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Anastasy [175]
2 years ago
10

7)

Mathematics
1 answer:
krek1111 [17]2 years ago
6 0

Answer:

A) 10

Step-by-step explanation:

Let the first integer be a+1. Then we wish to solve for the following:

(a+1) + (a+2) + \cdots + (a + n) + 100 = (a + (n + 1)) + (a + (n + 2)) + \cdots + (a + (2n))\\10a + (1 + 2 + \cdots + n) + 100 = 10a + ((n + 1) + (n + 2) + \cdots + (2n))\\\frac{1}{2}(n)(n + 1) + 100 = \frac{1}{2}(n)(3n + 1)\\n(n + 1) + 200 = n(3n + 1)\\n^2 + n + 200 = 3n^2 + n\\2n^2 = 200\\n^2 = 100\\n = 10 \quad \text{(because $n > 0$)}

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A swim meet has 13 contestants signed up for the 100-meter butterfly event. The first heat has 6 swimmers. How many different wa
tino4ka555 [31]

Answer:

6 swimmers in the first heat can be arranged in 1716 different ways.

Step-by-step explanation:

A swim meet has 13 contestants signed up. To calculate the arrangement of first 6 swimmers in first heat we will use combinations because order doesn't matter.

So to select 6 swimmers out of 13 contestants number of different ways

= ^{13}C_{6}

= \frac{13!}{(6!)(13-6)!}

= \frac{13\times 12\times 11\times 10\times 9\times 8\times 7!}{6!\times 7!}

= \frac{13\times 12\times 11\times 10\times 9\times 8}{6\times 5\times 4\times 3\times 2\times 1}

= \frac{1235520}{720}

= 1716

Therefore, 6 swimmers in the first heat can be arranged in 1716 different ways.

5 0
2 years ago
Question in picture above ^
Andrei [34K]
[ 4(4) x 4(3) ] / 4(5)

= [4(4+3)] / 4(5)

= 4(7) / 4(5)

= 4(7-5)

= 4(2)
5 0
2 years ago
What are the coefficients in the expression -8y^ + 12x + 5y + 7
schepotkina [342]

Answer:

-8  12  5  

Step-by-step explanation:

they are the numbers attached to the variables

8 0
3 years ago
Due at 11:59 PLS HELP
Lelechka [254]
The answer is the last one
8 0
2 years ago
What is the slope of the line?
riadik2000 [5.3K]

Answer:

The slope of the line must be 3

Step-by-step explanation:

<u><em>The picture of the question in the attached figure</em></u>

step 1

we know that

The volume of a rectangular prism is equal to

V_r_p=Bh ----> equation A

where

B is the area of the base of the prism

h is the height of the rectangular prism

step 2

The volume of a square pyramid is equal to

V_s_p=\frac{1}{3}Bh -----> equation B

where

B is the area of the square base of pyramid

h is the height of the pyramid

step 3

substitute equation A in equation B

V_s_p=\frac{1}{3}V_r_p

Find the relationship between the volume of  a rectangular prism and the volume of a square pyramid

\frac{V_r_p}{V_s_p}=3

therefore

The slope of the line must be 3

let's check it

To solve for the slope of the line, you must choose two coordinates first and use the formula

m=\frac{y2-y1}{x2-x1}

Choosing the points (2,6) and (3,9)

substitute

m=\frac{9-6}{3-2}=3 ----> is correct

8 0
3 years ago
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