The sum of three numbers is -2. the sum of three times the first number, twice the second number, and the third number is nine. the difference between the second number and half the third is 10. find the numbers.

The numbers are 3, 5, -10.

Step-by-step explanation:

Let, the numbers are X, Y, Z.

Given, sum of the three numbers are -2.  

So, the equation is X + Y+ Z = -2 (i)

Again, for 2nd condition, the equation will be  

3X + 2Y + Z = 9   (ii)

Again, for the third condition, the equation will be

Y - (Z/2) = 10 (iii)

Multiplying the equation (i) by 3 and the equation (ii) by 1, we get

                     3X + 3Y+ 3Z = -6

                     3X + 2Y +  Z =  9

(Deduct)                  Y + 2Z = -15 (iv)  

Solving equation (iii) and (iv) we get,

                         Y - (Z/2) = 10

                         Y + 2Z   = -15

(Deduct)        -(Z/2) - 2Z = 25

or, (-Z-4Z)/2 = 25

or, -5Z = 25*2

or, Z = 50/(-5)

Therefore, Z = -10

Putting the value of Z into equation (iv) we get,

Y + 2*(-10) = -15

or, Y - 20 = -15

or, Y = 20 - 15

Therefore, Y = 5

Putting the value of Y and Z into equation (i) we get,

X + 5 + (-10) = -2

or, X + 5 - 10 = -2

or, X - 5 = -2

or, X = 5 - 2

Therefore, X = 3

So, the numbers are, X = 3; Y = 5; and Z = -10.

step-by-step explanation:

let

we know that

the y-intercept is the y-coordinate of the point when the value of x is equal to zero

so

the y-coordinate of the point a is the y-intercept

the answer part a) is

the value of y-intercept is

part b) find the slope m

we know that

the value of the slope is equal to

substitute the values

therefore

the answer part b) is

the value of the slope is equal to

the general answer is

the slope is

the value of y-intercept is

total of apples - take away four

6-4 = 2

answer is 2 apples