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2 years ago

PLEASE HELP!!

Mathematics

1 answer:

ad-work [718]2 years ago

3 0

Step-by-step explanation:

5^-2= 1/25 (as when taken up 25 it becomes 5^-2).
2^5= 32 (when we multiply 2 for 5 times, we get 32).(2×2×2×2×2)
2^-4=1/16 (as when we take up 16 we get 2^-4)
5^3=125 (when we multiply 5 for 3 times we get 125)(5×5×5)

Hope it helps...

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Factor f(x) = 15x^3 - 15x^2 - 90x completely and determine the exact value(s) of the zero(s) and enter them as a comma separated

Illusion [34]

Answer:

$x=-2,0,3$

Step-by-step explanation:

We have been given a function $f(x)=15x^3-15x^2-90x$ . We are asked to find the zeros of our given function.

To find the zeros of our given function, we will equate our given function by 0 as shown below:

$15x^3-15x^2-90x=0$

Now, we will factor our equation. We can see that all terms of our equation a common factor that is $15x$ .

Upon factoring out $15x$ , we will get:

$15x(x^2-x-6)=0$

Now, we will split the middle term of our equation into parts, whose sum is $-1$ and whose product is $-6$ . We know such two numbers are $-3\text{ and }2$ .

$15x(x^2-3x+2x-6)=0$

$15x((x^2-3x)+(2x-6))=0$

$15x(x(x-3)+2(x-3))=0$

$15x(x-3)(x+2)=0$

Now, we will use zero product property to find the zeros of our given function.

$15x=0\text{ (or) }(x-3)=0\text{ (or) }(x+2)=0$

$15x=0\text{ (or) }x-3=0\text{ (or) }x+2=0$

$\frac{15x}{15}=\frac{0}{15}\text{ (or) }x-3=0\text{ (or) }x+2=0$

$x=0\text{ (or) }x=3\text{ (or) }x=-2$

Therefore, the zeros of our given function are $x=-2,0,3$ .

7 0

3 years ago

How to make an equation with numbers 0.25, 7.00, and 27

shepuryov [24]

There are many ways to do this.

One way could be 0.25x+7.00=27

8 0

3 years ago

HELPPP!! Plzzzz can’t do any more points so 10

Anestetic [448]

3. Answer: a) RT

b) XZ

c) TS

4. Answer: a) 26

b) 58

c) 21.5

d) 127

Step-by-step explanation:

2(PT) = AE 2(CP) = AN 2(CT) = EN

2(13) = AE 2(29) = AN 2(CT) = 43

26 = AE 58 = AN CT = 21.5

Perimeter = AE + AN + EN

= 26 + 58 + 43

= 127

4 0

2 years ago

Show tan(???? − ????) = tan(????)−tan(????) / 1+tan(????) tan(????) .

anyanavicka [17]

Answer:

See the proof below

Step-by-step explanation:

For this case we need to proof the following identity:

$tan(x-y) = \frac{tan(x) -tan(y)}{1+ tan(x) tan(y)}$

We need to begin with the definition of tangent:

$tan (x) =\frac{sin(x)}{cos(x)}$

So we can replace into our formula and we got:

$tan(x-y) = \frac{sin(x-y)}{cos(x-y)}$ (1)

We have the following identities useful for this case:

$sin(a-b) = sin(a) cos(b) - sin(b) cos(a)$

$cos(a-b) = cos(a) cos(b) + sin (a) sin(b)$

If we apply the identities into our equation (1) we got:

$tan(x-y) = \frac{sin(x) cos(y) - sin(y) cos(x)}{sin(x) sin(y) + cos(x) cos(y)}$ (2)

Now we can divide the numerator and denominato from expression (2) by $\frac{1}{cos(x) cos(y)}$ and we got this:

$tan(x-y) = \frac{\frac{sin(x) cos(y)}{cos(x) cos(y)} - \frac{sin(y) cos(x)}{cos(x) cos(y)}}{\frac{sin(x) sin(y)}{cos(x) cos(y)} +\frac{cos(x) cos(y)}{cos(x) cos(y)}}$

And simplifying we got:

$tan(x-y) = \frac{tan(x) -tan(y)}{1+ tan(x) tan(y)}$

And this identity is satisfied for all:

$(x-y) \neq \frac{\pi}{2} +n\pi$

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2 years ago

Amy has a piece of wood that measures 42 inches. The model shows the length remaining after she cut a piece from the 42-inch pie

Hitman42 [59]

Answer:

She has 42 pieces of wood each of 1 inch of length.

Step-by-step explanation:

Amy has 42 inches piece of wood.

She has to cut an inch.

After cutting pieces of inch each she counts the pieces to be 42.

Mathematically

Total length / unit lenght = Number of pieces

42 inches/ 1 inch= 42 pieces.

She has 42 pieces of wood each of 1 inch of length.

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2 years ago