What is one of the solutions to the following system of equations?

y2 + x2 = 65
y + x = 7

a (8, −1)
b (1, 6)
c (6, 1)
d (9, −2)

(8,-1)

Step-by-step explanation:

Given :  

To Find: solution of given system of equations.

Solution:

Equation a :  

Equation b :  

Substitute the value of y from equation b in equation a

y from equation b : y = 7-x

Now substitute value of y in equation a

Thus equation a becomes:

⇒ x= -1 and x = 8

Now substitute values of x  in equation b to obtains values of y

⇒

for x = -1

⇒

⇒

⇒

Thus (x,y)=(-1,8)

For x =8

⇒

⇒

⇒

Thus (x,y)=(8,-1)

Hence Option A is the correct solution .

.19875994384

step-by-step explanation:

1699/ 8548

a) 40 more; b) old factory:   10%, new factory:   16%; c) week 4

explanation:

a) at week 0, we see in the graph that the new factory produces 190 specialty items.  

using the function, substituting 0 in for w,

this is a difference of 230-190 = 40.

b) the function for the old factory is written in the form f(x) = a(1+r)ˣ, where a is the original amount, x is the amount of time and r is the growth rate.   the equation for the old factory is ; 230 is in place of a and is the original amount; w is the amount of time; which means 1+r = 1.1.   this means that r must be 0.1 or 10%.

for the new factory, we find the percent of increase to find the growth rate; the formula for this is

between the first two points, the amount of change is 220-190 = 30; this gives us

30/190 = 0.158 ≈ 0.16 = 16%

c) at week 0, the old factory has 230 while the new factory has 190.

at week 1, the old factory has 230(1.1) = 253 while the new factory has 220.

at week 2, the old factory has 230(1.1²) = 278.3 while the new factory has 252.

at week 3, the old factory has 230(1.1³) = 306.13 while the new factory has 290.

at week 4, the old factory has 230(1.1⁴) = 336.743 while the new factory has 337.   this is the first week that the new factory surpasses the old.