There is a pair of parallel sides in the following shape.


What is the area of the shape?

The ratio of the point C on the line segment is 3 : 5

The line segment that completes the question is added as an attachment

On the attached line segment, we have the following points assuming that the point A is at A = 0

So, we have

A = 0

C = 3

B = 8

The above means that

AB : CB = C - A : B - C

So, we have

AB : CB = 3 - 0 : 8 - 3

Evaluate the difference

AB : CB = 3 : 5

Hence, the ratio of the point C on the line segment is 3 : 5

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Check the picture below.

[tex]~\hfill \stackrel{\textit{\large distance between 2 points}}{d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2}}~\hfill~ \\\\[-0.35em] ~\dotfill\\\\ A(\stackrel{x_1}{-4}~,~\stackrel{y_1}{0})\qquad B(\stackrel{x_2}{2}~,~\stackrel{y_2}{3}) ~\hfill AB=\sqrt{(~~ 2- (-4)~~)^2 + (~~ 3- 0~~)^2} \\\\\\ ~\hfill AB=\sqrt{( 6 )^2 + ( 3)^2}\implies \boxed{AB=\sqrt{45}}[/tex]

[tex]B(\stackrel{x_1}{2}~,~\stackrel{y_1}{3})\qquad C(\stackrel{x_2}{6}~,~\stackrel{y_2}{0}) ~\hfill BC=\sqrt{(~~ 6- 2~~)^2 + (~~ 0- 3 ~~)^2} \\\\\\ ~\hfill BC=\sqrt{( 4)^2 + ( -3)^2}\implies \boxed{BC=5} \\\\\\ C(\stackrel{x_1}{6}~,~\stackrel{y_1}{0})\qquad D(\stackrel{x_2}{0}~,~\stackrel{y_2}{-3}) ~\hfill CD=\sqrt{(~~ 0- 6~~)^2 + (~~ -3- 0~~)^2} \\\\\\ ~\hfill CD=\sqrt{( -6)^2 + ( -3)^2}\implies \boxed{CD=\sqrt{45}}[/tex]

[tex]D(\stackrel{x_1}{0}~,~\stackrel{y_1}{-3})\qquad A(\stackrel{x_2}{-4}~,~\stackrel{y_2}{0}) ~\hfill DA=\sqrt{(~~ -4- 0~~)^2 + (~~ 0- (-3)~~)^2} \\\\\\ ~\hfill DA=\sqrt{( -4)^2 + ( 3)^2}\implies \boxed{DA=5} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{\LARGE Perimeter}}{\sqrt{45}~~ + ~~5~~ + ~~\sqrt{45}~~ + ~~5 ~~ \approx ~~ \text{\LARGE 23.42}}[/tex]

Answer:

.........................................................

Step-by-step explanation:

.................................................

The volume of the given three-dimensional figures are:

So, the volume of the cube: a³

(1) a³ = 4³ = 64ft³

The volume of the cuboid: whl

(2) whl = 4 × 6 × 3 = 72ft³

(3) whl = 2 × 3 × 5 = 30ft³

(4) whl = 2 × 5 × 8 = 80ft³

Therefore, the volume of the given three-dimensional figures are:

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Answer:

No

Step-by-step explanation:

substitute x = - 4 and y = - 17 into the left side and compare the result obtained to the right side.

2y - 3x

= 2(- 17) - 3(- 4) = - 34 + 12 = - 22 < 12

thus (- 4, - 17 ) is not a solution of the inequality

-1/2 = 3/8y
Answer:

y = -4/3

answer is y= -4/3

step by step

-1/2 = 3/8y

divide both sides by 3/8 to solve for y

-1/2 divided by 3/8 = 3/8 divided by 3/8y

when you divide fractions you flip the divisor and multiply

-1/2 x 8/3 = y

-8/6 or simplified to -4/3

you can check your work by substituting your y value of -4/3 into your original equation

-1/2= 3/8y

-1/2 = (3/8) (-4/3)

-1/2 = -12/24

-1/2 = -1/2

They equal so problem solved!

Answer:

Step-by-step explanation:

Brooke and Samuel each had 56 marbles as represented by the bar model.

In mathematics, a bar model is a visual representation of a subject or problem where the known and unknown quantities are represented by bars or boxes.

Let us consider that each had x marbles. Now Brooke gave away 20 marbles and Samuel gave away 44 marbles :

∴ x - 20 = 3 (x - 44)

or, x -20 = 3x - 132

or, -2x = -112

or, x = 66

Brooke and Samuel each have 56 marbles as calculated from the bar models.

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Answer: 1 inch 7/8

Step-by-step explanation: 65 1/4 inches is the same and 65 2/8 inches. its now just as simple as finding the difference.

                  <-----------take 8/8 or 1 away from the 65 and add it to the 2/8                 65 2/8

-  63 3/8

----------------          

   64 10/8           <------now the equation looks like this

-   63 3/8             <----10-3 is 7    ----   64 - 63 is 1

----------------

  1 inch and 7/8

The dimensions of the region which enclose the maximal area is 61.5 feet by 41 feet .

Let the length of the rectangular plot be "L" and width be "w"

It is given that farmer wants to do fencing of 246 feet which means all the boundary will be covered which is given by

            [tex]L+L+w+w+w=246\\2L+3w=246\\2L=246-3w\\\\L=\frac{246}{2} -\frac{3w}{2} \\\\L=123-\frac{3w}{2}[/tex]  ...(2)

Putting the value of "L" in equation (1) , we get

       [tex]A=({123-\frac{3w}{2}}) \times w\\\\A=123w-\frac{3w^2}{2}[/tex] ....(3)

 Now , we are asked to find the maximum area then , put

            [tex]\frac{dA}{dw}=0[/tex]

           [tex]123-\frac{6w}{2} =0\\123-3w=0\\123=3w\\w=41[/tex]

Putting w = 41 in equation (3) , we will get the maximum area

  [tex]A=123(41)-\frac{3(41)^2}{2} \\\\A=5043-2521.5\\\\A=2521.5[/tex]

Putting w = 41 in equation (2) , we will get the length

   [tex]L=123-\frac{3(41)}{2} \\L=123-61.5\\L=61.5feet[/tex]

Hence , the dimensions will be 61.5 feet by 41 feet .

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Answer:

2

Step-by-step explanation:

Monthly income and expenditure of Ganesh will be-16680

Let Ganesh's monthly income be x

The problem can be solved using linear equation

The amount of 60% of his salary is spent which can be written as 60% of x or 0.6x

The amount of money saved by Ganesh = total salary - amount spent

                                                                     = x - 0.6x

                                                                     = 0.4x

The amount of savings made by Ganesh  as per the question = 11120

Lets equate both the equation

                          0.4x = 11120

                               x = (11120 × 100)/ 40

                              x = 27800

Hence, Ganesh's monthly salary comes out to be 27800

Ganesh's monthly expenditure = 0.6 x= 0.6 × 27800 =16680

What is a linear equation in math?

A linear equation only has one or two variables. No variable in a linear equation is raised to a power greater than 1 or used as the denominator of a fraction. When you find pairs of values that make a linear equation true and plot those pairs on a coordinate grid, all of the points lie on the same line

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Answer:

Slope = (4/5)

Step-by-step explanation:

Point 1: (-2, 0); Point 2: (3, 4)

            (x₁, y₁)               (x₂, y₂)

       y₂ - y₁         4 - 0             4            4

m = ----------- = ------------ = ------------ = ------

       x₂ - x₁         3 - (-2)        3 + 2         5

y - y₁ = m(x - x₁)

y - 0 = (4/5) (x - (-2)

y - 0 = (4/5) (x + 2)

y - 0 = (4/5)x + (8/5)

y = (4/5)x + (8/5)

I hope this helps!

Answer:6.75 miles per half hour

Step-by-step explanation:6..75 miles per half hour

Answer:

Step-by-step explanation:

a Whar grsde are u even in >:/

Answer:

The function which has a slope of 4 will be that function or line which is going through the points (2, 0) and (3, 4).

What is a linear function?

A straight line on the coordinate plane is represented by a linear function.

A linear function always has the same and constant slope.

The formula for a linear function is f(x) = ax + b, where a and b are real values.

In another word, a linear function is a function that varies linearly with respect to the changing variable.

In the given question is saying for the second case the line goes through points  (2, 0) and (3, 4) so the slope will be

(4 - 0)/(3 - 2) = 4 hence, it will be the correct answer because it is the only line that has a slope of 4.

Answer:

On a coordinate plane, a line goes through points (2, 0) and (3, 4).

Step-by-step explanation:

Answer:

(2m+5)

2

=

Use binomial theorem (a+b)

2

=a

2

+2ab+b

2

 to expand (2m+5)

2

.

4m

2

+20m+25

Answer - 4m + 2 + 20m + 25

Step-by-step explanation:

help

The required equation that is a representation of the associative property of addition is 5 + (6 + 2) = (5 + 6) + 2

Expressions are mathematical statements that are represented by variables, coefficients and operators

The expression is given as

-15 + 0

The associative property of addition states that

(x + y) + z = x + (y + z)

This means that

(x + y) + z = x + (y + z) is a representation of the associative property of addition

From the list of given options, we have

5 + (6 + 2) = (5 + 6) + 2

The above is a perfect illustration of (x + y) + z = x + (y + z)

So, 5 + (6 + 2) = (5 + 6) + 2 is a representation of the associative property of addition

Hence, the required equation that is a representation of the associative property of addition is 5 + (6 + 2) = (5 + 6) + 2

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Answer:

5 + (6 + 2) = (5 + 6) + 2

Step-by-step explanation:

The fraction of those who were cast got major roles is 1 / 5.

Any number of equal parts is represented by a fraction, which also represents a portion of a whole. A fraction is a number that is a component of a whole. By breaking a whole into a number of parts, it is evaluated.

Given that ninety students auditioned for the school play. One-third of those who auditioned were cast, 6 in major roles.

The fraction will be calculated as below:-

Fraction of the students cast = 90 / 3 = 30

Fraction of the students selected for major roles = 6 / 30 = 1 / 5

Therefore, the fraction of those who were cast got major roles is 1 / 5.

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The amount that will be left based on the information will be 60100 - 23s - 28t - 14r.

Total number of soles = 60100

From the information, she bought 23 stoves, 28 television, and 14 refrigerators.

Therefore, the amount that will be left based on the information will be:

= 60100 - 23s - 28t - 14r

where s = stove

t = television

r = refrigerator

Therefore, the amount that will be left based on the information will be 60100 - 23s - 28t - 14r.

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Answer:

3x, where x = the price of a football ticket

The scale is equal to 1:500.

The ratio between a distance on a map and its corresponding distance on the ground is referred to as the "map scale."

if 1 cm on the map corresponds to 100 cm on actual ground then the scale of the map is given by the ration 1:100.

Scale of map is widely used in cartography and constructions.

The given condition states that 3 cm to 15 m.

We know that 1 cm =100 meters

Hence 15 meters = 15 × 100 cm =1500 cm

Therefore length on map = 1 cm

Length on ground = 1500 cm

Scale = distance on map : distance on ground

or, Scale = 3 : 1500

or, Scale = 1: 500.

Therefore the scale is 1: 500.

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20 people likes movies, such that  12 of these also like music, then the probability is just the quotient between:

Q = 12/20 = 0.6

The probability that a person likes music given that he/she lies movies is 0.6 or 60%

Notice that there are 5 + 7 common elements between movies and music, and a total of 20 people likes movies, such that 5 + 7 = 12 of these also like music, then the probability is just the quotient between the numbers of total people that likes movies which we know is 20, and the people that likes movies and also music.

So the quotient between 12 and 20, that will gave us the probability we want to find.

The probability that a person likes music given that he/she lies movies is 0.6 or 60%

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Answer:

17.37

Step-by-step explanation:

In a normal distribution, x = 9 and z = −1.21. This tells you that x = 9 is 1.21 standard deviations to the left the mean.

The z-score is a mathematical measure that allows us to see how much above or below the mean a value in a distribution is in terms of standard deviation.

When the value is above or right of the mean, the z-score would be positive and when the z-score is left or below the mean, the z-score would be negative.

In this instance, x = 9 has a z-score of -1.21 which means that it is 1.21 standard deviations to the left of the mean.

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According to the plot, it looks like [tex]y=3.5[/tex] when [tex]x=4[/tex], and [tex]y=7[/tex] when [tex]x=5[/tex]. Then the average rate of change from [tex]x=4[/tex] to [tex]x=5[/tex] is

[tex]\dfrac{\Delta y}{\Delta x} = \dfrac{7 - 3.5}{5 - 4} = 3.5[/tex]

The solution of the system of equation are as follows:

The system of equation can be solved as follows;

2x + 2y = 4

2x + 4y = 66

subtract equation(i) from equation(ii)

4y - 2y = 66 - 4

2y = 62

divide both sides by 2

y = 62 / 2

y = 31

Therefore, substitute the value of y in equation(i)

2x + 2(31) = 4

2x + 62 = 4

2x = 4 - 62

2x = -58

divide both sides by 2

x = -58 / 2

x = - 29

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The proof based on the triangle was done based on the fact that they are congruent triangles.

In this question we have  ΔABC ≅ ΔBAD

We have the following congruent sides in this triangle.

These are:

AB ≅ BA;

AC ≅ BD;

BC ≅ AD

These are corresponding angles too

∠ABC ≅ ∠BAD;

∠BCA ≅ ∠ADB;

∠CAB ≅ ∠DBA.

From the question we can see that the angles A and D can be said to be common. Hence we can say that

AE ≅ EB

Then CD would bisect AB

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Answer:

f'(x) = 0

Step-by-step explanation:

the derivative of a constant is zero , that is

f(x) = 5 ( a constant ) , then

f'(x) = 0