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3 years ago

In triangle ABC, if an exterior angle drawn at vertex C

Mathematics

1 answer:

Lorico [155]3 years ago

3 0

Answer:

Part 1) Option D. must be an acute angle

Part 2) m∠A=70°

Step-by-step explanation:

Part 1) In triangle ABC, if an exterior angle drawn at vertex C measures 45, then angle B...

we know that

An exterior angle of a triangle is equal to the sum of the opposite interior angles

The measure of an exterior angle at C is equal to the sum of the interior angles at A and B

we have that

45°=m∠A+m∠B

therefore

m∠B < 90°

Angle B must be an acute angle

Part 2)

we know that

An exterior angle of a triangle is equal to the sum of the opposite interior angles

The measure of an exterior angle at B is equal to the sum of the interior angles at A and C

m∠A+m∠C=2m∠C+5

m∠C=m∠A-5 ----> equation A

m∠C=65° ----> equation B

substitute equation B in equation A

65°=m∠A-5

m∠A=(65+5)°=70°

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What are 5 numbers that have 5, 11, and 2 as prime factors

Firdavs [7]

110, 220, 330, 440, 550

hope this helps

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4 years ago

Find the distance between the lines with equations -4x+7y+9=0 and y=4/7x-9

uysha [10]

Answer:

54/sqrt(65)

Step-by-step explanation:

You can only find the distance between two lines that are parallel. If they are not parallel they are different lengths everywhere. So first lets check they are parallel. i am going to write them in slope intercept form, which is y = mx + b

-4x+7y+9=0

-4x + 9 = -7y

y = 4/7 x - 9/7

y = 4/7x - 9

the slopes (m) are the same so theya re parallel.

Now, to find the distance we want a line that is perpendicular to the two, find where that line intersects both lines, then find the distance between those two points. Easy right?

First a line that is perpendicular. Super easy, a perpendicular line as a slope of -1/m. for these two functons m = 4/7 so slope for this perpendicular equation is -7/4.

so the most simple function is y = -7/4 x so let's use that.

Now when does y = -7/4 x intersect y = 4/7 x - 9/7 and y = 4/7x - 9? just set them equal to each other.

-7/4 x = 4/7 x - 9/7

-7/4 x - 4/7 x = -9/7

(-49 - 16)/28 x = -9/7

-65/28 x = -9/7

x = 252/455

x = 36/65

Just double check, plug this into both equations and you should get the same answer.

-7/4 x

-7/4 (36/65)

-63/65

4/7 x - 9/7

4/7 (36/65) - 9/7

-63/65

So the point is (36/65, -63/65) Fun. Next

-7/4 x = 4/7x - 9 Just gonna do this in one step.

x = 252/65

so now -7/4 252/65 = 4/7 252/65 - 9 = -441/65 So the point is (252/65, -441/65)

Now, we want the distance between (36/65, -63/65) and (252/65, -441/65)

sqrt((252/65 - 36/65)^2 + (-441/65 - -63/65)^2) = 54/sqrt(65)

So that's the distance between the two lines.

6 0

3 years ago

2/3x(-3)+(-2)-1/3x hurry i need this answered

mrs_skeptik [129]

Answer:

-7x/3 - 2

Step-by-step explanation:

7 0

3 years ago

You have 8 gallons of lemonade to sell. You use cone-shaped cups that are 9 centimeters in diameter and 12 centimeters tall. Eac

andre [41]

You will need 119 cups to sell all of the lemonade.

Step-by-step explanation:

Given,

Diameter of cups = 9 cm

Radius of cup = $\frac{Diameter}{2}=\frac{9}{2}=4.5\ cm$

Height of cups = 12 cm

We will find volume of cup.

$Volume = \frac{1}{3}\pi r^2h\\$

Putting all the values

$Volume=\frac{1}{3}(3.14)(4.5)^2(12)\\\\Volume=\frac{1}{3}(3.14)(20.25)(12)\\\\Volume= \frac{763.02}{3}\\\\Volume= 254.34\ cm^3$

Therefore;

Each cup can hold 254.34 cubed centimeter of lemonade.

Number of gallons = 8

1 gallon = 3785 cm³

8 gallons = 3785*8 = 30280 cm³

Let,

x = Number of cups

Volume of lemonade in one cup * Number of cups = Volume of 8 gallons

254.34x=30280

Dividing both sides by 254.34

$\frac{254.34x}{254.34}=\frac{30280}{254.34}\\x=119.05$

Rounding off to nearest whole number

x = 119

You will need 119 cups to sell all of the lemonade.

Keywords: volume, division

Learn more about volume at:

#LearnwithBrainly

4 0

3 years ago

Can you answer this and explain it please! for 100 points

pashok25 [27]

Answer:

D) -12

Step-by-step explanation:

$3(x-4)+(2-x)-x^2$

Replace X With 5

$3(5-4)+(2)(5)-5^2$

$=-12$

I Hope This Helps

Please Mark Me As Brainliest :)

6 0

2 years ago