Solve the simultaneous equations j-k= 2 and j2 + 2k=8. Give the answer in three decimal places.

Answer is j=2.606, j=4.606 and k=0.606, k=-6.606

Can you show me how to do it step by step

Step-by-step explanation:

hello :

here is an solution :

j=2.606, j=-4.606 and k=0.606, k=-6.606

Step-by-step explanation:

First step is to merge the formulas so that you are left with one combined equation with only one variable. Let's go for j, so we won't have to fiddle with the quadratic term:

First we convert j-k=2 to k=j-2, then we plug in this value for k in the other equation:

j² + 2(j-2) = 8

j² +2j -4 = 8

j² + 2j -12 = 0

This we can solve using the quadratic formula:

j = (-2 ± √(2²-4·1·-12) ) / 2

= (-2 ± √52)/2

= -1 ± √13

So j ≈ 2.6056 or j≈-4.6056

k can be found by subtracting 2.

the number of possible outcomes that do not show a 1 on the first spinner and show the number 4 on the second spinner is 2.

spinner 1 spinner 2

1                     1

1                     2

1                     3

1                     4

2                   1

2                   2

2                   3

2                   4   = not 1, and 4

3                   1

3                   2

3                   3

3                   4 = not 1, and 4

only 2 outcomes have passed the given condition.

step-by-step explanation:

hello!

to begin with, we're given that on earth, a rock weighs 20 pounds, and while on jupiter, that same rock weighs 42 pounds. now, we're trying to find the weight of a rock that weighs 10.5 pounds on earth, on jupiter.

to solve this, first, set up a proportion, cross-multiply, and solve it algebraically.

setting up the proportion is the hardest and the most confusing part of the problem, but it's simple.

if on earth, the rock weighs 20 lbs, and on jupiter it weighs 42 lbs, our first part of our proportion is 20/42 lbs. the second part has to be equal to each other. this means that 10.5 has to be on the numerator of the fraction, and x, the value we're trying to find, has to be on the denominator. remember that the rock weighs 10.5 lbs on earth, and we're trying to find the weight of it on jupiter (which is x).

20/42 = 10.5/x

next, you would cross-multiply.

20x = 42(10.5)

20x = 441

now, solve it algebraically by using division.

x = 22.05 lbs

this can be rounded to 22.1 lbs.

therefore, the weight of the rock on jupiter is 22.1 lbs, the fourth choice.