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goldenfox [79]
3 years ago
5

If BE = 2x + 2, BD = 5x – 3, and AE = 4x – 6, what are the values of x and AC?

Mathematics
1 answer:
Keith_Richards [23]3 years ago
3 0

Answer: x=7 and AC = 44 unuts.

Step-by-step explanation:

We know that the diagonals of a parallelogram bisect each other. (i)

Here in parallelogram ABCD , AC and Bd are diagonals intersecting at E.

BE = 2x + 2, BD = 5x – 3, and AE = 4x – 6

Using (i)

BE=\dfrac{BD}{2}\\\\2x+2=\dfrac{5x-3}{2}\\\\ 2(2x+2)=5x-3\\\\ 4x+4= 5x-3\\\\ 5x-4x=4+3\\\\ x= 7

Now , AE = 4(7)-6 = 28-6 = 22

AC =2 AE = 2 (22) =44 units.

Hence, x=7 and AC = 44 unuts.

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Write in point-slope form an equation of the line that passes through the point (8, 9) with slope 7.
Lina20 [59]

Answer:

<h2>y=7x-47</h2>

Step-by-step explanation:

(8,9)=(x1,y1) \\ m=7 \\ y−y1=m(x−x1) \\ y−9=7(x−8)

y - 9 = 7x - 56 \\ y = 7x - 56 + 9 \\ y = 7x - 47

8 0
3 years ago
Joseph needs 6 1/2 cups of cooked rice for a recipe of nasi gorang. If 2 cups of uncooked rice with 2 1/2 cups of water make 4 1
liraira [26]

Answer:

The number of the cups of uncooked rice is 3 cups

The number of the cups of water is 3\frac{3}{4} cups

Step-by-step explanation:

* Let us read the recipe of Nasi Gorang

- 2 cups of uncooked rice need 2\frac{1}{2} cups of water to

  make 4\frac{1}{3} cups of cooked rice

- Joseph needs 6\frac{1}{2} cups of cooked rice

- We need to know how many cups of uncooked rice Joshep needs

  for this recipe and how much water should be added

* We can solve this problem by using the ratio method

⇒ uncooked cups   :   water cups   :   cooked cups

⇒ 2                           :   2\frac{1}{2}                   :  4\frac{1}{3}

⇒  x                           :   y                     :  6\frac{1}{2}

- By using cross multiplication

∵ x ( 4\frac{1}{3} ) = 2 ( 6\frac{1}{2} )

∵ 4\frac{1}{3} = \frac{13}{3}

∵ 6\frac{1}{2} = \frac{13}{2}

∴ x ( \frac{13}{3} ) = 2 ( \frac{13}{2} )

∴ \frac{13}{3} x = 13

- Divide both sides by \frac{13}{3}

∴ x = 3

∴ The number of the cups of uncooked rice is 3 cups

- By using cross multiplication

∵ y ( 4\frac{1}{3} ) =  ( 2\frac{1}{2} )( 6\frac{1}{2} )

∵ 2\frac{1}{2} = \frac{5}{2}

∵ 6\frac{1}{2} = \frac{13}{2}

∵ 4\frac{1}{3} = \frac{13}{3}

∴ \frac{13}{3} y = ( \frac{5}{2} )( \frac{13}{2} )

∴ \frac{13}{3} y = \frac{65}{4}

- Divide both sides by \frac{13}{3}

∴ y = 3\frac{3}{4}

∴ The number of the cups of water is 3\frac{3}{4} cups

6 0
2 years ago
Find the circumference and area of a circle with a diameter of 14 inches. Leave your answers in terms of pi.
Y_Kistochka [10]

Answer:

A=153.94

C=43.98

Step-by-step explanation:

CIRCUMFERENCE

C=2πr

C=2π7

C=43.98

AREA

A=πr²

A=π7²

A=153.94

8 0
3 years ago
There are 20 people competing in a contest, first place earns $100, second place earns $50 and third place earns $25. how many w
Tresset [83]
20*19*18, or 6840 ways
7 0
3 years ago
What is the area of a square with a perimeter of 64 mm
pashok25 [27]

Answer:

A =256 mm^2

Step-by-step explanation:

The perimeter of a square is given by the formula

P = 4s where s is the length of a side

64 = 4s

Divide each side by 4

64/4 =4s/4

16 = s

To find the area of a square, use the formula

A =s^2

A = 16^2

A =256 mm^2

5 0
2 years ago
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