Which one of the following is an ordered pair? {-3, 5} (2, 4, 0) (0, 6) 1, 3

Which number in the monomial 215x18y3z21 needs to be changed to make it a perfect cube?

hoa [83]

We need to remember that:
xyz = (x)(y)(z)
if x, y and z are perfect cubes, then xyz would also be a perfect cube

Also,
(x^n)^m = x^(mn)
if it is a perfect cube, then it can be factored into the expression (x^n)^3, wherein n is a whole number.

All should be a perfect cube, given

215x^18(y^3)(z^21)

By writing the terms separately, we would see which one is to be changed.

215 = 5*43, we see this is not a perfect cube, we could changed it to 6^3 or 216

x^18=(x^6)^3

y^3=y^3
z^21=(z^7)^3

The other terms are perfect cubes except for the first one. So the correct answer would be the last option, 215 should be changed.

4 0

3 years ago

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Point J(-2, 1) and point K(4, 5) form the line segment jk. for the point p that partitions jk in the ratio 3:7 what is the y coo

kumpel [21]

Answer:

$\frac{11}{5}$

Step-by-step explanation:

Using the section formula

$y_{P}$ = $\frac{3(5)+7(1)}{3+7}$ = $\frac{15+7}{10}$ = $\frac{22}{10}$ = $\frac{11}{5}$

7 0

3 years ago

What expression is equivalent to -3+2/3y-4-1/3y

Neko [114]

Answer:

The simplified form of the given expression is $-7 + (\frac{1}{3})y$

Step-by-step explanation:

Here, the given expression is:

$-3 + (\frac{2}{3}) y - 4 - (\frac{1}{3})y$

Now to simplify the given expression, perform operations on LIKE TERMS:

We get:

$-3 + (\frac{2}{3}) y - 4 - (\frac{1}{3})y =( -3 - 4) + [(\frac{2}{3}) y- (\frac{1}{3})y]\\= - 7 + [(\frac{2}{3}) -(\frac{1}{3})]y = -7 + [\frac{2-1}{3}]y\\ = -7 + (\frac{1}{3})y\\ \implies -3 + (\frac{2}{3}) y - 4 - (\frac{1}{3})y = -7 + (\frac{1}{3})y$

Hence the simplified form of the given expression is $-7 + (\frac{1}{3})y$

6 0

3 years ago

A manufacturer is planning to sell a new product at the price of 210 dollars per unit and estimates that if x thousand dollars i

sattari [20]

Answer:

Development costs: $2757

Promotion costs: $3155

Step-by-step explanation:

This might seem like a two-variable problem, but in actuality it's not - because the demand function is a sum of two components, each being independent and using only one variable, we can solve for the two separately.

Moreover, the price per unit and cost per unit is constant, so each product yields exactly $80 ($210 - $130).

Let's solve separately.

We need to maximize:

$80 * 160y/(y+4) - 1000y = $12800 * y/(y+4) - $1000*y

$80 * 170x/(x+7) - 1000x = $13600 * x/(x+7) - $1000*x

Let's go:

$12800 * y/(y+4) - $1000*y = $12800 * (1 - 4/(y+4)) - $1000y = $12800 - $51200/(y+4) - $1000*y

we analyze the derivative. $12800 is a constant, so we can skip it. Derivative of 1/(y+4) is -(y+4)^-2, derivative of $1000y is $1000.

deriv = $51200/(y+4)/(y+4) - $1000

We find the changepoints by analyzing $51200/(y+4)/(y+4) - $1000 = $0. We don't need to worry about y+4 = 0 because we cannot spend negative money on development/advertisement.

(y+4)^2 = $51.2

y+4 ~= 7.155417528 (or -y-4 = 7.1554... but it doesn't make sense because negative budget so we don't analyze).

y ~= 3.155417528

lastly, we should check that it's actually a maximum there - but it is, the original function goes to negative infinity.

rounding $1000y to the nearest dollar gives us $3155

Let's do the same for x:

$13600 * x/(x+7) - $1000*x = $13600 * (1 - 7/(x+7)) - $1000x = $13600 - $95200/(x+7) - $1000*x

deriv = $95200/(x+7)/(x+7) - $1000

$95200/(x+7)/(x+7) - $1000 = $0

(x+7)^2 = 95.2

(x+7) ~= 9.75704873412

x ~= 2.75704...

rounding $1000x to the nearest dollar yields $2757

3 0

3 years ago

79=11x+13 <br> Solve each equation by using the properties of equality and justify each step

neonofarm [45]

Solution: X=6

Detailed explanation:

In this problem we're asked to find "x" or the unknown.

The first step is to subtract 11x from both sides.

$---\mapsto\boldsymbol{-11x+79=13}$

Next, subtract 79 from both sides.

$---\mapsto\boldsymbol{-11x=-66}$

To finish this off, divide both sides by -11.

$---\mapsto\boldsymbol{x=6}$

Voila! There's our answer!

<h2><em>Cheers!! ^-^</em></h2>

___________________

Hope I helped. Best wishes.

Reach far. Aim high. Dream big.

___________________

8 0

2 years ago

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