M.N and O are 60 degree. And you have to know that 30 60 and 90 triangle. if 30 degrees opposite is measuring A , 60 is A square root 3 and the 90's opposite is being 2A. So 90 degree opposite is 16 square root 3 and 30 degree is being 8 square root 3 and 60 is
$8 \sqrt{3} \times \sqrt{3} = 24$
the height is 24 .

6 0

3 years ago

Read 2 more answers

Place the indicated product in the proper location on the grid. (4x^3+7y^3 z^ 4) ^2

ella [17]

Answer:

$16x^{6} +56x^{3}y^{3} z^{4} +49y^{6} z^{8} \\$

Step-by-step explanation:

To solve this type of problems first need to review some laws of exponents:

When you are multiplying the same base, you need to add the exponents.

$x^{2} +x^{8} = x^{2+8} = x^{10}$

When you are raising a base with power to another power, you should keep the base and multiply the exponents:

$(x^{2} y^{5})^3 = x^{2*3} y^{5*3} = x^{6} y^{15}$

Now for the expression $(4x^{3} + 7y^{3} z^{4} )^2$

Write the multiplying factors:

$(4x^{3} + 7y^{3} z^{4} )(4x^{3} + 7y^{3} z^{4} )$

Multiply the term $4x^{3}$

$(4x^{3} + 7y^{3} z^{4} )(4x^{3} + 7y^{3} z^{4} ) = 16x^{3+3} + 28x^3y^{3} z^{4}$

Then multiply the term $7y^{3}z^{4}$

$(4x^{3} + 7y^{3} z^{4} )(4x^{3} + 7y^{3} z^{4} ) = 16x^{3+3} + 28x^3y^{3} z^{4}\\\\+ 28x^3y^{3} z^{4} + 49y^{3+3} z^{4+4}$

Simplify the exponents:

$(4x^{3} + 7y^{3} z^{4} )(4x^{3} + 7y^{3} z^{4} ) = 16x^{6} + 28x^3y^{3} z^{4}\\\\+ 28x^3y^{3} z^{4} + 49y^{6} z^{8}$

Add like terms:

$= 16x^{6} + 56x^3y^{3} z^{4} + 49y^{6} z^{8}$

5 0

3 years ago

Marty made a $220 bank deposit using $10 bills and $5 bills. She gave the teller a total of 38 bills, how many $5 bills were in

Luda [366]

ANSWER: 32 five-dollar bills

======

EXPLANATION:

Let x be number of $5 bills

Let y be number of $10 bills

Since we have total of 38 bills, we must have the sum of x and y be 38

x + y = 38 (I)

Since the total amount deposited is $220, we must have the sum of 5x and 10y be 220 (x and y are just the "number of" their respective bills, so we multiply them by their value to get the total value):

5x + 10y = 220 (II)

System of equations:

$\left\{ \begin{aligned} x + y &= 38 && \text{(I)} \\ 5x + 10y &= 220 && \text{(II)} \end{aligned} \right.$

Divide both sides of equation (II) by 5 so our numbers become smaller

$\left\{ \begin{aligned} x + y &= 38 && \text{(I)} \\ x + 2y &= 44 && \text{(II)} \end{aligned} \right.$

Rearrange (I) to solve for y so that we can substitute into (II)

$\begin{aligned} x + y &= 38 && \text{(I)} \\ y &= 38 - x \end{aligned}$

Substituting this into equation (II) for the y:

$\begin{aligned} x + 2y &= 44 && \text{(II)} \\ x + 2(38 - x) &= 44\\ x + 76 - 2x &= 44 \\ -x &= -32 \\ x &= 32 \end{aligned}$

We have 32 five-dollar bills

======

If we want to finish off the question, use y = 38 - x to figure out number of $10 bills

$y = 38 - 32 = 6$

32 five-dollar bills and 6 ten-dollar bills

7 0

4 years ago