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3 years ago

Which expressions are equivalent to {22c + 33d}

Mathematics

2 answers:

charle [14.2K]3 years ago

7 0

Here it is really easy if you think about it. (all it requires is 50 years of constant grinding on your homework :P Jk)

Alright so we have {22c + 33d}

First i would question myself....common factors....YES!

i see a 11!

factor out the 11

you get 11(2c+3d)

:DDDDDD

Arturiano [62]3 years ago

5 0

Answer: A C and E for KHAN ACADEMY

Step-by-step explanation:

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9) Which of the following shows the Associative Property of Addition

makvit [3.9K]

The answer is D that is (18+41)+12 = 18+(41+12)
because A,B,C can be only be associative when
(A+B)+C= A+(B+C)
So by comparing the associative law with the options above , you will be able to get your answer

3 0

3 years ago

Suppose a home improvement contractor is painting the walls and ceiling of a rectangular room. The volume of the room is 288 cub

ratelena [41]

Answer:

The minimum cost is $17.30c

Step-by-step explanation:

Given

$V = 288$ --- Volume

$C_1 = 0.06$ --- cost of wall paint

$C_2 = 0.16$ ---cost of ceiling paint

Required

Minimum cost of paint

The volume is calculated as:

$V =xyz$

Substitute 288 for V

$288 =xyz$

Make z the subject

$z = \frac{288}{xy}$

The surface area is calculated as:

$Area = 2(yz + xz) + xy$

Because xy represent the dimension of the ceiling and the opposite of the ceiling (the floor) will not be painted. Hence, it does not require a coefficient of 2

The cost is:

$C = 0.06 * 2(yz + xz) + 0.16 * xy$

Substitute $z = \frac{288}{xy}$

$C = 0.06 * 2(y*\frac{288}{xy} + x*\frac{288}{xy}) + 0.16 * xy$

$C = 0.06 * 2(\frac{288}{x} + \frac{288}{y}) + 0.16 * xy$

$C = 0.12(\frac{288}{x} + \frac{288}{y}) + 0.16 * xy$

$C = (\frac{34.56}{x} + \frac{34.56}{y}) + 0.16 * xy$

$C = (\frac{34.56}{x} + \frac{34.56}{y}) + 0.16 xy$

Differentiate w.r.t x and y

$C_x = -\frac{34.56}{x^2} + 0.16y$

$C_y = -\frac{34.56}{y^2} + 0.16x$

By comparison: $x = y$

Set them equal to 0

$C_y = -\frac{34.56}{y^2} + 0.16x=0$

$-\frac{34.56}{y^2} + 0.16x=0\\$

Substitute x for y

$-\frac{34.56}{x^2} + 0.16x=0$

$0.16x=\frac{34.56}{x^2}$

Cross multiply

$0.16x^3 = 34.56$

$x^3 = \frac{34.56}{0.16}$

$x^3 = 216$

Take the cube root of both sides

$x = \sqrt[3]{216}$

$x = 6$

$x=y= 6$

Substitute 6 for x and for y in $C = (\frac{34.56}{x} + \frac{34.56}{y}) + 0.16 xy$

$C = (\frac{34.56}{6} + \frac{34.56}{6}) + 0.16 * 6* 6$

$C = (\frac{2*34.56}{6}) + 5.76$

$C = 11.52 + 5.76$

$C = 17.28$

$C = 17.3$ --- approximated

8 0

3 years ago

What is the slope of the line that passes through the points (8,8) and (20,-2)?

vesna_86 [32]

Answer: Slope = -5/6

Step-by-step explanation:

(y1-y2) / (x1-x2)

(-2-8) / (20-8)

-10/12

-5/6

Hope this helps!

6 0

3 years ago

Read 2 more answers

What is the solution for x in the given equation? The square root of 9x +7 + the square root of 2x = 7

cestrela7 [59]

Answer:

The solution is x =2 for the given equation $\sqrt{9x+7} +\sqrt{2x}=7$

Step-by-step explanation:

We need to find the solution for x in the given equation.

$\sqrt{9x+7} +\sqrt{2x}=7$

Solving:

Subtract $\sqrt{2x}$ from both sides

$\sqrt{9x+7} =7-\sqrt{2x}$

Taking square on both sides

$(\sqrt{9x+7})^2 =(7-\sqrt{2x})^2\\Using\,\, (a-b)^2 = a^2-2ab-b^2\\9x+7=(7)^2-2(7)(\sqrt{2x})+(\sqrt{2x})^2\\9x+7=49-14\sqrt{2x}+2x\\9x-2x+7-49=-14\sqrt{2x}\\7x-42=-14\sqrt{2x}\\Taking\,\,square\,\,on\,\,both\,\,sides\\(7x-42)^2=(-14\sqrt{2x})^2\\49x^2-2(7x)(42)+(42)^2= 196(2x)\\49x^2-588x+1764=392x\\49x^2-588x+1764-392x=0\\49x^2-980x+1764=0\\Using \,\,quadratic \,\, equation \,\,to \,\, find \,\, value \,\, of \,\, x \\x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}\\a= 49, \, b= -980 \,\,and\,\, c = 1764$

Putting values and solving

$x=\frac{-(-980)\pm\sqrt{(-980)^2-4(49)(1760)}}{2(49)}\\x=\frac{980\pm\sqrt{614656}}{98}\\Solving\\x=18 \,\, and x =2$

Verifying the solution by putting values of x in given equation

Putting x=18

$\sqrt{9x+7} +\sqrt{2x}=7\\\sqrt{9(18)+7} +\sqrt{2(18)}=7\\\sqrt{169} +\sqrt{36}=7\\13+6=7\\19\neq 7$

So, x=18 is not solution o given equation.

Putting x = 2

$\sqrt{9x+7} +\sqrt{2x}=7\\\sqrt{9(2)+7} +\sqrt{2(2)}=7\\\sqrt{25} +\sqrt{4}=7\\5+2=7\\7=7$

So, x=2 satisfies the equation

The solution is x =2 for the given equation $\sqrt{9x+7} +\sqrt{2x}=7$

7 0

3 years ago

Rick needs to hire a new employee. Current projections indicate that the department will generate $5 million USD in gross revenu

Dima020 [189]

The maximum salary that Rick can offer a new employee based on the budgeted and current projections is <u>$93.750</u>.

<h3>What is a budget projection?</h3>

A budget projection is qualitative and quantitative data developed for making a long-term prediction of estimated future financial results.

<h3>Data and Calculations:</h3>

Projected gross revenue = $5 million

The annual profit margin on cost = 25%

Annual profit in dollars = $962,500 ($3,850,000 x 25%)

Projected expenses for the year = $3,850,000

Actual cost of an employee = $187,500 ($5,000,000 - $3,850,000 - $962,500)

The expected maximum salary for the new employee = $93,750 ($187,500/2)

Thus, Rick cannot avoid offering a new employee more than <u>$93,750</u> if he must maintain a 25% annual profit margin on cost.

Learn more about budget projections at brainly.com/question/24940564

#SPJ1

3 0

2 years ago