All categories

2 years ago

I'm confused on how to do this question

Mathematics

1 answer:

laila [671]2 years ago

3 0

Answer:

CE = 35

Step-by-step explanation:

Based on the Triangle Proportionality Theorem, BD divides AC and CE proportionally. This implies that:

BC:AB = DC:DE

Plug in the values

(x - 5)/6 = 14/(2x + 3)

(x - 5)(2x + 3) = 14*6

x(2x + 3) -5(2x + 3) = 84

2x² + 3x - 10x - 15 = 84

2x² - 7x - 15 - 84 = 0

2x² - 7x - 99 = 0

Factorize

2x² - 18x + 11x - 99 = 0

2x(x - 9) +11(x - 9) = 0

(2x + 11)(x - 9) = 0

2x = -11

x = -11/2

x = 9

Let's take the positive value of x

Thus:

CE = 14 + 2x + 3

Plug in the value of x

CE = 14 + 2(9) + 3

CE = 14 + 18 + 3

CE = 35

You might be interested in

Please simplify! 1+x-1+12x=12x-3

Zina [86]

Answer:

x = - 3

Step-by-step explanation:

1 + x - 1 + 12x = 12x - 3

Subtract 12x from both sides.

1 + x - 1 = - 3

Combine like terms on the left side.

x = - 3

8 0

3 years ago

Read 2 more answers

Monica scored 32 points for her team at team at the Science Bowl. She got 5 four-point question correct, and the rest of her poi

NikAS [45]

4. She got 5 four point questions correct, 5x4=20. Then, you count by 3's from 20 until you get to 32.

3 0

3 years ago

Read 2 more answers

Please help me:( The volume of the above solid is

iren2701 [21]

Answer:

the volume of cylinder = πr²h

h = 5cm

r = 6cm

volume = π × 6² × 5

= π × 6 × 6 × 5

= 180πcm³

3 0

1 year ago

Staci is attending a music festival. The ticket to the festival costs $87.96. Staci plans to purchase $30.00 t-shirt from the ev

prohojiy [21]

First, we have to calculate the remaining amount of money after the cost of the ticket. It is 200 - 87.96 = 112.04 Dividing this number to 30, we can find the maximum number of t-shirts she can buy. It is less 4 and more than 3. So that, the final answer is 3.

4 0

3 years ago

Someone please help me with this

Sedbober [7]

Answer:

The area of the shaded figure is:

<u>20 units^2</u>

Step-by-step explanation:

To obtain the area of the shaded figure, first, you must calculate this as a rectangle, with the measurements: wide (4 units), and long (6 units):

Area of a rectangle = long * wide
Area of a rectangle = 6 * 4
Area of a rectangle = 24 units^2

How the figure isn't a rectangle, you must subtract the triangle on the top, so, now we calculate the area of that triangle with measurements: wide (4 units), and height (2 units):

Area of a triangle = $\frac{wide*height}{2}$
Area of a triangle = $\frac{4*2}{2}$
Area of a triangle = $\frac{8}{2}$
Area of a triangle = 4 units^2

In the end, you subtract the area of the triangle to the area of the rectangle, to obtain the area of the shaded figure:

Area of the shaded figure = Area of the rectangle - Area of the triangle
Area of the shaded figure = 24 units^2 - 4 units^2
<u>Area of the shaded figure = 20 units^2</u>

I use the name "units" because the exercise doesn't say if they are feet, inches, or another, but you can replace this in case you need it.

5 0

2 years ago