How do you solve a table of equivalent ratios

Which of the following is equal to 4 and 2/3 ÷ by 3 and 1/2

Marina CMI [18]

the answer is 4/3 fraction form

4 0

3 years ago

Given right triangle ABCABC with altitude \overline{BD} BD drawn to hypotenuse ACAC. If BC=10BC=10 and DC=5,DC=5, what is the le

Helen [10]

Answer: $\overline{AC}=$ 12.5

Step-by-step explanation: The triangle ABC and its altitude $\overline{BD}$ is represented in the figure below.

Altitude is a segment of line that link a vertex and the opposite side, forming a right angle.

So, because of $\overline{BD}$ , now we have two similar triangles, which means that ratios of corresponding sides are equal:

$\frac{\overline{BD}}{\overline{BC}} =\frac{\overline{AD}}{\overline{BD}}$

$\overline{BD}^{2}=\overline{BC}.\overline{AD}$ (1)

This is always true for a right triangle and a altitude drawn to the hypotenuse.

Triangle BDC is also right triangle. So, we can use Pythagorean theorem to determine the missing side.

$\overline{BC}^{2}=\overline{CD}^{2}+\overline{BD}^{2}$

$\overline{BD}^{2}=\overline{BC}^{2}-\overline{CD}^{2}$ (2)

Substituting (2) into (1):

$\overline{BC}^{2}-\overline{CD}^{2}=\overline{BC}.\overline{AD}$

We want to find f, so:

$\overline{AD}=\frac{\overline{BC}^{2}-\overline{CD}^{2}}{\overline{BC}}$

$f=\frac{10^{2}-5^{2}}{10}$

f = 7.5

The length of $\overline{AC}$ is

$\overline{AC}=f+5$

$\overline{AC}=7.5+5$

$\overline{AC}=12.5$

The length of the hypotenuse of triangle ABC is 12.5 units.

5 0

3 years ago

Read 2 more answers

Felix has $50 in a savings account that earns 5% interest, compounded annually. To the nearest cent, how much interest will he e

qwelly [4]

Answer:

$55.13

Step-by-step explanation:

50 * 1.05 = 52.5

We do this step twice because the interest is for 2 years.

52.5 * 1.05 = 55.125

This rounds up to 55.13, your final answer!

8 0

3 years ago

What is 9-3y=x I don't know this one

torisob [31]

The answer is
y= - x-9/3 I believe.
1- Subtract 9 from both sides.
-3y = x - 9
2- Divide both sides by -3
y = - x-9/3

4 0

3 years ago

Read 2 more answers

The height of a triangle is 12 centimeters more than its base. The area of the triangle is 189 square centimeters Find the base

telo118 [61]

Answer:

C

Step-by-step explanation:

the area of a triangle is

baseline × height / 2

so, we know in our case

b(b+12) = 189 cm²

b² + 12b - 189 = 0

let's try to solve this by completing the square.

that means we try to find the expression

(b + k)² + c

that is equal to

b² + 12b - 189

(b + k)² + c = b² + 2kb + k² + c = b² + 12b - 189

so,

2k = 12

k = 6

and then

k² + c = -189

6² + c = -189

36 + c = -189

c = -225

(b + 6)² - 225 = 0

(b + 6)² = 225

b + 6 = 15

b = 9

so, the baseline b = 9 cm.

the height b+12 = 9+12 = 21 cm.

6 0

2 years ago