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2 years ago

Determine the unit rate. Use mental math when you can. 6 golf balls for $15

Mathematics

1 answer:

Lena [83]2 years ago

4 0

Answer:

1 golf ball : $2.50

Step-by-step explanation:

You can first divide 6 and 15 by 3, and get 2 and 5.
Then, you divide 5 by 2, which is 2.5
Therefore, the unit rate is 1 golf ball : $2.50

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The circumference of Earth at the equator is about 40,074 kilometers. Find the diameter of Earth to the nearest kilometer.

PtichkaEL [24]

Answer:

C.62,884

Step-by-step explanation:

8 0

3 years ago

2D - 5F = 30 <br><br> Solve for F

Allushta [10]

Answer:

F = -6 + 2d/5

Step-by-step explanation:

2d-5f=30

subract 2D from each side

-5f=30-2d

divide both sides by -5

f= -6 +2d/5

5 0

4 years ago

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Please help with imaginary numbers worksheet!

mihalych1998 [28]

Problem 5

<h3>Answer: 6i</h3>

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

Explanation:

We have these four identities

i^0 = 1
i^1 = i
i^2 = -1
i^3 = -i

Notice how computing i^4 leads us back to 1. So i^4 = i^0. The pattern repeats every 4 terms. So we divide the exponent by 4 and look at the remainder. We ignore the quotient entirely. We can see that 28/4 = 7 remainder 0. Meaning that i^28 = i^0 = 1.

We can think of it like this if you wanted

i^28 = (i^4)^7 = 1^7 = 1

Then the sqrt(-36) becomes 6i

So overall, we end up with the final answer of 6i

=============================================

Problem 6

<h3>Answer: -3i</h3>

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

Explanation:

We'll use the ideas mentioned in problem 5

46/4 = 11 remainder 2

i^46 = i^2 = -1

sqrt(-9) = 3i

The two outside negative signs cancel out, but there's still a negative from -1 we found earlier. So we end up with -3i

In other words, here is one way you could write out the steps

$-i^{46}*-\sqrt{-9}\\\\-i^{2}*-3i\\\\i^{2}*3i\\\\-1*3i\\\\-3i\\\\$

=============================================

Problem 7

<h3>Answer: -1</h3>

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

Work Shown:

i^10 = i^2 because 10/4 = 2 remainder 2

i^19 = i^3 because 19/4 = 4 remainder 3

i^7 = i^3 because 7/4 = 1 remainder 3

Again, all we care about are the remainders.

$i^{10}+i^{19} - i^{7}\\\\i^{2}+i^{3} - i^{3}\\\\i^{2}\\\\-1$

=============================================

Problem 8

<h3>Answer: -1 + i</h3>

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

Work Shown:

i^22*i^6 = i^(22+6) = i^28

Earlier in problem 5, we found that i^28 = i^0 = 1

So,

$i^1 - \left(i^{22}*i^{6}\right)\\\\i^1 - i^{28}\\\\i^1 - i^{0}\\\\i - 1\\\\-1+i$

8 0

3 years ago

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((PLEASE ANSWER WITH A B C or D))

natali 33 [55]

Answer:

D. 60°

Step-by-step explanation:

The mnemonic SOH CAH TOA reminds you that the relationship of interest is ...

Sin = Opposite/Hypotenuse

sin(M) = ON/OM = 4(√3)/8 = (√3)/2

M = sin⁻¹((√3)/2) = 60°

8 0

3 years ago

How many extraneous solutions does the equation below have?

aev [14]

Answer:

A solution is said to be extraneous, if it is a zero of the equation, but it does not satisfy the equation,when substituted in the original equation,L.H.S≠R.H.S.

The given equation consisting of variable , m is

$\frac{2 m}{2 m+3} -\frac{2 m}{2 m-3}=1\\\\ 2 m[\frac{1}{2 m+3} -\frac{1}{2 m-3}]=1\\\\ 2 m\times \frac{[2 m-3 -2 m- 3]}{4m^2-9}=1\\\\ -6 \times 2 m=4 m^2 -9\\\\ 4 m^2 +1 2 m -9=0\\\\m=\frac{-12 \pm\sqrt{12^2-4 \times 4 \times (-9)}}{2\times 4}\\\\m=\frac{-12 \pm \sqrt {144+144}}{8}\\\\m=\frac{-12 \pm \sqrt {288}}{8}\\\\m=\frac{-12 \pm 12 \sqrt{2}}{8}\\\\m=\frac{3}{2}\times(-1 \pm \sqrt{2})$

None of the two solution

$m=\frac{3}{2}\times(-1 +\sqrt{2}) and , m=\frac{3}{2}\times(-1 -\sqrt{2})$ , is extraneous.

Here, L.H.S= R.H.S

Option A: 0→ extraneous

8 0

3 years ago

Read 2 more answers