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3 years ago

7

on the blueprint of the house 44 millimeters represents 8 meters. the length of the living room is 33 millimeters on the bluepri

nt. what is the actual length of the living room?

1 answer:

Scilla [17]3 years ago

6 0

So if 44=8 and 33=x, solve for x.
The problem would look like this : 44mm = 8m
33mm = x
You would cross multiply giving you this : 44x = 264
Then divide 264 by 44 to isolate x, then you should get this : x = 6
6m will be your answer.

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Help me figure out the last two please

yawa3891 [41]

Answer:

$1)\ x = 5$

$2)\ x = 14$

$3) \ x = 15,\ y = 2$

Step-by-step explanation:

1) Given that M<1 = 95 + 7x and M<2 = 55 - x, you should look on the diagram to see what type of angles M<1 and M<2 are.

On the diagram at the top, angles 1 and 2 appear to be supplementary angles, meaning they add up to 180 degrees. You can apply this information to creating an equation:

M<1 + M<2 = 180°

$(95 + 7x) + (55 - x) = 180$

Now you can solve this equation by combining like terms on the left-hand side of the equation.

$150+6x=180$

Subtract 150 from both sides of the equation in order to isolate the variable x.

$6x=30$

Divide both sides of the equation by 6 in order to isolate the variable x completely.

$x=5$

2) You are given that M<3 = 5x + 12 and M<4 = 7x - 16, so look on the diagram at the top to find out what type of angles they are.

Angles 3 and 4 appear to be alternate exterior angles, meaning that they are equal to each other as stated by the Alternate Exterior Angles Theorem. You can use this information to make an equation where M<3 = M<4.

M<3 = M<4

$5x+12=7x-16$

Subtract 5x from both sides of the equation, and add 16 to both sides of the equation.

$28=2x$

Divide both sides of the equation by 2 to isolate the variable x completely.

$14=x \rightarrow x=14$

3) Given that M<1 = 7y + 16, M<2 = 2x, and M<3 = 4x - 30, look on the diagram at the bottom to find out what type of angles they are.

Since angles 2 and 3 include an "x" variable, you should start with them first in order to be able to solve for x. Angles 2 and 3 are complementary angles, meaning that they are equal to each other based on the Complementary Angles Theorem. Translate this information into an equation:

M<2 = M<3

$2x=4x-30$

Subtract 2x from both sides of the equation and add 30 to both sides of the equation.

$30=2x$

Divide both sides of the equation by 2 in order to isolate the variable x completely.

$15=x \rightarrow x=15$

Now to solve for y - based on the diagram, you can see that angle 1 and angle 2 are vertical angles, meaning that they are equal to each other based on the Vertical Angles Theorem.

You can make them equal to each other in an equation:

M<1 = M<2

$7y+16=2x$

We solved for x and know that it is 15, so substitute 15 into the equation for x.

$7y+16=2(15)$
$7y+16=30$

Subtract 16 from both sides of the equation.

$7y=14$

Divide both sides of the equation by 7 to isolate the variable x.

$y=2$

Hope this helped! Comment below if you have any clarifying questions.

3 0

3 years ago

A climbing gym charges $10 to climb each day. A pair of climbing shoes costs $84. It costs $169 to buy 6 days of climbing, one p

xxTIMURxx [149]

Answer for this question is $25

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3 years ago

Determined the quadrant for an angle with the following characteristics: cotθ>0 and cscθ>0.

oee [108]

$\csc\theta=\dfrac1{\sin\theta}>0\implies\sin\theta>0$

This happens whenever the terminal point of $\theta$ lies in either the first or second quadrants.

Meanwhile,

$\cot\theta=\dfrac1{\tan\theta}=\dfrac{\cos\theta}{\sin\theta}>0\implies\cos\theta>0$

since you already know sine is positive. Cosine is positive when the angle lies in the first or fourth quadrant.

Sine and cosine are both positive only when $\theta$ is the first quadrant, which means this angle's terminal point lies in the first quadrant (A).

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3 years ago

Read 2 more answers

Write the word phrases into an algebraic expression : 4 less than 5 times a number "p"

shusha [124]

Answer: 5p - 4

5 times ‘p’ = 5p
4 less than ‘p’ = p - 4

Therefore,
=> 5p - 4

4 0

2 years ago

Factor 3x^2y^2 − 2xy^2 − 8y^2. Show your work.

docker41 [41]

<span>3x^2y^2 − 2xy^2 − 8y^2 =
y^2 (3x^2 - 2x - 8) =

factoring with leading coefficient:

for ax2+bx+c find two numbers n,m, that m*n = a*c and m+n = b
</span><span><span>
3x^2 - 2x - 8
a=3, b=-2, c=-8
</span>a*c = 3*(-8) = -24
-24=(-6)*4 and -6+4=-2, so m=-6 and n=4

replace bx with mx + nx and factor by grouping
</span><span>
3x^2 - 2x - 8 = </span>3x^2 -6x + 4x -8 = 3x(x-2) + 4(x-2) = (3x+4)(x-2)

answer:
<span>3x^2y^2 − 2xy^2 − 8y^2 = y^2(3x+4)(x-2)</span>

7 0

3 years ago