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2 years ago

What numbers have a sum of 20 and the difference is 4

Mathematics

2 answers:

kvv77 [185]2 years ago

8 0

Answer:

The numbers are 12 and 8

Step-by-step explanation:

let the numbers be x and y :

$x + y = 20 - - - (a) \\ x - y = 4 - - - (b)$

add (a) and (b):

$2x + 0y = 24 \\ 2x = 24 \\ x = 12$

find y:

$x + y = 20 \\ 12 + y = 20 \\ y = 20 - 12 \\ y = 8$

balu736 [363]2 years ago

6 0

Answer:

16 and 2

Step-by-step explanation:

I'm not sure honestly if this is correct, but I hope this helps.

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(3x-2)(2x^2+3x-1), after I distribute how would I get an exponent of three, for the 6x?

Aliun [14]

Because when multiplying you add the number of variables, and there are 3 X's so it would be 6x with an exponent of 3

7 0

2 years ago

Mrs. Chip bought 2 sheets and a blanket and paid $41. Mrs. Dale bought a sheet and 4 blankets and paid $80.

Katyanochek1 [597]

Answer:

Sheet = $12
Blanket = $17

Step-by-step explanation:

Let the cost of a sheet be s and cost of a blanket be b

2s + b = 41
s + 4b = 80

From the first equation we get:

b = 41 - 2s

Substitute in the second equation

s + 4*(41 - 2s) = 80
s + 164 - 8s = 80
7s = 84
s = 12

Then

b = 41- 2*12 = 17

6 0

2 years ago

What is the following product?

VMariaS [17]

For this case we must find the product of the following expression:

$\sqrt {12} * \sqrt {18}$

We combine using the product rule for radicals:

$\sqrt [n] {a} * \sqrt [n] {b} = \sqrt [n] {ab}$

So, we have:

$\sqrt {12 * 18} =\\\sqrt {216} =$

We rewrite the 216 as $6 * 6 * 6 = 6 ^ 3 = 6 ^ 2 * 6$

$\sqrt {6 ^ 2 * 6} =$

By definition of properties of powers and roots we have:

$\sqrt [n] {a ^ n} = a ^ {\frac {n} {n}} = a$

Then, the expression is:

$6 \sqrt {6}$

Answer:

Option D

6 0

2 years ago

Read 2 more answers

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:

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

8 0

2 years ago

HELP!!! 30 points!

user100 [1]

Basically, the equator is like the x-axis of the world and the prime meridian is like the y-axis. You locate places by distances from these lines.

7 0

3 years ago

Read 2 more answers