If using the method of completing the square to solve the quadratic equation
x2 + 7x – 27 = 0, which number would have to be added to "complete the
square"?

Answers

Answer 1

To determine the constant that makes the expression (x² + kx) a perfect square,

Take the coefficient of the second term which is k and ÷2

In this case, it is (7/2)²

At the end it looks like

x² + 7x + (7/2)² = 27 + 49/4

(x + 7/2)² = 157/4

Answer 2

The  number is added is 7/2² or 49/4.

What is Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given:

x² + 7x – 27 = 0.

Now, we have to half the coefficient of x and then add and subtract the square of half the coefficient of x

So, x² + 7x – 27 +7/2² - 7/2² = 0.

( x+ 7/2)² – 27- 49/4 = 0.

( x+ 7/2)² = 157/4

Hence, the number is added is 7/2² or 49/4.

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Related Questions

6. Simplify the expression.
3n+5-12n-8+6p

Answers

Answer

-9n-3+6p

Step-by-step explanation:

Answer:

-9n - 3 + 6p

Step-by-step explanation:

You have to remember that you can add or subtract only LIKE terms. In other words, you can't add 3n + 5, so separate them.

In this equation: 3n + 5 - 12n - 8 + 6p,

1. 3n - 12n

2. 5 - 8

3. 6p

= -9n - 3 + 6p

0.2(k + 2.4) = 3.2k. Please help me. ​

Answers

Answer:

k = 0.16

Step-by-step explanation:

First, use distributive property on the left side:

[tex]0.2(k+2.4)=3.2k\\0.2k+0.48=3.2k\\0.48 = 3k\\k = 0.16[/tex]

Answer:

k = 0.16

Step-by-step explanation:

Use distributive property, meaning individually multiply 0.2 to each number/variable within the parameters

0.2 × k = 0.2k

0.2 × 2.4 = 0.48

0.2k + 0.48 = 3.2k

You cannot add a number and a variable so instead we should isolate the variable

Subtract 0.2k from both sides

0.48 = 3.2k - 0.2k

0.48 = 3.0k

0.48 = 3k

Divide both sides by 3

0.16 = k

A teepee is designed to have a diameter of 10 ft and a volume of 366ft³ what is the height? A.15ft , b.14 ft, c 5ft, or 1 ft

Answers

Answer:

B.  14 ft approx

Step-by-step explanation:

Given data

A teepee  has a conical shape

Diameter= 10ft

radius= 5 ft

Volume = 366ft³

Height = ????

The expression for the volume is

V= 1/3πr^2 h

substitute

366= 1/3*3.142*5^2*h

366= 1/3*78.55*h

366= 26.18h

h= 366/26.18

h=13.98 ft

h= 14 ft approx

Hence the Height is 14 ft approx

Answer:

14 ft

Step-by-step explanation:

a p e x!

SYMBOL THAT INDICATES THE ROOT OF THE NUMBER

Answers

Answer:

The root symbol (√ ) is used to represent the square root of any number.

Answer:

[tex]\sqrt{x}[/tex]

Square Root

Convert the decimal below to a fraction in simplest form. 0.689

Answers

Answer:

689 / 1000 is the answer

Step-by-step explanation:

zzzzzzzzzzzzz

Hi! PLS HELP!!! 20 POINTS!


A children's pool contains 17,500 milliliters. How many liters are in the pool?

1.75 liters
17.5 liters
175 liters
1,750 liters

pls help!
If u put something of the topic imma report u
Have a great day! :)
(its not a I did it and got it wrong!!)

Answers

Answer:

17.5 liters

Step-by-step explanation:

hope its the answer your looking for

17.5 liters hope this helps

What is the least common multiple of 8 and 12?
24
48
96

Answers

Answer:

The least common multiple of 8 and 12 is 24

Explanation:

Find and list the multiples each number until the first common multiple is found.

This is the lowest common multiple .

Multiples of 8

8, 16, 24, 32,40

Multiples of 12

12,24, 36,48

Therefore,

LCM of 8 and 12 is 24

Answer: The answer is 24

Step-by-step explanation: One easy way to find least common multiples is to take the large number and multiply it by increasing numbers (1,2,3,etc.) until a number is found that is also divisible by the smaller number.

In this case, we can multiple 12 by increasing numbers until we find a number that is also divisible by 8.

12

1

=

12

This is not divisible by 8.

12

2

=

24

This is divisible by 8.

8

3

=

24

Therefore, the least common multiple is 24.

what are all the equivalent ratios for 48:32

Answers

Step-by-step explanation:

There are infinitely many ratios for 48:32, so I'll just list a few:

24:16

6:4

3:2

9:6

480:320

240:160

60:40

30:20

90:60

what type of polygon is this​

Answers

Answer:

enneagon

Step-by-step explanation:

Nonagon :) that’s bc of the nine sides in the polygon

A nurse wants to simulate the number of male and female births at the hospital where she
works using a random digit table.
Which of the following best simulates this situation?

Answers

Answer:

Let the digits 0,1,2,3 and 4 represent the birth of a boy, and let digits 5,6,7,8, and 9 represent the birth of a girl. Use a table of random digits. Choose the first 10 digits in the table and record the number of boy and girl births. Continue to choose batches of 10 digits for a total of 100 times, recording the number of boy and girl births. (possibly B)

I need help with these 2

Answers

For the first one you need to do
x+2+x+2+2x+4+2x+4
=6x+12

When doing this kind of problem you should use FOIL
First, Outer, Inner, Last
(x+2)(2x+4)
First- x•2x= 2x^2
Outer- x•4= 4x
Inner- 2•2x= 4x
Last- 2•4= 8

Combined you have
=2x^2+8x+8

sole this question ?
30÷5+(9×5)-3²=

Answers

Answer:

30÷5+(45)-96+45-942I do exams and quizzes if ur interested

Answer:

42

Step-by-step explanation:

30/5 + ( 9)(5)−32

= 6 + ( 9)(5)−32

= 6 + 45−32

= 51 − 32

= 51 − 9

= 42

hope I helped!!

Hey, guys I need help :D

Answers

Answer:

D

Step-by-step explanation:

Dilating BC to B'C' by a factor of 1/2 makes each side of the triangle halved. Originally BC is 16, so when it's halved, it becomes 8

We know when triangle are similar and are changed only by a scale factor, the angle will not change. Angle A' = 28 degrees

Circumscribe a circle about the given triangle. ​

Answers

Answer:

Step-by-step explanation:

To circumscribe a circle to a given triangle implies constructing a circle outside the triangle, so that it touches the three vertices of the given triangle externally.

The step requires bisecting two sides of the triangle so as to locate the center of the circle. Then with the center and one of the edges, draw a complete circle. The circles should be outside the triangle and passing through its three vertices.

The construction is as shown in the attachment to this answer.

Brainliest!! + Thanks and 5 stars :>
(08.05)What conclusion can be determined from the dot plot below?


A dot plot showing five dots above 9, six dots above 10, three dots above 11, and one dot above 12.


The number of observations is 10.

The median of the data set is 10.

The mean of the data set is 15.

The range of the data set is 12.

Answers

Answer:

Option 2

Step-by-step explanation:

Go through until you find a true statement:

- The number of observations is 10

Count the number of data points. You should end up with 15, so this option is not correct.

-The median of the data set is 10

To find the median, you know that there are a total of 15 data points, so the median would be the mean of the 7th and 8th (because those are the middle numbers). If you look at the data points, the 7th and 8th points are at 10. The mean of 10 and 10 is just 10,  so that means the median of the set is 10.

This is the correct answer.

If you want, you can also go through the other options and see that none of them work.

Answer:

The person above is correct it would be option two!

Step-by-step explanation:

The explanation makes alot of sence. I took the test to make sure it was correct i gotten a 100~!!! ty!

Which of the following values are solutions to the inequality 6≥4x−5?

Answers

Answer:

The solution to the inequality is:

[tex]6\ge \:4x-5\quad :\quad \begin{bmatrix}\mathrm{Solution:}\:&\:x\le \frac{11}{4}\:\\ \:\mathrm{Decimal:}&\:x\le \:2.75\\ \:\mathrm{Interval\:Notation:}&\:(-\infty \:,\:\frac{11}{4}]\end{bmatrix}[/tex]

-5 and -6 are the solution values.

Step-by-step explanation:

Given the inequality

[tex]6\ge \:4x-5[/tex]

Let us solve the inequality

[tex]6\ge \:4x-5[/tex]

switch sides

[tex]4x-5\le \:6[/tex]

Add 5 to both sides

[tex]4x-5+5\le \:6+5[/tex]

Simplify

[tex]4x\le \:11[/tex]

Divide both sides by 4

[tex]\frac{4x}{4}\le \frac{11}{4}[/tex]

Simplify

[tex]x\le \frac{11}{4}[/tex]

Thus, the solution to the inequality is:

[tex]6\ge \:4x-5\quad :\quad \begin{bmatrix}\mathrm{Solution:}\:&\:x\le \frac{11}{4}\:\\ \:\mathrm{Decimal:}&\:x\le \:2.75\\ \:\mathrm{Interval\:Notation:}&\:(-\infty \:,\:\frac{11}{4}]\end{bmatrix}[/tex]

In our case, we are given the values -6, 8, and -5

We have already determined that the solution is x ≤ 2.75.

Since the solution is x ≤ 2.75, so -5 and -6 come under the solution set because -5 and -6 are less than 2.75.

Hence, -5 and -6 are the solution values.

The graph of the solution of the inequality is also attached below.

The solutions to the inequality 6 ≥ 4x − 5 is x ≤ 11/4.

What is inequality?

A statement of an order relationship-greater than, greater than or equal to, less than, less than or equal to- between two numbers or algebraic equations.

Now the given inequality is,

6 ≥ 4x − 5

Adding 5 both the side we get,

6 + 5 ≥ 4x − 5 + 5

⇒ 11 ≥ 4x

Dividing both the side by 4 we get,

11/4 ≥ 4x/4

⇒  11/4 ≥ x

or, x ≤ 11/4

this is the required solution of the given inequality.

Thus, the solutions to the inequality 6 ≥ 4x − 5 is x ≤ 11/4.

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holly has 368 pet pal cards Dara has 243 cards how much more does holly have then Dara

Answers

Answer:

125

Step-by-step explanation:

Answer:

125

Step-by-step explanation:

368 - 243 = 125

4x - 2y = 24
y=-3x - 2


someone help me?

Answers

Step-by-step explanation:

I've used substitution method over here and got the value of X and Y

Hi how is your day going

x2 = 36 solve for x please answer

Answers

Step-by-step explanation:

Given

x² = 36

x² =( +6)²

x = +6

Hope it will help :)

Answer:

x= 18

Step-by-step explanation:

Divide both sides by 2

2 and 2 cancel out

36/2=18

check that it fits

2 x 18=36

18 is correct

Hope this helps ^-^

kayden mixed two solutions together which causes a chemical reaction and the solution becomes warm. which statement best describes what has happened

A. energy has been transformed from one form to another

B. energy has been created, where it did not exist before

C. the chemicals energy of the solution had been described

D. more energy has been created than has been destroyed

Answers

The answer is B because before mixing the solution together nothing happened and it wasn’t warm, now that kayden mixed the solutions causing a chemical reaction making it to become warm. There for it will be B

According to law of conservation of energy, the statement  which best describes what has happened is that energy has been transformed from one form to another.

What is law of conservation of energy?

According to law of conservation of energy, it is evident that energy  is neither created nor destroyed rather it is restored at the end of a chemical reaction .

Law of conservation of mass and energy are related as mass and energy are directly proportional which is indicated by the equation E=mc².Concept of conservation of mass is widely used in field of chemistry, fluid dynamics.

Law needs to be modified in accordance with laws of quantum mechanics under the principle of mass and energy equivalence.This law was proposed by Julius Robert Mayer in the year 1812.

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chase bought his dream car ,a chevy corvette, for $58,735. sales tax is 5% where chase lives what is the total price chase paid for the corvette?

Answers

Answer:

$61,671.75

Step-by-step explanation:

There is a calculator called "Sales Tax Calculator" and if you put in your Before Tax Price and your Sales Tax Rate you will receive your answer of $61,671 and 75 Cents. ($61,671.75)

what is the precent of change from 12 to 19

Answers

Answer:

158%

Step-by-step explanation:

19/12 = 1.58

Whoever receives this get's the brainliest crown all you have to say is 1st

Answers

Answer:

1st

Step-by-step explanation:

1st !!!!!!!!!!!Lolllllllllll

what is (9m)4 without exponents

Answers

Answer:

The answer is 36m

Step-by-step explanation:

Multiply 9m by 4, and you'll get (9x4)m, which is (36)m, which can be simplified into 36m.

x varies directly with
y. If x = 60 when
y = 75. find x when
y = 32.

Answers

Answer:

x=17

Step-by-step explanation:

Answer:

25.6

Step-by-step explanation:

find constant of variation ('k'):

y = kx

75 = 60k

k = 75/60 or 5/4

32 = 5/4x

cross-multiply:

5x = 128

x = 25.6

please answer this question​

Answers

Answer:

activity2

1. ( 14.4) adn

2.(0.616) adn

3.( 5-36) adn

Find the Values of x and y

Answers

the answer is x = 2 and y = 17

Please help me solve this

Answers

Answer:

Q. 11 x=29

Q. 12 x=24

Step-by-step explanation:

Q.11

sum of all sides of triangle = 180°

(2x+20)+(x+10)+(2x+5)=180°

5x+35=180°

5x=180°-35

5x=145°

x=145/5

x=29°

Q.12

sum of all sides of triangle=180°

96+(2x)+(x+12)=180°

3x+108=180°

3x=180-108

3x=72

x=72/3

x=24

What he said is correct

here you can get free question answer things, so

1+0 = ?

u can get free “helped people”by this

Answers

Answer:

the answer is 1

........

1+0=1

Because anything plus zero equals itself (Example) :

3+0=3, 4+0=4, etc

Therefore

1+0=1

Have a good day!

Help I will be marking brainliest!!!!

A. 274
B. 300
C. 306
D. 316

Answers

Answer:

300 units

Step-by-step explanation:

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