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3 years ago

Using the following image, apply what you have learned about linear pairs and solve for x.

Mathematics

1 answer:

luda_lava [24]3 years ago

8 0

Answer:

Step-by-step explanation:

Linear pair, so sum of both angles is 180

x - 2 + 2 +4x = 180

Add the like terms

5x +0 = 180

5x = 180

Divide both sides by 5

x = 180/5

x = 36

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Some types of algae have the potential to cause damage to river ecosystems. Suppose the accompanying data on algae colony densit

kondor19780726 [428]

Answer:

The equation of the regression line is:

$y~=~234.56158 ~-~ 2.95835 \cdot x$

Step-by-step explanation:

The Least Squares Regression Line is the line that makes the vertical distance from the data points to the regression line as small as possible. It’s called a “least squares” because the best line of fit is one that minimizes the variance.

We have the following data:

$\begin{array}{c|ccccccccc}X&50&55&50&79&44&37&70&45&49\\Y&152&48&22&35&43&171&13&185&25\end{array}$

To find the line of best fit for the points:

Step 1: Find $X\cdot X$ and $X\cdot Y$ as it was done in the table

Step 2: Find the sum of every column:

$\sum{X} = 479 ~,~ \sum{Y} = 694 ~,~ \sum{X \cdot Y} = 32784 ~,~ \sum{X^2} = 26897$

Step 3: Use the following equations to find a and b:

$\begin{aligned} a &= \frac{\sum{Y} \cdot \sum{X^2} - \sum{X} \cdot \sum{XY} }{n \cdot \sum{X^2} - \left(\sum{X}\right)^2} = \frac{ 694 \cdot 26897 - 479 \cdot 32784}{ 9 \cdot 26897 - 479^2} \approx 234.56158 \\ \\b &= \frac{ n \cdot \sum{XY} - \sum{X} \cdot \sum{Y}}{n \cdot \sum{X^2} - \left(\sum{X}\right)^2} = \frac{ 9 \cdot 32784 - 479 \cdot 694 }{ 9 \cdot 26897 - \left( 479 \right)^2} \approx -2.95835\end{aligned}$

Step 4: Assemble the equation of a line

$\begin{aligned} y~&=~a ~+~ b \cdot x \\y~=~234.56158 ~-~ 2.95835\cdot x\end{aligned}$

The graph of the regression line is:

5 0

4 years ago

Write a rule for a function with a parabolic graph that contains the x-intercepts (-20,0) and (40,0) and a maximum point whose y

lakkis [162]

Step-by-step explanation:

Since the x-intercepts are -20 and 40, the line of symmetry is x = (-20 + 40)/2 = 10.

Now we have y = a(x - 10)² + 30, where a is an unknown constant. We can find a by using an x-intercept point.

=> (0) = a[(40) - 10]² + 30

=> 900a + 30 = 0, a = -1/30.

Hence the rule is y = -(x - 10)²/30 + 30.

7 0

3 years ago

A and B together can do a work in 6 days. If A alone can do it in 15 days. In how many days can B alone do it.

Nina [5.8K]

Answer:

10 days to complete

Step-by-step explanation:

for mixed rate problems, the sum of each individual reciprocal rates equals the sum of the combined rate

i.e

$\frac{1}{A's rate} + \frac{1}{B's Rate} = \frac{1}{combined rate}$

we are given,

A's rate = 15 days to complete

Combined rate = 6 days to complete

B's rate = need to find

substituting' the given info into the equation above,

1/15 + 1/ (B's Rate) = 1/6

1 / (B's Rate) = 1/6 - 1/15 (convert right side to same denominator)

1 / (B's Rate) = 5/30 - 2/30

1 / (B's Rate) = 3/30

1 / (B's Rate) = 1/10 (taking reciprocal of both sides)

B's rate = 10 days to complete

4 0

4 years ago

Read 2 more answers

A merry go round revolves 2 times per minute, jack is 10 feet from the center while bob is 14 feet from the center

Nesterboy [21]

Answer:

Jack's linear speed is 126ft/min

Bob's linear speed is 176ft/min

Step-by-step explanation:

First of all, find the circumference of both circles given the radius; Jack, 2pir (10)=63ft. Bob 2pir(14)=88ft. Now, realize that the merry go round revolves 2 times per min; 2rpm, so multiply each result by 2 and there you go.

5 0

3 years ago

Add: (2^3 − + 4) + (5^2 − 6 + 3)

BlackZzzverrR [31]

Answer:26!

Step-by-step explanation:

((23) - 4) + ((52 - 6) + 3)

(23 - 4) + 22

Hope this helps! ^w^

7 0

2 years ago