5 points Two lines are represented by equations: 10x - 15y = 21 and y = kx + 5. What value of k will make lines perpendicular?

Michelle is measuring the dimensions of her living room so she can install new flooring. She measures the length at 4√12 feet wi

Aneli [31]

The question is incomplete. Here is the complete question.

Michelle is measuring the dimensions of her living room so she can install new flooring. She measures the length at $4\sqrt{12}$ fett with her radical measure tape, and then measures the width at $3\sqrt{8}$ feet.

1. Determine the area of the living room. Leave your answer as a simplified radical expression and include units.

2. Michelle decided she only wants to cover $\frac{3}{4}$ of the room in the new flooring. Determine the area of the flooring she will need to cover $\frac{3}{4}$ of the room. Leave your answer as a simplified radical expression and include units.

3. For the remaining portion of the living room not covered by the new flooring, Michelle wants to paint the concrete. After carefully measuring the exposed concrete, she determines 6 square feet are already painted and the remaining unpainted area forms a square with side length x. The entire concrete, including the painted and unpainted portions, is a total of 31 square feet. write an expression that could be used to find the unpainted square side length x.

4. After installing the new flooring, Michelle palns to install new baseboards around the perimeter of the room. Help Michelle by determining the perimeter of the room, leaving your answer as a simplified radical expression.

5. When Michelle goes to the local hardware store to purchase the baseboards, the shop owner tell her his conversion calculator is broken and he only has 14 yards of baseboard in stock. Help Michelle by converting the perimeter to yards and determine if the hardware store has enough baseboard for her room. Hint: 3 feet are 1 yard.

Answer: 1. $48\sqrt{6}$ ft²

2. $36\sqrt{6}$ ft²

3. $x^{2}+6=31$

4. $(16\sqrt{3}+12\sqrt{2})$ ft

5. No, because perimeter is 15 yards.

Step-by-step explanation:

1. Michelle's living room is a rectangle. Area of a rectangle is calculated as

A = length*width

$A=(4\sqrt{12})(3\sqrt{8})$

$A=12\sqrt{96}$

Square root of 96 is not an exact number, so we can only simplify it:

$A=12\sqrt{2^{4}.6}$

$A=12.4\sqrt{6}$

$A=48\sqrt{6}$

Living room has area of $48\sqrt{6}$ square feet.

2. If only 3/4 of the room will be floored, she will need:

$A_{1}=\frac{3}{4}.48\sqrt{6}$

$A_{1}=36\sqrt{6}$

Michelle will need $36\sqrt{6}$ square feet of flooring.

3. According to her measure, 6 square feet is painted and a square of size x is unpainted. Both the total of both area is 31.

Area of a square is given by

A = side²

Area of the unpainted square :

$A_{s}=x^{2}$

Total area is the sum of unpainted and painted area. Then:

$x^{2}+6=31$

The equation used to determine the unpainted area is $x^{2}+6=31$

4. <u>Perimeter</u> is the sum of all the sides of a polygon. Since rectangle has two parallel, equal and opposite sides, perimeter is

P = 2*length + 2*width

$P=2(4\sqrt{12})+2(3\sqrt{8})$

$P=8\sqrt{12}+6\sqrt{8}$

Simplifying, we have:

$P=8\sqrt{2^{2}.3}+6\sqrt{2^{2}.2}$

$P=16\sqrt{3}+12\sqrt{2}$

Perimeter of the room is $(16\sqrt{3}+12\sqrt{2})$ feet.

5. Converting feet to yard

3 ft --------------------- 1 yard

$(16\sqrt{3}+12\sqrt{2})$ ---------- x

$x=\frac{16\sqrt{3}+12\sqrt{2} }{3}$

$x=\frac{16\sqrt{3} }{3} +4\sqrt{2}$

Knowing that $\sqrt{3} =1.73$ and $\sqrt{2}=1.41$ , x is approximately

x ≈ 15 yards

So, the hardware store won't have enough baseboard for the room.

4 0

3 years ago

Use the number line to complete the statements.A number line going from negative 10 to positive 10 in increments of 2.The opposi

g100num [7]

Answer:

-4 and 8

Step-by-step explanation:

When looking at the number line to get the opposite of a number take your number and count that many numbers on the opposite side of the 0 (zero).

So if your number is -4 count that many on the opposite side of the zero to get 4.

8 0

3 years ago

9. Jennifer is now 3 years older than Peter. If, in 12 years, the sum of their ages will be 61, how

zaharov [31]

Answer:

20

Step-by-step explanation:

In 12 years, the sum of their ages will be 24 more than it is now. The sum of their ages now is 61-24 = 37.

If Jennifer is 3 years older than Peter, we have ...

j + (j -3) = 37

2j = 40 . . . . . . add 3

j = 20 . . . . . . . divide by 2

Jennifer is now 20 years old.

_____

Peter is now 17 years old. In 12 years, they will be 29 and 32, so their ages will sum to 61.

7 0

3 years ago

The diagram shows a scale drawing of a playground the scale of the drawing is 1:500 work out the perimeter of the real playgroun

liraira [26]

Answer:

Check Explanation

Step-by-step explanation:

The complete question plus diagram is presented in the attached image to this solution.

From the attached image, the dimensions of the playground drawn will be a bit variable now as zooming and some editing might have tampered with the original intended dimensions to be measured.

But still, let us assume that on measuring the rectangular playground shown, we obtain approximately that the length is 4.5 cm and the breadth is 2 cm.

The scale to convert to real life is 1;500 indicating that

1 cm on the drawing = 500 cm lenght units of the real playground.

So,

4.5 cm on the drawing = 4.5 × 500 = 2250 cm of the playground

2 cm on the drawing = 2 × 500 = 1000 cm of the playground.

Hence, the real life dimensions of the playground is 2250 cm by 1000 cm.

In meters, that is 2.25 m by 1 m

The perimeter of a rectangular figure is given as

Perimeter = 2(Length + Breadth)

= 2(2.25 + 1)

= 6.5 m

Hope this Helps!!!

5 0

3 years ago

A recipe calls for an oven to be preheated to 400 °F. What is the approximate temperature of the preheated oven in Celsius degre

Anton [14]

Answer:204.4

Step-by-step explanation:

5 0

4 years ago

Read 2 more answers

5 points Two lines are represented by equations: 10x - 15y = 21 and y = kx + 5. What value of k will make lines perpendicular?​

5 points Two lines are represented by equations: 10x - 15y = 21 and y = kx + 5. What value of k will make lines perpendicular?