was the expression a^2-b^2 = (a+b)(a-b) invented or discovered?

Answer:

Proved

Step-by-step explanation:

The given data is:

[tex]11^n - 6[/tex] not [tex]11^{n - 6[/tex]

Required

Prove by induction that it is divisible by 5

Assume [tex]n = k[/tex]

So, we have:

[tex]11^k - 6 = 5p[/tex] where p is a positive digit

Rewrite as:

[tex]11^k = 5p + 6[/tex]

To solve further, we have to prove that [tex]11^k - 6[/tex] is true for [tex]n=k+1[/tex]

So, we have:

[tex]11^{k+1} - 6[/tex]

[tex]11^{k+1} - 6 = 11^k * 11 - 6[/tex]

Add 0

[tex]11^{k+1} - 6 = 11^k * 11 - 6 + 0[/tex]

Replace 0 with [tex]-5 +5[/tex]

[tex]11^{k+1} - 6 = 11^k * 11 - 6 - 5 + 5[/tex]

[tex]11^{k+1} - 6 = 11^k * 11 - 11- 5[/tex]

Factorize

[tex]11^{k+1} - 6 = 11 (11^k - 1)- 5[/tex]

Substitute [tex]11^k = 5p + 6[/tex]

[tex]11^{k+1} - 6 = 11 (5p + 6- 1)- 5[/tex]

[tex]11^{k+1} - 6 = 11 (5p + 5)- 5[/tex]

Factorize

[tex]11^{k+1} - 6 = 11 *5(p + 1)- 5[/tex]

Factorize

[tex]11^{k+1} - 6 = 5[11(p + 1)- 1][/tex]

The 5 outside the bracket implies that it is divisible by 5

Answer:

20 = x

Step-by-step explanation:

All interiror angles in this triangle will equal 180

Set your formula up as 180 = x+5+7x-5+x then solve for x

180 = x+5+7x-5+x

180 = x + 7x + x +5 - 5

180 - 5 + 5 = 9x

180 = 9x

180 / 9 = x

20 = x

You can check your result by pluging in 20 for all x

180 = 20+5+7*20-5+20

180 = 180

Answer:

[tex]49\frac{3}{5}[/tex]

Step-by-step explanation:

Answer:

49 3/5

Step-by-step explanation:

First, convert 12 2/5 into an improper fraction. You should get 62/5. We know that dividing fractions is the same thing as multiplying by the other fraction's reciprical (flip). So, 62/5 divided by 1/4 is the same thing as 62/5*4/1 (4). Lastly multiply straight across to get 248/5. Simplify to get 49 3/5.

Hope this helps

Answer:

what is your question friend? :)

Answer:

[tex]x = 3\ or\ x = 7[/tex]

Step-by-step explanation:

Given

[tex]x^{2}-8x+14=2x-7[/tex]

Required

Solve

Equate to 0

[tex]x^{2}-8x-2x+14+7=0[/tex]

[tex]x^{2}-10x+21=0[/tex]

Expand

[tex]x^{2}-7x-3x+21=0[/tex]

Factorize

[tex]x(x-7)-3(x-7)=0[/tex]

Factor out x - 7

[tex](x-3)(x-7)=0[/tex]

Split

[tex]x - 3 = 0\ \ x - 7 = 0[/tex]

Solve

[tex]x = 3\ or\ x = 7[/tex]

9514 1404 393

Answer:

  infinite number of solutions

Step-by-step explanation:

The two equations describe the same line.

Adding 9y+15 to the second equation makes it be ...

  15 = 6x +9y

Dividing that by 3 gives you ...

  5 = 2x +3y . . . . . . identical to the first equation

The lines intersect at every point, so there are an infinite number of solutions.

Answer:

A. 8

Step-by-step explanation:

sqrt{64} is 8 (8*8)

Answer:

8

Step-by-step explanation:

There are 8 members in each row

the sum of two numbers that is 45 and their difference is 7 it is 39 and 6 more like 39+6

Answer:

d 243

Step-by-step explanation:

The solution of given function is 243

A limit defined as the value which a function approaches as that function's inputs get closer and closer to some number

[tex]lim\ (3x-3)^\frac{5}{2} \\x\to 4[/tex]

[tex](3(4)-3)^\frac{5}{2}[/tex]

[tex](12-3)^\frac{5}{2}[/tex]

[tex](9)^\frac{5}{2}[/tex]

[tex](3^2)^\frac{5}{2}[/tex]

[tex]3^5[/tex]

243

Hence, the solution of given function is 243

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Answer:$6.25

Step-by-step explanation:we have that

x------------------> represent the number of hours Steven babysits

y----------------- > represent the amount he charges

for x=6 hours

y=$37.50 ----------------> y/x=37.5/6=6.25

for x=8 hours

y=$50---------------------> y/x=50/8=6.25

therefore

y=6.25x

Answer:

What is 1/3 of 814

Step-by-step explanation:

What is 1/3 of 814

Answer: I think C

Step-by-step explanation:

Answer:

[tex]x - 2y=5[/tex]

Step-by-step explanation:

Given

[tex]x = -5; y=-5[/tex]

[tex]x - 2y[/tex] --- missing from question

Required

Evaluate

We have:

[tex]x - 2y[/tex]

Substitute for x and y

[tex]x - 2y=-5 - 2*-5[/tex]

[tex]x - 2y=-5 +10[/tex]

[tex]x - 2y=5[/tex]

Answer:

0

Step-by-step explanation:

5x+10-4=13-7x-7

5x+6=6-7x

5x+0= -7x

0=-12x

Divide and u get x=0

Answer:

The answer is below

Step-by-step explanation:

Given that k(x) = -125x² +670x - 125, where x is the charge per cone and P = k(x) is the weekly profit

a) The maximum profit is at P'(x) = 0. Therefore we have to find the derivative of the profit equation and equate it to 0.

P'(x) = k'(x) = 0

k'(x) = -250x + 670 = 0

-250x + 670 = 0

250x = 670

x = $2.68

P = k(2.68) = -125(2.68²) + 670(2.68) - 125 = $772.8

Hence the maximum profit is $772.8 when the price of each ice cream cone is $2.68

b) At break even, the profit is 0. Hence P= k(x) = 0

-125x² + 670x - 125 = 0

x = 5.17 or x = 0.19

Therefore to break even, the price of the ice cream cone needs to be $0.19 or $5.17

c) g(x) = k(x - 2)

g(x) = -125(x - 2)² + 670 (x -2) - 125

Maximum profit is at g'(x) = 0

g'(x) = -250(x-2) + 670

-250(x-2) + 670 = 0

-250x + 500 + 670 = 0

250x = 1170

x = 4.68

g(4.68) = -125(4.68 - 2)² + 670(4.68 -2) - 125 = $772.8

Therefore function g has the same maximum value as function k

Answer:

? = 1

Step-by-step explanation:

4/8 = ?/2

Change the ? into a variable so it's easier to calculate:

Variable x = ?

4/8 = x/2

Cross multiply:

4 × 2 = 8 × x

8 = 8x

Divide both sides by 8 to isolate the variable:

1 = x

Check your work:

4/8 = 1/2

4 × 2 = 8 × 1

8 = 8

Correct!

Answer:

36 minutes

Step-by-step explanation:

The equation to determine the time together is

1/a + 1/b = 1/c  where a and b are the times alone and c is the time together

1/90  + 1/ 60 = 1/c

Multiply each side by 180c to clear the fractions

180c( 1/90  + 1/ 60 = 1/c)

2c + 3c = 180

5c = 180

Divide each side by 5

5c/5 = 180/5

c =36

Answer:

x-intercept = 5

y-intercept = 15

Step-by-step explanation:

Change the equation to slope-intercept form: y = -3x + 15

You have the y-intercept in that equation already, so you know it's 15. To find the x-intercept, substitute 0 in for y and solve algebraically.

0 = -3x + 15

-15 = -3x

5=x

On expanding the expression, we get - 7x + 21.

We have the following expression -

f(x) = 7(x + 3)

We have to write its equivalent expression.

Expanding we get -

f(x) = [tex]$\pi \sqrt{x} + 5\pi[/tex]

According to the question, we have -

7(x + 3)

On expanding, we get -

7(x + 3) = 7x + 21

Hence, on expanding the expression, we get - 7x + 21.

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9514 1404 393

Answer:

  B

Step-by-step explanation:

If the probability of event "A" is 'p', then the probability of the event "not A" is

  P(not A) = 1 - P(A) = 1 - p

For p=0.5, this is ...

  P(not A) = 1 -0.5 = 0.5 . . . . . matches choice B

Answer:

○B. 0.5 is the proof the outcome (not A).

Answer:

i believe it is 497 after the 30% mark down

Step-by-step explanation:

i subtracted 30% from 710

Answer:

A. 21

Step-by-step explanation:

Recall: inscribed angle in a semicircle equals 90°

m<K is an inscribed angle in a semicircle = (4x + 6)°

Therefore,

4x + 6 = 90°

Solve for x. Subtract both sides by 6

4x + 6 - 6 = 90 - 6

4x = 84

Divide both sides by 4

4x/4 = 84/4

x = 21

Answer:

the quotient of w and 7

is it correct?

Step-by-step explanation:

Answer:

The value of ∠b = 180°

Step-by-step explanation:

Given that;

ABC is a straight line

Another angle is 137°

Find:

The value of ∠a

The value of ∠b

Computation:

We know that, ABC is a straight line

So,

137 + The value of ∠a = 180

The value of ∠a = 180 - 137

The value of ∠a = 43°

The value of ∠b = 360 - 137 - The value of ∠a

The value of ∠b = 360 - 137 - 43

The value of ∠b = 180°

Answer:

g = -8, 6

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Equality Properties

Algebra I

Step-by-step explanation:

Step 1: Define

Identify

g² + 2g - 48 = 0

Step 2: Solve for g

Answer:

a= 250

b= 50

250 + 50 = 300

Step-by-step explanation:

There's many solutions but this was the first one I could come up with.

Answer:

my opinion is seince a+b=300 then the sqaure of 300= 17.3?

Step-by-step explanation: