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3 years ago

What is 0.021 in fraction form?

1 answer:

7 0

Convert the decimal to a fraction by placing the decimal number over a power of ten. Since there are three numbers to the right of the decimal point, place the decimal number over 10^3 (1000)
= 21/1000

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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

In Exercise find the derivative of the functions.<br> f(x) = (4x - 3)(x2 + 9)

pashok25 [27]

Answer: $f'(x)=12x^2 - 6x+36$

Step-by-step explanation:

According to the product rule of derivatives.

$f'(x)=u'(x)v(x)+u(x)v'(x)$

The given function : $f(x) = (4x - 3)(x^2 + 9)$

here , $u(x) = 4x - 3$ and $v(x)=x^2 + 9$

Differentiate both sides with respect to x, we get

$u'(x) = 4+0=4$ and $v(x)=2x +0=2x$

$[\because \dfrac{d(ax)}{dx}=a\ , \dfrac{d(a)}{dx}=0 \ \&\ \ \dfrac{d(x^n)}{dx}=nx^{n-1}]$

Then, Tge derivative of withe respect to x will be :

$f'(x)=u'(x)v(x)+u(x)v'(x)$

$=4(x^2 + 9)+( 4x - 3)(2x)$

$=4x^2 +36+8x^2 - 6x$

$=12x^2 - 6x+36$

Hence, the derivative of the function is $f'(x)=12x^2 - 6x+36$ .

7 0

4 years ago

5pn-8p=7n-7. Solve for n.

Firlakuza [10]

Answer:

-8p + 7

n = --------------

8 - 5p

Step-by-step explanation:

Let's group the n terms in 5pn-8p=7n-7 .

Subtract 5pn from both sides. This results in -8p = 7n - 7 - 5pn

Now add 7 to both sides. This will group the n terms on the right side:

-8p + 7 = 7n - 5pn

Factor n out of 7n - 5pn:

-8p + 7 = n(7 - 5p)

Finally, divide both sides by (7 - 5n) to isolate n:

-8p + 7

n = --------------

8 - 5p

8 0

3 years ago

Can somebody help and explain this plzz

8_murik_8 [283]

A) Every T is worth 7 points, and every F is worth 3 points. So if we let T = 7 and F = 3, we can count how many T's and F's each team scored and write it as an expression.

So for the East Side Bulldogs, they have 7 touchdowns and 6 field goals, thus the expression for them is:

7T + 6F

For the West Side Bulldogs, they have 5 touchdowns and 5 field goals, thus the expression for them is:

5T + 5F

B) The difference would be written as:
7T + 6F - (5T + 5F) = 2T + F

C) To determine how many more points the winning team has than the losing team, calculate the scores of the two teams. Then subtract the smaller number from the larger number to determine the score differential.

8 0

4 years ago

Jorge's friend Anna planted a garden with the same ratio of tulips to daisies. Anna's garden has 21 tulips. How many total flowe

olasank [31]

Answer:

48 flowers

Step-by-step explanation:

Since, the ratio of tulips to daisies are the same.

Hence, if we have x number of daisies, then the number of tulips will also be x.

Therefore, with number of tulips being 21 and equal ratio of daisies will also mean that Anna has 21 daisies .

The total number of flowers will be :

Number of tulips + Number of daisies

21 + 21 = 42 flowers

8 0

3 years ago