What is the function written in vertex form?

f(x) = 4(x + 6)2 + 10
f(x) = 4(x + 6)2 – 26
f(x) = 4(x + 6)2 – 134
f(x) = 4(x + 6)2 + 154

Answer:

43 9

Step-by-step explanation:

sum of their ages is 52

let Jack's age be x = 5×x= 5x

his father's age is 2<5x

Answer:

(53.812 ; 58.188) ; 156

Step-by-step explanation:

Given that :

Sample size (n) = 51

Mean (m) = 56

Standard deviation (σ) = 9.5

α = 90%

Using the relation :

Confidence interval = mean ± Error

Error = Zcritical * (standard deviation / sqrt (n))

Zcritical at 90% = 1.645

Error = 1.645 * (9.5 / sqrt(51))

Error = 1.645 * 1.3302660

Error = 2.1882877

Hence,

Confidence interval :

Lower boundary = 56 - 2.1882877 = 53.8117123

Upper boundary = 56 + 2.1882877 = 58.1882877

Confidence interval = (53.812 ; 58.188)

2.)

Margin of Error (ME) = 1.25

α = 90%

Sample size = ((Zcritical * σ) / ME)^2

Zcritical at 90% = 1.645

Sample size = ((1.645 * 9.5) / 1.25)^2

Sample size = (15.6275 / 1.25)^2

Sample size = 12.502^2 = 156.3000

Sample size = 156

Answer: 8 units

Step-by-step explanation:

Answer:

a=2

Step-by-step explanation:

Slope is found by (y2-y1)/(x2-x1)

Using the points, that is (5-a)/(4a-2) = 1/2

multiply both sides by the denominator 4a-2

5-a = (1/2)(4a-2)

5-a=2a-1

put like terms on opposite sides by adding a to both sides so a terms on the right, adding 1 on both sides so numbers are on the left

6=3a

divide both sides by 3

a=2

please give thanks :)

Answer:

9

5

Step-by-step explanation:

Wyatt's class:

Each group of 3 students eats 1 1/2 pizzas.

There are 18 students.

18/3 = 6

There are 6 groups of 3 students.

Since each group of 3 students eats 1 1/2 pizzas, 6 groups eat

6 * 1 1/2 = 6 * 3/2 = 18/2 = 9

Answer: 9 pizzas

Jennifer's class:

There are 15 students. Each student eats 1/3 of a pizza.

15 * 1/3 = 15/3 = 5

Answer: 5 pizzas

Answer:

9

5

Answer:

The answer is x=y/6 - 0.383 (3 being repeated) , hope this helps you.

Step-by-step explanation:

Isolate the variable by dividing each side by factors that don't contain the variable.

Answer:

I think it is x=y/6 - 0.383 (3 being repeated)

Step-by-step explanation:

Hope this helped have an amazing day!

Answer: Um, I think is [tex]\frac{x}{2-3}[/tex].

Step-by-step explanation:

9514 1404 393

Answer:

  y = 1/4x^1 -x -4

Step-by-step explanation:

Same question as previous parts. The working is identical, using different numbers.

Focus-vertex distance is (y-difference) p = -4-(-5) = 1. Vertex is (h, k) = (2, -5). Putting these values into the vertex form and expanding to standard form, you get ...

  y = (1/(4p))(x -h)^2 +k

  y = 1/4(x -2)^2 -5 . . . . . . . . fill in the values for p, h, k

  y = 1/4(x^2 -4x +4) -5 . . . .  expand the square

  y = 1/4x^2 -x +1 -5 . . . . . . . use the distributive property to eliminate parens

  y = 1/4x^1 -x -4 . . . . . . . . . collect terms

_____

Additional information may be found at ...

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Answer:

The 30, goes all the way down, in the empty spot by the 2, put in a 5, then below it a 10

Step-by-step explanation:

Answer:

30/ [5x2]

30/ 10=3

Step-by-step explanation:

Answer:

The number of cars that go through the intersection each minute X has Poisson distribution with parameter λ = 11.5

and the PMF of X is;

P (X = x) = e^-λ ( λˣ / x! ); where x = 0, 1, 2, 3, , , , , ,

Step-by-step explanation:

Given that;

on average eleven and a half  cars go through the intersection each minute and It takes an average person ten seconds to walk across the intersection.

Therefore

The number of cars that go through the intersection each minute X has Poisson distribution with parameter λ = 11.5

and the PMF of X is;

P ( X = x ) = e^-λ ( λˣ / x! ) ;

where x = 0, 1, 2, 3, , , , , ,

Answer:

[tex]\displaystyle \frac{118}{125}[/tex]

Step-by-step explanation:

Trigonometry

Calculate

[tex]\sin (3\sin^{-1}(2/5))[/tex]

We use the formula for the sine of triple angle:

[tex]\sin 3x=3\sin x-4\sin^3 x[/tex]

And recall:

[tex]\sin \sin^{-1}x=x[/tex]

For this problem, we set:

[tex]x=\sin^{-1}(2/5)[/tex]

Thus:

[tex]\sin 3x=3\sin (\sin^{-1}(2/5))-4\sin^3 (\sin^{-1}(2/5))[/tex]

[tex]\displaystyle \sin 3x=3*\frac{2}{5}-4\left(\frac{2}{5}\right)^3[/tex]

[tex]\displaystyle \sin 3x=\frac{6}{5}-4*\frac{8}{125}[/tex]

[tex]\displaystyle \sin 3x=\frac{6}{5}-\frac{32}{125}[/tex]

[tex]\displaystyle \sin 3x=\frac{6*25}{125}-\frac{32}{125}[/tex]

[tex]\displaystyle \sin 3x=\frac{150-32}{125}[/tex]

[tex]\mathbf{\displaystyle \sin 3x=\frac{118}{125}}[/tex]

Answer:

  c)  $51,450

Step-by-step explanation:

  Current payroll:

     21 * 49000 = $1,029,000

  Payroll after 5% increase:

     1029000 * 1.05 = $1,080,450

  Difference between after increase and current payroll:

     1080450 - 1029000 = $51,450

Answer:

(x, y)

(-1,0)

since the rest of the points aren't in the multiple choice well it's (-1,0)

The solution is :  the correct option is (B) (-1, 0), is an x-intercept of the graphed function.

Here, we have,

We are given to find the x-intercepts of the graphed function.

We know that

x-intercepts of a function are the points on the X-axis through which the graph of the function is crossing.

From the graph, we see that

the curve is crossing the X-axis at the points (-2, 0) and (-1, 0) .

Therefore, the x-intercept of the given function is (-1, 0).

Option (B) is CORRECT.

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Step-by-step explanation:

Answer

[tex] {a}^{3} - {b}^{2} [/tex]

[tex] = {3}^{3} - { \frac{1}{2} }^{2} [/tex]

[tex] = 27 - \frac{1}{4} [/tex]

[tex] = \frac{107}{4} [/tex]

[tex] = 26 \frac{3}{4} [/tex]

sorry if wrong :)

Answer:

use your scientific calculator and click shift + mode or just mode , after that select the table option and enter the equation that u see and then set the step to 1 (start = -2 , end = 3) and step =1

Answer:

solution

or, (N+1) th item

_

2

or ,8+1 th item

_

2

or,9

_

2

or,4.5 th item hence the median is4

The median of the given numbers will be 8.5.

The Median is the middlemost value of the numbers arranged in ascending orders. If the number of the data is an odd number so the median will be a middle number if the number of the data is even then the median is the mean of the middle two numbers.

The given data is:-

1 , 1.23 , 2 , 3 , 4 , 13 , 22 , 26.8

The total numbers of the data are 8 so the median will be calculated as:-

Median = ( 4 + 13 ) / 2

Median = 17 / 2

Median = 8.5

Therefore the median of the given numbers will be 8.5.

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Answer:

the highest common factor of the polynomial is (x + 2) (x - 3)

Step-by-step explanation:

The computation of the highest common factor of the polynomial is as follows:

According to the question, the following equation is given

'[tex]x^2 - x - 6[/tex]

Now do the factorization

[tex]x^2 -3x + 2x - 6[/tex]

x(x - 3) +2 (x - 3)

(x + 2) (x - 3)

hence, the highest common factor of the polynomial is (x + 2) (x - 3)

The same is to be considered

Answer:

The amount of intrest gained was B. $7.50

Step-by-step explanation:

Mark invested $125.

He gaines 3% per year and he did it for 2 years.

.03 x 2 =.06

125 x .06 = 7.50

B. $7.50

Hope this helps!

:)

Answer:

Did you want me to simplify the expression???

Step-by-step explanation:

3f+5b+3d+8

Answer:

A or B

Step-by-step explanation:

Its more likely B

Answer:

c. 2640

Step-by-step explanation:

20 x 12 x 11 = 2640

Answer: C. 2,640

Step-by-step explanation:

Answer:

the answer is 70

Step-by-step explanation:

Answer: Irrational

Step-by-step explanation:

Answer:

1/12

Step-by-step explanation:

When we roll 2 dice, there are 36 possible rolls

How can we get 4

1and 3, 3 and 1, 2 and2 = 3 different rolls

P( 4) = number of rolls with sum of 4/ total rolls

        = 3/36 = 1/12

Answer:

the answer is d because it