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4 years ago

Which term correctly describes the figure shown below?

Mathematics

1 answer:

Step2247 [10]4 years ago

6 0

Answer:

it is triangle probality acute or scalene triangle

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Select the correct answer.

DedPeter [7]

Answer: The correct option is (D) (4, -6).

Step-by-step explanation: Given that the areas of the triangles ADC and DCB are in the ratio 3 : 4.

We are to find the co-ordinates of point C.

From the diagram, we note that

the co-ordinates of point A and B are A(1, -9) and B(8,-2).

So, the length of the line segment AB, calculated by distance formula, is

$AB=\sqrt{(1-8)^2+(-9+2)^2}=\sqrt{49+49}=7\sqrt2.$

Now, area of ΔADC is

$A_{ABC}=\dfrac{1}{2}\times AC\times CD,$

and area of ΔDCB is

$A_{DCE}=\dfrac{1}{2}\times BC\times CD.$

According to the given information, we have

$A_{ADC}:A_{DCB}=3:4\\\\\\\Rightarrow \dfrac{A_{ADC}}{A_{DCE}}=\dfrac{3}{4}\\\\\\\Rightarrow \dfrac{\frac{1}{2}\times AC\times CD}{\frac{1}{2}\times BC\times CD}=\dfrac{3}{4}\\\\\\\Rightarrow \dfrac{AC}{BC}=3:4.$

So, the point C divides the line segment AB internally in the ratio 3 : 4.

We know that

if a point divides a line segment with end-points (a, b) and (c, d) internally in the ration m : n, then its co-ordinates are

$\left(\dfrac{mc+na}{m+n},\dfrac{md+nb}{m+n}\right).$

Since point C divides the line segment AB with end-points A(1, -9) and B(8, -2) internally, so the co-ordinates of point C will be

$\left(\dfrac{3\times 8+4\times 1}{3+4},\dfrac{3\times (-2)+4\times (-9)}{3+4}\right)\\\\\\=\left(\dfrac{28}{7},\dfrac{-42}{7}\right)\\\\\\=(4, -6).$

Thus, the co-ordinates of point C are (4, -6).

Option (D) is correct.

3 0

3 years ago

Read 2 more answers

Can u guys PLEASE explain the difference between 2 x 10 to the power of 4 and 2 to the power of 4

Alexxx [7]

Answer:

see explanation

Step-by-step explanation:

2 × $10^{4}$

= 2 × 10 × 10 × 10 × 10

= 2 × 100 × 100

= 200 × 100

= 20000

And

$2^{4}$

= 2 × 2 × 2 × 2

= 4 × 4

= 16

7 0

4 years ago

Bob won a $200,000 lottery. He invests part of the money in real estate with an annual return of 3% and the rest in a money mark

SVETLANKA909090 [29]

Answer:

Bob invested $50,000 in real state and $150,000 in a money market.

Step-by-step explanation:

Assuming that x is the investment in real state:

(200,000-x)*0.045 + x * 0.03 = 8,250

Apply distributive property:

(200,000*0,045) - 0.045x +0.03x = 8,250

9,000 - 0.045x +0.03x = 8,250

We must clear x:

- 0.045x +0.03x = 8,250 - 9,000

-0.015x = -750

x = -750/-0.015

x = 50,000

So, the invest in real state is $50,000.

$200,000 - $50,000 = $150,000 is the invest in a money market.

4 0

3 years ago

See screenshot...need help its due today

Pani-rosa [81]

Answer:

Step-by-step explanation:

f=20

Im a god bro

4 0

3 years ago

5. Stephanie has an aquarium. What is the volume capacity of the aquarium?

Luden [163]

Answer: 2520 inches.

I hope this helped! Please mark me brainliest :)

3 0

3 years ago