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3 years ago

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The average distance is 92,950,000 miles between earth and sun but the distance can vary 1,550,000 miles from the average. find

an absolute value equation that models the situation and has a minimum and maximum distance between the earth and sun as solutions

1 answer:

Semenov [28]3 years ago

7 0

Answer:

|x -92,950,000| = 1,550,000

Step-by-step explanation:

The positive difference (x) from average will be ...

|x -92,950,000|

We want that to be 1,550,000 so that the only solutions to the equation are the minimum and maximum values of distance.

|x -92,950,000| = 1,550,000 . . . . . where x is earth-sun distance

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How many solutions does the equation have, x1 + x2 + x3 = 10 , where x1 , x2, and x3 are non-negative integers?

MAVERICK [17]

Non-negative integers are positive integers or zero.

1. When $x_1=0,$ then there are such possible cases for $x_2$ and $x_3:$

$x_2=0,\ x_3=10;$
$x_2=1,\ x_3=9;$
$x_2=2,\ x_3=8;$
$x_2=3,\ x_3=7;$
$x_2=4,\ x_3=6;$
$x_2=5,\ x_3=5;$
$x_2=6,\ x_3=4;$
$x_2=7,\ x_3=3;$
$x_2=8,\ x_3=2;$
$x_2=9,\ x_3=1;$
$x_2=10,\ x_3=0.$

In total 11 solutions for $x_1=0.$

2. For $x_1=1,$ there are such possible cases for $x_2$ and $x_3:$

$x_2=0,\ x_3=9;$
$x_2=1,\ x_3=8;$
$x_2=2,\ x_3=7;$
$x_2=3,\ x_3=6;$
$x_2=4,\ x_3=5;$
$x_2=5,\ x_3=4;$
$x_2=6,\ x_3=3;$
$x_2=7,\ x_3=2;$
$x_2=8,\ x_3=1;$
$x_2=9,\ x_3=0.$

In total 10 solutions for $x_1=1.$

3. This process gives you

for $x_1=2$ - 9 solutions;
for $x_1=3$ - 8 solutions;
for $x_1=4$ - 7 solutions;
for $x_1=5$ - 6 solutions;
for $x_1=6$ - 5 solutions;
for $x_1=7$ - 4 solutions;
for $x_1=8$ - 3 solutions;
for $x_1=9$ - 2 solutions;
for $x_1=10$ - 1 solution.

4. Add all numbers of solutions:

$11+10+9+8+7+6+5+4+3+2+1=66.$

Answer: there are 66 possible solutions (with non-negative integer variables)

8 0

3 years ago

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Please factorise the equations in the doc bellow ASAP. please show full working

ad-work [718]

Answer:

b. x² + 8x + 12 =

1. use the factoring X (see attachment)

2. 6 x 2 = 12; 6 + 2 = 12

3. (x + 6)(x + 2) = 0

4. x = -6, -2

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1. 12 x 1 = 12; 12 + 1 = 13

2. (x + 12)(x + 1) = 0

3. x = -12, -1

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2. (x +4)(x - 3) = 0

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1. 12 x 3 = 36; 12 + 3 = 15

2. (x + 12)(x + 3) = 0

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I need this one asap

gizmo_the_mogwai [7]

Answer:

c

Step-by-step explanation:

because it has 3 different parts that cannot be combined

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Maslowich

Answer:

D.

Step-by-step explanation:

R is remainder and to have equal amounts in each bin she could not put them in one.

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Sergeeva-Olga [200]

Answer:

x=1/4

y = -2

(1/4, -2)

b

Step-by-step explanation:

4x -y =3

y =-8x

substitute y =-8x into the first equation. Everywhere you see y put 8x

4x -y =3

4x - (-8x) =3

4x+8x=3

combine like terms

12x = 3

divide by 12

12x/12x = 3 /12

x = 1/4

now we need to find y

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y = -8 * 1/4

y = -2

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