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3 years ago

Pleaseeee help! I'm really confused.

Mathematics

1 answer:

cluponka [151]3 years ago

8 0

You treat this problem as though it's a regular triangle.

You plug the numbers 24 and 45 into the equation for a triangle which is A=1/2 (L x W)

So what you get is A= 1/2 (24 x 45)

Which can be simplified to A= 12 x 45.

In the end that totals to 540 meters.

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Function f(x)=|x| is transformed to create function g(x)=|x+4|+3. What transformations are performed to function f to get functi

Ahat [919]

Answer:

Step-by-step explanation:

Function f(x)=|x| is transformed to create function g(x)=|x+4|+3. What transformations are performed to function f to get function g? Select each correct answer.

Function f is translated 4 units to the right.

Function f is translated 3 units to the left.

Function f is translated 4 units down.

(this one is correct) Function f is translated 3 units up.

Function f is translated 4 units up.

(this one is correct) Function f is translated 4 units to the left.

Function f is translated 3 units to the right.

Function f is translated 3 units down.

3 0

2 years ago

A total of $12,000 is invested in two corporate bonds that pay 7.5% and 9% simple interest. The invest wants an annual interest

nlexa [21]

Answer:

$13,200

Step-by-step explanation:

You need to use the simple interest formula

I = P * r * t

I = Interest accrued

P = Principal amount invested

r = Interest rate you need to divide by 100 to get it in decimal form

t = time, in years if you are given a partial year, divide the months by 12

P = $12,000

r = 7.5% = .075

t = 1

But, because we want I to equal $990 then I is

I = $990

So we ignore our P and instead solve for the P that will give us the desired result.

I = P * r * t

$990 = P * .075 * 1

$990 = P.075 Divide each side by .075

$990/.075 = P.075/.075

$990/.075 = P

$13,200 = P

So, to earn an annual interest income of $990, $13,200 will have to be invested in the 7.5% bond.

6 0

3 years ago

Solve the following recurrence relation: <img src="https://tex.z-dn.net/?f=A_%7Bn%7D%3Da_%7Bn-1%7D%2Bn%3B%20a_%7B1%7D%20%3D

-Dominant- [34]

By iteratively substituting, we have

$a_n = a_{n-1} + n$

$a_{n-1} = a_{n-2} + (n - 1) \implies a_n = a_{n-2} + n + (n - 1)$

$a_{n-2} = a_{n-3} + (n - 2) \implies a_n = a_{n-3} + n + (n - 1) + (n - 2)$

and the pattern continues down to the first term $a_1=0$ ,

$a_n = a_{n - (n - 1)} + n + (n - 1) + (n - 2) + \cdots + (n - (n - 2))$

$\implies a_n = a_1 + \displaystyle \sum_{k=0}^{n-2} (n - k)$

$\implies a_n = \displaystyle n \sum_{k=0}^{n-2} 1 - \sum_{k=0}^{n-2} k$

Recall the formulas

$\displaystyle \sum_{n=1}^N 1 = N$

$\displaystyle \sum_{n=1}^N n = \frac{N(N+1)}2$

It follows that

$a_n = n (n - 2) - \dfrac{(n-2)(n-1)}2$

$\implies a_n = \dfrac12 n^2 + \dfrac12 n - 1$

$\implies \boxed{a_n = \dfrac{(n+2)(n-1)}2}$

4 0

2 years ago

Make x the subject of the formula 6x+a=5

Tatiana [17]

You would -a to get 6x=5-a then divide by 6 which you would get your final answer which is x=5-a/6

7 0

3 years ago

Please help with 1-9 43 points

Paul [167]

Remark

I'll do two from each group, leaving you with 1. I just leave the answer for the one I don't do or a hint it it is long. That's more than we are instructed to do (which is three parts per posted question).

One

Two ratios form a proportion because they both equal the same thing when you reduce them to the point where the ratios are prime to each other.

3/4 = 12/16

3/4 can't be reduced any further. When both 12 and 16 are divided by 4, the result is 3/4

Two

Formula

Sale Price/Original Price = 3/4

Solve

Sale Price / 64 = 3/4 Multiply both sides by 64

Sale Price = (3/4)*64

Sale Price = 48

Three

682 Trillion atoms of hydrogen.

Four

Formula

rotations / 40 seconds = rotations / second

Solve

2000 / 40 seconds = rotations / 1 second Just divide

50 rotations/1 second = rotations / second.

Five

Formula

Herd of cows / Total pounds of milk = 1 cow / pounds of milk

Given

Herd = 12

pounds total = 224998

Solve

12/224998 = 1 / x Cross multiply

12x = 224998

x = 18750 pounds of milk for 1 cow.

Six

0.5 m in 1 second.

Seven

Formula

Pages / hour = pages / minute

pages / hour = 4.5

1 hour = 60 minutes.

Solve

4.5 / 1 hour. But 1 hour = 60 min

4.5 pages / 60 min = 0.075 pages per minute.

Note this is not a true proportion. You just have to know how it is done.

Eight

This is also not a true proportion. The best way to do this is called unit analysis.

$\dfrac{18feet}{2seconds} * \dfrac{1 mile}{5280 feet}\dfrac{3600sec}{1hour}$

Each set of units on the right will cancel with a set of units on the left until all that you area left with is miles / hour. Then just multiply the numerator numbers together and denominator numbers together.

numerator: 18 * 1 * 3600 = 64800

denominator: 2 * 5280 * 1 = 10560

Now divide the numerator by the denominator.

answer: numerator/denominator = 64800/10560 = 6.14 miles per hour.

Nine

Note: there are 1760 yards in a mile.

1 gallon will take you 32000 yards or 18 miles. Do this the same way eight was done.

7 0

4 years ago

Read 2 more answers