In ΔIJK, i = 340 cm, ∠I=120° and ∠J=59°. Find the area of ΔIJK, to the nearest 10th of a square centimeter.

A child is hopping along a sidewalk. The ratio below shows the comparison between the number of hops and the distance traveled.

blagie [28]

Answer:

Find the ratio of hops to distance traveled (1: 1.5), then multiply 150 by 1.5.

Step-by-step explanation:

A child is hopping along a sidewalk. The ratio table below shows the comparison between the number of hops and the distance traveled. Hopping Number of hops Distance traveled (ft) 20 30 50 75 80 120 150 ?

Which statement correctly explains how to find the distance traveled after 150 hops? Subtract 120 – 75 to get 45, then add that number to 120. Add 30 + 75 + 120. Find the ratio of hops to distance traveled (1:1.5), then multiply 150 by 1.5. Find the ratio of hops to distance traveled (1:1.5), then divide 150 by 1.5.

Solution:

The table is:

No. of hops Distance traveled

20 30

50 75

80 120

150 ?

From the table, for every 30 increase in the number of hops, the distance travelled increase by 45 feet

Find the slope of the line:

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

m=slope of the line

y2-y1 = change in distance travelled

x-2 - x1 = Change in number of hops

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

m = (75-30) / (50-20)

=45 / 30

m = 1.5

Then, the line is:

y = 1.5x

We substitute x = 150

y = 1.5x

y = 1.5 × 150

y = 225

7 0

2 years ago

A drinking glass has sides following the shape of a hyperbola. The minimum diameter of the glass is 45 millimeters at a height o

Alinara [238K]

Answer:

The answer is a= 128.95 and b = 14.75

Step-by-step explanation:

Solution

Given

let the equation of the hyperbola be denoted as x2/a2 - y2/b2 = 1 here, we will consider the foci on the x-axis. All units are considered to be in mm.

From question stated, with x and y coordinates represents height and radius respectively,

Then,

When x = 83 + a, y is = 45/2 = 22.5 and

At x = 180 + a, y is = 57/2 = 28.5

It is important to know that, the height is estimated from the focus so we a a is included to the heights.

Thus,

(83+a)2/a2 - 22.52/b2 = 1 and (180+a)2/a2 - 28.52/b2 = 1

By using a calculator we have, a = 128.95 and b = 14.75

Therefore a= 128.95 and b = 14.75

3 0

2 years ago

Isabella filled her pool with water at a constant rate.

AlladinOne [14]

(184-94)/5=18

This means that she fills up 18 liters every minute. Thus she will be done in->

184(original amount)+(2 minutes (time passed during first data point)*18(rate of water)=184+36=220

To find the total time taken we divide 220 by 18 which is 220/18=12 2/9

6 0

2 years ago

Read 2 more answers

The average rate of change from x = 0 to x = 15 is about −4.667. How does the average rate of change from x = 0 to x = 20 compar

Amanda [17]

First we calculate the ambio rate from x = 0 to x = 15:
We have:
R = ((80-10) / (0-15))
R = -4.666666667
We now calculate for the entire interval:
from x = 0 to x = 20:
R = ((80-2) / (0-20))
R = -3.9
Answer:
What is the average rate of change over the entire slide?
R = -3.9
The average rate of change from x = 0 to x = 15 is about -4.667. How does the average rate change from x = 0 to x = 20 compare to this number?
The percentage difference is:
(-3.9 / -4.666666667) * (100) = 83.57142857%
100-83.57142857 = 16.42857143%

6 0

2 years ago

You and a friend each randomly draw a card from a standard deck. What is the probability that at least one of you is holding a f

Andreyy89

Answer:

0.24

Step-by-step explanation:

Total cards = 52

Face cards = heart {K,Q,J} , Spade {K,Q,J} , Club {K,Q,J} , Diamond{K,Q,J} = 12

Now we are given that You and a friend each randomly draw a card from a standard deck.

Probability that no one getting face card:

Favorable events = total cards - face cards = 52 -12= 40

Total cards = 52

So, probability that no one is getting face card = $\frac{40}{52} =0.76$

Now we are supposed to find the probability that at least one of you is holding a face card

So, probability = 1 - probability that no one is getting face card

=1 - 0.76

= 0.24

So, probability that at least one of you is holding a face card is 0.24

8 0

2 years ago

Read 2 more answers