Round 44.3 to the nearest whole number

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

Plz quick hurry help !!

tankabanditka [31]

The answer is A. it is 4 multiplied 3 times

6 0

3 years ago

Does this table represent a function? Why or why not?

artcher [175]

Answer:

NO. B is the answer

Step-by-step explanation:

because there are two of the same x values, causing there to not form a straight line.

Hope this helped! Have a nice day! Plz mark as brainliest!!! :D

-XxDeathshotxX

5 0

3 years ago

The expression on (3+i)(4+5i) can be written in form a+bi, where a and b are integers. What are the values of a and b? (Show you

gregori [183]

$(3 + i)(4 + 5i) \\ 12 + 15i + 4i + 5 {i }^{2} \\ 12 + 19i - 5 \\ 7 + 19i$

Therefore, a is 7 aka real part and b is 19 which is imaginary part.

8 0

3 years ago

The height, h, of the equilateral triangle is given by h =5cotΘ, where Θ is 30 degrees. Can someone help me with this? I don't u

Hoochie [10]

You don't even need the picture to solve this one.

You said that h = 5 cot(Θ) , and you said that Θ is 30 degrees.
All you need now is to find the cotangent of Θ, plop that into the equation,
and the solution practically jumps off the paper into your lap.

To find the cotangent of 30 degrees, you can use a calculator, look it up
in a book, read it off of a slide rule if you have one, draw a picture of a
30-60-90 right triangle etc. You'll find that the cotangent of 30 degrees
is √3 . That's about 1.732 .

So your equation is h = 5 (1.732) = 8.66 (rounded)

Apparently, somebody gave you the equation, and asked you to find 'h'.
Once you had the equation, you didn't even need to know that 'h' has
anything to do with a triangle.

5 0

3 years ago