What is a perfect square? Why is [tex]x^{2} + 8x +16[/tex] a perfect square?

Answers

Answer 1

Answer:

It is a perfect square. Explanation below.

Explanation:

Perfect squares are of the form

(

a

+

b

)

2

=

a

2

+

2

a

b

+

b

2

. In polynomials of x, the a-term is always x.(

(

x

+

c

)

2

=

x

2

+

2

c

x

+

c

2

)

x

2

+

8

x

+

16

is the given trinomial. Notice that the first term and the constant are both perfect squares:

x

2

is the square of x and 16 is the square of 4.

So we find that the first and last terms correspond to our expansion. Now we must check if the middle term,

8

x

is of the form

2

c

x

.

The middle term is twice the constant times x, so it is

2

×

4

×

x

=

8

x

.

Okay, we found out that the trinomial is of the form

(

x

+

c

)

2

, where

x

=

x

and

c

=

4

.

Let us rewrite it as

x

2

+

8

x

+

16

=

(

x

+

4

)

2

. Now we can say it is a perfect square, as it is the square of

(

x

+

4

)

.


Related Questions

PLS HELP I WILL GIVE BRAINLIEST THANK U PLSSS

Answers

The answer is A. A is not correct. B is correct. A is not correct because look at the lines on the angles. they don’t match up. But they do in B.
A is not correct because the angles are different

Can anyone help me with this question...please i really need your help....

(Express the variable in the brackets as the subject of formula​)

Answers

9514 1404 393

Answer:

  p = q/(2 -3q)

Step-by-step explanation:

  [tex]\dfrac{2p}{3p+1}=q \qquad\text{given}\\\\2p=q(3p+1) \qquad\text{multiply by the denominator}\\\\ 2p=3pq+q \qquad\text{eliminate parentheses}\\\\ 2p -3pq = q \qquad\text{subtract $3pq$}\\\\ p(2-3q)=q \qquad\text{factor out $p$}\\\\ \boxed{p=\dfrac{q}{2-3q}} \qquad\text{divide by the coefficient of p}[/tex]

HELPPP ME PLEASEEE!!!!

Answers

You need a common denominator in your case 2x4=8 ( because those are the demoninators) then 1x2=2 and 2x4=8 8/8 2/4 meaning it’s one half

Solve using substitution. x − 6y = –8 x + 6y = 16 please help imma fail

Answers

Answer:

x=−16/7

Step-by-step explanation:

happy to help ya :)

Answer:

x = 4, y = 2

Step-by-step explanation:

x - 6y = - 8 is the same as x = 6y - 8

sub that into x + 6y = 16 :

6y - 8 + 6y = 16

12y = 16 + 8

y = 2

sub that into x = 6y - 8:

x = 12 - 8 = 4

                     

please help and explain

is the square root of 16/9 rational or irrational
is 0.30300 rational or irrational?

Answers

Answer:

√169

Step-by-step explanation:

its is a rational, thats all I can help with

What is 73 x 4 + 13?

Answers

Answer:

73 x 4 + 13 is 305

Answer:

305

explaination:

73 x 4 = 292

292 + 13 = 305

Determine the geometric mean of 11 and 8.

Answers

Answer:

[tex]\sqrt{88}[/tex]

Step-by-step explanation:

The geometric mean of 11 and 8 is equal to [tex]\sqrt{88}[/tex].

According to the question it is clear that we have to calculate the geometric mean of two positive numbers 11 and 8.

The geometric mean of two positive numbers a and c is the positive number b in such a way that it satisfies the condition

[tex]\frac{a}{b}=\frac{b}{c}[/tex]

The geometric mean of a and b is √ab if a and b are both positive numbers and it will be −√ab if a and b are negative numbers.

The geometric mean is the positive square root of the product of two numbers.

For a square the geometric mean of two numbers a and b, is the length of one side of a square whose area is equal to the area of a rectangle with the sides of a and b lengths.

If we talk about the n numbers then the geometric mean is the nth root of the product of n numbers. If n positive values are given then the geometric mean is the nth positive root of the product of that n numbers.

So, the geometric mean is equal to [tex]\sqrt{a.b}[/tex]

Here, a = 11 and b = 8

The geometric mean of this is equal to = [tex]\sqrt{11.8}[/tex] = [tex]\sqrt{88}[/tex]

Learn more about geometric mean at:

https://brainly.com/question/29199001

#SPJ2

An ordinary dice is rolled. What is the probability that the number
of dots on the upper face is -
(a) 3
(c) an even no
(b) less than 3
(d) 7​

Answers

Answer:

A) 1/6

B) 1/3

C)1/2

D) 1/6

Answer:

1/6 , 1/3 , 1/2 , 0

Step by Step Explanation:

An ordinary die has numbers from 1 to 6

Number of dots on the face = number that face represent

Dots on face can be 1 , 2 , 3 , 4 , 5 , 6

1. Number of 3 Dots

Probaility = 1/6

2. Number of Dots less than 3 = 1 or 2 Dots

Probability = 2/6 = 1/3

3 . An even number = 2 , 4 , 6

Probability = 3/6 = 1/2

4 7 Dots not possible Hence

Probability = 0

Learn more:

A die is rolled. What is the probability that the number appearing on ...

brainly.in/question/4334466

An unbiased die is thrown .what is the probability of getting a ...

brainly.in/question/7707663

Chen rode his skateboard 3 1/4 miles in 1/2 of an hour. What was his average speed in miles per hour.

Answers

Answer:

6.5 MPH

Step-by-step explanation:

Since he rode his skateboard for half an hour, you must multiply 2, that way he rode 1 hour. Since you multiply the 1/2 hour, you must also multiply 3 1/4, to get 6 1/2, or 6.5. Even though we know he didn't ride a full hour, if he had, and at the same rate, he would have rode 6.5 miles per hour.

Hope this helps! ;)

A man with a height of 5ft casts a shadow of 2ft. What will be the height of a tree that casts a shadow of 40ft at the same time?

Answers

Answer:

19

Step-by-step explanation:

Answer:

100 ft.

Step-by-step explanation:

Let x = height of tree

height/height = shadow length/shadow length

5/x = 2/40

2x = 200

x = 100 ft.

In the rhombus,
mZ1 =15x, mZ2 = x+y, and m/3 =9z.
Find the value of each variable. The diagram
is not to scale.
2 | 1
a. x = 12, y = 84, z = 20
b. x = 6, y = 174, z = 20
c. X= 6, y = 84, z = 10
d. x = 12, y = 174, z = 10

Answers

For the M1 angle, we can conclude the size of angle is 90°. Do the angle equation like this :

15x=90

x = 90/15

x = 6

Do the same thing in M2 :

Subtitute the x value to equation, then evaluate the value by using 90 because it's the same.

x+y=90

6+y=90

y=90-6

y=84

M3 value is same, 90°

9z=90

9z/9 = 90/9

z=10

Hope this helps

Horse kg of grass in 12 days how much how much does he eat in 9 days​

Answers

Step-by-step explanation:

The horse eats 9/12 in 9 days.

-2 + b < 3





.............

Answers

Answer:

I believe we are solving for b. b<5

Step-by-step explanation:

25% of N is 12. Solve for N. Just put the number.

Answers

Answer:

25% of 48 = 12

Step-by-step explanation:

12 ÷ 25% = 12 ÷ 0.25 = 48

Answer: Divide each term by 25 % and simplify.

N = 48

Step-by-step explanation:

#2 Find the value of x. Round to the nearest degree.

Answers

Answer:

49°

Step-by-step explanation:

arccos x = 15/23

Name all the quadrilaterals that have the given property.


two pairs of parallel sides and all angles congruent


a

rectangle, square

b

trapezoid

c

rhombus, square

d

rhombus

Answers

Answer:

A) rectangle and square

Step-by-step explanation:

Answer:

A) rectangle and square

Step-by-step explanation:

 

 Hope it work

Brainliest plz

I am in need of help

Answers

Answer:

The last one

Step-by-step explanation:

best answer will get brainlist

Answers

Answer: 482x-4y%742

Step-by-step explanation: if you put the compexules and then you suntract then times the sublactus

HELP ASAP!!Solve for x. Enter the solutions from least to greatest.
X squared minus 5x minus 14=0
lesser x=
greater x=

Answers

x^2 - 5x - 14 = 0

what multiplies to negative 14 and adds to negative 5? -7 and positive 2.

(x - 7) (x + 2) = 0

Lesser x = -2
Greater x = 7

A number cube with faces labeled from 1 to 6 was rolled 20 times. Each time the number cube was rolled, the number showing on the top face was recorded. The table shows the results.


Based on these results, what is the experimental probability that the next time the number cube is rolled it will land with 5 or 6 showing on the top face?



PLEASE ANSWER ASAP!!!

Answers

Step-by-step explanation:

dkdjfjfjfjureuwuweee

What is the percentage of sugar in the syrup made of 10kg of water and 5kg of sugar? Hi and have a good day :D

Answers

Answer:

33.33%

Step-by-step explanation:

the syrup has a total of 15kg of ingredients, 5kg of it is sugar, so 15/5 which will end as 33.33%

Answer:

33.33%

Step-by-step explanation:

the syrup has a total of 15kg of ingredients, 5kg of it is sugar, so 15/5 which will end as 33.33%

11. If AB = BC and BC = CD, which property shows AB = CD?

Answers

Answer:

i belive its the transitive property

sry if im incorrect

There are 6 balls. Half of the balls are blue. One ball is red. The rest are green. Write the fraction for the green balls.

Answers

2/6 of the balls are green or 1/3

Answer:

1/3 (Minimized) 2/6

Step-by-step explanation:

5/7=12/y solve for y.

Answers

I believe the answer is 84/5

Answer:

Step-by-step explanation:

5/7 = 12/y

5y = 84

y = 84/5

14 =2b HELP ME PLEASE

Answers

Answer:

The answer is b = 7

Step-by-step explanation:

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

~Hoped this helped~

Divide 2b by 2 to get b. Then divide 14 by 2 to get 7. b=7

solve CORRECTLY for brainly and 20 points

Answers

Answer:

k/4 + 3 = 14

k = 44

Step-by-step explanation:

Step 1: k + 12 = 56

Step 2: k = 56 - 12

Step 3: k = 44

Multiply both sides of the equation by 4Subtract from both sidesSubtract 12 from 56 to get 44

Answer:

The answer are

t=4

f=4

e=2

k=44

a=-4

n=11


[tex] {x}^{3} - 3 {x}^{2} + x - 3[/tex]
how do I solve for x?​

Answers

Answer:(x−3)(x^2+1)

Step-by-step explanation:

(x + 7)^2 – 11 = 0
lesser =
greater =

Answers

Answer:

Lesser = -[tex]\sqrt{11}[/tex] - 7 = -10.317

Greater = +[tex]\sqrt{11}[/tex] - 7 = -3.683

Step-by-step explanation:

I am assuming you are asking for the lesser x solution and greater x solution.

(x + 7)^2 – 11 = 0

(x + 7)^2 = 11

x+7 = ±[tex]\sqrt{11}[/tex]

x = ±[tex]\sqrt{11}[/tex] - 7

Lesser = -[tex]\sqrt{11}[/tex] - 7 = -10.317

Greater = +[tex]\sqrt{11}[/tex] - 7 = -3.683

Answer:

lesser= -14

greater= 0  (:

Solve - x/6 less than or equal to 3

Answers

Answer: x is greater than or equal to 18

Step-by-step explanation:

Answer:

x ≤ - 2

Step-by-step explanation:

- x/6 ≤ 3

- x/2 ≤ 1

- x ≤ 2

x ≤ - 2

i need helpppppppppppppp​

Answers

Answer:

B

Step-by-step explanation:

Factor out 1/4.

1/4 - 3/4 x = (1/4)(1 - 3x)

Answer: B

b because 1/4*1 = 1/4 and 1/4*-3 = -3/4
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