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Thepotemich [5.8K]

3 years ago

6

Solve the following equation. Then place the correct number in the box provided. 2(x + 1 ) - 3(x + 5) ≥ 0

1 answer:

larisa86 [58]3 years ago

5 0

Answer:

13

Step-by-step explanation:

2x+2-3x-15>0

-x+13>0

-x>0-13

x>-13/-1

x>13

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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

Help fast please???

blagie [28]

The answer would be C. 8 cm, 15 cm, 22cm.
The rule is that the two smaller sides when added, have to be bigger than the largest side. 8 + 15= 23 and the largest side is 22. 23 is greater than 22. The other options do not work with this rule

4 0

3 years ago

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I NEED THIS ASAP PLZ

miskamm [114]

Answer:

96

Step-by-step explanation:

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What is the Answer to this

kari74 [83]

First collect like terms for x^2:
x^2 + 3x^2 = 5x^2
Then collect like terms for x:
-2x + 5x = 3x
Collect like terms for normal numbers:
7 + - 3 = 4

Put them altogether:

5x^2 + 3x + 4

5 0

3 years ago

What is $125 billion in scientific notation

Angelina_Jolie [31]

$125 billion in scientific notation is 1.25*1011

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