WILL MARK BRAINLIEST
If a + b = 10, and ab = 16, then find the value of the following: i .a2 + b2 ii. a3 – b3

Answers

Answer 1

Answer:

a² + b² = 68

a3 + b3 = 520

Step-by-step explanation:

Given :

a + b = 10 (1)

ab = 16 (2)

A. Find a² + b²

(a + b)² = a² + 2ab + b² (3)

Substitutite the values of (1) and (2) into (3)

(10)² = a² + 2(16) + b²

100 = a² + 32 + b²

Subtract 32 from both sides

100 - 32 = a² + b²

a² + b² = 68

B. a^3 + b^3

(a + b)^3 = a^3 + b^3 + 3ab(a + b)

(10)^3 = a^3 + b^3 + 3*16(10)

1000 = a^3 + b^3 + 480

a^3 + b^3 = 1000 - 480

a3 + b3 = 520


Related Questions

Find the square root of 1764 using prime factorization with explanation and solution.

Answers

Answer:

42

Step-by-step explanation:

The product of the prime factors of 1764 is

1764 = 2² × 3² × 7² , thus

[tex]\sqrt{1764}[/tex]

= [tex]\sqrt{2^{2}(3^{2} )(7^{2} ) }[/tex]

= [tex]\sqrt{2^{2} }[/tex] × [tex]\sqrt{3^{2} }[/tex] × [tex]\sqrt{7^{2} }[/tex]

= 2 × 3 × 7

= 42

Water Use
50
40
30
Water used (gal)
20
10
O
2 4 6 8 10
Time (min)
O y = 10x
O y = 5x
O y=1/10
O y = 1/5



HEEELLLLPPPP MEEEE ASAP!!!!!!!!!!!

Answers

The answer to your question would be B

I need an answer asap! ​

Answers

Answer:

Step-by-step explanation:

(x + 11)/-2 = -8

x + 11 = 16

x = 5

All 60 students in the seventh grade must choose a fall sport in which they will participate. If 2/5 of them choose volleyball, 25% of them choose soccer, and the remainder choose softball, how many students choose softball?

Answers

Answer:

21

Step-by-step explanation:

24 play volleyball

15 play soccer

Softball= 60-(24+15)=21

or

2/5 = 40%

100% -(40+25)= 35%

60x0.35=21

Angle A equals 30 degrees side a equals 7 and side b equals 12

Answers

Answer:

to make chocolate milk, the lunch lady uses 4 cups of white milk for each cup of chocolate milk

Step-by-step explanation:

Side c = 11° (hope this is the answer u were looking for)

What value of x is in the solution set of 2(3x - 1) = 4x - 6?
EO
-10

Answers

Answer:

D) -1

Step-by-step explanation:

6x-2≥4x-6

6x-4x≥-6+2

2x≥-4

x≥-4÷2

x≥-2

Only -1 is greater than -2 in the list.

Answer:

x = - 1

Step-by-step explanation:

Given

2(3x - 1) ≥ 4x - 6 ← distribute parenthesis on left side

6x - 2 ≥ 4x - 6 ( subtract 4x from both sides )

2x - 2 ≥ - 6 ( add 2 to both sides )

2x ≥ - 4 ( divide both sides by 2 )

x ≥ - 2

The only value in the list greater than - 2 is - 1

x = - 1 is in the solution set

Mount Kosciuszko is the highest mountain in Australia, with a peak of about 2,228 meters above sea level. Lake Erye has the lowest point at 15 meters below sea level. What is the difference in elevation between Mount Kosciuszko and Lake Eyre? You must show your work on your sheet on notebook paper.
A)2,243
B)2,213
C)2,250
D) 2,210​

Answers

Answer:

Option (A)

Step-by-step explanation:

Heights above the sea level are denoted with positive notations and depths below the sea level with negative.

Height of the highest peak of the mountain = +2228 meters

Lowest point of the lake = -15 meters

Difference between these elevations = 2228 - (-15)

                                                              = 2243 meters

Therefore, Option (A) will be the correct option.

5. Tinh Tran is a physical therapist. He earns $49,830 a year and is
single with no dependents. The state income tax rate is 5% of
taxable income. What amount is withheld from his biweekly
pay for state income tax?

Answers

Answer:

2491.50$ oooooooooooooooooooooooo

The amount withheld from his biweekly pay for state income tax is $2491.5.

What is the percentage?

The percentage is defined as a ratio expressed as a fraction of 100.

What are Arithmetic operations?

Arithmetic operations can also be specified by subtracting, dividing, and multiplying built-in functions.

We have been given that the physical therapist earns $49,830 a year and is single with no dependents.

To determine the amount withheld from his biweekly pay for state income tax.

Since the state income tax rate is 5% of taxable income.

So the amount withheld from his biweekly pay for state income tax as:

⇒ 5 % of 49,830

⇒ (5/100)49,830

⇒ (0.05)49,830

⇒ 2491.50

Therefore, the amount withheld from his biweekly pay for state income tax is $2491.5.

Learn more about the percentages here:

brainly.com/question/24159063

#SPJ2

WILL GIVE BRAINLIEST! LOOK AT THE IMAGE ATTACHED!

Answers

Answer:

x²-√3 x+1/2

Step-by-step explanation:

(√3-1)/2 and (√3+1)/2

the quadratic equation:

x²-(sum of the root)x +product of the roots

x²-((√3-1)/2 + (√3+1)/2)x+((√3-1)/2) )(√3+1)/2)

x²-(2√3/2)x+ (3-1)/4

x²-√3 x+1/2

x²-x√3 +1/2

If you're going 60 miles per hour, how many hours is that? So, in other words, what does "per" mean? How many is "per"?

Answers

Answer:

Per pretty much means 1. So for example if I say I'm going 12 miles PER hour it means 12 miles every 1 hour.

Please help! I dont understand this, I will give 15 points!

Answers

Answer:

Step-by-step explanation:

common denominator is the multiplication of the two denominator or the least common multiple of the two

                    common denominator 24              10                 12

13/24 +7/12                   ☑ ☑

7/6+(-5/12)                                                                                  ☑  ☑

-3/4+(-2/3)                                                                                  ☑  ☑

5-7/10                                                                     ☑  ☑

1/8 - 5/3                          ☑  ☑

3/2 - 4/5                                                                  ☑  ☑

Distribute to find the product:(p+3)(2p - 1)
B
2p2 + 5p-3
A
7p-3
С
2p2 +p-3
D
9p + 3

Answers

Answer:

B. 2p² + 5p -3

Step-by-step explanation:

Foil method:

2p² -p + 6p -3

2p² + 5p -3

Which of the following is NOT a subset of the rational numbers

Integers
Whole Numbers
Perfect square integers
Irrational numbers

Answers

Whole numbers is the correct answer

f(5)= 2(5)+ 4
Thanks

Answers

Answer: I HOPE IT HELPS OR WATCH  VIDOES  ABOUT IT

Step-by-step explanation:

Two unique points define a line.  Other geometric figures also may pass through those two points (you will learn those later).

There are several forms of the equation of a line:

     Standard form                           Ax + By = C

     Slope-intercept form                  y = mx + b

     Point-slope form                        y – y1 = m(x – x1)

     Two-point form              y – y1 = [ (y2 – y1)/(x2 – x1) ](x – x1)

O.K., you picked the two-point form, right?    

               The points are  P1:  (5,5) and P2: (7,-4)

    y - 5 = [ ((-4) - 5)/(7 - 5) ] (x - 5)          (put in x and y values of points)

    y - 5 = [  -9 / 2 ](x - 5)                         (simplify)

    y - 5  =  -9/2x  + 45/2                           (distribute -9/2)

     y =  f(x) = -9/2x + 55/2                   (add 5 to both sided)

Check (very important):

  Is (5,5) on the line?      5 = (-9/2)(5) +  55/2  ?

                                         5 =  -45/2   +  55/2  ?

                                          5 =  10/2         yes.

  Is (7,-4) on the line?     -4 = (-9/2)(7) + 55/2       ?

                                          -4  =  -63/2   + 55/2   ?

                                          -4  =   -8/2   ?       yes.

Let C be between D and E. Solve for x
DC = 5x + 8
CE = 3x + 5
DE = 61

Answers

DE/2 = 30.5
CE=30.5
DC=30.5

3x + 5 = 30.5
3x = 30.5 - 5
3x = 25.5
25.5/3 =8.5
x=8.5

- 60= - 24 + 12r
How do I solve this problem and what are the steps to solve the problem

Answers

Answer:

r = -3

Step-by-step explanation:

- 60= - 24 + 12r

Add 24 to each side

- 60+24= - 24+24 + 12r

-36 = 12r

Divide each side by 12

-36/12 = 12r/12

-3 =r

6x+2y=12 how do I show my work solve for y :) please help me

Answers

Answer:

x=2

Step-by-step explanation:

6x+2y=12

6x+2x0=12

6x+0=12

6x=12

x=2

Use the distributive Property to simplify: (x-7)(x-8)

Answers

Answer:

[tex]x^2-15x+56[/tex]

Step-by-step explanation:

Use the FOIL distributive method: [tex]\left(a+b\right)\left(c+d\right)=ac+ad+bc+bd[/tex]

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

Thus, [tex]\left(x-7\right)\left(x-8\right)=x\times x +x\left(-8\right)+\left(-7\right)x+\left(-7\right)\left(-8\right)[/tex]

Multiply them to get:

[tex]x^2-8x-7x+56[/tex]

[tex]x^2-15x+56[/tex]

I don't know. can someone help please??​

Answers

A if I’m not mistaking

Can the common ratio of geometric sequence be equal to 0?

Answers

Answer:

No it cant

Step-by-step explanation:

it cant

The pre-image is...
What does a pre image mean

Answers

Answer:

i think it means pre image (plural pre images) (mathematics) For a given function, the set of all elements of the domain that are mapped into a given subset of the codomain; (formally) given a function ƒ : X → Y and a subset B ⊆ Y, the set ƒ−1(B) = {x ∈ X : ƒ(x) ∈ B}. The pre image of under the function is the set .

Step-by-step explanation:

Answer:

I forgot what the letter was for this option but The Pre image is a geometric shape BEFORE a transformation occurs ( I think that's option B but u should read it to be sure)

Step-by-step explanation:

Hope this helps I was kinda paying attention

I NEED HELP !!!!!!!!!

Answers

Answer:

b

d

e

Step-by-step explanation:

the standar form is

[tex]ax^{2} +bx+c=0[/tex]

so it's

[tex]0.5x^{2} -3.2x+5.8=0\\\\-x^2-3x+20=0\\\\\frac{1}{2}x^2+4x-3=0\\\\[/tex]

only that

42 is 6 times larger than which number

Answers

Answer:

The answer is 7

Step-by-step explanation:

6*7=42

Answer:

252

Step-by-step explanation:

42 x 6 = 252

To cheek the answer: 252 ÷ 42 = 6

a patio has an area of 120 square feet. the length of the patio is 12 feet. what is its width

Answers

Answer:

w = 10 feet

Step-by-step explanation:

Area formula

A = l×w

120ft² = 12ft×w

w = 120ft²/12ft

w = 10 feet

is an example of _____.

Answers

Answer:

The distributive property

Step-by-step explanation:

The equation 3+7x

URGENT PLS HELP

BD bisects ABC. Find each of the following
1. Find the measure of angle ABD if the measure of angle ABD = 6x + 4 and
the measure of angle DBC = 8x - 4
2. Find the measure of angle ABC if the measure of angle ABD = 5y - 3 and the
measure of angle DBC = 3y + 15.

Answers

I hope this helps. If you are still confused just tell me and I’ll explain it again

Find the value of x for the following situation: the line containing (8,7) and (7,-6) is perpendicular to the line containing (2,4) and (x,3)

Answers

Answer:

x=14

Step-by-step explanation:

Answer: x=14

Step-by-step explanation:

Find JH if I is the midpoint.

Answers

Answer:

158

Step-by-step explanation:

If I is the midpoint of JH, JI= IH

JH= JI +IH

JH= JI +JI (subst. IH= JI)

JH= 2(JI)

Since JI= 79,

JH= 2(79)

JH= 158

What is the square root of 1/23?

Answers

0.04347826086

Step-by-step explanation:

this is the anwser,just round to whatever you need to

Answer:

0.20851

Step-by-step explanation:

[tex]\sqrt{\frac{1}{23} } \\\\Refine \\=0.20851\dots[/tex]

The ratio of teachers to students in the eighth grade it’s in proportion to the ratio of teacher to students in the entire school. If the eighth grade has four teachers and 84 students, how many students are there if there are 25 students in the entire school?

Answers

Answer:

525 students

Step-by-step explanation:

84/4 is 21. The ratio is 1 teacher to every 21 students. There are 25 teachers in the entire school. If you multiply that by 21, there are 525 students in the entire school.

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