Which of the following is the greatest common factor of 60 and 64?

Answer: The two integers are 8 and 9.

Step-by-step explanation: Let n represent the number.

n^2 + (n + 1)^2 = 145

By foiling, this can be rearranged to:

n^2 + n^2 + 2n + 1 = 145

Subtract 145 from both sides:

2n^2 + 2n - 144 = 0

Divide both sides by 2:

n^2 + n - 72 = 0

Factor the polynomial:

(n + 9)(n - 8) = 0

Solve for n:

n = -9, n = 8

Since they need to be consecutive, make the 9 positive. It will be positive either way because it is being squared.

Now, n = 9 and n = 8.

These are your two integers. Hope this helps!

Answer:

Perpendicular lines are lines that are at right angles to each other.

For perpendicular lines, the product of their slopes is -1.

[tex]\implies m_2=\dfrac{-1}{m_1}[/tex]

(where [tex]m_1[/tex] and [tex]m_2[/tex] are the slopes of perpendicular lines)

The slope of the given equation is -3.  Therefore, to find the slope of the line that is perpendicular:

[tex]m_2=\dfrac{-1}{-3}=\dfrac13[/tex]

Now we have the slope, we can use the point-slope form of a linear equation with [tex]m=\dfrac13[/tex] and [tex](x_1,y_1)=(2,-6)[/tex] to find the equation of the perpendicular line:

[tex]\implies y-y_1=m(x-x_1)[/tex]

[tex]\implies y-(-6)=\dfrac13(x-2)[/tex]

[tex]\implies y+6=\dfrac13x-\dfrac23[/tex]

[tex]\implies y=\dfrac13x-\dfrac{20}3[/tex]

The formula Sabine should use for calculating the variance and standard deviation for the random sample of bamboo stalks are,

[tex]s^2=\dfrac{(x_1-\overline x)^2(x_2-\overline x)^2...(x_n-\overline x)^2}{n-1}[/tex]

[tex]s=\sqrt{\dfrac{(x_1-\overline x)^2(x_2-\overline x)^2...(x_n-\overline x)^2}{n-1}}[/tex]

The variance of the data is the measure of average level by which every point is differed from the mean.

It can be calculated as,

[tex]s^2=\dfrac{(x_1-\overline x)^2(x_2-\overline x)^2...(x_n-\overline x)^2}{n-1}[/tex]

The standard deviation of the data is the half of the difference of the highest value and mean of the data set.

It can be calculated as,

[tex]s=\sqrt{\dfrac{(x_1-\overline x)^2(x_2-\overline x)^2...(x_n-\overline x)^2}{n-1}}[/tex]

Sabine records the daily heights of a random sample of bamboo stalks, in inches.

They are: 20, 19, 17, 16, 18, 15, 20, 21

For this data Sabine wants to calculate the variance and standard deviation, which can be done using the above formula.

Hence, the formula Sabine should use for variance is,

[tex]s^2=\dfrac{(x_1-\overline x)^2(x_2-\overline x)^2...(x_n-\overline x)^2}{n-1}[/tex]

The formula should Sabine use for standard deviation,

[tex]s=\sqrt{\dfrac{(x_1-\overline x)^2(x_2-\overline x)^2...(x_n-\overline x)^2}{n-1}}[/tex]

Learn more about the variance and standard deviation here;

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Answer:

First Part: A and B

Second Part: 4.5 and 2.12

Step-by-step explanation:

edge 2022

Answer:

Step-by-step explanation:

Outlier is a data point that is different from the rest of the data. The outliers in the dataset will be 20 and 78.

A scatter plot is also known as a scatter chart, a scatter graph that uses dots to represent values for two different numeric variables. Each dot on the graph represents particular data on both axes.

An outlier is a data point that is different from the rest of the data.

If we keenly observe the data set that is given to us, 48, 52, 56, 64, 61, 20, 48, 51, 58, 48, 78; the range of the data set that is given to us lies mostly between the 48 to 68, therefore, the data point that is the outlier for this data set are 20 and 78.

Hence, the outliers in the dataset will be 20 and 78.

Learn more about Outlier:

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Answer:

Only 20 is an outlier.

Step-by-step explanation:

Took the test.

Answer:

8 miles.

Step-by-step explanation:

Travelling down Alley street is 20 miles

Travelling along Polk and Fernwood = 12 + 16 = 28 miles.

Answer:

4+2+1=7 Make me brainlist please

Answer:

- 4

Step-by-step explanation:

the minimum value of the parabola is the value of the y- coordinate of the vertex.

given a parabola in standard form

y = ax² + bx + c ( a ≠ 0 )

then the x- coordinate of the vertex is

x = - [tex]\frac{b}{2a}[/tex]

y = x² - 2x - 3 ← is in standard form

with a = 1 and b = - 2 , then

[tex]x_{vertex}[/tex] = - [tex]\frac{-2}{2}[/tex] = 1

substitute x = 1 into the equation for corresponding y- coordinate

y = 1² - 2(1) - 3 = 1 - 2 - 3 = - 4

then minimum value is - 4

Check the picture below.

The value of variables x and y are,

x = 1 and y = 188

An angle is a combination of two rays (half-lines) with a common endpoint. The latter is known as the vertex of the angle and the rays as the sides, sometimes as the legs and sometimes the arms of the angle.

Given that;

In the diagram, quadrilateral HIJK is inscribed in circle L.

Now, We know that;

sum of opposite angle are 180 degree.

Hence, We get;

∠H + ∠J = 180

67 + (y - 75) = 180

y - 8 = 180

y = 180 + 8

y = 188

And, We get;

∠I + ∠K = 180°

96 + (x + 83) = 180

x + 179 = 180

x = 180 - 179

x = 1

Thus, The value of variables x and y are,

x = 1 and y = 188

Learn more about the angle visit:;

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#SPJ2

3 + 7x - (2 + 9x )

3 + 7x - 2 -9x

1-2x

Answer:

1-2x

Step-by-step explanation:

3+7x-(2-9x)

(if there's a minus in front of parenthesis then you have to change the sign in the parenthesis)

3+7x-2-9x(take out from parenthesis)

1-2x(combine/simplify like terms)

Step-by-step explanation:

£22.25 pls mark brainliest thanks

Answer:

41%

Step-by-step explanation:

Answer:

13

Step-by-step explanation:

AB = 5

AC = 10

BC = ~11

P = 11 + 10 + 5 = 26

26 / 2 = 13

Answer:

25%

Step-by-step explanation:When you divide 7 and 28 you get 0.25 which makes 25%

Answer:

82.82in^2

Step-by-step explanation:

Answer:

Yes, Wendy's conclusion is valid.

Step-by-step explanation:

40 divided by 15= 2.666666666666667

Therefore, 1000 divided by 2.666666666666667= 374.999999999999953 which can be rounded to 375

Answer:

B. Line segment

Step-by-step explanation:

A line segment starts with a point and ends with a point.

Answer:

Slope:-2

Step-by-step explanation:

You have to do y-y divided by x-x so 3-9 which equals -6 and 5-2 which equals 3 and then you have -6/3 and simplifying that you get -2.

Answer:

Your answer is: y = 5/8x -1/8

Step-by-step explanation:

Hope this helped : )

Step-by-step explanation:

Because 3^-3=0.037 and 1/27 also equals 0.037 so they are equivalent thats why.

Answer: See below

Step-by-step explanation:

Sophie's speed is --> s miles/hour

Yesterday, Sophie biked for --> t hours

Distance = speed * time

Distance = (s miles/hour)(t hours)

Distance = (s)(t)

Therefore, Sophie's route was s*t or st miles long

The student should compute 6*180 = 1080 because of the formula

S = 180(n-2)

We have n = 8 sides which leads the n-2 part to become n-2 = 8-2 = 6

Answer:

x = 20

Step-by-step explanation:

given a line parallel to a side of a triangle and intersecting the other two sides, then it divides those sides proportionally , that is

[tex]\frac{10}{5x+10}[/tex] = [tex]\frac{11}{121}[/tex] = [tex]\frac{1}{11}[/tex] ( cross- multiply )

5x + 10 = 110 ( subtract 10 from both sides )

5x = 100 ( divide both sides by 5 )

x = 20

Answer:

(0, -3)

explanation:

If reflected over y axis, there will be additive inverse in x unit

use the formula:  (x,y) → (−x, y)

Then if translated vertically, there will be change in y axis:

(0, -7+4) → (0, -3)

Answer:

c

Step-by-step explanation:

c because

if you use a number such as -4 for x, you do

-3/2*-4 is 12/2 which is 6

6-2 is 4

the coordinate would be (-4,4)

it fits graph c

Option D is the correct answer

Answer:

4.  x=3

5. 27

Step-by-step explanation:

4.  6(x+1) = 24,  because you work the equation backwards and the opposite way,  24/6 then - 1

5. put the numbers from lowest to highest temperature

9'c,  -3'c,  22'c,  -5'c,  11'c,  15'c

-5'c,  -3'c,  9'c,  11'c, 15'c,  22'c

range - is the highest number - lowest

22--5 =22+5 , therefore range is 27