If using the method of completing the square to solve the quadratic equation x^2-16x+37=0 which number would have to be added to "complete the square"?

Answers

Answer 1

Answer:

-27

(negative number)

Step-by-step explanation:

-b/2a = -(-16)/2(1) = 16/2 = 8

                       x       +          8

                 x   x^2                8x

                 +

                 8    8x                64

So we got 64, but 64 is not 37 so we need to change that by subtracting 27 from it.

64 - 27 = 37

So the final answer (in vertex form) is:

(x+8)^2 - 27

(-27) is the number being added


Related Questions

given the slope of the line and one point the passage through (2,-1) m=5/4

Answers

Answer:

slope intercept form:

y = [tex]\frac{5}{4}[/tex] x - [tex]\frac{7}{2}[/tex]

Step-by-step explanation:

m = 5/4

x = 2   from the point (2,-1)

y = -1   from the point (2,-1)

y = mx + b

-1 = [tex]\frac{5}{4}[/tex] ([tex]\frac{2}{1}[/tex]) + b

-1 = [tex]\frac{10}{4}[/tex] + b

-1 = [tex]\frac{5}{2}[/tex] + b   Subtract [tex]\frac{5}{2}[/tex] from both sides

[tex]\frac{-2}{2}[/tex] -+ [tex]\frac{-5}{2}[/tex] = b

[tex]\frac{-7}{2}[/tex] = b

y = mx + b

y = [tex]\frac{5}{4}[/tex] x - [tex]\frac{7}{2}[/tex]

Answer:

if you need the equation: y + 1 = [tex]\frac{5}{4}[/tex] (x-2) or y + 1 = [tex]\frac{5}{4}[/tex] x  [tex]-\frac{5}{2}[/tex]

the answer: y = [tex]\frac{5}{4}[/tex] x [tex]-\frac{7}{2}[/tex]  

Step-by-step explanation:

Kind of explanatory you have a slope and a point, your formula is going to be y-y₁ = m(x-x₁)

What percentage of 2000 is 1200

Answers

The percentage of 2000 that is 1200 is
= 60%

9(2n+1) help please brooooooo

Answers

Answer:

18n + 9

Step-by-step explanation:

Distribute 9 into the expression.

9*2n = 18n

9*1 = 9

18n + 9

a group of four numbers has an average of 15. The first three numbers are 12,19 and 7. What is the other number

Answers

Answer:

22

Step-by-step explanation:

12 + 19 + 7 + _?_ = 15

38 + _?_ = 15

-38             -38

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

? = 23

12 + 19 + 7 + 23 = 61

                    -1

             

12 + 19 + 7 + 22 = 60

60 ÷ 4 = 15

I hope this helps!

A fence is to be built to enclose a rectangular area of 1250 square feet. The fence along three sides is to be made of material that costs $6 per foot. The material for the fourth side costs $18 per foot. Find the dimensions of the rectangle that will allow for the most economical fence to be built

Answers

The dimensions of the rectangle for the most economical fence are length, L = 50 feet and width, W = 25 feet

How to find the dimensions of the rectangle for the most economical fence?

Given: Area =  1250 square feet, , cost of material along three sides = $6 per foot, cost of material for fourth sides = $18 per foot

In order to calculate the dimension of the fence

Let L and W represent the length and width of the fence respectively

Thus, the area of the fence can be represented as:

A = L × W = 1250  ---- (1)

L = 1250/W

Let the total cost to construct the fence be 'C' can be obtained if we construct the shorter side with material with a cost of $18 per foot

C = 6×(2W + L) + 18×L

C = 12W + 24L  ---- (2)

Substituting the value of L from equation 1 into equation 2 we have:

C = 12W + 24×(1250/W)

To minimize the cost we differentiate both sides with respect to W and equate the result to zero:

C = 12W + 24×(1250/W)

dC/dW = d/dW (12W + 30000/W)

0 = 12 - 30000/W²

12W² = 30000

W² = 2500

W = 50 feet

Since L = 1250/W

L = 1250/50

L = 25 feet

Therefore, the dimensions of the rectangle are length of 25 feet and width of 50 feet

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Susan has a collection of 60 nickels and dimes. If the number of nickels is four times the number of​ dimes, how many nickels and how many dimes does she​ have?

Answers

Answer: 12 dimes, 48 nickles.

Step-by-step explanation:

Let x = the number of dimes

Let 4x = the number of nickels

x + 4x = 60

5x = 60

x = 12 dimes

4x = 48 nickles

She has 48 nickels and 12 dimes.

Equation

At first, we have to express the sentence into equation:

Given:

x = nickels

y = dimes

Susan has a collection of 60 nickels and dimes  --> x + y = 60 ............. (1)

the number of nickels is four times the number of dimes --> x = 4y ......(2)

then we must input the equation (2) into the equation (1):

x + y = 60

4y + y = 60

5y = 60

y = 60/5

y = 12

As we know the value of y, we can calculate the value of x from the equation (2):

x = 4y

x = 4 * 12

x = 48

Thus, Susan has 48 nickels and 12 dimes

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The weather report suggested that your city’s temperature increased from -10 degree celsius to 20 degree celsius. What is the rise in temperature?

Answers

Answer:

The temperature increased in 30 degrees Celsius

Step-by-step explanation:

The diagram shows a shape with all side lengths measured in centimetres. All the angles are right angles.
Write an expression, in terms of
x, for the total shaded area.

Answers

The expression for the total shaded area is in terms of x is

Area = (x + 5)(x - 3)

How to find the total shaded area

The top side of the diagram shows that the dimension for the shaded area has length = x + 5

The width of the shaded area is x - 3

Area of a rectangle is given by the formula

Area = Length * width

Area = (x + 5) * (x - 3)

Area = x² - 3x + 5x - 15

Area =  x²+ 2x - 15

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Explain why the slope(m) of this line is
2/6

Answers

The slope is 2/6 because the rise is 2 while the run is 6

rise             2

-------    =    -------

run              6

question below answer quick

Answers

The x-intercept is (5,0)

The y-intercept is (0,10)

What is intercept ?

A y-intercept, also known as a vertical intercept, is the point where the graph of a function or relation intersects the y-axis of the coordinate system in analytical geometry, using the widely used convention that the horizontal axis represents a variable x and the vertical axis represents a variable y. As a result, x = 0 is satisfied at these sites.

A line's x-intercept and y-intercept are the points at which the x- and y-axes cross, respectively.

To find x-intercept we put y = 0 to the equation

4x + 2y = 20

4x = 20

x = 5

To find y-intercept we put x = 0 to the equation

4x + 2y = 20

2y = 20

y = 10

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The power P (in W) generated by a particular windmill is given by P=0.015V where V is the velocity of the wind (in
mph). Find the instantaneous rate of change of power with respect to velocity when the velocity is 5.9 mph. Round
your answer to the nearest tenth.
OA. 0.3 W/mph
OB. 3.5 W/mph
OC. 1.6 W/mph
D. 6.2 W/mph

Answers

The instantaneous rate of change of power with respect to velocity is 1.6 W/mph.

What is the rate of change function?

The pace at which one quantity changes in relation to another is known as the rate of change function.

Given, P = 0.015[tex]V^{3}[/tex]

Differentiating P with respect to V:

P′=(0.015)(3)[tex]V^{2}[/tex]

At V = 5.9 mph, then

P′=(0.015)(3)[tex]5.9^{2}[/tex] = 1.6 W/mph

Hence, the instantaneous rate of change of power is 1.6 W/mph.

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Jason uses his car for business. he must keep accurate records so his company will reimburse him for his car expenses. when he started his trip, the odometer read 43,156.1. Jason's car gets 35 miles per gallon. his tank was full at the beginning of the trip. when he filled the tank, it cost $34.24. what price did he pay per gallon of gas on this fill-up?

Answers

The price Jason paid per gallon of gas on this fill-up is $0.03 per gallon

What is the price per gallon?

Based on the given task content; this can be solved using the division method.

Total miles = 43,156.1Jason's miles per gallon = 35 miles per gallonTotal cost to fill Jason's car = $34.24

Total 35 miles in Jason's odometer = Total miles / 35

= 43,156.1 / 35

= 1233.031428571428

Approximately,

1,233.03 of 35 miles per gallon

Amount Jason paid per gallon of gas on this fill-up = 1,233.03 / $34.24

= 0.027768991833126

Approximately,

$0.03 per gallon

In conclusion, the amount Jason paid per gallon of gas is $0.03 per gallon

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Does the table represent a
function? Explain.
x
-3 -2 0 -3 -2
y 9 4 0 -9 -4

Answers

keeping in mind that a function does not have any X-Repeats, that is, the 1st coordinate in every pair never repeats, Check the picture below.

In an animal rescue facility are 21 animals.14 cats and 7 dogs. During the day 5 animals were adopted.what is the probabity that 3 cats and 2 dogs were adopted? Review ch 7 on probability

Answers

Answer:

0.3756

Step-by-step explanation:

I believe this is a combinatorics probability problem.

We first figure out in how many ways we can choose 3 cats out of 14 cats

Then we figure out how many ways we can choose 2 dogs out of 7 dogs

The total number of ways to select 3 cats and 2 dogs will be the product of these two

We then figure out in how many ways we can select 5 animals out of a total of 21 animals

The product we computed divided by the above number will give the probability

The number of ways we can choose k items out of n items is given by nCk i.e n Choose k

The formula is rather complicated but almost all calculators should be able to compute this given n and k

Let's deal with the selection of 3 cats from the population of 14 cats

This is given by 14C₃ which works out to 364

Number of ways for selecting 2 dogs from 7 dogs = 7C₂ = 21

Number of ways of selecting 5 animals from 21 = 21C₅ = 20349

The probability of selecting 3 cats and 2 dogs is therefore:

[tex]\dfrac{364 \times 21}{20349} = 0.3756[/tex]

That, I believe is the answer. Please let me know if it is correct and if you need more info.

One rectangle is "framed" within another. Find the area of the shaded region if the "frame" is 2 units wide. 7 and 2

Answers

24 units is the area of the shaded region if the "frame" is 2 units wide.

What is Area of Rectangle?

The area of Rectangle is length times of width

We know that the frame is 2 units wide, and the measure of the rectangle and the frame are:

width = 7 units

length = 12 units

Now, if we remove the frame, we will remove 2×2 units = 4 units for each measure (because for each measure we have the frame in both sides).

So the measures for the shaded rectangle are:

width = 7 units - 4 units = 3 units

length = 12 units - 4 units = 8 units.

And the area of a rectangle is given by the product between the width and length, then we have:

A = (3 units)*(8 units) = 24 square units.

Hence, 24 units is the area of the shaded region if the "frame" is 2 units wide.

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Can somebody help me with this please?

Answers

Answer: -16.66

Reason: 10*-5/3=−16.66666667 or −50/3​

A party rental company has chairs and tables for rent. The total cost to rent 2 chairs and 6 tables is $54 . The total cost to rent 5 chairs and 3 tables is $36 . What is the cost to rent each chair and each table?

Answers

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

The cost of each chair is $2.25.

The cost of each table is $8.25.

What is an equation?

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

Example: 2x + 4 = 5 is an equation.

We have,

Cost of each chair = x

Cost of each table = y

Now,

2x + 6y = 54 _____(1)

5x + 3y = 36 ______(2)

From (1) we get,

2x = 54 - 6y

x = (54 - 6y)/2 ______(3)

Now,

Putting (3) in (2) we get,

5(54 - 6y)/2 + 3y = 36

270/2 - 30y/2 + 3y = 36

135 - 15y + 3y = 36

99 = 12y

y = 99/12

y = 8.25 ______(4)

Now,

Putting 4 in (3) we get,

x = (54 - 6 x 8.25) / 2

x = 4.5/2

x = 2.25

Thus,

The cost of each chair is $2.25.

The cost of each table is $8.25.

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Sydney’s fitness app says she has completed `70\%` of her goal for the week. Her goal is `50` miles. How far has she biked?

Answers

Sydney has biked `35` miles.

Find the present value​ (the amount that should be invested now to accumulate the following​ amount) if the money is compounded as indicated.
​$6800 at ​4% compounded quarterly for 3 years

Answers

The present value​ the amount that should be invested now to accumulate is $7662.24.

What is meant by compound interest?

Compound interest is the adding of interest to the principal amount of a loan or deposit, or interest on interest + principal. It is the outcome of reinvesting interest, or adding it to lent capital, rather than paying it out or requesting payment from the borrower, so that interest is received on the principle sum plus previously accumulated interest in the next month. In finance and economics, compound interest is common.

Compound interest differs from simple interest in that previously collected interest is not added to the current period's main amount, resulting in no compounding. The simple annual interest rate is calculated by multiplying the interest amount per period by the number of periods in a year.

Given,

Principle P=$6800

T=3 years

And also given that the money is compounded quarterly.

Present value=P[tex](1+(R/4)^{4t}[/tex]

=6800[tex](1+(4/400)^{12}[/tex])

=6800[tex](1+(1/100))^{12}[/tex]

=6800[tex](101/100)^{12}[/tex]

=6800[tex](1.01)^{12}[/tex]

=6800×1.1268

=$7662.24

The present value​ the amount that should be invested now to accumulate is $7662.24

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Ahmed earns $450/week. He receives a 4% increase in pay.

What is Ahmed’s weekly pay after his increase?

Answers

The answer to this question is $468

what is the slope of a line that is parallel to the line connecting point O (-5,1) and point P (2,3)?

Answers

Answer:

2/7

Step-by-step explanation:

2 parallel lines have the same slope

we just need to find the slope of the line with the point’s connecting O and P

We use y2-y1/x2-x1 to find slope

3-1/2-(-5)

2/7

2/7 is the slope

Hopes this helps please mark brainliest

pls help me with this question ​

Answers

Answer:

[tex]\frac{13}{30}[/tex]

Step-by-step explanation:

In your own words, tell me the difference between a geometric and an arithmetic sequence.

Answers

As several differences are there between them and is differentiated below.

What is Sequence?

A list of numbers in a specific order is called a sequence. The terms of the sequence are the various numbers that appear in it.

Let a sequence's terms be a1, a2, a3,..., an,..., etc.

The term's position is indicated by the subscripts. That implies,

Initial phrase = a1

term two = a2

term three Equals a3

….

The nth term, indicated by an, is the number that appears in the sequence at the nth place. This phrase is also known as the sequence's general phrase.

Geometric Sequence:

It is a sequence of numbers in which each new term is calculated by multiplying by a non-zero and fixed number.Multiplication or Division is done in every step.A common ratio between 2 successive terms is the common ratio.It is of the Exponential Form.

Arithmetic Sequence:

It is a list of numbers, in which every new term alters from another preceding term by a definite quantity.Addition or Subtraction is done in every step.A common ratio between 2 successive terms.It is of the Linear Form,

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Jordan is helping his dad build a doghouse. The floor is rectangle-shaped with a width of 5 feet and an area of 36.25 ft2. What is the length of the rectangular floor?​

Answers

The length is 7.25 feet

Here the detail

The formula for rectangled-shaped area is multiply length and width

Area = Length x Width

In this case, we know that the area is 36.25 ft2 and the width is 5 feet

so we can divided the area and the width to solve the length

Area = Length x Width

36.25 = Length x 5

Length = 36.25 : 5

Length = 7.25 feet

Hence the length of the rectangular floor is 7.25 feet

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Malik spent $7.00 for a drink and a sandwich. His drink cost $ 2.00. Did he have a ham sandwich for $ 3.00, a tuna sandwich for $ 5.00, or a turkey sandwich for $ 4.00 Use the equation s + 2.00 = 7.00 to justify your answer.

Answers

Answer: tuna sandwich

Step-by-step explanation: 2+5=7

during basketball season josh made 3 out of every 7 free throw attempts in the last game josh attempted 28 free throws how many free throws would he have been expected to make

Answers

There are 12 free throws would he have been expected to make.

What is mean by Ratio?

A ratio indicates how many times one number contain in another number. The ratio of two number is written as x : y, which is equivalent to x/y. Where, x and y are individual amount of two quantities.

Given that;

During basketball season josh made 3 out of every 7 free throw attempts in the last game.

Now,

Since, During basketball season josh made 3 out of every 7 free throw attempts in the last game.

Hence, Let number of free throws would he have been expected to make for attempted 28 free throws = x

So, We can formulate;

⇒ 3/7 = x/28

Solve for x as;

⇒ 3 × 28 / 7 = x

⇒ x = 3 × 4

⇒ x = 12

Thus, There are 12 free throws would he have been expected to make.

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What does absolute value represent?

Answers

Step-by-step explanation:

The distance from zero that a number is on the number line without considering Direction

Jaxon goes to a restaurant and the subtotal on the bill was x dollars. A tax of 8% is applied to the bill. Jaxon decides to leave a tip of 23% on the entire bill (including the tax). Write an expression in terms of x that represents the total amount that Jaxon paid.

Answers

Answer:

Step-by-step explanation:

If the equation is going off of what is the traditional, and correct way to tip, the tip would be based off the total BEFORE tax.

Therefore, the expression for the total cost would be: x + .23x +.08x, which, simplified, would be 1.33x.

15 points!! Is the triangle a right triangle?

Answers

Answer: Yes.

Step-by-step explanation:

Answer:

yes, it is because the right side is the bigger side.

Step-by-step explanation:

See in a right triangle, the side that is opposite of the 90° angle is the longest side of the triangle, and is called the hypotenuse.

Can you guys awnser the questions in the boxes below

Answers

Answer:35 divide by 10.50= 3.33 = 4 hrs

Step-by-step explanation:

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