This figure represents a specialty design for an art print, made of a square and 3 identical triangles.


What is the area of 4 of these designs?



77 cm²


91 cm²


364 cm²


532 cm²

Answer: How to Calculate Slope of a Line

Calculate slope, m using the formula for slope:

Slope Formula

m=(y2−y1)(x2−x1)

m=riserun=ΔyΔx=y2−y1x2−x1

Here you need to know the coordinates of 2 points on a line, (x1, y1) and (x2, y2).

How to Find Slope of a Line

Find the difference between the y coordinates, Δy is change in y

Δy = y2 - y1

Find the difference between the x coordinates, Δx is change in x

Δx = x2 - x1

Divide Δy by Δx to find slope

m = Δy/Δx

Example: Find the Slope

Say you know two points on a line and their coordinates are (2, 5) and (9, 19). Find slope by finding the difference in the y points, and divide that by the difference in the x points.

The difference between y coordinates Δy is

Δy = y2 - y1

Δy = 19 - 5

Δy = 14

The difference between x coordinates Δx is

Δx = x2 - x1

Δx = 9 - 2

Δx = 7

Divide Δy by Δx to find slope m

m=142

m=7

Line Equations with Slope

There are 3 common ways to write line equations with slope:

Point slope form

Slope intercept form

Standard form

Point slope form is written as

y - y1 = m(x - x1)

Using the coordinates of one of the points on the line, insert the values in the x1 and y1 spots to get an equation of a line in point slope form.

Lets use a point from the original example above (2, 5), and the slope which we calculated as 7. Put those values in the point slope format to get an equation of that line in point slope form:

y - 5 = 7(x - 2)

If you simplify the point slope equation above you get the equation of the line in slope intercept form.

Slope intercept form is written as

y = mx + b

Take the point slope form equation and multiply out 7 times x and 7 times 2.

y - 5 = 7(x - 2)

y - 5 = 7x - 14

Continue to work the equation so that y is on one side of the equals sign and everything else is on the other side.

Add 5 to both sides of the equation to get the equation in slope intercept form:

y = 7x - 9

Standard form of the equation for a line is written as

Ax + By = C

You may also see standard form written as Ax + By + C = 0 in some references.

Use either the point slope form or slope intercept form equation and work out the math to rearrange the equation into standard form. Note that the equation should not include fractions or decimals, and the x coefficient should only be positive.

Slope intercept form: y = 7x - 9

Subtract y from both sides of the equation to get 7x - y - 9 = 0

Add 9 to both sides of the equation to get 7x - y = 9

Slope intercept form y = 7x - 9 becomes 7x - y = 9 written in standard form.

Find Slope From an Equation

If you have the equation for a line you can put it into slope intercept form. The coefficient of x will be the slope.

Example

You have the equation of a line, 6x - 2y = 12, and you need to find the slope.

Your goal is to get the equation into slope intercept format y = mx + b

Start with your equation 6x - 2y = 12

Add 2y to both sides to get 6x = 12 + 2y

Subtract 12 from both sides of the equation to get 6x - 12 = 2y

You want to get y by itself on one side of the equation, so you need to divide both sides by 2 to get y = 3x - 6

This is slope intercept form, y = 3x - 6. Slope is the coefficient of x so in this case slope = 3

How to Find the y-Intercept

The y-intercept of a line is the value of y when x=0.  It is the point where the line crosses the y axis.

Using the equation y = 3x - 6, set x=0 to find the y-intercept.

y = 3(0) - 6

y = -6

The y-intercept is -6

How to Find the x-Intercept

The x-intercept of a line is the value of x when y=0.  It is the point where the line crosses the x axis.

Using the equation y = 3x - 6, set y=0 to find the x-intercept.

0 = 3x - 6

3x = 6

 OTHER WORDS: D. M = 10

Step-by-step explanation:

Answer:If you search up what grade u need to get in order to pass a grade in middle school you need a D at the lowest and i'm pretty sure

Step-by-step explanation:

Answer:

yes you can pass with a D

Step-by-step explanation:

An E, you will fial

Complete the square:

F(x) = -3x² - 6x - 5

F(x) = -3 (x² + 2x) - 5

F(x) = -3 (x² + 2x + 1 - 1) - 5

F(x) = -3 ((x + 1)² - 1) - 5

F(x) = -3 (x + 1)² + 3 - 5

F(x) = -3 (x + 1)² - 2

The y-intercept has x-coordinate equal to 0, so it corresponds to the value of F(0) :

F(0) = -3 (0 + 1)² - 2 = -3 - 2 = -5

The axis of symmetry is the vertical line running through the vertex of this parabola, so we'll come back to this.

The vertex of the parabola is (-1, -2). This represents the maximum value of F(x), which follows from

(x + 1)² ≥ 0   ⇒   -3 (x + 1)² ≤ 0   ⇒   -3 (x + 1)² - 2 ≤ -2

This is to say, every point on the parabola has a y-coordinate no greater than -2.

As mentioned earlier, the axis of symmetry is the vertical line through the vertex, and its equation is determined by the x-coordinate of the vertex. Hence the AoS is the line x = -1.

Answer:

The variables are 1,400, 360, and two to represent the jobs he worked over the summer. System of equations, I would do 1,400+360 divided by two. 1,400+360 divided by two equals 880. To answer the last question, he earned $880 at each job.

Step-by-step explanation:

Hope this helps! Please tell me if I'm wrong. Have a wonderful rest of your day or night! ^w^

Answer:

anything close to 9 feet

Step-by-step explanation:

b²=c²-a²

b=√c²-a²

b = √10²-4²

b=√100-16

b=√84 ≈ 9.12

Answer:

5 * 8 * 6 * 3 = 40 * 18 = 720. so it would be 720 cm squared

Step-by-step explanation:

Answer:

75

51

54

Step-by-step explanation:

Let me know if you need an explanation

Answer:

D. the absolute deviation is 3

Step-by-step explanation:

Given:

MAD:

[tex]\displaystyle \large{\dfrac{1}{n}\sum_{i=1}^{n}|x_i-m| = \dfrac{|x_1-m|+|x_2-m|+|x_3-m|+...+|x_n-m|}{n}}[/tex]

Therefore:

[tex]\displaystyle \large{MAD=\dfrac{|7-12|+|10-12|+|10-12|+|14-12|+|14-12|+|17-12|}{6}}\\\displaystyle \large{MAD=\dfrac{5+2+2+2+2+5}{6}}\\\displaystyle \large{MAD=\dfrac{18}{6}}\\\displaystyle \large{MAD = 3}[/tex]

Therefore, absolute deviation is 3

Answer:

IQR = 8

Step-by-step explanation:

IQR is Q3-Q1.

Lets split into quarters.

21, 23, 25, 29, 30, 31, 33, 34

Median is 29.5.

Q1 is 24.

Q3 is 32.

32-24=8

Step-by-step explanation:

2x° + 2x° + 76° = 180° ( being supplementary angle )

4x° = 180° - 76°

4x° = 104°

x = 104/4

x = 26°

Answer:

x = 30°

The angles:

Step-by-step explanation:

Hello!

The sum of all the angles in a triangle is 180°. So we can set up an equation for this question.

Solve the equation:

We can replace 30° for all the angles.

The measures are:

2x = 60

3x = 90

x = 30

All triangles have 3 angles that add up to 180 degrees. We can use the information to create an equation.

Finding x

First, add all of the angles together and set them equal to 180

Next, combine like terms

Finally, divide both sides by 6

Solve For Missing Angles

Now that we have x, we can solve from each of the missing angles. Do this by plugging in 30 for the x-values.

2x

3x

x

We can check our answers by adding all of these together. Because 60+90+30 equals 180, these answers must be correct.

Answer:

[tex]\huge\boxed{\sf w = -14}[/tex]

Step-by-step explanation:

Given Equation:

6 + w = -8

Subtract 6 to both sides

w = -8 - 6

w = -14

[tex]\rule[225]{225}{2}[/tex]

Answer:

w = -14

Step-by-step explanation:

6 + w = -8

move 6 to the other side of the = sign

to do that you must subtract from both sides (of the equal sign) it since it is a positive number

6 + w = -8

-6          -6

this makes the 6 cancel out

-8 - 6 = -14

w = -14

your answer is -14

hope this helps :)

Answer:

(For page 1) volume=Length x width x height

so area is Length x width, therefore you would just take 2,025 and divide by 9 to get 225 sq. ft for the area. (For page 2) the volume of the aquarium is V= Lx wx H

it is already given that V=11.25 cubic feet, so 11.25=LxWxH

H height and it is the aquarium's depth

H=11.25 / L xW= 11.25/2.5x1.5= 3 feet

Step-by-step explanation:

Hope this helps :>

Answer: Perimeter of the shape,

= 2*pi*r + 3*10*10

= 2*pi*r + 300

r = 10

So,

Perimeter = 20*pi + 300

Step-by-step explanation:

Answer:

lowest value-0

lower quartile(or first quartile)-1.25

median-4.25

upper quartile-6.75

highest value-7

Step-by-step explanation:

lowest value=is the lowest number of a set

lower quartile(first quartile)=the number between the median and th   minimum or if there is a  even amount of values you find the mean of the values between the minimum and maximum

median=the middle number of a set

upper quartile(third quartile)=the middle number between the median and the maximum.

highest value(maximum)=the highest number in the set

Answer:

Lowest Value = 0

Lower Quartile = 1.5

Median = 4.5

Lower Quartile = 6.5

Highest Value = 7

Step-by-step explanation:

Given values:  

0, 1, 2, 3, 6, 6, 7, 7

Before determining the quartiles, place the values of the data set in order of size.

To find the position of the lower quartile (Q1) first work out n/4 (where n is the number of data values in the set).

If n/4 is a whole number, then the lower quartile is halfway between the values in this position and the position above.

⇒ 8/4 = 2, so the Lower Quartile is halfway between the 2nd and 3rd values.

⇒ Lower Quartile = 1.5

The median is the value in the middle of the data set when all the data values are placed in order of size.

To find the position of the median (Q2) first work out n/2.

If n/2 is a whole number, then the median is halfway between the values in this position and the position above.

⇒ Median = 4.5

To find the position of the upper quartile (Q3) first work out 3n/4 (where n is the number of data values in the set).

If 3n/4 is a whole number, then the lower quartile is halfway between the values in this position and the position above.

⇒ (3 x 8)/4 = 6, so the Lower Quartile is halfway between the 6th and 7th values.

⇒ Lower Quartile = 1.5

The lowest value is the smallest value in the data set = 0

The highest value is the largest value in the data set = 7

Answer:

[tex]\huge\boxed{\bf\:m=-3}[/tex]

Step-by-step explanation:

Slope can be found using the following formula [tex]\downarrow[/tex]

[tex]\boxed{m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}}[/tex]

Here,

[tex]\star \: x_{1} = 1\\\star \:x_{2} = 6\\\star \:y_{1} = 5\\\star \:y_{2} = -10[/tex]

Then,

[tex]Slope \: (m)\\= \frac{-10-5}{6-1}\\= -\frac{15}{5}\\= \boxed{\bf\:-3}[/tex]

[tex]\rule{150pt}{2pt}[/tex]

Answer:

b in number 1, a in number 2, and c in number 3

Step-by-step explanation:

Just did test

Answer:

1. 30.5

2. 23

Step-by-step explanation:

1. Find the middle of 30 and 31.

2. 21, 22, 23, 24, 25...now cross of a number from each side at a time until you get to the middle.

You put the numbers from smallest to biggest and cross off one number at a time from each side until you get to the middle.

If at the end you have two numbers left, you find the middle for these two numbers.

Answer:

1) 30.5

2) 23

3) 50

4) 2

5) 100

Step-by-step explanation:

First of all, order your data from lowest to highest value. Next, if you have an even number of observations (like in question n. 1 and n. 3) you have to add the middle two observations and divide the result by two. If you have an uneven number of observations, your median is simply going to be the number in the middle. Here, I'll show you:

- Question 1 has 2 observations, meaning you have to compute 30+31 = 61. Now you divide 61 by 2:

61/2 = 30.5 and that's your median.

- In question 2 you firstly have to order the data from lowest to highest number. Since it's an uneven number, your median is going to be 23.

- Question 3 has 4 observations, meaning you have to firstly order in ascending order and find the middle 2 numbers, which are 30 and 70. You add them: 30 + 70 = 100.

100/2 = 50 and that's your median.

- In question 4, after you order in ascending order you can clearly see that your median is 2.

- In question 5, after you order in ascending order you can clearly see that your median is 100.

Answer:

5(x-3)(x-3)

Step-by-step explanation:

First we can divide everything by 5:

[tex]\frac{5x^{2} -30x+45}{5} = x^{2} -6x+9[/tex]

Now we find 2 numbers that multiply to give +9 and add to give -6:

This would be -3 and -3. Now we substitute these numbers inside of -6 by splitting -6x into -3x and -3x:

[tex]x^{2} -3x-3x+9[/tex]

Now we factor the first 2 terms:

[tex]x(x-3)[/tex]

Now we factor the last 2 terms:

[tex]-3(x-3)[/tex]

Now we only copy one bracket and the things outside the bracket we put them into 1:

(x-3)(x-3)

Now we multiply everything by 5 :

5(x-3)(x-3)

Answer:

5(x-3)( x-3)

Step-by-step explanation:

First we notice that all the factors are divisible by 5 because the ending of the coefficients is 0 or 5

5 (x² -6x+9)

5 ( x -3) ² , because x² -6x+9 = 9x-3)²

5 (x-3)( x-3)

11 is the absolute devtion

set : { 19 16 4 9 7 }

Answer:  5.

Reasoning: How you get the absolute deviation of a number in a set is to

1. Find the median (add all the numbers together, then divide it by the amount of numbers) (19+16+4+9+7=55, then 55 divided by 5 to get 11)

2. Find the difference between the number (16 in this case) and the median (11) (16-11=5)

and i also did the quiz

Hope this helps! :))

Answer:

49.70

Step-by-step explanation:

commission = total sales revenue  mutliplied by the commission rate.

Answer:

Height = 20 ; Base = 5

Step-by-step explanation:

Triangle Area = Base x Height x 1/2

50 = 1x × 4x × 1/2

50 = 4x^2 × 1/2

50 = 2x^2

25 = x^2

x=5

Height equals to 4x -> 4 × 5 = 20

Base equals to x -> 1 × 5 = 5

Answer:

1928

Step-by-step explanation:

1927.83505155 rounded to the nearest whole number is 1928. A whole number is a number with no decimal places, so we'll have to look at the number directly to 7's right (the first decimal) in order to find out whether we'll be rounding up or down. This number is 8, which is closer to 10 than it is to 0, so we'll be rounding up.

1927 + 1 = 1928, and this is our final answer. Hopefully this was helpful! Let me know if you have any further questions on the subject.