3 (x - 4) = 5 + 3x + 2

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

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22% of _ peaches is 11 peaches

Neko [114]

I’m pretty sure it’s 50 peaches

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Isla walked 3/4 miles each way to and from the school Wednesday. How many miles did Isla walk that day?

jolli1 [7]

All you have to do is multiply 3/4 of a mile times two because she walked round trip. The answer is 1.5 miles

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A shoreline is eroding at a rate of 1/3 3 foot per 3 months. How many feet are eroding per year?

salantis [7]

7ft if 3+1/3 hopefully this helps i did hwat i can

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4 years ago

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A2-b2 ÷5a-5b factorise

katrin2010 [14]

Answer:

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "b2" was replaced by "b^2". 1 more similar replacement(s).

STEP

1

:

5a + 5b

Simplify ———————

a2 - b2

STEP

2

:

Pulling out like terms

2.1 Pull out like factors :

5a + 5b = 5 • (a + b)

Trying to factor as a Difference of Squares:

2.2 Factoring: a2 - b2

Theory : A difference of two perfect squares, A2 - B2 can be factored into (A+B) • (A-B)

Proof : (A+B) • (A-B) =

A2 - AB + BA - B2 =

A2 - AB + AB - B2 =

A2 - B2

Note : AB = BA is the commutative property of multiplication.

Note : - AB + AB equals zero and is therefore eliminated from the expression.

Check : a2 is the square of a1

Check : b2 is the square of b1

Factorization is : (a + b) • (a - b)

Canceling Out :

2.3 Cancel out (a + b) which appears on both sides of the fraction line.

Final result :

5 / a -b

Step-by-step explanation:

3 0

3 years ago