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3 years ago

The distance from the Sun to Mars is an average of 2.1 repeating.

Mathematics

1 answer:

Anna007 [38]3 years ago

7 0

Answer:

19/9

Step-by-step explanation:

We are given repeating decimal number 2.1¯.

We know 2.1¯ = 2.1111..... repeating 1's.

Let us assume x is a fraction equals given repating decimal number.

And set it as a first eqaution.

x = 2.1111..... ------------- (equation 1).

Multiplying equation both side by 10 ( because only one digit is repeating after decimal, we multiply by 10).

On multiplying by 10 we get

10*x = 10*2.1111.....

10x = 21.1111...... ----------------- (equation 2)

Subtracting equation 1 from equation 2, we get

10x = 21.1111......

-x = -2.1111.....

_____________

9x = 19.

Now, dividing both sides by 9. we get

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Given:

lys-0071 [83]

Answer:

$PS=13\text{ units}$

Step-by-step explanation:

So, we know that PR is 20, SR is 11, and QS is 5.

We also know that PQ is perpendicular to QR, forming the right angle at ∠Q.

We know all the side lengths except for PQ and PS (the one we want to find). Notice that if we find PQ first, we can then use the Pythagorean Theorem to find PS since we already know QS.

So, let's find PQ.

We can see that we can also use the Pythagorean Theorem on PQ. PQ, QR, and PR (the hypotenuse) will be our sides. So:

$(PQ)^2+(QR)^2=(PR)^2$

We know that PR is 20.

QR is the combined length of QS+SR, so QR is 5+11 or 16.

So, substitute:

$(PQ)^2+(16)^2=(20)^2$

Solve for PQ. Square:

$(PQ)^2+256=400$

Subtract 256 from both sides:

$(PQ)^2=144$

Take the square root of both sides:

$PQ=12$

So, the side length of PQ is 12.

Now, we can use the Pythagorean Theorem again to find PS. Notice that PQ, QS, and PS also form a right triangle, with PS being the hypotenuse. So:

$(PQ)^2+(QS)^2=(PS)^2$

We already know that QS is 5. We also just determined that PQ is 12. Substitute:

$(12)^2+(5)^2=(PS)^2$

Square:

$144+25=(PS)^2$

Add:

$169=(PS)^2$

Take the square root of both sides:

$PS=13$

Therefore, the length of PS is 13 units.

And we're done!

7 0

4 years ago

Help me I keep getting it wrong

gtnhenbr [62]

Answer:

see explanation

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = $\frac{2}{3}$ x - 6 ← is in slope- intercept form

with slope m = $\frac{2}{3}$

Parallel lines have equal slopes , then

y = $\frac{2}{3}$ x + c ← is the partial equation

To find c substitute (9, 2) into the partial equation

2 = 6 + c ⇒ c = 2 - 6 = - 4

y = $\frac{2}{3}$ x - 4 ← equation of parallel line

-------------------------------------------------------------------

Given a line with slope m then the slope of a line perpendicular to it is

$m_{perpendicular}$ = - $\frac{1}{m}$ = - $\frac{1}{\frac{2}{3} }$ = - $\frac{3}{2}$ , then

y = - $\frac{3}{2}$ x + c ← is the partial equation

To find c substitute (9, 2) into the partial equation

2 = - $\frac{27}{2}$ + c ⇒ c = 2 + $\frac{27}{2}$ = $\frac{31}{2}$

y = - $\frac{3}{2}$ x + $\frac{31}{2}$ ← equation of perpendicular line

4 0

3 years ago

100 points and brainleist

Assoli18 [71]

Answer:

582 (C)

Step-by-step explanation:

The side closest to us (and the back too) is 9*9 + (15-9)*(15) = 81 + 90 = 171 *2 sides = 342

The top and bottom faces are: 15*4 = 60 * 2 sides = 120

The left side + right side = 15*4 * 2sides = 120

120+120+342 =

582

6 0

4 years ago

I’m confused please help

Degger [83]

This is completing the square.

So x^2-6x-12=0

Add 12 to both sides so x^2-6x=12

Now take half the x term and square it. Add this number to both sides.

So x^2-6x+9=12+9

Which is the same as (x-3)^2=21

This is answer 2.

6 0

3 years ago

The scale of a map is 1in:15miles. How many miles is it from Philadelphia, Pa to Boston, Ma if they are 20.4 inches apart on the

cupoosta [38]

Answer:

if 1in=15miles

then20.4in=? miles

1in by ? miles and 20.4in by 15miles

1in ? miles= 306in miles

divide both sides by 1in

? miles= 306 miles

therefore 20.4in = 306miles

4 0

2 years ago