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nadezda [96]
2 years ago
6

Function rule how to solve ​

Mathematics
1 answer:
JulsSmile [24]2 years ago
7 0

Step-by-step explanation:

please mark me as brainlest

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10) Determine which of the following are functions. 11) What are the domain and range of the following relation?
Sauron [17]

Answer:

10) The first 2 on the left are functions and the one on the top right is a function, but the bottom right is not.

11) Domain = (2, 8, -1, 0) Range = (5, -2, 4, 5)

3 0
3 years ago
Some types of algae have the potential to cause damage to river ecosystems. Suppose the accompanying data on algae colony densit
Phantasy [73]

Answer:

y=-2.95836 x +234.56159

Step-by-step explanation:

We assume that th data is this one:

x: 50, 55, 50, 79, 44, 37, 70, 45, 49

y: 152, 48, 22, 35, 43, 171, 13, 185, 25

a) Compute the equation of the least-squares regression line. (Round your numerical values to five decimal places.)For this case we need to calculate the slope with the following formula:

m=\frac{S_{xy}}{S_{xx}}

Where:

S_{xy}=\sum_{i=1}^n x_i y_i -\frac{(\sum_{i=1}^n x_i)(\sum_{i=1}^n y_i)}{n}

S_{xx}=\sum_{i=1}^n x^2_i -\frac{(\sum_{i=1}^n x_i)^2}{n}

So we can find the sums like this:

\sum_{i=1}^n x_i =50+ 55+ 50+ 79+ 44+ 37+ 70+ 45+ 49=479

\sum_{i=1}^n y_i =152+ 48+ 22+ 35+ 43+ 171+ 13+ 185+ 25=694

\sum_{i=1}^n x^2_i =50^2 + 55^2 + 50^2 + 79^2 + 44^2 + 37^2 + 70^2 + 45^2 + 49^2=26897

\sum_{i=1}^n y^2_i =152^2 + 48^2 + 22^2 + 35^2 + 43^2 + 171^2 + 13^2 + 185^2 + 25^2=93226

\sum_{i=1}^n x_i y_i =50*152+ 55*48+ 50*22+ 79*35+ 44*43+ 37*171+ 70*13+ 45*185+ 49*25=32784

With these we can find the sums:

S_{xx}=\sum_{i=1}^n x^2_i -\frac{(\sum_{i=1}^n x_i)^2}{n}=26897-\frac{479^2}{9}=1403.556

S_{xy}=\sum_{i=1}^n x_i y_i -\frac{(\sum_{i=1}^n x_i)(\sum_{i=1}^n y_i)}=32784-\frac{479*694}{9}=-4152.22

And the slope would be:

m=-\frac{-4152.222}{1403.556}=-2.95836

Nowe we can find the means for x and y like this:

\bar x= \frac{\sum x_i}{n}=\frac{479}{9}=53.222

\bar y= \frac{\sum y_i}{n}=\frac{694}{9}=77.111

And we can find the intercept using this:

b=\bar y -m \bar x=77.1111111-(-2.95836*53.22222222)=234.56159

So the line would be given by:

y=-2.95836 x +234.56159

7 0
3 years ago
Given klmn is a trapezoid, kl = mn, m<1 = m<2, lm/kn = 8/9, pklmn = 132. Find: the length of the legs
Ilia_Sergeevich [38]

Answer:

The length of legs lm, mn, and lk is 32 while that of kn is 36.

Step-by-step explanation:

The diagram is attached in the answer.

As both the angles are equal thus the two forms isosceles triangles. This is true because the converse of base angle theorem is applicable here. The theorem clearly states that when a trapezoid is divided by the diagonal, it forms two set of angles where m<1=m<2 and m<lmk=m<nmk

This leads the two set of legs such as

\dfrac{lm}{kn}=\dfrac{8}{9}

Or this could be written as

lm=8x\\kn=9x

Now the remaining two sides are given as

lk=lm as this form an isosceles triangle so

lk=8x

Similarly

mn=lm\\

Or

mn=8x

Now the perimeter is given as

\text{perimeter}=lm+mn+kn+lk\\

Here perimeter is given as 132 so this gives:

\text{perimeter}=lm+mn+kn+lk\\132=8x+8x+8x+9x\\132=33x\\x=\dfrac{132}{33}\\x=4

So the four legs are of length as given below:

lm=8x=8\times 4=32\\mn=8x=8\times 4=32\\lk=8x=8\times 4=32\\kn=9x=9\times4=36

So the length of legs lm, mn, and lk is 32 while that of kn is 36.

6 0
3 years ago
Find the perimeter of the shape shown below.
sukhopar [10]

perimeter = turn of the figure

P = 6 + 3 + 4 + 4 + 3 + 6 + 3 + 4 + 3 = 36

the triangle has 2 équal sides => isosceles

and 1 angle is 60° so the triangle is equilateral

 

7 0
2 years ago
Solve for F:<br> C=5(F-32)/9
puteri [66]
C = 5(F-32)/9      Multiply each side by 9
9C = 5(F-32)       Distribute
9C = 5F - 160     Add 160 to each side
9C + 160 = 5F     Divide each side by 5
9/5C + 32 = F
5 0
3 years ago
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