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Ivahew [28]
3 years ago
15

If these two shapes are similar, what is the measure of the missing length g?

Mathematics
1 answer:
Sophie [7]3 years ago
4 0
So if the shapes are similar, they have to have a number multiple from to get the other triangle. If you divide 63 by 42, you get 1.5. Then you have to divide 54 by 1.5 to get G and that would be 36.

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Suppose we want to choose 4 colors, without replacement, from 18 distinct colors.
amm1812

Answers:

  • (a) 73440
  • (b)  3060

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

Explanation for part (a)

Consider four slots labeled A,B,C,D.

We have

  • 18 choices for slot A
  • 17 choices for slot B
  • 16 choices for slot C
  • 15 choices for slot D

We started at 18 and counted down until we filled the four slots. The countdown is because we cannot repeat a color. Multiply out those values to get the answer: 18*17*16*15 = 73440

You can use the nPr permutation formula as an alternative method

_nP_r = \frac{n!}{(n-r)!}

in this case n = 18 and r = 4. The exclamation marks indicate factorial.

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

Explanation for part (b)

Let's say we had color labels A,B,C,... all the way up to R which is the 18th letter in the English alphabet. From those 18 letters, we can only pick four. Let's say we pick D,E,F,G.

Focusing solely on the set {D,E,F,G}, we only have one set and the order doesn't matter. So {D,E,F,G} is the same as {D,E,G,F}.

There are 4*3*2*1 = 24 ways to arrange those four items meaning that we'll need to divide the result of part (a) by 24 to get the result of part (b)

73440/24 = 3060

You could use the nCr combination formula to get the same result

_nC_r = \frac{n!}{r!(n-r)!}

where n = 18 and r = 4 are the same from last time.

The connection between nPr and nCr is this

_nC_r = \frac{_nP_r}{r!}

which can be rearranged into

_nP_r = r!*\left( _nC_r \right)

these formulas are handy to help us go back and forth between nCr or nPr.

8 0
3 years ago
Eric cell phone service cost $40.00 a month for unlimited calls he also pays $0.02 for each text message he send. whichbis equat
Marianna [84]

Given :

Service cost , c = $40.

Amount paid for each message , m = $0.02 .

To Find :

Equation represents the total cost C in dollars for a month when eric send t text message.

Solution :

Let , total cost be C .

It is an linear equation with slope equal to 0.02 and y-intercept equal to 40.

So ,

C=mt+c\\\\C=0.02t +40

Hence, this is the required solution.

5 0
3 years ago
What are two different way of factoring -3x-9? Select all that apply
Ghella [55]

Options:

A. –3(x + 3)

B. 3(x + 3)

C. 3(–x – 3)

D. –3(x – 3)

Answer:

A and C

Step-by-step explanation:

Given

-3x - 9

Required

Factorize

The options are not given; So, I'll answer on a general term

-3x - 9

Express -9 as -3 * 3

-3x - 9 = -3x - 3 * 3

Then factorize 3 out of the expression as:

-3x - 9 = 3(-x - 3)

Another way is to factor -3 out of the expression as:

-3x - 9 = -3x - 3 * 3

-3x - 9 = -3(x + 3)

3 0
3 years ago
Find the value of s if 57+s=68
olga2289 [7]

Answer

s = 11

Step-by-step explanation:

Find the value of S:

57 + s = 68

Substract 57 from both sides of the equation

s = 68 - 57

s = 11

6 0
3 years ago
Read 2 more answers
Which of the following is NOT a Pythagorean triplet?
maxonik [38]
I believe the answer is A. 20, 30, 40 is NOT a pythagorean triple.
4 0
3 years ago
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