Which long division problem can be used to prove the formula for factoring the difference of two perfect cubes?

Answer:

[tex]Area = 60x - x^2[/tex]

Step-by-step explanation:

Given

[tex]Perimeter = 120[/tex]

[tex]Side\ 1 = x[/tex]

Required

The area of the garden

First, we calculate the length of the other side using:

[tex]Perimeter = 2 *(Side\ 1 + Side\ 2)[/tex]

This gives:

[tex]120 = 2 *(x + Side\ 2)[/tex]

Divide both sides by 2

[tex]60 = x + Side\ 2[/tex]

Make Side 2 the subject

[tex]Side\ 2 = 60 - x[/tex]

So, the area of the garden is:

[tex]Area = Side\ 1 * Side\ 2[/tex]

[tex]Area = x * (60 - x)[/tex]

Expand

[tex]Area = 60x - x^2[/tex]

Answer:

B) 5

Step-by-step explanation:

We are given the function:

[tex]f(x)=x(x+3)[/tex]

We are given that f(a) = 40 and a > 0 and we want to determine the value of a.

Substitute:

[tex]f(a)=40=a(a+3)[/tex]

Distribute:

[tex]a^2+3a=40[/tex]

Subtract 40 from both sides:

[tex]a^2+3a-40=0[/tex]

We can factor using 8 and -5. Hence:

[tex](a+8)(a-5)=0[/tex]

By the Zero Product Property:

[tex]a+8=0\text{ or } a-5=0[/tex]

Solve for each case:

[tex]\displaystyle a=-8\text{ or } a=5[/tex]

Since a > 0, we can eliminate the first solution. Hence:

[tex]a=5[/tex]

Our answer is B.

Hi!

y = ax + b

y = 14x + 2 → a = 14 ∧ b = 2

Parallel lines have the same slope factor (a) so line parallel to the line with the equation y = 14x + 2 will be y = 14x - 12

Answer:

option 4

Step-by-step explanation:

The equation of a circle in standard form is

(x - h)² + (y - k)² = r²

where (h, k) are the coordinates of the centre and r is the radius

(x + 1)² + (y - 12)² = 25 ← is in standard form

with centre = (- 1, 12 ) and radius = [tex]\sqrt{25}[/tex] = 5

Answer:

Step-by-step explanation:

[tex]\dfrac{7}{25} =0.28=28\%\\\\\dfrac{2}{3} \approx 0.67=67\%\\\\\dfrac{3}{8} =0.375=37.5%[/tex]

Answer:

15

Step-by-step explanation:

Use the distributive property

4x+4=64, then subtract

4x=60, then divide

x=15

[tex] \huge\boxed{\mathfrak{Answer}}[/tex]

[tex]4(x + 1) = 64 \\ 4x + 4 = 64 \\ 4x = 64 - 4 \\ 4x = 60 \\ x = \frac{60}{4} \\ x = 15[/tex]

=> The answer is 15.

Answer:

6

Step-by-step explanation:

Follow 1 hour on the y axis to where it meets the line of best fit. In this case it is about 6 puzzles.

Answer:

Correct answer 1

Step-by-step explanation:

Answer:

1.3

Step-by-step explanation:

The Rest Of Them Are Writen As Fractions

Answer:

[tex]\sqrt{10}[/tex]

NOTE: the other answer is WRONG...

irrational means can not be written as a fraction (with whole numbers)

4/3 = 1.33333333333

Step-by-step explanation:

Answer:

1

Step-by-step explanation:

64+32 =96 that'd how I got the answer

Answer:

[tex]{ \tt{8(2v + 8) = 96}} \\ { \tt{2v + 8 = 12}} \\ { \tt{2v = 4}} \\ { \bf{v = 2}}[/tex]

Answer:

The circumference of Earth's equator is 40,080 km.

Step-by-step explanation:

Given that every 24 hours, Earth makes a full rotation around its axis, and Earth's speed of rotation at the equator is 1,670 km per hour, to determine what is the circumference of Earth's equator the following calculation must be performed:

24 x 1,670 = X

40,080 = X

Therefore, the circumference of Earth's equator is 40,080 km.

Answer:

x = 17

Step-by-step explanation:

If AB // DE, then angle 5 and angle 6 are alternate interior angle and they should be congruent.

5x + 16 = 3x + 50

Subtract 16 from both sides

5x = 3x + 50 - 16

5x = 3x + 34

Subtract 3x from both sides

5x - 3x = 34

2x = 34

Divide both sides by 2

x = 34/2

x = 17

Answer:

3x + 50 = 5x + 16

5x - 3x = 50-16

2x = 34

x = 17

Answer:

$124.42.

Step-by-step explanation:

Given data

Principqp= $100

Rate= 5.5%

time=4 years

First, convert R as a percent to r as a decimal

r = R/100

r = 5.5/100

r = 0.055 rate per year,

Then solve the equation for A

A = P(1 + r/n)^nt            // Since we are compounding quarterly

A = 100.00(1 + 0.055/4)(^4)(4)

A = 100.00(1 + 0.01375)^(16)

A = $124.42

Summary:

The total amount accrued, principal plus interest, with compound interest on a principal of $100.00 at a rate of 5.5% per year compounded 4 times per year over 4 years is $124.42.

Answer:

Zoe rode [tex]\frac{5}{6}[/tex] of a mile more than she walked.

Step-by-step explanation:

[tex]\frac{11}{12}-\frac{1}{12} =\frac{5}{6}[/tex]

Answer:

$765

Step-by-step explanation:

[tex]interest \: = \frac{prt}{100} \\ = \frac{(450)(5)(14)}{100} \\ = 315 \\ total \: money \: = 315 + 450 \\ = 765[/tex]

A(n) = 450 + (n – 1)(0.05 • 450); $765.00

Answer:

Step-by-step explanation:

(cos 4a*cos 2a+sin 4a*sin 2a)/sin 4a

=[cos (4a-2a)]/sin 4a

=(cos 2a)/sin 4a

=(cos 2a) /(2 sin 2a cos 2a)

=1/(2 sin 2a)

=1/2 csc 2a

Answer: Amy is incorrect. The answer is -5 points.

Step-by-step explanation:

From the question, we are informed that Amanda earned 20 points for winning a sprint in the first race but got -25 points in the second race.

Based on the information above, Amanda's total score now will be:

= 20 + (-25)

= 20 - 25

= -5

The answer is -5 points.

Amy is wrong because (+) × (-) = (-)

the sum of interior angle is 180:

[tex]x + 160 = 180 \\ x = 180 - 160 \\ x = 20[/tex]

Answer:

Yes, it shows direct variation

Step-by-step explanation:

Given

The above table

Required

Is it a direct variation?

The constant of variation (k) is:

[tex]k = y/x[/tex]

For each pair x and y, we have:

[tex]k = 5/15 = 1/3[/tex]

[tex]k = 6/18 = 1/3[/tex]

[tex]k =9/27 = 1/3[/tex]

Since the calculate constant have the same value for all pair or x and y, then the table shows direct variation

Answer:1

Step-by-step explanation:3/3=1

Answer:

19.005 ounces

Step-by-step explanation:

I believe that all you have to do is mutilply the 2 numbers which is 543 and 0.035 to find the amount of ounces it weighs. So 543 × 0.035 = 19.005. The answer is 19.005 ounces. (i hope)

Answer:

Can't See 7 clearly

8) (9,9)

Step-by-step explanation:

[tex]\frac{10+8}{2}[/tex] , [tex]\frac{10+8}{2}[/tex]

Add x's and divide by 2

Add y's and divide by 2

Like taking the average of the coordinates.

Answer:

The probability that this occurs is 25%, as 3/6 (chance to roll an odd number) multiplied by 1/2 (chance to flip a head) is .25.

Step-by-step explanation:

Answer:

a shipping container ,the ones they use in large cargo ships

Answer:

every single angle is 90°

Step-by-step explanation:

remember that,

4 angles will form if two lines intersect and the sum of those 4 angles is 360°

we are given the sum of 3 angles i.e 270

so one of the angles should be

[tex] \displaystyle {360}^{\circ} - {270}^{\circ}[/tex]

simplify substraction:

[tex] \displaystyle {90}^{\circ}[/tex]

therefore since one of the angles is 90° the intercepting lines are Perpendicular as a result every single angle formed by the two intercepting lines is 90°

Answer:

90°

Step-by-step explanation:

We know that sum of angle around a point is 360° . Here its already given that sum of three Angles out of 4 is 270°

Therefore :-

Measure of remaining one angle ,

Therefore the measure of the fourth angle is 90°

B.

the solution is in the picture

Answer: [tex]55,811.91[/tex]

Step-by-step explanation:

Given

Principal amount is 25,000

Time Period is [tex]t=15\ yr[/tex]

Rate of interest [tex]r=5.5\%[/tex]

Amount in compound interest is given by

[tex]\Rightarrow A=P\left(1+r\%\right)^t[/tex]

Insert the values

[tex]\Rightarrow A=25,000(1+\dfrac{5.5}{100})^{15}\\\\\Rightarrow A=25,000(1.055)^{15}\\\Rightarrow A=55,811.91[/tex]

Therefore, [tex]55,811.91[/tex] must be paid back

Answer:

(a) [tex]x\³ - 6x - 6[/tex]

(b) Proved

Step-by-step explanation:

Given

[tex]r = $\sqrt[3]{2} + \sqrt[3]{4}$[/tex] --- the root

Solving (a): The polynomial

A cubic function is represented as:

[tex]f = (a + b)^3[/tex]

Expand

[tex]f = a^3 + 3a^2b + 3ab^2 + b^3[/tex]

Rewrite as:

[tex]f = a^3 + 3ab(a + b) + b^3[/tex]

The root is represented as:

[tex]r=a+b[/tex]

By comparison:

[tex]a = $\sqrt[3]{2}[/tex]

[tex]b = \sqrt[3]{4}$[/tex]

So, we have:

[tex]f = ($\sqrt[3]{2})^3 + 3*$\sqrt[3]{2}*\sqrt[3]{4}$*($\sqrt[3]{2} + \sqrt[3]{4}$) + (\sqrt[3]{4}$)^3[/tex]

Expand

[tex]f = 2 + 3*$\sqrt[3]{2*4}*($\sqrt[3]{2} + \sqrt[3]{4}$) + 4[/tex]

[tex]f = 2 + 3*$\sqrt[3]{8}*($\sqrt[3]{2} + \sqrt[3]{4}$) + 4[/tex]

[tex]f = 2 + 3*2*($\sqrt[3]{2} + \sqrt[3]{4}$) + 4[/tex]

[tex]f = 2 + 6($\sqrt[3]{2} + \sqrt[3]{4}$) + 4[/tex]

Evaluate like terms

[tex]f = 6 + 6($\sqrt[3]{2} + \sqrt[3]{4}$)[/tex]

Recall that: [tex]r = $\sqrt[3]{2} + \sqrt[3]{4}$[/tex]

So, we have:

[tex]f = 6 + 6r[/tex]

Equate to 0

[tex]f - 6 - 6r = 0[/tex]

Rewrite as:

[tex]f - 6r - 6 = 0[/tex]

Express as a cubic function

[tex]x^3 - 6x - 6 = 0[/tex]

Hence, the cubic polynomial is:

[tex]f(x) = x^3 - 6x - 6[/tex]

Solving (b): Prove that r is irrational

The constant term of [tex]x^3 - 6x - 6 = 0[/tex] is -6

The divisors of -6 are: -6,-3,-2,-1,1,2,3,6

Calculate f(x) for each of the above values to calculate the remainder when f(x) is divided by any of the above values

[tex]f(-6) = (-6)^3 - 6*-6 - 6 = -186[/tex]

[tex]f(-3) = (-3)^3 - 6*-3 - 6 = -15[/tex]

[tex]f(-2) = (-2)^3 - 6*-2 - 6 = -2[/tex]

[tex]f(-1) = (-1)^3 - 6*-1 - 6 = -1[/tex]

[tex]f(1) = (1)^3 - 6*1 - 6 = -11[/tex]

[tex]f(2) = (2)^3 - 6*2 - 6 = -10[/tex]

[tex]f(3) = (3)^3 - 6*3 - 6 = 3[/tex]

[tex]f(6) = (6)^3 - 6*6 - 6 = 174[/tex]

For r to be rational;

The divisors of -6 must divide f(x) without remainder

i.e. Any of the above values  must equal 0

Since none equals 0, then r is irrational