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butalik [34]
3 years ago
7

I need help understanding this ASAP plz, I have a quiz over this next week!!!!

Mathematics
1 answer:
scZoUnD [109]3 years ago
6 0

Answer:

Step-by-step explanation:

With any two points, you can find the line between them with:

y = mx + b\\where\\m = \frac{y_2-y_1}{x_2-x_1}

#1:

(-1, 1) -> (1, 3) m = \frac{3-1}{1-(-1)} = 1, 3 = 1(1) + b, b = 2, y = x + 2

(3, 4) -> (0, 2) m = \frac{4-2}{3-0} = \frac{2}{3}, 2 = \frac{2}{3}(0) + b, y = \frac{2}{3}(x)+2

(0, 1) -> (3, 3) m = \frac{3-1}{3-0} = \frac{2}{3}, 1 = 2/3(0) + b, y = \frac{2}{3}(x) + 1

Lines b and c are parallel because they have the same slopes

#2 is a bit easier

a: 2y = x + 12, y = \frac{1}{2}(x) + 6

b:2y - x = 5, y = \frac{1}{2}(x) + \frac{5}{2}

c: 2y + x = 4, y = \frac{-1}{2}(x) + 2

Since lines a and b have the same slope, they are parallel

#3:

(1, 3), y = 2x - 5

We have to find a line with a slope of 2 that passes through the two points

y = 2x + b\\3 = 2(1) + b\\b = 1\\\\y = 2x + 1

#4:

(-2, 1) , y = -4x + 3

We have to find a line with a slope of-4 that passes through the line

y = -4x + b\\1 = -4(-2) + b\\1 = 8+ b\\b = -7\\y = -4x - 7

#5:

(-2, 3) (1, -1), m = \frac{3-(-1)}{-2-1} = \frac{-4}{3}, 3 = \frac{8}{3} + b, b = \frac{1}{3}, y = \frac{-4x}{3} + \frac{1}{3}

(-3, 1) (1, 4), m = \frac{4-1}{1-(-3)} =\frac{3}{4}, 4 = \frac{3(1)}{4} + b, y = \frac{3}{4}(x) + \frac{13}{4}

(0, 2) (3, -2) m = \frac{2-(-2)}{0-3} = \frac{-4}{3} , 2 = b, y = \frac{-4}{3}(x) + 2

Since lines c and b have negative reciprocal slopes, they are perpendicular

#6:

a: y = -4x + 7

b: x = 4y + 2, y = \frac{x}{4} - \frac{1}{2}

c: -4y + x = 3, y = \frac{x}{4} - \frac{3}{4}

since lines a and c have negative reciprocal slopes, they are perpendicular

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The summer olympic occurs every 4 years. Every 6 years, a US senator runs for reelection. If both events occurred last year how
deff fn [24]

Answer:

12 years

Step-by-step explanation:

every 4 years, olympic occurs.

Every 6 years, senator reelection.

if last year was 2020

in 2024 olympic will occur

in 2026 the reelection will occur

in 2028 olympic will occur

in 2032 olympic and reelection will occur will occur

2032 - 2020 = 12

12 years is the answer

7 0
3 years ago
Need answers ASAP
andrew-mc [135]
Data:
r (radius) = 14 m
h (height) = 6 m
v (volume) = ?

Formula:
V =  \pi *r^2*h

Solving:
V = \pi *r^2*h
V =  \pi *14^2*6
V =  \pi *196*6
\boxed{\boxed{V = 1176 \pi\:m^3}}\end{array}}\qquad\quad\checkmark
4 0
3 years ago
If a 4 x 16 rectangle has the same area as a square, what is the length of a side of the square?
Licemer1 [7]

Answer:

Option D. 8 units

Step-by-step explanation:

step 1

Find the area of rectangle

The area of rectangle is

A=(4)(16)=64\ units^2

step 2

Find the length side of the square with the same area of rectangle

The area of a square is

A=b^2

where

b is the length side of the square

we have

A=64\ units^2

substitute

64=b^2

take the square root both sides

b=8\ units

therefore

The length side of the square is 8 units

7 0
3 years ago
. Two bicyclists, Sarah and Emily, depart from the same location. Sarah heads N55°E at an average speed of 6 km/hr. Emily heads
Liula [17]

Answer:

The distance between them after 30 minutes is 6.5 km.

Step-by-step explanation:

Speed = \frac{distance}{time}

Sarah's speed = 6 km/hr = 1.6667 m/s

Emily's speed = 10 km/hr = 2.7778 m/s

The measure of angle between their bearings = 105^{o}

After 30 minutes (1800 seconds);

distance = speed x time

Sarah would have covered a distance = 1.6667 x 1800

                               = 3000 m

                               = 3 km

Emily would have covered a distance = 2.7778 x 1800

                               = 5000 m

                               = 5 km

The distance between them, a, can be determined by applying the cosine rule;

a^{2} = b^{2} + c^{2} - 2bcCos A

   = 5000^{2} + 3000^{2} -2(5000 x 3000) Cos 105

   = 5000^{2} + 3000^{2} -2(5000 x 3000) x (-0.2588)

   = 2.5 x 10^{7} + 9 x 10^{6} + 7764000

   = 41764000

a = \sqrt{41764000}

  = 6462.5073

a = 6462.5 m

The distance between them after 30 minutes is 6.5 km.

4 0
2 years ago
Is it possible to draw an acute isosceles triangle with side lengths of 6 cm, 9 cm, and 12 cm and angles of 30°, 50°, and 100° ?
bagirrra123 [75]

Answer:

Yes

Step-by-step explanation:

A full triangle is 180 degrees. 100 + 30 + 50 = 180.

I hope you get it right! :D

(i hope i get brainlist)

5 0
2 years ago
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