Factorize: a^3-1+ a-1

Law of Exponent

[tex] \displaystyle \large{( \frac{a}{b} )^{n} = \frac{ {a}^{n} }{ {b}^{n} } }[/tex]

From the expression.

[tex] \displaystyle \large{( \frac{2}{3} )^{2} = \frac{ {2}^{2} }{ {3}^{2} } = \boxed{\frac{4}{9} } }[/tex]

Jerome's mistake is that Jerome forgot to evaluate 2^2 or forgot to add 2^2. The denominator is correct but the numerator is wrong.

Answer:

64/672/882(986)*866772

Answer:

[tex]0=x[/tex],  [tex]3=x[/tex]

Step-by-step explanation:

One is given the following equation:

[tex]y=6x-2x^2[/tex]

Factor this expression:

[tex]y=-2x(x-3)[/tex]

Set the equation equal to (0), then use the zero-product property to solve for (x). The zero product property states that any number times zero equals zero. Thus, one can apply this here to solve for (x):

[tex]0=-2x(x-3)[/tex]

[tex]0=-2x[/tex]          [tex]0=x-3[/tex]

Inverse operations,

[tex]0=-2x[/tex]          [tex]0=x-3[/tex]

[tex]0=x[/tex]               [tex]3=x[/tex]

Answer:

the answer is A)  

Step-by-step explanation:

combine like terms

4p+14

a=

2x2p+2x7

hope this helps

Answer:

v=-155

Step-by-step explanation:

167 = 12 - v

subtract both sides by 12

155= -v

multiply both sides by -1

-155= v

Answer:

no solutions

Step-by-step explanation:

2x-4=2x-7 (subtract 2x by the 2x on the other side)

-4 = -7 ( add 4 to negative 4 and add 4 to negative 7)

0 ≠ -3 (0 zero does not equal -3, if the solution had one solution then you would find x. if the solution had infinitely solutions then the numbers would be equal [like -3 = -3])

Since the equation ended with an invalid answer ( 0 ≠ -3) it has no solutions. hope this helps!

Answer: -13 + 10i

Step-by-step explanation: ((-6) + (2 * i)) - (7 - (8 * i)) = -13+10i

Answer:30%

Step-by-step explanation:

GAIN = 156- 120=$ 36

% GAIN = [tex]\frac{gain}{old cost price } X 100%\\[/tex]

= [tex]\frac{36}{120} X 100%[/tex]

=30%

Answer:

q = 108/p

Explanation:

the initial statement is q  ∝  1 /p

to convert to an equation multiply by k the constant of variation  

⇒  q  =  k × 1 /p  = k /p

to find k use the given condition

q  =  k/ p  

⇒  k  =  q/ p  =  3 /2  ×  72  = 108

equation is   q = 108/ p

Answer:

q = 48

Step-by-step explanation:

Given q is inversely proportional to p then the equation relating them is

q = [tex]\frac{k}{p}[/tex] ← k is the constant of proportion

To find k use the condition q = 120 when p = 2 , then

120 = [tex]\frac{k}{2}[/tex] ( multiply both sides by 2 )

240 = k

q = [tex]\frac{240}{p}[/tex] ← equation of proportion

When p = 5 , then

q = [tex]\frac{240}{5}[/tex] = 48

Answer:

BC = 12

Step-by-step explanation:

23 - (2 + 9)

23 - 11 = 12

BC = 12

Answer:

4800

Step-by-step explanation:

80 × 60 = 4800

Answer:

0.0089

Step-by-step explanation:

i dont know how to show my work i did it online, pls give me brainliest :(

Fun Fact: Octopuses lay 56,000 eggs at a time

Answer:

13/3

Step-by-step explanation:

SEE THE IMAGE FOR SOLUTION

HOPE IT HELPS

HAVE A GREAT DAY

[tex]\frac{4}{\pi}\left[x*\sin^{-1}(x)+\sqrt{1-x^2}\right]-x+C\\\\[/tex]

====================================================

Proof:

Apply the derivative to choice A. The goal is to prove the derivative is equivalent to the given integrand.

[tex]y = \frac{4}{\pi}\left[x*\sin^{-1}(x)+\sqrt{1-x^2}\right]-x+C\\\\\frac{dy}{dx} = \frac{4}{\pi}\left[\sin^{-1}(x)+\frac{x}{\sqrt{1-x^2}}-\frac{x}{\sqrt{1-x^2}}\right]-1\\\\\frac{dy}{dx} = \frac{4}{\pi}\sin^{-1}(x)-1\\\\[/tex]

It's far from obvious, but we can apply a bit of algebra like so

[tex]\frac{dy}{dx} = \frac{4}{\pi}\sin^{-1}(x)-1\\\\\frac{dy}{dx} = \frac{4}{\pi}\sin^{-1}(x)-\frac{\pi}{\pi}\\\\\frac{dy}{dx} = \frac{4\sin^{-1}(x)-\pi}{\pi}\\\\[/tex]

Next, we divide every term by 2. This is so we can replace the pi terms with pi/2

[tex]\frac{dy}{dx} = \frac{4\sin^{-1}(x)-\pi}{\pi}\\\\\frac{dy}{dx} = \frac{2\sin^{-1}(x)-\frac{\pi}{2}}{\frac{\pi}{2}}\\\\[/tex]

We do this to take advantage of the trig identity [tex]\sin^{-1}(x)+\cos^{-1}(x) = \frac{\pi}{2}[/tex]

So we'll be replacing every instance of "pi/2" with the left hand side of that equation just mentioned.

Therefore,

[tex]\frac{dy}{dx} = \frac{2\sin^{-1}(x)-\frac{\pi}{2}}{\frac{\pi}{2}}\\\\\frac{dy}{dx} = \frac{2\sin^{-1}(x)-\left(\sin^{-1}(x)+\cos^{-1}(x)\right)}{\sin^{-1}(x)+\cos^{-1}(x)}\\\\\frac{dy}{dx} = \frac{2\sin^{-1}(x)-\sin^{-1}(x)-\cos^{-1}(x)}{\sin^{-1}(x)+\cos^{-1}(x)}\\\\\frac{dy}{dx} = \frac{\sin^{-1}(x)-\cos^{-1}(x)}{\sin^{-1}(x)+\cos^{-1}(x)}\\\\[/tex]

This shows that differentiating the expression in choice A leads to the given integrand.

If we reverse all of the steps mentioned, then we can show that:

[tex]\displaystyle\frac{dy}{dx} = \frac{\sin^{-1}(x)-\cos^{-1}(x)}{\sin^{-1}(x)+\cos^{-1}(x)}\\\\\\ \int\frac{dy}{dx}dx = \int\frac{\sin^{-1}(x)-\cos^{-1}(x)}{\sin^{-1}(x)+\cos^{-1}(x)}dx\\\\\\y = \frac{4}{\pi}\left[x*\sin^{-1}(x)+\sqrt{1-x^2}\right]-x+C\\\\[/tex]

since integrals and derivatives are tied together through inverse processes (one undoes the other more or less).

Answer:

22 divided 5 I would think

Step-by-step explanation:

Answer:

35/100 if I remembered correctly, XD

Answer:

[tex]\frac{35}{100}[/tex]

Step-by-step explanation:

if you want to convert decimal to fraction you first have to observe the decimal point

here the decimal point is after 2 numbers so

u will take 100 to be divided with

[tex]\frac{35}{100}[/tex]

Hey there! I'm happy to help!

We see that this is an isosceles triangle. This means that two sides are the same length. . We can see that the sides DE and EF are marked with two orange lines, which shows that they are congruent.

We want to find the measure of angle D. We see that our two lines of equal length both create an angle with the hypotenuse DF. Since these lines are the exact same length, they are going to have to create the same angle. Even if you just eyeball it, the angles look to be the same.

So, our measure of angle D is going to be the same as angle F. Let's call this measure m and put it into an equation.

2m+92=180 (sum of all angle measures in a triangle is 180)

Subtract 92 from both sides.

2m=88

Divide both sides by 2

m=44

So, the measure of angle D is B. 44°.

Have a wonderful day and keep on learning! :D

Answer:

-1.22

Step-by-step explanation:

Answer:Of the ones mentioned here, I'd say that 3, redefine addition, is the easiest way to use and work with to get lots of self consistent theories that have 2 + 2 = 5.

Step-by-step explanation:

First, it’s easy to prove that 2 + 2 =4. You just need the rule x + Sy = S(x + y) where Sx means the successor of x, or x + 1. With some more steps, with simple natural axioms, you can also derive a contradiction from 2 + 2 = 5. Proof indented so it’s easy to skip.

Answer:

A. 3(2m+9) and 6m+27

Step-by-step explanation:

Use the distributive property to solve 3(2m+9).

3×2m+3×9

6m+27.

I hope this helps!  

pls ❤ and mark brainliest pls!

Explanation:

Think of the problem as x-3 = 2 where x is the blank that we need to fill in.

Adding on -3 is the same as subtracting 3, so that's why x+(-3) is the same as x-3.

To solve x-3 = 2, we add 3 to both sides and we'll get x = 5

Then note how 5-3 = 2 to help confirm the answer.

Answer:

5

Step-by-step explanation:

5 + (-3) = 5 - 3

Answer:

26.6 miles

Step-by-step explanation:

distance = speed × time ( time is in hours )

              = 7.6 × 3.5

             = 26.6 miles

Answer:

$9170 per year , or ≈ $3.92 per hour

Step-by-step explanation:

We can solve this by putting both of these in terms of yearly salary and going from there.

The first job is already in terms of yearly salary.

The hourly rate job is $26 per hour. There are 45 hours worked per week, and we add $26 for each hour. Another way of saying this is  26 * 45 = total amount earned for the week = $1,170 .

There are 52 weeks in a year, and you make $1,170 per week on the hourly job. This means that over 52 weeks, you will earn 1170 * 52 = 60840. This is the yearly rate for the second job.

The difference between the two jobs is

60840 - 51670 = $9170 per year. Dividing by 52 to get the weekly gain, we get ≈ $176.35 more for the hourly job each week. Dividing by 45 to get the hourly gain, we get ≈ $3.92 dollars from taking the second job

Answer:

4

Step-by-step explanation:

(-1.5) + 3.5+2

-1.5 + 3.5 + 2

2 + 2

= 4

Answer:

< then >

Step-by-step explanation:

11 7/8 can be written as (11 + 7/8). If we find (11+7/8)², we know that √(11+7/8)² = (11+7/8), so we can compare (11+7/8)² with 129 and see which is bigger.

(11+7/8)² = (11+7/8) * (11+7/8)

= 121 + 7/8 * 11 + 7/8 * 11 + (7/8)²

= 121 + 77/8 + 77/8 + (7/8)²

77/8 is greater than 9 (8*9 = 72) but less than 10 (8*10=80). Rounding down to 7, we have

121 + 7 + 7 + (7/8)²

= 135 + (7/8)²

Even when rounding down, (11+7/8)² is greater than 129. Therefore,

129 < (11+7/8)²

square root both sides

√129 < (11+7/8)

We can apply a similar process for the next one.

(3+5/6)² = (3+5/6) * (3+5/6)

= 9 + 5/6 * 3 + 5/6 * 3 + (5/6)²

= 9 + 15/6 + 15/6 + (5/6)²

15/6 is less than 3 (6*3 = 18) but greater than 2 (6*2 = 12). Rounding down to 2, we have

9 + 2 + 2 + (5/6)²

= 13 + (5/6)² > 10

Even when rounding down, (3+5/6)² is greater than 10

(3+5/6)² > 10

square root both sides

(3+5/6) > √10

Answer: The bill with a discount is $18.59

Step-by-step explanation:

Given information

2 boxes of $3.49 cereal

3 cartons of $2.99 ice-cream

6 packs of $1.99 soda

1/3 discount off total bill

Given expression

Bill = (1 - 1/3) (2 × 3.49 + 3 × 2.99 + 6 × 1.99)

Simplify values in parentheses

Bill = (2/3) (6.98 + 8.97 + 11.94)

Simplify by addition

Bill = (2/3) (27.89)

Simplify by multiplication

Bill = $18.59 (Rounded to the nearest hundredth because the usual money ends in nearest cent)

Hope this helps!! :)

Please let me know if you have any questions

Answer:

Step-by-step explanation:

Inverse variation equation:

We have:

Work out the value of k by substituting the values of x and y:

The equation is:

Answer:

y = -6/x

Step-by-step explanation:

y varies inversely as x

So, y = k/x, where k is the constant of proportionality.

If y = -1 when x = 6,

Then, -1 = k/6 ===> k = -6

Therefore, y = -6/x