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3 years ago

5

What is 10 x

}{5} " align="absmiddle" class="latex-formula"> show your work

1 answer:

djverab [1.8K]3 years ago

3 0

First, convert the 10 into a fraction. This easy since anything over 1 is that number.

10 = $\frac{10}{1}$

Now multiply.

$\frac{10}{1} * \frac{4}{5} = \frac{40}{5}$ = 8

So, 8 is the answer.

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Three of these fractions are equivalent: B. 12 C . 21 D. 74 30 A. . 70 Which one is the odd one out?

IrinaVladis [17]

Answer:

12/30

Step-by-step explanation:

Here is the complete question

Three of these fractions are equivalent A.30/70 B.12/30 C.9/21 D.6/14 which one is the odd one out

to determine the equivalent fractions, convert the fractions to percentage

$\frac{30}{70}$ × 100 = 42.86%

$\frac{12}{30}$ × 100 = 40%

$\frac{9}{21}$ × 100 = 42.86%

$\frac{6}{14}$ x 100 = 42.86%

Another method is to convert the fraction to its simplest form

30/70

To transform to the simplest form. divide both the numerator and the denominator by 10 = 3/7

12/30

To transform to the simplest form. divide both the numerator and the denominator by 6 = 2/5

9/21

To transform to the simplest form. divide both the numerator and the denominator by 3 = 3/7

6/14

To transform to the simplest form. divide both the numerator and the denominator by 2 = 3/7

Using either methods, 12/30 is the odd one out

4 0

2 years ago

The price, P, of a sweater was discounted by 10% in

aalyn [17]

Answer:

In terms of P, the price of the sweater after the discount is 0.72P.

Step-by-step explanation:

Since the price P would represent 100% and the price was discounted by 10%, you can calculate 10% of 100% and subtract that amount, which would be:

100*10%=10

100-10=90%

This means that the price paid would be 90% of P. Then, the statement says that the price was discounted by another 20%. So, you have to calculate 20% of the price and subtract that amount from the price:

90*20%=18

90-18=72%

According to this, this means that in terms of P, the price of the sweater after the discount is 0.72P.

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2 years ago

Find the distance between a point (– 2, 3 – 4) and its image on the plane x+y+z=3 measured across a line (x + 2)/3 = (2y + 3)/4

dimaraw [331]

Answer:

Distance of the point from its image = 8.56 units

Step-by-step explanation:

Given,

Co-ordinates of point is (-2, 3,-4)

Let's say

$x_1\ =\ -2$

$y_1\ =\ 3$

$z_1\ =\ -4$

Distance is measure across the line

$\dfrac{x+2}{3}\ =\ \dfrac{2y+3}{4}\ =\ \dfrac{3z+4}{5}$

So, we can write

$\dfrac{x-x_1+2}{3}\ =\ \dfrac{2(y-y_1)+3}{4}\ =\ \dfrac{3(z-z_1)+4}{5}\ =\ k$

$=>\ \dfrac{x-(-2)+2}{3}\ =\ \dfrac{2(y-3)+3}{4}\ =\ \dfrac{3(z-(-4))+4}{5}\ =\ k$

$=>\ \dfrac{x+4}{3}\ =\ \dfrac{2y-3}{4}\ =\ \dfrac{3z+16}{5}\ =\ k$

$=>\ x\ =\ 3k-4,\ y\ =\ \dfrac{4k+3}{2},\ z\ =\ \dfrac{5k-16}{3}$

Since, the equation of plane is given by

x+y+z=3

The point which intersect the point will satisfy the equation of plane.

So, we can write

$3k-4+\dfrac{4k+3}{2}+\dfrac{5k-16}{3}\ =\ 3$

$=>6(3k-4)+3(4k+3)+2(5k-16)\ =\ 18$

$=>18k-24+12k+9+10k-32\ =\ 18$

$=>\ k\ =\dfrac{13}{8}$

So,

$x\ =\ 3k-4$

$=\ 3\times \dfrac{13}{8}-4$

$=\ \dfrac{7}{4}$

$y\ =\ \dfrac{4k+3}{2}$

$=\ \dfrac{4\times \dfrac{13}{8}+3}{2}$

$=\ \dfrac{19}{4}$

$z\ =\ \dfrac{5k-16}{3}$

$=\ \dfrac{5\times \dfrac{13}{8}-16}{3}$

$=\ \dfrac{-21}{8}$

Now, the distance of point from the plane is given by,

$d\ =\ \sqrt{(x-x_1)^2+(y-y_1)^2+(z-z_1)^2}$

$=\ \sqrt{(-2-\dfrac{7}{4})^2+(3-\dfrac{19}{4})^2+(-4+\dfrac{21}{8})^2}$

$=\ \sqrt{(\dfrac{-15}{4})^2+(\dfrac{-7}{4})^2+(\dfrac{9}{8})^2}$

$=\ \sqrt{\dfrac{225}{16}+\dfrac{49}{16}+\dfrac{81}{64}}$

$=\ \sqrt{\dfrac{1177}{64}}$

$=\ 4.28$

So, the distance of the point from its image can be given by,

D = 2d = 2 x 4.28

= 8.56 unit

So, the distance of a point from it's image is 8.56 units.

4 0

3 years ago