Consider the function f(x) = x2 + 8x +1. Which equation shows function f written in vertex form?
f() = (x + 8)2 +1
f(x) = (x – 4)²+1
f(x) = (x – 8)² – 17
f()= (x +4)2 - 15​

The domain of the function h(x) = 4·㏒₂(x - 6) + 1, using interval notation is (6, ∞)

The domain of a function is the set of the possible input values of the function, which is denoted as dom(f).

The domain of the function f: X → Y, is defined as the values of X

The given function is; h(x) = 4·㏒₂(x - 6) + 1

The domain of a function is the set of the possible input (x-values) of the function.

The values which the function ㏒₂(x - 6) can have as input, which is the domain of the function, ㏒₂(x - 6) is; 0 < x - 6 < ∞

Which gives: 6 < x < ∞

The domain of the function, h(x) = 4·㏒₂(x - 6) + 1 is 6 < x < ∞, which using interval notation is (6, ∞)

Learn more about the domain and range of a function here:

https://brainly.com/question/10197594

#SPJ1

So first, lets caculate how much you get in one day

10x7= 70$

So, in one day you make 70$.

Since we make 70$ in one day, we need to find out if we worked all week.

70x7 = 490$

So in one week,we make $490.

~NatLikesAnime~

[tex]\text{Given that,}\\\\1-\cos A = \dfrac 12\implies \cos A = 1-\dfrac 12 = \dfrac 12\\\\\text{L.H.S}\\\\=\tan^2 A + 4 \sin^2 A\\\\=\dfrac{\sin^2 A}{\cos^2 A}+4(1-\cos^2 A)\\\\\\=\dfrac{1-\cos^2 A}{\cos^2 A} +4-4\cos^2 A\\\\\\=\dfrac{1-\left( \dfrac 12 \right)^2 }{\left(\dfrac 12 \right)^2 } +4 -4 \left( \dfrac 12 \right)^2\\\\\\=\dfrac{1- \dfrac 14}{\dfrac 14}+4-4\cdot \dfrac 14\\\\\\=\dfrac{\tfrac 34}{\tfrac 14}+4-1\\\\\\=\dfrac 34 \cdot 4 +3\\\\=3+3\\\\=6\\\\=\text{R.H.S}[/tex]

Answer:

106.6 minutes

Step-by-step explanation:

49.2/6 = 8.2

8.2x13 = 106.6

Answer:

$216

Step-by-step explanation:

Find how much Mary made per hour by dividing 144 by 8 to get 18. Then, multiply that number by 12 which $216

Answer:

$216

Step-by-step explanation:

First, find out what Mary makes every hour. To find this, we divide 144 by 8.

144/8 = $18

This means that Mary makes $18 per hour.

Now, we find out how much Mary would make if she worked for 12 hours:

x = # of hours worked

18n

18(12)

$216

Therefore, Mary would make $216 in 12 hours.

Hope this helps!

The direct variation of x to y implies that x and y increases at the same time, and the formula of x in terms of z is [tex]x = 4z^3[/tex]

The direct proportion of x to y is represented as:

[tex]x\ \alpha\ y^2[/tex]

As an equation, we have:

[tex]x\ =\ ky^2[/tex]

The direct proportion of y to z is represented as:

[tex]y\ \alpha\ z^3[/tex]

As an equation, we have:

[tex]y\ =\ kz^3[/tex]

Square both sides

[tex]y^2 = k^2z^3[/tex]

Substitute [tex]y^2 = k^2z^3[/tex] in [tex]x\ =\ ky^2[/tex]

[tex]x =k^3z^3[/tex]

When z = 2, x = 32.

So, we have:

[tex]32 =k^3 * 2^3[/tex]

Evaluate

[tex]32 =k^3 * 8[/tex]

Divide both sides by 8

[tex]k^3 =4[/tex]

Substitute [tex]k^3 =4[/tex] in [tex]x =k^3z^3[/tex]

[tex]x = 4z^3[/tex]

Hence, the formula of x in terms of z is [tex]x = 4z^3[/tex]

Read more about direct variation at:

https://brainly.com/question/6499629

Answer:

c

[tex]6.46 \geqslant \frac{ { {x \sqrt[ |)x \frac{ {?}^{?} }{?} | ]{?} }^{?} }^{2} }{?} [/tex]

d

The graph of the inequality is attached to the solution.

A graph can be defined as a pictorial representation or a diagram that represents data or values.

Given is an inequality, y+4 < 3x - 1/2x - 2, we need to graph it,

This graph represents inequality y+4 < 3x - 1/2x - 2,

Learn more about graph,

brainly.com/question/16608196

#SPJ7

Answer:

Proportional relationships are relationships between two variables where their ratios are equivalent.

So if one of your answers have equivalent ratios, that is your answer

Answer:

x = 2-√13/3

Step-by-step explanation:

If the classmates donate $230 each, then the answer would be:

( 230   ×   17 )   +   300 =   4,210

If they donated 230 altogether, then the answer would be:

300   +   230 =   530

Answer:

g(x) = x² - 6

h(x) = x² + 3

   g(x) = h(x) + k

 x² - 6 = (x² + 3) + k

 x² - 6 = x² + 3 + k

- x²       - x²

     -6 = 3 + k

    - 3  - 3

     -9 = k

The value of k is -9.

Step-by-step explanation:

MathPapa.com

As a wife, Mrs. Mallard was not free. That's why, when she heard her husband had died, she was not sad. She thought of all the hours that would now be hers alone. She no longer had to obey anyone -- she was finally free.

Answer:

12

Step-by-step explanation:

The measure of length EF is the triangle EFG has an area of 70 m² is 7.38m

A triangle is a 2-dimensional shape with 3 sides and angles. The formula for calculating the area of a triangle is expressed as:

A = (EF)(FG) sin theta

If the ratio of EF to FG is 1:2, then FG = 2EF
A = (EF)(2EF) sin theta
70 = 2EF²sin40
70 = 1.2856EF²
EF² = 54.474
EF = 7.38m

Hence the measure of length EF is the triangle EFG has an area of 70 m² is 7.38m

Learn more on area of triangle here: https://brainly.com/question/17335144

Answer:

8 is 5/2, 9 is an undefined slope

Step-by-step explanation:

8 rise 5 and runs 2 and 9 is a vertical line so there is no slope meaning its undefined.

Answer:  

[tex]\mathrm{Slope = \dfrac{1}{2}}[/tex]

Step-by-step explanation:

To find the slope of a graph, we use the formula below:

[tex]\mathrm{m =\dfrac{y\x_{2}-y\x_{1}}{x\y_{2}-x\y_{1}}}[/tex]

m = slope

(x1, y1) = coordinates of first point in the line

(x2, y2) = coordinates of second point in the line

Step 1: Find any two points on the line

Lets choose: (0, 3) and (2, 4)

Step 2: Put these points into the slope formula

[tex]\mathrm{m =\dfrac{y\x_{2}-y\x_{1}}{x\y_{2}-x\y_{1}}}[/tex]

Step 3: Substitute points into formula

[tex]\mathrm{m =\dfrac{4-3}{2-0}}[/tex]

Step 4: Subtract 3 from 4 and 0 from 2

[tex]\mathrm{m =\dfrac{1}{2}}[/tex]

----------------------------------------------------------------------------------------------------------

Another way you could easily do this is:

Step 1:  Find two ponts on the line

For this problem, let's use (0, 3) and (2, 4)

Step 2: Then from the first point, how much do you need to go up and to the left or right to get to the second point

For this problem, we start on the on the point (0, 4) and go up by 1 and then to the right by 2

Step 3: Then you do rise over run to get the slope

The slope is rise over run:

Rise = 1

Run = 2

So, the slope is 1/2

________________________________________________________[tex]\mathrm{Answer:\dfrac{1}{2}}[/tex]                                                                                                                     ----------------------------------------------------------------------------------------------------------    

Answer:

the sum of 6 and a number g

Answer:

I believe it is 6 but I'm not sure

Step-by-step explanation:

Sorry I am unsure

Step-by-step explanation:

the function for x≥—1 is x²—3

so f(3) = 3²—3=9—3=6

Answer:
7

Step-by-step explanation:

because if you spinned it , it has a 1/5 chance, if we divide 35 by 5 we can see its 7 meaning she could exect a average of 7 spins.

Answer:

it would mean that the anwser is positive

Step-by-step explanation:

Answer:

ill say C too

Step-by-step explanation:

Answer:The answer is 400

I hope this helps have a great day!

Step-by-step explanation:

I am not sure about my answer.But I guess it may be correct.Hope the picture will help you..

first im guessing its 4 and 1/2

and the second is 3

Answer:

40%

Step-by-step explanation:

20+45=60

100-60=40

Answer:

-276^10 c + 156^6 c ^6 - 21b^4 c ^6

Step-by-step explanation:

The expected score of each at bat if he earns 1 point for each hit that is not a home run and 5 points for each home run is 0.57

It is defined as the ratio of the number of favorable outcomes to the total number of outcomes, in other words the probability is the number that shows the happening of the event.

Number of bats = 369

Number of hits = 127

Number of home runs = 21

The probability of a hit:

[tex]=\frac{127}{369}[/tex]   (includes home run)

The probability of home run:

[tex]=\frac{21}{369}[/tex]

The probability of hit run(without home run)

[tex]=\frac{127}{369}-\frac{21}{369}[/tex]

[tex]=\frac{106}{369}[/tex]

The probability of no hit:

[tex]=\frac{369-127}{369}[/tex]

[tex]=\frac{242}{369}[/tex]

For home run, the score will be 5 points.

If not, a home run score will be 1 points.

If Miguel does not get hit, score will be zero point.

Expected value of Miguel hit at each bat is (without home run):

For 5 hit:

[tex]=\frac{106}{369}[/tex]

For 21 home runs, the points will be 21×5 = 105  (5 points for each home run)

The expected value for this:

[tex]\frac{105}{369}[/tex]

Adding both expected hits, we get:

[tex]=\frac{106}{369}+\frac{105}{369}[/tex]

[tex]=\frac{211}{369}[/tex]

= 0.571 ≈ 0.57

Thus, the expected score of each at bat if he earns 1 point for each hit that is not a home run and 5 points for each home run is 0.57

Learn more about the probability here:

brainly.com/question/11234923

Answer:

0.57

Step-by-step explanation:

Answer:

1) Y

2) Y

3) N

4) N

5) N

steps

1) How many bananas did Joe eat yesterday?

The word "many" tells you that its talking about variability.

2) What is the population of Austin, Texas?

The phrase "What is the population..." tells you that its talking about variability.

3) What kind of sandwiches does your class like?

Doesn't talk about variability.

4) What is the name of your teacher?

Doesn't talk about variability.

5) How much do televisions cost?

Doesn't talk about variability.

(YYNNN)

Inequalities help us to compare two unequal expressions.  The value of x which is the solution set of 9(2x+1)<9x–18 is -4.

Inequalities help us to compare two unequal expressions. Also, it helps us to compare the non-equal expressions so that an equation can be formed.

It is mostly denoted by the symbol <, >, ≤, and ≥.

To know which value will satisfy the inequality we need to substitute each of the values into the inequality,

A) x=-4

[tex]9(2x+1) < (9x-18)\\\\9[2(-4)+1] < [9(-4)-18]\\\\9(-8+1) < (-36-18)\\\\9(-7) < -54\\\\-63 < -54[/tex]

Since the inequality is satisfied this is the solution set of the inequality.

Thus, the value of x which is the solution set of 9(2x+1)<9x–18 is -4.

Learn more about Inequality:

https://brainly.com/question/19491153