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Contact [7]
4 years ago
13

Given: AB ∥ DC

Mathematics
1 answer:
RSB [31]4 years ago
5 0

Answer:

A=1,720.16\ units^2

Step-by-step explanation:

we know that

The area of the trapezoid is equal to

A=\frac{1}{2}(DC+AB)DE

step 1

Find the measure of angle DAE

m∠ADC+m∠DAE=180° -----> by consecutive interior angles

we have

m∠ADC = 134°

substitute

134°+m∠DAE=180°

m∠DAE=180°-134°=46°

step 2

In the right triangle ADE

Find the length side AE

cos(∠DAE)=AE/AD

AE=cos(46\°)(40)\\AE=27.79\ units

step 3

In the right triangle ADE

Find the length side DE

sin(∠DAE)=DE/AD

DE=sin(46\°)(40)\\DE=28.77\ units

step 4

Find the area of ABCD

A=\frac{1}{2}(DC+AB)DE

we have

DC=32\ units\\AB=DC+2(AE)=32+2(27.79)=87.58\ units\\DE=28.77\ units

substitute

A=\frac{1}{2}(32+87.58)28.77

A=1,720.16\ units^2

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Evaluate each expression for g = -7 and h = 3 and match it to its value.
Arturiano [62]

Answer:

The values of given expressions are:

1. gh = -21

2. g^2 - h = 46

3. g + h^2 = 2

4. g + h  = -4

5. h - g  = 10

6. g - h = -10

Step-by-step explanation:

Given values of g and h are:

g = -7

h = 3

<u>1. gh</u>

The two numbers are being multiplied

Putting the values

gh = (-7)(3) = -21

<u>2. g^2-h</u>

Putting the values

=(-7)^2-3\\=49-3\\=46

<u>3. g+h^2</u>

Putting the values

= -7 + (3)^2\\=-7+9\\=2

<u>4. g+h</u>

Putting the values

= -7+3\\=-4

<u>5. h-g</u>

Putting the values

= 3 - (-7)\\=3+7\\=10

<u>6. g-h</u>

Putting values

=-7-3\\=-10

Hence,

The values of given expressions are:

1. gh = -21

2. g^2 - h = 46

3. g + h^2 = 2

4. g + h  = -4

5. h - g  = 10

6. g - h = -10

4 0
3 years ago
Read 2 more answers
James has eight coins in his pocket. All the coins are either dimes or quarters.The total value of the coins is $1.25. How many
Goshia [24]

Answer:

he has 5d+3q

Step-by-step explanation:

since every d is .10 and every q is .25 the equation can be changed to 5(.10)+3(.25) which is equal to .5+.75 which adds up to 1.25

i did this by assuming that the amount of d is 8 at first, then change one of the 8 d to a q which will give you 7d+q, then assume another d is a q which will give you 6d+2q, repeat this until the amount of d and q add up to 1.25

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3 years ago
Belle runs 16 times around a track that measures 1/4 mile long.
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16/4 which could be simplified to be the whole number 4
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Given this rectangular prism with length
34kurt

Answer: width = 36 m

Step-by-step explanation:

Width = Volume / (height x length)

Width = 13500 / (25 x 15)

= 13500/375

= 36 m

4 0
3 years ago
Which of the following is most likely the next step in the series? Choices: 10A, 21b, 32C, 43d, 54E, 65f. . A.66g. B.76g. C.76G.
Katena32 [7]
First, we pay attention to the numerical coefficients of the terms in the series: 10, 21, 32, 43, 54, 65. Conclusively they form an arithmetic sequence with a common difference of 11. Thus, the next numerical coefficient is 76. Then, we pay attention to the letters which are just arrange alphabetically. The next letter ought to be G which needs to be capitalized. Thus, the answer is letter C. 76G. 
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