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

5 consecutive odd number between 40 and 60​

Answers

Answer:

47 49 51 53 55

Step-by-step explanation:

Consecutive: following one another in uninterrupted succession or order; successive: six consecutive numbers, such as 5, 6, 7, 8, 9, 10. marked by logical sequence. Grammar. expressing consequence or result: a consecutive clause.

Odd number between 40 and 60​: 41, 43, 45, 47, 49, 51, 53, 55, 57, 59

Answer:

The answer is 41, 43, 47, 49 and 51

Write your answer in scientific notation.
(5.1x10^7)+(1.3 x 10^6)

Answers

the answer is 5.23*10^7

One half of a watermelon is shared among 6 people what is the fraction of how much each will get?

Answers

Answer:

1/12

Step-by-step explanation:

In comparing the two written forms of a sequence, which is easier to find a50, the explicit form or the recursive form?

Answers

Answer:

Explicit

Step-by-step explanation:

Given

[tex]Term: a_{50[/tex]

Required

Explicit or Recursive; which is easier

The explicit form is easier.

Take for instance, the explicit form of the sequence is:

[tex]a_n = 2n + 1[/tex]

And the recursive form is:

[tex]a_n = a_{n-1} + 2[/tex]

To find [tex]a_{50}[/tex] in [tex]a_n = 2n + 1[/tex]

You simply substitute 50 for n and then solve for [tex]a_n[/tex]

Which gives:

[tex]a_{50} = 2*50 + 1 = 101[/tex]

The case is different in: [tex]a_n = a_{n-1} + 2[/tex]

First, you substitute 50 for n

[tex]a_{50} = a_{50-1} + 2[/tex]

[tex]a_{50} = a_{49} + 2[/tex]

Next, you need to calculate a49.

This action continues until you get to a1

Then you evaluate the corresponding expressions from a1 to a49 before you get a50.

Hence, the explicit form is easier.

In a recent survey of 655 working americans ages 25-34, the average weekly amount spent on lunch was $43.29 with standard deviation $2.75. The weekly amounts are approximately bell-shaped

Answers

Answer:

99.7%

Step-by-step explanation:

Given that:

sample size (n) = 655

sample mean ([tex]\overline x[/tex]) = 43.29

Standard deviation [tex]\sigma[/tex] = 2.75

Let's assume we are to estimate the percentage between $33.72 and $51.54

Then;

The test statistics at 33.72 is :

[tex]Z = \dfrac{X - \mu}{\sigma}[/tex]

[tex]Z = \dfrac{33.72 -43.29}{2.75}[/tex]

[tex]Z = -3.48[/tex]

Z at 51.54

[tex]Z = \dfrac{X - \mu}{\sigma}[/tex]

[tex]Z = \dfrac{51.54 -43.29}{2.75}[/tex]

[tex]Z = 3.00[/tex]

Using the empirical standard rule, the percentage will be 99.7%

AP Calc BC help!
Can someone explain how to do these problems? I care more about the explanation than the actual answer! My course never taught me how to do these kinds of problems.
Thank you!!

Answers

Answer:

Question 1) 72

Question 2) 40

Question 3) Both C and D.

Question 4) Both A and C.

Step-by-step explanation:

Question 1)

We are given that:

[tex]\displaystyle \int_1^5f(x)\, dx=8\text{ and we want to find} \int_1^5xf'(x)\, dx[/tex]

We will use integration by parts, given by:

[tex]\displaystyle \int_a^b u\, dv=uv-\int_a^b v\, du[/tex]

We will let:

[tex]u=x\Rightarrow du=dx\text{ and } dv=f'(x)\, dx \Rightarrow v=f(x)[/tex]

Therefore:

[tex]\displaystyle \int_1^5xf'(x)\, dx=xf(x)\Big|_1^5-\int_1^5f(x)\, dx[/tex]

Substitute:

[tex]\displaystyle \int_1^5xf'(x)\, dx=(5(f(5))-(1(f(1))-(8)[/tex]

Evaluate:

[tex]\displaystyle \int_1^5xf'(x)\, dx=75-(-5)-8=72[/tex]

Question 2)

Similarly, we will let:

[tex]\displaystyle u=x\Rightarrow du=dx\text{ and } dv=f'(x)\, dx \text{ so } v=f(x)[/tex]

Hence:

[tex]\displaystyle \int_0^3 xf'(x)\, dx=xf(x)\Big|_0^3-\int_0^3f(x)\, dx[/tex]

Evaluate:

[tex]\displaystyle \int_0^3 xf'(x)\, dx=(3f(3))-(0(f(0))-(2)[/tex]

Thus:

[tex]\displaystyle \int_0^3 xf'(x)\, dx=3(14)-2=40[/tex]

Question 3)

We are given:

[tex]\displaystyle g(x)=\int_4^xf(x)\, dx[/tex]

By the Fundamental Theorem of Calculus:

[tex]g'(x)=f(x)>0[/tex]

The derivative of g is always positive. So, the values of g are always increasing.

The tables that reflect this are C and D.

And there are, as I understand it, no way to determine their exact values. Both C and D are correct.

Question 4)

Similarly, we are given:

[tex]\displaystyle g(x)=\int_{-2}^xf(x)\, dx[/tex]

By the FTC:

[tex]g'(x)=f(x)<0[/tex]

So, g should be decreasing for all x.

The tables that reflect this are A and C.

So, both A and C are correct.

please help me I will give brainlist

Answers

Answer:

3 + 2n

Step-by-step explanation:

2 + 1 = 3.

2n cannot be added into this because it has a letter in front of it. Therefore, it stays on its own.

2n + 3

1 and 3 are like terms, and because there are no more variables, the 2n will stay alone :)

What are the answers
2x = 10; x=?

-3x = 21;x=?

1/3x=6; x=?

-1/2x = -7;x?

Answers

Answer:

1) 5 2)7 3)18 4) 14

Step-by-step explanation:

Find (-5x + 6) - (-2x - 7)

Answers

The answer is: -3x +13

I need help with this question!

Answers

Answer:

sorry but don't know this answer

What is the ratio of the length of the rectangle to its width. 24 and 20

Answers

6:5 is the ratio
Hope this helps!

If the cocoa to water ratio for a hot chocolate recipe is 1 tablespoon cocoa to 1⁄4 cup water, how much cocoa do you need if you use 1.5 cups of water?

Answers

6 tablespoons of cocoa for 1.5 cups of water

Can someone solve these for me I have no idea what to do and it has to be turns in within an hour

Answers

Answer:

Step-by-step explanation:

Subtract second equation from first equation to eliminate x

2x+6y-2x+10y=17-9

16y=8

y=1/2, use either original equation to solve for x

2x+6y=17 becomes

2x+6(1/2)=17

2x+3=17

2x=14

x=7 so the solution is the point (7, 1/2)

We can multiply the first by -2 and add it to second equation to eliminate x.

-2(3x-4y)+6x+3y=-2(-10)-42

-6x+8y+6x+3y=20-42

11y=-22

y=-2 using 3x-4y=-10 becomes

3x-4(-2)=-10

3x+8=-10

3x=-18

x=-6 so the solution is the point (-6,-2)

So you should be able to see how to solve the other two.

Answer:

Question 1: x = 7, y = [tex]\frac{1}{2}[/tex]

Question 2: x = -6, y = -2

Question 3: x = -1, y = 9

Question 4: There is no solution.

I don't understand how to do this problem 3x + y =9

Answers

Answer:

35

Step-by-step explanation:

A movie theater is offering a special summer pass. Passholders pay $8 per movie for the first 5 movies and watch additional movies for free, up to a maximum of 15 movies. The function C gives the total cost, in dollars, for a passholder to watch n movies.
Is function C a piecewise function? Explain your reasoning.

Answers

probably it's 8 or 4. and as $8 is the initial fee, that sounds like the starting value. :-)

the line equation you need is the slope intercept form y = mx + b where m = gradient and b = y intercept.

in this case, y = 4x + 8 where x = number of movies seen, and y = total cost in $

for this line m = 4 and b = 8. hence, indeed, the y intercept is 8

Mark as brainlist

Answer:

Step-by-step explanation:

C is a piecewise function because it represents more than one type of deal.

hi can u please help solve this. something with conjugnates.

Answers

Answer:

Use mathcway its 2 ez with that page trust me bro

Step-by-step explanation:

No cap

5 10 okey espero te sirva

answer Pls Gyys Options i ​

Answers

Answer:

Step-by-step explanation:

1301/100 is the correct answer

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

6/3 + -1/6 reduce this equation to the simplest form

Answers

Answer:

12/6-1/6=11/6 simplified to 1 5/6

Step-by-step explanation:

to make this easier make sure all fractions have the same denominator 6/3x2/2=12/6 since they now have the same denominator add 12/6+-1/6=11/6

adding a negative(6/3+-1/6) is the same as subtracting a positive(6/3-1/6)

Answer:

1 5/6

hope this helps :)........

a worded math problem that = 5

Answers

Answer:

Seven take away two is equals to five

Step-by-step explanation:

Because,

Seven take away two is equals to five

is the same to

7 - 2 = 5

Select the correct answer from each drop-down menu. Simplify the given polynomial and use it to complete the statement. The polynomial simplifies to an expression that is a with a degree of .

Answers

Answer:

The answer is below

Step-by-step explanation:

Select the correct answer from each drop-down menu. Simplify the given polynomial and use it to complete the statement.

(-5x² - 2x + 4) + (8x² - x - 1) + (x + 2)(x - 5)

.The polynomial simplifies to an expression that is a____

A.quadratic

B.liner

C.constany

A.trinomial

B.binomial

C.monomial

with a degree of____

A.1

B.2

C.0

Solution:

A polynomial is an expression involving operations of addition, subtraction, multiplication, exponents which consists of variables and their coefficient. A trinomial is a polynomial consisting of three terms, while a binomial consist of two terms and a monomial consist of one term.

The degree of a polynomial is the highest degree of any of the terms of the polynomial. If it has a degree of 0 it is a constant, a degree of 1 it is linear while for a degree of 2 it is quadratic.

(-5x² - 2x + 4) + (8x² - x - 1) + (x + 2)(x - 5)

= (-5x² - 2x + 4) + (8x² - x - 1) + (x² -5x + 2x - 10)

= (-5x² - 2x + 4) + (8x² - x - 1) + (x² - 3x - 10)

= (-5x² + 8x² + x² - 2x - x - 3x + 4 - 1 - 10)

= 4x² - 6x - 7

Therefore:

.The polynomial simplifies to an expression that is a quadratic trinomial of degree 2.

hey can u answer my math question look atbthe picture to see
the pic.​

Answers

Answer:

4 3/4 yards

Step-by-step explanation:

5 1/4 + 2 1/2 = 7 3/4

(1/2 is equal to 2/4)

12 1/2 - 7 3/4 = 4 3/4

Hope this helps, mark me brainliest if it does! :)

Answer:

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

Jotted Solution:

circumference and area of radius 42

Answers

Answer:

Area = 5542.488 unit^2

Circumference= 263.9 units

Step-by-step explanation:=

Given data

Radius= 42 units

Circumference= 2πr

C= 2*3.142*42

C=263.9 units

Area= πr^2

A= 3.142* 42^2

A= 3.142* 1764

A= 5542.488 unit^2

answer asap!!! PLS HELP.
what is the value of x in the figure??
a. 90
b. 60
c. 120
d. 30

Answers

Answer:

Step-by-step explanation:

the x is 30

60=2x

x=30

Answer:

d

Step-by-step explanation:

its d i think

Find the slope of the line represented by the table of values.
A)
12
5
B)
D)

Answers

Answer:

B 4456448444424346464646464664646464

solve : 105/103 = _____

Answers

Answer:

1.02

Step-by-step explanation:

the square of a number is 16 do you know the number

Answers

Answer:

4

Step-by-step explanation:

4 squared, which is the same thing as 4 times 4, is 16.

[tex]4^2=16[/tex]  or [tex]4 * 4 = 16[/tex]

you can check your answer by finding the square root of 16.

[tex]\sqrt{16}=4[/tex]

i hope this helps! have a nice day <3

EDGE20 ASSIGNMENT, WILL MARK BRAINLIEST FOR WHOLE ASSIGNMENT Quadratic in Form Polynomials
Assignment
Active
Practice writing as a quadratic.
ASSIGNMENT

Answers

Answer:

[tex] \bold{ \red{{y}^{2} + 7y - 8 = 0}}[/tex]

Step-by-step explanation:

[tex] {(3x + 2)}^{2} + 7 {(3x + 2)} - 8 = 0 \\ \\ plug \: (3x + 2 )= y \\ \\ so \: above \: quadratic \: equation \: \\transforms \: to \\ \\ \bold{ \red{{y}^{2} + 7y - 8 = 0}}[/tex]

A spherical balloon has a diameter of 4 feet. Approximate how many cubic feet of air this balloon holds. Use 3.14 as an approximation for pie, and give a numerical answer.

Answers

Answer:

3.764

Step-by-step explanation:

just try matgs is a tough de partoe

¿ Cómo surge la estadística?

Answers

Answer:

surgiendo dah

jjhhjjklnt7ikkkkvvh

Answer:

Los métodos matemáticos de la estadística surgieron de la teoría de probabilidades, la cual tiene sus raíces en la correspondencia entre Pierre de Fermat y Blaise Pascal (1654). ... En su libro, Bernoulli introdujo la idea de representar certeza completa como el número 1 y la probabilidad como un número entre cero y uno.

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What questions do you think remain unanswered in "The Wife's Lament"? Temperature transducers of a certain type are shipped in batches of 50. A sample of 60 batches was selected, and the number of transducers in each batch not conforming to design specifications was determined, resulting in the following data: 2 1 2 4 0 1 3 2 0 5 3 3 1 3 2 4 7 0 2 3 0 4 2 1 3 1 1 3 4 1 2 3 2 2 8 4 5 1 3 1 5 0 2 3 2 1 0 6 4 2 1 6 0 3 3 3 6 1 2 3Required:a. Determine frequencies and relative frequencies for the observed values of x = number of nonconforming transducers in a batch.b. What proportion of batches in the sample have at most six nonconforming transducers?c. What proportion have fewer than six? (Enter your answer to three decimal places.)d. What proportion have at least six nonconforming units? 5 functions of the secretary of of state in the british colonial adminstration The Strange Machine My uncle is an inventor. One day, I was sedarching through the attic of my uncle's house. I found a very strange machine with buttons, knobs, dials, and levers. I had never seen a machine like it before. On one side there was a button that said 'on.'Directions: After reading the introduction (beginning) to "The Strange Machine," write a body (middle) and a conclusion (end). Make sure the story is logical and has a good flow with the existing paragraph. Use details and descriptive words to make your writing interesting. Make sure to indent each paragraph and proofread your work. how does afforestation help to control and landslide Chloe has 85 floral beads. She uses 4 floral beads to make each bracelet. She makes as many bracelets as possible. How many floral beads will she have left? According to monetary theory, which of the following is the main driver in changing economic activity? A. Exchange rate B. Money supply C. Taxes D. Employment rate a b c d e f g h i j k l m n o p q r s t u v w x y z Because most of the parts for its irrigation systems are standard, Waterways handles the majority of its manufacturing as a process cost system. There are multiple process departments. Three of these departments are the Molding, Cutting, and Welding departments. All items eventually end up in the Packaging Department, which prepares items for sale in kits or individually. The following information is available for the Molding department for January. Work in process beginning: Units in process 24,100 Stage of completion for materials 80% Stage of completion for labor and overhead 30% Costs in work in process inventory: Materials $168,470 Labor 68,020 Overhead 17,160 Total costs in beginning work in process $253,650 Units started into production in January 59,800 Units completed and transferred in January 58,300 Costs added to production: Materials $281,593 Labor 311,150 Overhead 60,120 Total costs added into production in January $652,863 Work in process ending: Units in process 25,600 Stage of completion for materials 50% Stage of completion for labor and overhead 10%Required:Prepare a production cost report for Waterways using the weighted-average method. Please help with ALEKS >-< .................................. A tractor pulls a 1,000 kg wagon with a force of 4,000N. What is the wagons acceleration in m/s2? * Which pair of numbers has a sum of 100? ( A) 39,61(B) 49,61(C) 59, 51(D) 39,51 4. Los derechos humanos se clasifican en dos grandes grupos que se recogen en dos tratados distintos edectadosdespus de la DUDH.a-Derechos primarios y derechos secundarios-Derechos civiles y polticos, y derechos econmicos, sociales y culturalesDerechos fundamentales y derechos integrales Michael ordered the food and drinks below for himself and three friends. 3 hot dogs for $2.99 each 3 bags of French fries for $1.99 each 2 hamburgers for $3.99 each 4 drinks for $0.79. Michael and his friends will share the total cost of the food and drink equally. What was the cost per person? true or false:Bills may start in either house of Congress. Please help me with How did North Carolina contribute to World War I the force required to lift a load of 800 Newton by using a Lever having a mechanical advantage of 1.6 is Figure A is original and Figure B is the copy. can someone pls help me? the due is tmrrw