What is the area of the obtuse triangle given below?

Agata [3.3K]

Both problems give you a function in the second column and the x-values. To find out the values of a through f, you need to plug in those x-values into the function and simplify!

You need to know three exponent rules to simplify these expressions:
1) The negative exponent rule says that when a base has a negative exponent, flip the base onto the other side of the fraction to make it into a positive exponent. For example, $3^{-2} =
\frac{1}{3^{2} }$ .
2) Raising a fraction to a power is the same as separately raising the numerator and denominator to that power. For example, $(\frac{3}{4}) ^{3} = \frac{ 3^{3} }{4^{3} }$ .
3) The zero exponent rule says that any number raised to zero is 1. For example, $3^{0} = 1$ .


Back to the Problem:
Problem 1
The x-values are in the left column. The title of the right column tells you that the function is $y = 4^{-x}$ . The x-values are:
1) x = 0
Plug this into $y = 4^{-x}$ to find letter a:
$y = 4^{-x}\\
y = 4^{-0}\\
y = 4^{0}\\
y = 1$

2) x = 2
Plug this into $y = 4^{-x}$ to find letter b:
$y = 4^{-x}\\ 
y = 4^{-2}\\ 
y = \frac{1}{4^{2}} \\ 
y= \frac{1}{16}$

3) x = 4
Plug this into $y = 4^{-x}$ to find letter c:
$y = 4^{-x}\\ 
y = 4^{-4}\\ 
y = \frac{1}{4^{4}} \\ 
y= \frac{1}{256}$


Problem 2
The x-values are in the left column. The title of the right column tells you that the function is $y = (\frac{2}{3})^x$ . The x-values are:
1) x = 0
Plug this into $y = (\frac{2}{3})^x$ to find letter d:
$y = (\frac{2}{3})^x\\
y = (\frac{2}{3})^0\\
y = 1$

2) x = 2
Plug this into $y = (\frac{2}{3})^x$ to find letter e:
$y = (\frac{2}{3})^x\\ y = (\frac{2}{3})^2\\ y = \frac{2^2}{3^2}\\
y = \frac{4}{9}$

3) x = 4
Plug this into $y = (\frac{2}{3})^x$ to find letter f:
$y = (\frac{2}{3})^x\\ y = (\frac{2}{3})^4\\ y = \frac{2^4}{3^4}\\ y = \frac{16}{81}$

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Answers:
a = 1
b = $\frac{1}{16}$ 
c = $\frac{1}{256}$
d = 1
e = $\frac{4}{9}$
f = $\frac{16}{81}$

5 0

3 years ago

Is y=7.5x a proportional relationship and why

DerKrebs [107]

Direct Proportion functions look like this:

y=kx

'k' is the constant of proportionality and in this case its 7.5 or 15/2.

--------------------------------------------

When x=1, y=7.5
When x=2, y=15
When x=3, y=22.5

Therefore y is directly proportional to x.

--------------------------------------

DIRECT PROPORTION EXPLAINED:

Say a football costs £7.50. If you buy one football you'll have to pay out £7.50, but if you you buy two footballs you'll have to pay out £15.00. Therefore the cost of the football(s) is directly proportional to the amount of footballs you buy. C=cost, f=football(s) and C∝f, therefore C=kf, but as k=7.5, C=7.5f.

INVERSE PROPORTION EXPLAINED:

If it were to take 8 hours for one bricklayer to set up a wall, how long would it take for two bricklayers to set up a wall? The answer in this case would be 4 hours.

T=time to set up a wall
b=bricklayer(s)

Therefore T∝1/b, and T=k/b. In this case k=8 so T=8/b.

When b=1, T=8.
When b=2, T=4.

We'd say that the time it would take for bricklayers to set up a wall would be inversely proportional to the amount of bricklayers available.

4 0

3 years ago

Read Fred's conclusion. If the sum of the digits of a number is a multiple of 3. then the number is a multiple of 6. Which state

kolezko [41]

Answer:

the answer would be a because 42÷6=7 and 42÷3=14.

7 0

3 years ago

What is the answer to this

Sever21 [200]

I think it’s d I’m not sure though

8 0

3 years ago

Someone help pls :,)

Semenov [28]

Answer:

W = 87 degrees

Step-by-step explanation:

First we can rearrange the question so that W is isolated on the left side, which we do by dividing both sides by tan:

tanW/tan = 19.0811/tan

W = 19.0811/tan

Now we can use the inverse tan function on the calculator ( $tan^{-1}$ ) to calculate it:

W = 19.0811 x $tan^{-1}$

W = 87 degrees

Hope this helped!

8 0

3 years ago