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3 years ago

The line passing through (-4,6) and parallel to the line y=3x+8

1 answer:

6 0

y=3x+8
if it's parallel to this line, then the slope will also be 3.

slope = 3
x₁ = -4
y₁ = 6

for this question, we use point-slope
y - y₁ = m(x - x₁)

y + 4 = 3(x - 6)
y + 4 = 3x - 18

y = 3x - 14
this is your equation

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Find the area of the irregular figure. Round to the nearest hundredth.

RSB [31]

Answer:

$67.5\text{ [square units]}$

Step-by-step explanation:

The composite figure consists of one rectangle and two triangles. We can add up the area of these individual shapes to find the total area of the irregular figure.

Formulas:

Area of rectangle with base $b$ and height $h$ : $A=bh$
Area of triangle with base $b$ and height $h$ : $A=\frac{1}{2}bh$

By definition, the base and height must intersect at a 90 degree angle.

The rectangle has a base of 10 and a height of 5. Therefore, its area is $A=10\cdot 5=50$ .

The smaller triangle to the left of the rectangle has a base of 2 and a height of 5. Therefore, its area is $A=\frac{1}{2}\cdot 2\cdot 5=5$ .

Finally, the larger triangle on top of the rectangle has a base of 5 and a height of 5. Therefore, its area is $A=\frac{1}{2}\cdot 5\cdot 5=12.5$ .

Thus, the area of the total irregular figure is:

$50+5+12.5=\boxed{67.5\text{ [square units]}}$

7 0

3 years ago

Kaitlin, Tony, and Austin sent a total of 103 text messages over their cell phones during the weekend. Austin sent 4 times as ma

emmainna [20.7K]

The number of messages Kaitlyn, Tony and Austin sent are 13, 18 and 72 messages respectively.

<h3>How to write and solve equation?</h3>

let

Number of messages Kaitlyn sent = x
Number of messages Tony sent = x + 5
Number of messages Austin sent = 4(x + 5)
Total messages = 103

103 = x + (x + 5) + 4(x + 5)

103 = x + x + 5 + 4x + 20

103 = 6x + 25

103 - 25 = 6x

78 = 6x

x = 78/6

x = 13

Number of messages each sent:

Number of messages Kaitlyn sent = x

= 13 messages

Number of messages Tony sent = x + 5

= 13 + 5

= 18 messages

Number of messages Austin sent = 4(x + 5)

= 4(13 + 5)

= 4(18)

= 72 messages

Learn more about equation:

brainly.com/question/2972832

#SPJ1

3 0

2 years ago

There are 135 people in a sport centre. 73 people use the gym. 59 people use the swimming pool. 31 people use the track. 19 peop

wlad13 [49]

Answer:

Probability that the person doesn't use any facility = 0.0889

Step-by-step explanation:

Total number of people in a sports center = 135

Number of people using gym 'G' = 73

Number of people using swimming pool 'P' = 59

Number of people using track 'T' = 31

Number of people using gym and pool (G∩P) = 19

Number of people using pool and track (P∩T) = 9

Number of people using gym and track (G∩T) = 16

Number of people using all three facilities (G∩P∩T) = 4

Therefore, from the rule of compound probability,

P(GUPUT) = P(G) + P(P) + P(T) - P(G∩P) - P(G∩T) - P(P∩T) + p(G∩P∩T)

We know probability of an event = $\frac{\text{Favorable event}}{\text{Total outcomes}}$

We will plug in the values of probabilities of each event in the formula.

P(GUPUT) = $\frac{73}{135}+\frac{59}{135}+\frac{31}{135}-\frac{19}{135}-\frac{9}{135}-\frac{16}{135}+\frac{4}{135}$

= $\frac{1}{135}(73+59+31-19-9-16+4)$

= $\frac{123}{135}$

And probability that a person doesn't use any facility = 1 - P(GUPUT)

= 1 - $\frac{123}{135}$

= $\frac{135-123}{135}$

= $\frac{12}{135}$

= $\frac{4}{45}$ ≈ 0.0889

7 0

4 years ago

Read 2 more answers

The circumference of a circle is 6 pi cm what is the length of an arc of 140 degree

ValentinkaMS [17]

Since the total circumference of the circle is 60 pi cm which passes around 360˚, the length of an arc of 140˚ will be equal to 140/360 = 7/18 times the total length:
l = (7/18) * 60 pi cm = 23.3 pi cm

3 0

3 years ago

The sum of two numbers is 76 and their difference is 14. Find each of the numbers

Ludmilka [50]

The answers would be 24 and 52 hope this helped!

5 0

3 years ago

Read 2 more answers