Rewrite the function by completing the square.

f(x)=x^2-4x-26

Answer:

[tex]\textsf{a)} \quad y=(x+1)^2-4[/tex]

[tex]\textsf{b)} \quad y=2(x-4)^2-2[/tex]

Step-by-step explanation:

Vertex form of a parabola:  [tex]y=a(x-h)^2+k[/tex]

(where (h, k) is the vertex and [tex]a[/tex] is some constant)

Substitute the vertex into the formula:

[tex]\begin{aligned}\implies y &=a(x-(-1))^2-4\\y & =a(x+1)^2-4\end{aligned}[/tex]

Substitute the point (1, 0) into the formula:

[tex]\begin{aligned}\implies a(1+1)^2-4&=0\\4a-4&=0\\4a &=4\\a &=1\end{aligned}[/tex]

Therefore, the equation of the parabola in vertex form is:

[tex]y=(x+1)^2-4[/tex]

Substitute the vertex into the formula:

[tex]\begin{aligned}\implies y &=a(x-4)^2+(-2)\\y & =a(x-4)^2-2\end{aligned}[/tex]

Substitute the point (6, 6) into the formula:

[tex]\begin{aligned}\implies a(6-4)^2-2&=6\\4a-2 & =6\\4a &=8\\a &=2\end{aligned}[/tex]

Therefore, the equation of the parabola in vertex form is:

[tex]y=2(x-4)^2-2[/tex]

Find a

So

Vertex form

#2

Find a

Vertex form

Check the picture below.

so the quadrilateral is really just a parallelogram below a triangle, so let's simply get the area of each and sum them up.

[tex]\stackrel{\textit{\Large Areas}}{\stackrel{parallelogram}{(6)(4)}~~ + ~~\stackrel{triangle}{\cfrac{1}{2}(6)(4)}}\implies 24~~ + ~~12\implies 36[/tex]

Answer:

Hexa is a prefix meaning six.

Step-by-step explanation:

An example of this would be a hexagon, it has six sides, and the word of course has the prefix, "hexa."

Step-by-step explanation:

867.5x ×2.8

is is equal to 2429x

Answer: 25cm

Step-by-step explanation:

Since the field is square we can understand each side is an equal length

This means we just have to use the formula...  

[tex]A^2 = 625[/tex]

[tex]\sqrt{a^2} = \sqrt{625}[/tex]

a = ±25

Since it is a real thing, we are only looking at positive values, therefore your answer is

25cm

Step-by-step explanation:

odd numbers cannot be divided by 2 without remainder.

so, H is

{5, 7, 9, 11}

Answer:

Step-by-step explanation:

2 2/9? maybe because 1/8 is 6 times bigger than 1/2, so if you add 6 to 2 2/3 it would be 2 2/9?

You would need 1/4 white paint to mix with 2 2/3 quarts of blue paint to make the same shade of paint.

The ratio is defined as a relationship between two quantities, it is expressed as one divided by the other.

The amounts of each type of paint as fractions of the total amount of paint: 1/2 quart of blue paint is 1/(1+1/2) = 2/4 = 1/2 of the total amount of paint, and 1/8 quart of white paint is 1/(1+1/2+1/8) = 1/8 of the total amount of paint.

So the ratio of blue paint to white paint in the original mixture is 1/2 to 1/8, or 4 to 1. To make the same shade of paint with 2 2/3 quarts of blue paint, we need to use the same ratio of blue paint to white paint.

So we need 1/4 as much white paint as blue paint, which is (1/4) × 2 2/3 quarts = 2/3 quart of white paint.

The error in the original solution was not correctly finding the ratio of blue paint to white paint in the original mixture, which is necessary to determine the correct amount of white paint to mix with a different amount of blue paint to create the same shade.

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Answer:x < 3/14

Step-by-step explanation:

-14x > -3

x < 3/14

Answer: x<3/14

Step-by-step explanation:

In this survey, the results can be trusted because more than half of the people responded which makes this sample to be representative.

This occurs when most of the people who were intended to be surveyed do not respond, which causes the results to be biased as the sample does not represent the population.

Considering more than 50% answer it is likely the results can be trusted as the sample is still representative.

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Answer:

How do I calculate interest rate on investment?

Calculate Total Amount Accrued (Principal + Interest), solve for A. A = P(1 + rt)

Calculate Principal Amount, solve for P. P = A / (1 + rt)

Calculate rate of interest in decimal, solve for r. r = (1/t)(A/P - 1)

Calculate rate of interest in percent. ...

Calculate time, solve for t.

Step-by-step explanation:

Hope this helps.

Answer:

SA = 76 cm²

Step-by-step explanation:

Surface Area (SA) of a cuboid: 2(lw) + 2(wh) + 2(hl)

SA = 2(lw) + 2(wh) + 2(hl)

Substitute the values above and multiply:

SA = 2(lw) + 2(wh) + 2(hl)

SA = 2(4)(2) + 2(2)(5) + 2(5)(4)

SA = 2(8) + 2(10) + 2(20)

SA = 16 + 20 + 40

SA = 76 cm²

Final answer: 76 cm²

Hope this helps!

Answer: 20 lawns can mowed in 7hrs

Step-by-step explanation:

Rate of the lawns to mow is [tex]\frac{5}{7}[/tex]lawns per hour.

" Rate is defined as the ratio of the comparison of two different quantity with different unit."

According to the question,

Given,

Number of hours to mow 5 lawns = 7hours

Rate of the lawns mowed = [tex]\frac{5}{7}[/tex] lawns per hour

Hence, rate of the lawns to mow is [tex]\frac{5}{7}[/tex]lawns per hour.

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The x-intercept of the graphed function is (-1,0)

The x-intercept of the graphed function is the point where the function has a value of 0

i.e. the x value when y = 0

From the complete question, we have:

x = -1 when y = 0

Hence, the x-intercept of the graphed function is (-1,0)

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Answer:

The parents of the seventh grade students

Answer:

19

Step-by-step explanation:

I don't really have explanation but imagine putting boxes into boxes that are always a little bigger(+5 cm)

so you go from the smallest one 10cm and gradually keep adding 5cm until you reach 100cm.

10,15,20,25,30,........,100

Answer:

Step-by-step explanation:

Comment

The formula for density is D = m/V

Therefore the units of density is

Density = grams/cm^3

If one person received 25 messages. Then the number of messages received by each friend will be 26.

The division of something into distinct portions, or the sharing of something among other persons, locations, or things, is referred to as division.

A group of 9 friends received a combined total of 233 text messages in two hours. One person received 25 messages.

Then the number of the remaining messages will be

→ 233 - 25

→ 208

Then the number of the text messages that each of the other 8 friends receives is the same number of the messages. Then we have

Let each friend has an equal number of the messages be x. Then

[tex]\rm x = \dfrac{208}{8}\\\\x = 26[/tex]

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Answer:

64x^3 + 996x^2 + 48x + 8

Step-by-step explanation:

Answer:

12x+6

Step-by-step explanation:

[tex](4x+2)3[/tex]

Use the distributive property to multiply (4x+2) by 3:-

[tex]12x+6[/tex]

Answer:

39/50 is larger than 3/5.

Step-by-step explanation:

2/3 is larger than 3/5.

The equation which equivalent to given expression − 3 ( x − 6 ) + 12 x − ( 8 x + 3 ) is

The Correct option is (C) and (E)

A linear equation is an equation of a straight line, written in one variable. The only power of the variable is 1. Linear equations in one variable may take the form ax+ b = 0.

The given equation is:− 3 ( x − 6 ) + 12 x − ( 8 x + 3 ) .

= -3x+18 + 12 x -8x-3

=x +15

The corresponding equation to the above equation is:

C. x+15

D. (12 x - 11x) + (3-18)

= x-15

E. (12 x - 11x) + (18-3)

= x+15

F. (12 x - 11x) + (-6+3)

= x-3

As from the above it can be seen that the equation which equivalent to given expression − 3 ( x − 6 ) + 12 x − ( 8 x + 3 ) . is

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Answer:

Mean - 3.3793103448276

Median - 3

Step-by-step explanation:

Define:

Mean ⇒ Average

Median ⇒ Middle Number

Solve:

Mean ( Adding all number then divide by total number in data set)

1 + 1 + 2+2+2+2+3+3+3+3+3+3+3+3+3+4+4+4+4+4+4+4+4+5+5+5+5+5=94

94/29 = 3.3793103448276

Mean - 3.3793103448276

Median ( Find Middle Number)

1,1,2,2,2,2,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,5,5,5,5,5

Kavinsky

Answer:

Step-by-step explanation:

What is the coefficient in the mathematical expression?

- 7

point 2 1/3 is on the right of 2 plus 2 small marks

point -5/6 is on the right of -1 plus 1 small mark

point -3 1/2 is on the left of -3 plus 1 small mark

sorry I don't know how to draw a number line on brainly

Answer:

- for the number line check out the attached photo

- 7

Step-by-step explanation:

- on the number line, each small mark represents 1/6 so to make it easier I made the fraction into 1/6 form

- a coefficent is a numerical value placed before and multiplying the variable in an algebraic expression (ex. 4x)

In this case 7 is before the m making 7 the coefficent

Hope this helps, Let me know if you have any other questions !

The area of the circle is the amount of space it occupies, and the area of the circle is 156.25π

The circumference, C is given as:

C = 25π

Start by calculating the radius using:

C = 2πr

So, we have:

2πr = 25π

Solve for r

r = 12.5

The area is then calculated using:

A = πr²

So, we have:

A = π * 12.5²

Evaluate

A = 156.25π

Hence, the area of the circle is 156.25π

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Using it's equation, it is found that the percent decrease in the annual mean thickness of the ice cover was of 33.69%.

It is given by the decrease divided by the initial amount and multiplied by 100%.

In this problem:

Hence the percent decrease is given by:

P = (1.25/3.71) x 100% = 33.69%.

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Answer:

68

Step-by-step explanation:

if tickets cost $12 for adults and there are 3 adult tickets being bought the total cost for adult tickets will be $36

Now for the kids, the tickets cost $4 and there are 8 kids, so the total cost for the kids tickets is $32

so the total price for 3 adult tickets and 8 kids tickets is $68

------

sorry if I didn't answer right I cant tell if the last part is a typo or a question

Answer:

see below

Step-by-step explanation:

ok so there are 8 children and $4 so 4x8=32 and 3 adults for $12 so 3x12=36

36 + 32

3+3=6

6+2=8

36+32= 68

Answer:

d

Step-by-step explanation:

The sun is the primary source because without it there will be nothing like renewable or nonrenewable energy

Answer: Store B

Step-by-step explanation:

So for Store A 5 bowls are $15

1 bowl = 15/5

          = 3

Same applies for all

Store b = $2

Store c = $3

Thus Store B is cheaper

Answer:

58 inches

Step-by-step explanation:

15+12=27+14=41+9=50+8=58

Answer:

use a dot plot because it can show you the the coordinate numbers on the graph.