What is the area of this trapezoid?



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A rectangle with a length of 3 and a height of 8 has two right triangles on each side of it with short leg lengths of 7.

Check the picture below.

Mind you that we have four 30-60-90 triangles.

The area of given rectangle before the piece was removed is 65 cm² approximately.

The area of a rectangle (A) is the product of its length 'a' and width or breadth 'b'. So, Area of Rectangle = (a × b) square units.

In Δ DEF,

∠EDF + ∠DEF + ∠DFE = 180° (angle sum property)

30° + 90° + ∠DFE = 180°

∠DFE = 60°

[tex]cos F = \frac{EF}{FD}(\frac{base}{hypotenuse}\\ \\ cos(60) = \frac{5}{FD}\\ \\FD = 5 * 2= 10[/tex]

[tex]cos D = \frac{ED}{FD}(\frac{base}{hypotenuse}\\ \\ cos(30) = \frac{ED}{10}\\ \\ED = \frac{\sqrt{3} }{2} * 10= 5\sqrt{3}[/tex]

In Δ AED,

∠AED + ∠EAD + ∠EDA = 180° ( angle sum property)

∠AED + 90° + 30°= 180°

∠AED = 60°

[tex]sinE = \frac{AD}{DE} (\frac{perpendicular}{hypotenuse}\\ \\sin(60) = \frac{AD}{5\sqrt{3} } \\\\AD= \frac{\sqrt{3} }{2}*5\sqrt{3} \\\\AD = 7.5[/tex]

In Δ DFC,

∠FDC + ∠DCF + ∠DFC = 180° (angle sum property)

30° + 90° + ∠DFC = 180°

∠DFC = 60°

[tex]sinF = \frac{DC}{DF} \\\\sin(60) = \frac{DC}{10}\\ \\\frac{\sqrt{3} }{2} *10 = DC\\\\DC = 5\sqrt{3}[/tex]

Area of rectangle = length * breadth = xy = AD * DC = [tex]7.5 * 5\sqrt{3} = 64.95[/tex]

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Answer:

Step-by-step explanation:

→ [tex]\left(6x\:+\:9x\right)^3[/tex]

→ [tex]\left(15x\right)^3[/tex]      [ add the x inside the bracket ]

→ [tex]15^3x^3[/tex]       [ remove the bracket ]

→ [tex]3375x^3[/tex]     [ final answer ]

Answer:

3x(3x² + 2x)

Step-by-step explanation:

6x + 9x³

rearrange tribe

9x³ + 6x

factor by grouping

3(3x³ + 2x)

3x(3x² + 2x)

The maturity value on the bond is equal to $493.93

Data;

This is calculated as the sum of face value and interest.

[tex]M.V = F.V + I[/tex]

Let's solve for the interest on the bond

[tex]I = PRT\\I = 473 * 0.085 * 190/365\\I = 20.93[/tex]

Let's add this up and solve

[tex]M.V = 473 + 20.93\\M.V = 493.93[/tex]

The maturity value on the bond is equal to $493.93

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Answer:

M>22

Step-by-step explanation:

Answer:

[tex]\boxed{\sf{m > 22}}[/tex]

Step-by-step explanation:

To solve this problem, first, you have to isolate it on one side of the equation.

First, divide by -1 from both sides.

[tex]\Longrightarrow: \sf{\dfrac{-m}{-1} < \dfrac{-22}{-1} }[/tex]

Solve.

Divide the numbers from left to right.

⇒ -22/-1=22

[tex]\Longrightarrow: \boxed{\sf{m > 22}}[/tex]

I hope this helps you! Let me know if my answer is wrong or not.

Answer: It is not the solution, the solution for side one is 15, and the solution for side 2 is 18.

Answer:

a-24, b-36, c-36

Step-by-step explanation:

a) 4(6)=24

b) 5(6)+6=36

c) (6)^2=36

Answer:

a) c -24

b) a - 36

c) d - 36

Step-by-step explanation:

a) When x = 6, what is the value of 4x?

4x

4(6) = 24

b) When x = 6, what is the value of 5x + x

5x + x

5(6) + 6

30 + 6

36

c) When x = 6, what is the value of x^2?

x^2

6^2

36

Hope this helps!

Please give Brainliest!

Answer:

60

Step-by-step explanation:

Get that A.

Answer:

-5

Step-by-step explanation:

Answer:

−5a+6

Step-by-step explanation:

hope this is right

Answer:

A function is a relation which describes that there should be only one output for each input (or) we can say that a special kind of relation (a set of ordered pairs), which follows a rule i.e., every X-value should be associated with only one y-value is called a function.

Step-by-step explanation:

Answer:

do u mean factorization​?

if so, In math, factorization is when you break a number down into smaller numbers that, multiplied together, give you that original number. When you split a number into its factors or divisors, that's factorization. For example, factorization of the number 12 might look like 3 times 4.

Step-by-step explanation:

Hope this helps!

Answer:  it   an operation of resolving a quantity into factors; also : a product obtained by factorization

Step-by-step explanation:  hope i help

Answer:

42 cm squared

Step-by-step explanation:

base times height, divided in half

Answer:

B. 1/5

Step-by-step explanation:

Start at point (1,-2)

Then, go right 1 and up 5 to reach point (2,3)

Yes, adding the matrices would give a meaningful result as it provides a measure of the total number of nutrient and calorie intake throughout the day.

Yes, subtracting the matrix from each other gives a measure of the surplus or deficit of nutrients and calorie intake between any pair of meals.

A matrix can only be added to (or subtracted from) another matrix if the two matrices are of the same dimensions .

Hence, it follows that to add or subtract two matrices, just add or subtract the corresponding entries, and place this sum or difference in the corresponding position in the matrix which results accordingly.

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Answer:

1/2  in fraction each kid will get 0.50 in decimal and 50% in percent

Step-by-step explanation:

Answer:

500 times

Step-by-step explanation:

Divide 10,000,000,000 by 20,000,000 to determine how many 20 millions can go into 10 billion.

10,000,000,000 ÷ 20,000,000 = ?

Eliminate 7 zeros:

1,000 ÷ 2 = 500.

20,000,000 can go into 10,000,000 500 times.

Step-by-step explanation:

a² + b²

difference of two square

= (a + b)(a - b)

Answer:

see explanation

Step-by-step explanation:

(a + b)(a - b)

each term in the second factor is multiplied by each term in the first factor, that is

a(a - b) + b(a - b) ← distribute parenthesis

= a² - ab + ab - b² ← collect like terms

= a² - b²

Answer:

$166.71

Step-by-step explanation:

210.19 - 43.48 = 166.71

Total cards signed:-

[tex]\\ \tt\longmapsto \dfrac{1}{4}+\dfrac{3}{5}[/tex]

[tex]\\ \tt\longmapsto \dfrac{5+12}{20}=\dfrac{17}{20}[/tex]

Cards left:-

[tex]\\ \tt\longmapsto 80-17/20(80)=80-68=12[/tex]

Answer:

18

Step-by-step explanation:

scale factor = 1.25

30 : 24 = 1.25

or

35 : 28 = 1.25

The scale factor of this parallelogram is 5/4

In this question, we need to find the scale factor;

This is a factor to which a certain unit is multiplied or divided by. In this question, we have to find the scale factor first in order to know the missing side of the parallelogram.

[tex]\frac{30}{24} = \frac{5}{4}[/tex]

We have check for one side, let us find the other side and compare

[tex]\frac{35}{28}=\frac{5}{4}[/tex]

The scale factor of this parallelogram is 5/4

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Given :-

To Find :-

Solution :-

Given equation is ,

[tex] 3x + 6y = 24 [/tex]

To find the y intercept set x = 0 , we have ,

[tex] 3(0) +6y = 24 [/tex]

Simplify ,

[tex] 6y = 24[/tex]

Divide both sides by 6 ,

[tex] y = 4 [/tex]

Hence the y intercept is 4 .

[tex]\rule{200}2[/tex]

Now again to find x intercept , set y = 0

[tex] 3x +6(0)= 24[/tex]

Simplify ,

[tex] 3x = 24 [/tex]

Divide both sides by 3 ,

[tex] x = 8 [/tex]

Hence the x intercept is 8 .

Answer:

1 1/2

Step-by-step explanation:                                                                                    15x2/4x-5   =30/-20        =1 1/2                                                                                          First:

Convert any mixed numbers to fractions.

Then your initial equation becomes:                                                                                             Applying the fractions formula for division,                                                                Simplifying 30/-20,                                                                        

Domain:-

Range:-

Yes it's a function as domains have unique range

Answer:

Domain = Planet

Range = number of solar congress reps

Function = YES (many-to-one)

Step-by-step explanation:

Domain : input values ⇒ planet

Range : output value ⇒ number of solar congress reps

Function : A function relates each element of a set with exactly one element of another set (possibly the same set).

One-to-many is not a function.

Many-to-one is a function.

From inspection, we can see that every element in the domain is related to exactly one element in the range.  Both Venus and Neptune are related to 18.  So this is a many-to-one function.

Answer:

19/31

Step-by-step explanation:

since there are 15 squares and 4 circles, both is 19

and since the total pieces 31

so the probability that he will grab a square or circle is 19/31

Answer:

Ans=B.1

Step-by-step explanation:

hope this helps

Answer:

listed below.

Step-by-step explanation:

So basically its 420x420 which is 176400 which applies to all of these.

SO insert 1600 into Data Set 1.

For Data set II will be 69x69=4761

That is all you need. STAY SAFE!

Answer:

x = 7, y = 2

Explanation:

equations given:

x + 7y = 21

x + 4y = 15

make "x" the subject:

x + 7y = 21

x = 21 - 7y .........equation 1

x + 4y = 15

x = 15 - 4y .......equation 2

Solving both the equations simultaneously:

15 - 4y = 21 - 7y

-4y + 7y = 21 - 15

3y = 6

y = 6 ÷ 3

y = 2

If y is 2

Then x = 21 -7y;

x = 21 - 7(2)

x = 21 - 14

x = 7

x + 7y= 21

7 goes to RHS = X+ y = 21/7-3

x + 4y = 15

4 goes to RHS= x+y = 15/4 = 3.75

Answer:

Step-by-step explanation:

1 pound of potato salad costs 2.96

0.75 pounds of potato salad costs x

1/0.75 = 2.96/x            Cross multiply

x = 0.75 * 2.96

x = 2.22  

0.75 pounds of potato salad costs 2.22 dollars.

Using an inequality, it is found that the maximum number of desks that Bella can assemble is of 4.

We consider that:

Hence:

[tex]35.5 + 45.5x < 240[/tex]

Then, solving the inequality:

[tex]x < \frac{240 - 35.5}{45.5}[/tex]

[tex]x < 4.49[/tex]

Considering the number of desks has to be an integer, maximum number of desks that Bella can assemble is of 4.

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