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3 years ago

What is the slope of the line that passes through the points (-9, 8) and (–21, 10)?

Mathematics

1 answer:

Aliun [14]3 years ago

5 0

Answer:

-1/6

Step-by-step explanation:

We can use the slope formula

m = ( y2-y1)/(x2-x1)

= ( 10-8)/(-21 - -9)

= ( 10-8)/(-21 +9)

= 2 /-12

= -1/6

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Ainat [17]

Answer:

a. 5.25cm

b. 374.6 cm^2

Step-by-step explanation:

The radius of the conical cup is half the length of the arc formed

Mathematically, the length of the arc would be;

L = theta/360 * 2 * pi * r

L = 135/360 * 2 * 22/7 * 14 = 33 cm

Now, the arc of this sector will become the base circumference of the circular base of the cone

Thus;

2 * pi * R = 33

2 * 22/7 * R = 33

R = (7 * 33)/44 = 5.25 cm

b. The volume of the cone

Kindly note that the radius of the circle becomes the height of the cone

Mathematically;

V = 1/3 * pi * r^2 * h

Kindly note that the radius of the circle will become the slang height of the cone

We can use pythagoras’ theorem to find the height of the cone

Pythagoras theorem states that the square of the hypotenuse equals the sum of the squares of the two other sides

So here, slant height l is the hypotenuse, h and r are the other two sides

So 14^2 -5.25^2 = h^2

h^2 = 168.4375

h = 12.98 cm

Volume is thus ;

1/3 * pi * 5.25^2 * 12.98 = 374.6 cm^3

3 0

4 years ago

Determine the values of x and y in the diagram and use them to determine the measures of the eight angles

AleksAgata [21]

Answer:

Part 1) $x=8$

Part 2) $y=12$

Part 3) $m\angle a=105^o$

Part 4) $m\angle b=75^o$

Part 5) $m\angle c=105^o$

Part 6) $m\angle d=75^o$

Part 7) $m\angle e=105^o$

Part 8) $m\angle f=75^o$

Part 9) $m\angle g=105^o$

Part 10) $m\angle h=75^o$

Step-by-step explanation:

see the attached figure with letters to better understand the problem

Part 1) Determine the value of x

we know that

$m\angle a=m\angle g$ ----> by alternate exterior angles

substitute the given values

$(17x-31)^o=(12x+9)^o$

solve for x

$17x-12x=9+31\\5x=40\\x=8$

Part 2) Determine the value of y

we know that

$m\angle c+m\angle d=180^o$ ----> by supplementary angles (consecutive interior angles)

substitute the given values

$(7y+21)^o+(5y+15)^o=180^o$

solve for y

$(12y+36)^o=180^o$

$12y=180-36$

$12y=144$

$y=12$

Part 3) Find the measure of angle a

we have

$m\angle a=(17x-31)^o$

substitute the value of x

$m\angle a=(17(8)-31)=105^o$

Part 4) Find the measure of angle b

we know that

$m\angle a+m\angle b=180^o$ ----> by supplementary angles (consecutive interior angles)

we have

$m\angle a=105^o$

substitute

$105^o+m\angle b=180^o$

$m\angle b=180^o-105^o$

$m\angle b=75^o$

Part 5) Find the measure of angle c

we know that

$m\angle c=m\angle a$ ----> by vertical angles

we have

$m\angle a=105^o$

therefore

$m\angle c=105^o$

Part 6) Find the measure of angle d

we know that

$m\angle d=m\angle b$ ----> by vertical angles

we have

$m\angle b=75^o$

therefore

$m\angle d=75^o$

Part 7) Find the measure of angle e

we know that

$m\angle e=m\angle a$ ----> by corresponding angles

we have

$m\angle a=105^o$

therefore

$m\angle e=105^o$

Part 8) Find the measure of angle f

we know that

$m\angle f=m\angle b$ ----> by corresponding angles

we have

$m\angle b=75^o$

therefore

$m\angle f=75^o$

Part 9) Find the measure of angle g

we know that

$m\angle g=m\angle c$ ----> by corresponding angles

we have

$m\angle c=105^o$

therefore

$m\angle g=105^o$

Part 10) Find the measure of angle h

we know that

$m\angle h=m\angle d$ ----> by corresponding angles

we have

$m\angle d=75^o$

therefore

$m\angle h=75^o$

6 0

3 years ago

Ms shoe kept 2 meatballs to herself then divided the others equally among her 14 children if each child got 5 meatballs how many

mart [117]

Meatballs Ms. Show kept for herself = 2

Meatballs each child got = 5

Number of children Ms. Shoe has = 14

Hence, total number of meatballs = 2 + (14 * 5) = 2 + 70 = 72

3 0

3 years ago

Use the numbers shown to complete the table for each value of m. Numbers may be used once, more than once, or not at all.

morpeh [17]

Answer:

20 ,24 go on mailboxes closest to the right

Step-by-step explanation:

4 0

3 years ago

Michelle's class is handing out balloon arrangement consisting of 4 balloons each each balloon has and equally likely chance of

lara [203]

Answer:

The answer is 1/30 or 0.0333333...

Step-by-step explanation:

The way to find experimental probability is by comparing the number of times the event occurs to the total number of trials. In this question, there has only been one arrangement that consists of ballooons that are all the same color. This means that 1 (the number of times the event occurred)/ 30 (total number of trials) is the answer. I hope you have a great day!!

3 0

3 years ago