = -2 -13

-3x = -15

Divide both side by -3

x = 5

Therefore ; total number he ran on Wednesday

x + 4

If x = 5

Therefore total number he ran on Wednesday = 5+4

= 9

Answer:

Tax on her normal wage is $ 6755

She can work 176 hours in a year and still remain in the same tax category

Step-by-step explanation:

Becky earns $633.81 for a 40 hour week.

Her normal monthly  wage is $ 633.81 *4 = $ 2535.24

Her annual income is $ 2535.2 *12=  $ 30,422.88

Tax on her annual income is  $30,422.88- $ 20,700= $9722.88

Tax on $ 20,700 is $ 3060

Tax on remaining $ 9722.88 is 0.38*9722.88=  $36,95

Total tax is $ 3060 + $ 3695= $ 6755

She can earn up to ( $ 36,000- $ 30, 423=) $ 5577 to remain in the same tax bracket.

She earns  $633.81/40= $ 15.84 in one hour

She gets twice the wage for the overtime  $ 31. 69

No of hours she can work = $5577/ $ 31.69 = 175.98 almost 176 hours

Answer:

y-4=-2(x+4)

Step-by-step explanation:

Perpendicular means negative reciprocal of the slope.

y-y1=m(x-x1)

y-4=-2(x-(-4))

y-4=-2(x+4)

The equation of the line that passes through the point (-4, 4) and is perpendicular to the line [tex]y = \frac{1}{2}x + 1[/tex] is [tex]y = -2x - 4[/tex].

To find the equation of the line that passes through the point (-4, 4) and is perpendicular to the line [tex]y = \frac{1}{2}x + 1[/tex], we need to do the following steps:

Determine the slope of the given line:
The slope of the given line [tex]y = \frac{1}{2}x + 1[/tex] is [tex]\frac{1}{2}[/tex].

Find the slope of the perpendicular line:
The slopes of two perpendicular lines are negative reciprocals of each other. Therefore, if the slope of the given line is [tex]\frac{1}{2}[/tex], the slope of the perpendicular line will be [tex]-2[/tex] (since [tex]-1 \div \frac{1}{2} = -2[/tex]).

Use the point-slope form to find the equation:
The point-slope form of a line is [tex]y - y_1 = m(x - x_1)[/tex], where [tex](x_1, y_1)[/tex] is a point on the line, and [tex]m[/tex] is the slope.
Here, the point is [tex](-4, 4)[/tex] and the slope [tex]m = -2[/tex].

Substituting these values into the point-slope form, we get:
[tex]y - 4 = -2(x + 4)[/tex]

Simplify the equation:
Distribute the slope on the right side:
[tex]y - 4 = -2x - 8[/tex]

Add 4 to both sides to solve for [tex]y[/tex]:
[tex]y = -2x - 4[/tex]

Answer:

Step-by-step explanation:

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Answer:

the answer is 1.3

Step-by-step explanation:

12+4.3 is 16.3

16.3-15 is 1.3

Answer:

9

Step-by-step explanation:

PEMDAS stands for Parenthesis, Exponents, Multiplication, Division, Addition, and Subtraction.

So, the first thing you would do is Multiply:

12+4*3-15

12+12-15

Then Add:

24-15

Finally Subtract:

9

The new equation will be:

[tex]g(x) =\frac{1}{x+4}+4[/tex]

OR

[tex]g(x) = \frac{x+5}{x+4}[/tex]

Step-by-step explanation:

The function transformations are defined as:

Shifting function upwards b units

[tex]f(x) => g(x) = f(x)+b[/tex]

Shifting functions to the left b units

[tex]f(x) => g(x) = f(x+b)[/tex]

Given function is:

[tex]g(x) = \frac{1}{x}[/tex]

Shifting the function 4 units to the left will give us:

[tex]g(x) => g(x+b)\\= \frac{1}{x+4}[/tex]

Now shifting the function 4 units upwards

[tex]g(x) = \frac{1}{x+4} + 4[/tex]

Simplifying

[tex]g(x) = \frac{1+x+4}{x+4}\\= \frac{x+5}{x+4}[/tex]

The new equation will be:

[tex]g(x) =\frac{1}{x+4}+4[/tex]

OR

[tex]g(x) = \frac{x+5}{x+4}[/tex]

Keywords: function, transformations

Learn more about functions at:

#LearnwithBrainly

Using the cross product property on this proportion gives us the following equation:

20 (2x - 9) = 10 (9)

Use the distributive property and multiply

40x - 180 = 90

Add 180 to both sides

40x = 270

Divide 40 from both sides

x = 270/40

Simplify fraction

x = 27/4

This should be your answer. Let me know if you need any clarifications, thanks!

The cross product is a type of multiplication between vectors that results in a vector product. It has the distributive property and is anticommutative.

The cross product is a type of multiplication between vectors that results in a vector product. It is denoted by the symbol A x B and is also known as the vector product.

The cross product has the distributive property, which allows us to distribute a vector across the sum of two other vectors. For example, A x (B + C) = (A x B) + (A x C).

The cross product is anticommutative, meaning that the order in which we multiply two vectors matters. A x B = -B x A.

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Answer:

y=4

Step-by-step explanation:

y-y1=m(x-x1)

y-4=0(x-2)

y-4=0

y=0+4

y=4

Step-by-step explanation:

[tex]a + b > 12 \\ [/tex]

but

[tex] \\ a > - 3 \\ [/tex]

if

[tex]a = - 3 \\ then \: \\ a + b > 12 \\ - 3 + b > 12 \\ b > 12 + 3 \\ b > 15[/tex]

Answer:

its -3

Step-by-step explanation:

Answer:

9(5r+7s+7)

Step-by-step explanation:

Answer:

9(5r+7s+7)

Step-by-step explanation:

Rewrite 63 as 7*9

Rewrite 63 as 7*9

Rewrite 45 as 5*9

=5 * 9r+ 7 * 9s + 7 * 9

Factor out common term: 9

= 9(5r+7s+7)

Answer:

[tex]4\dfrac{1}{6}\ \text{kilometers per minute}[/tex]

Step-by-step explanation:

The graph shows a proportional relationship between the number of kilometers traveled (y) and the number of minutes spent traveling (x). This graph passes through the point (75,30). This means that in 30 minutes (x = 30), it was traveled 75 kilometers.

To find unit rate, divide the number of kilometers by the number of minutes:

[tex]\dfrac{75}{30}=\dfrac{25}{6}=4\dfrac{1}{6}\ \text{kilometers per minute}[/tex]

Answer:

3/2

Step-by-step explanation:

Plug x into the equation.

We get 2/3(9/4)

Multiply the 2 fractions. Final answer, 3/2.

Answer:

43 earbuds

Step-by-step explanation:

Let x be the number of earbuds sold over the week

This implies that

1 earbud:$17

x earbud:$731

Writing an equation, we get

[tex] \frac{1}{17} = \frac{x}{731} [/tex]

cross multiplying, we obtain

17x=731

Dividing through by 17,we get

x=43

Answer:

first step divide 112 by 8 which is going to give you 14 per hours. second step 150 by 6 is going to give you 25 per hours

I'm assuming that you want to find the unit rate of both scenarios.

I'm going to assume that you meant 112 miles in 8 hours.

Divide to find the unit rate: 112 / 8 = 14 miles per hour.

150 miles in 6 gallons

Divide to find the unit rate: 150 / 6 = 25 miles per gallon.

Best of Luck!

Answer:

The two integers are -47 and -48.

Step-by-step explanation:

Let the two consecutive integers be [tex]$ (n - 1) $[/tex] and [tex]$ n $[/tex].

Given that their sum is -95.

⇒ (n - 1) + n = - 95

⇒ 2n - 1 = - 95

⇒ 2n = - 94

Dividing by 2 throughout, we get:

n = - 47

⇒ n - 1 = - 47 - 1 = - 48

Therefore, the two integers should be - 47 and - 48.

Answer:

410 / 23 = 17.8260869565

Lydia would need about 18 rolls of wallpaper to paper the walls of her kitchen.

Answer:

Step-by-step explanation:

so 2/5 of 100 contain chocolate...

2/5 * 100 = 200/5 = 40 <== contain chocolate

Answer:

-1

Step-by-step explanation:

The answer is minus one. The third quadrant only has all negative numbers therefore the answer is -1. All the other answers in the selection is positive.

Answer:

A. -1

Step-by-step explanation:

In the third quadrant, the x-coordinate and the y-coordinate are negative.

The x-coordinate must be a negative number.

Answer: A. -1

Answer:

x = -8

Step-by-step explanation:

-2x-16+0 = 0

Combine like terms.

-2x-16 = 0

Add 16 to both sides (to isolate the -2x from -16)

-2x = 16

Divide both sides by -2 to isolate the x from -2

x = -8

Answer:

[tex]\frac{2}{15}[/tex]

Step-by-step explanation:

Number of students participating in the competition = 13.

Total number of students in the school = 15.

Thus ,

the number of students who did not make to this competition =

Total number of students - number of students participated

= 15-13 = 2.

Now ,

probability of the student who do not makes it to the competition

= fraction of students who did not make to this competition from the total number of students .

=[tex]\frac{2}{15}[/tex].

Good morning,

Answer:

if h= 2​  ⇒  18 - (2 + 6h) = 4.

Step-by-step explanation:

if h= 2​ Then 18 - (2 + 6h) = 18 -(2+6×2) = 18 - 14 = 4.

:)