All categories

2 years ago

In △ABC, point D∈AC

Mathematics

1 answer:

Maslowich2 years ago

6 0

<h3>Answer:</h3>

ABDC = 6 in²
AABD = 8 in²
AABC = 14 in²

<h3>Explanation:</h3>

A diagram can be helpful.

When triangles have the same altitude, their areas are proportional to their base lengths.

The altitude from D to line BC is the same for triangles BDC and EDC. The base lengths of these triangles have the ratio ...

... BC : EC = (1+5) : 5 = 6 : 5

so ABDC will be 6/5 times AEDC.

... ABDC = (6/5)×(5 in²)

... ABDC = 6 in²

_____

The altitude from B to line AC is the same for triangles BDC and BDA, so their areas are proportional to their base lengths. That is ...

... AABD : ABDC = AD : DC = 4 : 3

so AABD will be 4/3 times ABDC.

... AABD = (4/3)×(6 in²)

... AABD = 8 in²

_____

Of course, AABC is the sum of the areas of the triangles that make it up:

... AABC = AABD + ABDC = 8 in² + 6 in²

... AABC = 14 in²

You might be interested in

How do I turn those numbers into a mixed number?

BigorU [14]

Number 2 is already a mixed number. But it says mixed number as a decimal. So -1 29/40 as a decimal is -1.725.

8 0

3 years ago

Toillet paper is sold in cases for 36 rolls for $14.99 what is the per price per roll?

Eva8 [605]

Alright, so the unknown value here we want to know is the price of one roll of TP. Let's call it "x".
36x=14.99
Divide both sides by 36 to get the price of a single roll.
x=.41638888....
We have to round this to hundredths because we're talking in cents, so...
x=.42
Each roll of toilet paper costs 42 cents.

8 0

3 years ago

Y=2x+9 what the answer

tekilochka [14]

Answer:

x=Y/2−9/2

Step-by-step explanation:

please mark brainliest :)

8 0

3 years ago

In a normal distribution, what is the probability that a data value will fall below the

Serga [27]

Answer:

A 99.96%

Step-by-step explanation:

The z score shows by how many standard deviations the raw score is above or below the mean. The z score is positive if the raw score is above the mean while the z score is negative if the raw score is below the mean. The z score is given by:

$z=\frac{x-\mu}{\sigma} \\\\where\ z=z-score,\ x=raw\ score,\mu=mean, \ \sigma=standard\ deviation\\\\For\ a\ sample\ size(n):\\\\z=\frac{x-\mu}{\sigma/\sqrt{n} }$

The probability can be gotten from the normal distribution table. Therefore from the normal table:

P(z < 3.37) = 0.9996 = 99.96%

8 0

2 years ago

Marcos purchased a sail boat for $56,900. He anticipates each year the boat will decrease in value by 8.1% from the previous yea

Varvara68 [4.7K]

Answer: $56,900\left( 0.919\right)^x$

Step-by-step explanation:

Given

Marcos purchased a sailboat for $\$56,900$

Each year the boat will decrease in value by $8.1\%$

After 1 year it is

$\Rightarrow 56,900-56,900\times 0.081\\\Rightarrow 56,900\left( 1-0.081\right)\\$

after another year it becomes

$\Rightarrow 56,900\left( 1-0.081\right)-56,900\left( 1-0.081\right)\times 0.081\\\Rightarrow 56,900\left( 1-0.081\right)\cdot \left( 1-0.081\right)\\\Rightarrow 56,900\left( 1-0.081\right)^2$

After $x$ years it is

$\Rightarrow 56,900\left( 1-0.081\right)^x$

$\Rightarrow 56,900\left( 0.919\right)^x$

5 0

2 years ago