Rectangle ABCD and right triangle DCE have the same area. They are joined to form a trapezoid, as shown. What is DE?

Answers

Answer 1

Answer: Since the areas are the same (5 x 6 = 30 units), and the height of the triangle (DC) is 5 so the length of the triangle must be 12. (1/2 of 5 x 12 is also 30)

So now we use the Pythagorean theorem

a² + b² = c² we have 5² + 12² = c² or 25 + 144 = c² or 169 = c²

The square root of 169 is 13 so side DE is 13 units.

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3/4 (4c + 16) = 2c ÷ 9. what is c

Answers

Distribute

(3/4)(4c)+(3/4)(16)=2c/9

3c+12=2/9 c

Now subtract 2/9 c from both sides

3c+12-2/9 c=2/9 c-2/9 c

25/9 c+12 =0

Now we need to subtract 12 from both sides

25/9 c+12-12=0-12

25/9 c=-12

Just multiply both sides by 9/25 so we find the value for c

25/9 *(25/9 c)=-12(9/25)

c= -108/25

I hope that's help:0

diller elementary is collecting money to donate to a charity. $103 is collected each month. how much money is collected in 9 months?

Answers

The correct answer is: 927

Step by step explanation: first I set up the equation which would be 103*9 when you multiply that you get 927

PLEASE MARK AS BRAINLIEST

The answer is 927 because 103 times 9 is 927

If a plant manufacturing carpet backing has a cylindrical tank that is 3 meters high and is 6 meters in diameter, what is the volume of the tank? Assume 3.14 for pi. A)28.3 m3 B)37.7 m3 C)56.5 m3 D)84.8 m3

Answers

the equation to find the volume of a cylinder is π∗r2∗h so if you plug in the correct values, you should have an equation of π∗32∗3 which is equal to π∗27 which equals approximately 84.823 meters^3

Hope this helps.

Sam needs at least 78 credits to get his college degree. At the end of his third year, Sam has a total of 52 credits. Which inequality represents the number of credits, C, Sam needs to get his degree?-
A - C is less than or equal to 26.
B - C is less than or equal to 78.
C - C is greater than or equal to 26.
D - C is greater than or equal to 52.

Answers

Coulld you please explain a little more? The number of credits sam needs to get his degree is 26.

Solve the system of equations.
4x + 3y + z= -6
x-3y + 2z=0
11x-2y + 3z = - 26

Answers

Answer:

y= - 271/71

x=755/71

z =4866/71

Step-by-step explanation:

For resolve a system you multiply an equation of the system or add two of the equation and replace the result in the system

Add the 1st and 2nd, and replace the 2nd

4x + 3y + z= -6 4x + 3y + z= -6 4x + 3y + z= -6

(-4) (x-3y + 2z=0) → -4x +12y -8z =0 → +15y -7z = -6

11x-2y + 3z = - 26 11x-2y + 3z = - 26 11x-2y + 3z = - 26

Add the 2nd and 1st, and replace the 1st

4x + 3y + z= -6 4x + 3y + z= -6 4x + z= -6

(-1/5)( 15y -7z = -6) → -3y -7/5z =6/5 → -3y -7/5z =6/5

11x-2y + 3z = - 26 11x-2y + 3z = - 26 11x-2y + 3z = - 26

Add the1st and 3rd, and replace the 3erd

(-3)( 4x + z= -6) -12x - 3z= 18 -12x - 3z= 18

-3y -7/5z =6/5 → -3y -7/5z =6/5 → -3y -7/5z =6/5

11x-2y + 3z = - 26 11x-2y + 3z = - 26 -x-2y = - 8

Add the1st and 3rd, and replace the 1st

(1/3)(-12x - 3z= 18 ) -4x - z= 6 -4x - z= 6

(5)(-3y -7/5z =6/5) → -15y - 7z = 6 → -15y - 7z = 6

-x-2y = - 8 (-4)(-x-2y = - 8) 4x + 8y= 32

Add the 1st and 2nd, and replace the 2nd

(-7)(8y - z =38) -56y +7z= 266 -56y +7z= 266

-15y - 7z = 6 → -15y - 7z = 6 → -71y=271 → y= - 271/71

(1/4)(4x + 8y= 12) x+2y=3 x+2y=3

-56y +7z= 266 → -8y + z =38 → z =4866/71

x+2y=3 → x=755/71

4 teammates share 5 granola bars equally

Answers

4÷5
4÷5=0.8
Each teammate will have .8 of a granola bar

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