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3 years ago

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Mathematics

1 answer:

lianna [129]3 years ago

7 0

Answer:

1) The slope of the line is $m=\frac{5}{2}$ or $m=2.5$

2) The equation of the line is $y=2.5x-4$

Step-by-step explanation:

step 1

Find the slope

we know that

The formula to calculate the slope between two points is equal to

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

take any two points from the values in the table

(2,1) and (4,6)

substitute the values in the formula

$m=\frac{6-1}{4-2}$

$m=\frac{5}{2}$

$m=2.5$

step 2

Find the equation of the line in point slope form

$y-y1=m(x-x1)$

we have

$m=2.5$

$point\ (2,1)$

substitute

$y-1=2.5(x-2)$

Convert to slope intercept form

isolate the variable y

$y-1=2.5x-5$

$y=2.5x-5+1$

$y=2.5x-4$

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A community pool that is shaped like a regular pentagon needs a new cover for the winter months. The radius of the pool is 20.10

boyakko [2]

Answer:

$960.42\text{ ft}^2$

Step-by-step explanation:

Please find the attachment.

We have been given that a community pool that is shaped like a regular pentagon needs a new cover for the winter months.

To find the area of community pool we will use area of pentagon formula.

$\text{Area of pentagon}=\frac{1}{2}a*p$ , where, a represents the apothem or perpendicular distance from the center of the pentagon and p represents perimeter of pentagon.

Let us find the perimeter of our given pentagon by multiplying each side length by 5.

$\text{Perimeter of community pool}=5\times 23.62$

$\text{Perimeter of community pool}=118.1$

Now let us find apothem of our pentagon by using Pythagoras theorem.

$a^2=20.10^2-11.81^2$

$a^2=404.01-139.4761$

$a^2=264.5339$

$a=\sqrt{264.5339}$

$a=16.2645$

Upon substituting our given values in above formula we will get,

$\text{Area of community pool}=\frac{1}{2}\times 16.2645\times 118.1$

$\text{Area of community pool}=8.13224907\times 118.1$

$\text{Area of community pool}=960.418615627971\approx 960.42$

Therefore, the area of the pool that needs to be covered is 960.42 square feet.

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3 years ago

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Twice the sum of 2 consecutive integers equals 106. determine the value of each integer

ivanzaharov [21]

26&27

Start by writing out the equation which would be: 106=2(n+n+1)

N: fist integer
N+1: is the consecutive integer

Then solve:
106=2(2n+1). Combine.
106=4n+2. Distribute.
104=4n. Move whole numbers to the left.
N=26. Divide
N+1=27 Plug in for second integer

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3 years ago

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inn [45]

Answer:

x=40 degrees

Step-by-step explanation:

a triangle is a total of 180 degrees. 180-120-20=40

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How can you determine if you need to use a combination or permutation to count the number of outcomes? Which will usually have m

Nadya [2.5K]

Answer with Step-by-step explanation:

Permutation : It is an arrangement of r elements out of n elements.

Combination : it is a selection of r element out of n elements .

Suppose we have a set

S={1,2,3}

If two elements are taken at a time then

Using permutation formula

Total number of outcomes= $3P_2$

Total number of outcomes= $\frac{3!}{(3-2)!}$

Total number of outcomes=3!= $3\times 2\times1=6$

Using combination formula

$\binom{n}{r}=\frac{n!}{r!(n-r)!}$

Total number of outcomes= $\binom{3}{2}=\frac{3!}{2!1!}$

Total number of outcomes= $\frac{3\times2!}{2!}$

Hence, total number of outcomes=3

Total number of outcomes determined by permutation have more outcomes.

Because permutation is an arrangement of elements therefore, it consider order of arrangement of element but combination is a selection of elements it does no consider order of elements

Arrangements of two elements out of 3 elements

{1,2},{2,3},{2,1},{3,2},{1,3},{3,1}

By using combination if two elements taken at a time then combination

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olganol [36]

Answer:

x=4

Step-by-step explanation:

Divide both sides by 6.

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