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3 years ago

Geometry! Please help! What is the area of this triangle?

Mathematics

1 answer:

djverab [1.8K]3 years ago

3 0

In both cases, the area of the triangle can be computed from the formula
A = (1/2)bh
where b is the length of the base, and h is the height perpendicular to the base.

1. It is convenient to use DE as the base. Its length is 4-1 = 3. Then the height is the distance from F to DE, which is 1-(-3) = 4. By the formula, the area is
A = (1/2)(3)(4) = 6

2. It is convenient to use LK for the base. Its length is 4-0 = 4. Then the height is the distance from J to the line y=-5, which is -1-(-5) = 4. By the formula, the area is
A = (1/2)(4)(4) = 8

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The current population of a town is 10,000 and its growth in years can be represented by P(t) = 10,000(0.2)^t, where t is the ti

DiKsa [7]

Answer:

1) 20%

2) Choice a.

Step-by-step explanation:

$P(t)=10000(0.2)^t$

1) $P(0)$ is the population initially.

$P(1)$ is the population after a year.

$\frac{P(1)}{P(0)}$ represents the population increase factor.

So let's evaluate that fraction:

$\frac{P(1)}{P(0)}$

$\frac{10000(0.2)^1}{10000(0.2)^0}$

$\frac{0.2^1}{0.2^0}=\frac{0.2}{1}=0.2$

0.2=20%

2) Let's figure out the population growth in terms of months instead of years.

$P(t)=10000(0.2)^{t}$

We want t to represent months.

A full year is 12 months, in a full year we have that $P(1)=10000(0.2)^1=10000(0.2)=2000$

So we want a new P such that $P(12)=2000$ since 12 months equals a year.

Let's look at the functions given to see which gives us this:

a) $P(12)=10000(0.87449)^{12}=2000 \text{approximately}$

b) $P(12)=10000(0.87449)^{12(12)}=0 \text{ approximately}$

c) $P(12)=10000(0.87449)^{\frac{1}{12}}=9889 \text{approximately}$

d) $P(12)=10000(0.87449)^{12+12}=400 \text{approximately}$

So a is the function we want.

Also another way to look at this:

$P(t)=10000(.2)^t$ where $t$ is in years.

$P(t)=10000(.2^\frac{1}{12})^t$ where $t$ is in months.

And $.2^\frac{1}{12}=0.874485 \text{approximately}$

8 0

3 years ago

What is the length of DE

Valentin [98]

Answer:

Step-by-step explanation:

3 0

3 years ago

14.

Readme [11.4K]

The domain is t=0 to t=3.2 and range is y = 0 to 57.125 feet.

<u>What are Domain and range of a Function?</u>

The range of values that we are permitted to enter into our function is known as the domain of a function.
The x values for a function like f make up this set (x). A function's range is the collection of values it can take as input.
After we enter an x value, the function outputs this sequence of values. The y values are those.
A function can be compared to a piece of equipment on an assembly line.
A few screws and nuts are located on one end of the assembly line, while a car is located on the other. The function is the device in the center. The domain is the screws and bolts that we insert into the machine. The car at the other can be thought of as the range.

Given function is : y = -16t^2 + 50t + 4

It hits the ground when y=0

0 = -16t^2 + 50t + 4

8t^2 -25t -2 = 0

t = 25/16 + (1/16)sqrt(625+64) = (25+26.25)/16 = 51.25/16 = 3.2 seconds

domain is t=0 to t=3.2 [3.2]

take the derivative and set it equal to zero to find maximum height

-32t +50 = 0

t = 50/32 = 25/16 = 1.5625 seconds

-16(25/16) + 50(25/16) + 4 = 34(25/16) + 64/16 = (17(25)+32)/8 = 57.125 = maximum height

range is y = 0 to 57.125 feet. the discus goes from 4 feet to 57 1/8 feet and back down to 0 feet.

Know more about Domain and Range with the help of the given link:

brainly.com/question/20349151

#SPJ4

8 0

2 years ago

10³ ÷ (25×4) = Please

Leviafan [203]

Answer:

Step-by-step explanation:

8 0

2 years ago

Read 2 more answers

Ali has q quarters. Tom has four more quarters than Ali.

Anna35 [415]

Answer: x(.25)+(4+x(.25))=y

Step-by-step explanation:

1. set up the equation-

Ali has an unknown amount of quarters so make that x.

We know quarters are 25 cents so .25 if he has one quarter you put that one quarter into x, 2 into x and so on

Tom has 4 more, since he has 4 more it is 4+x and one again times .25

2. that is it

7 0

2 years ago