Solve the system of equations using substitution.
3x + 2y = 7
y = –3x + 11

Answers

Answer 1

Answer: 3x + 2y = 7
y = -3x + 11

Solve the system of equation using substitution.

Substitute the y in the first equation by its value presented in the 2nd equation.

3x + 2y = 7
3x + 2(-3x + 11) = 7
3x - 6x + 22 = 7
-3x + 22 = 7
-3x = 7 - 22
-3x = -15
-3x/-3 = -15/-3
x = 5

Substitute x in the 2nd equation by its computed value. x = 5
y = -3x + 11
y = -3(5) + 11
y = -15 + 11
y = -4

x = 5 ; y = -4

Substitute x and y in the 1st equation with its corresponding values

3x + 2y = 7
3(5) + 2(-4) = 7
15 - 8 = 7
7 = 7

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Probability theory predicts that there is a 9% chance of a water polo team winning any particular match. If the water polo team playing two matches is simulated 10,000 times, in about how many of the simulations would you expect them to win exactly one match?A. 8281
B. 1638
C. 81
D. 819

Answers

The result is B. 1638.

To calculate this, we will use both an addition and a multiplication rule. The addition rule is used to calculate the probability of one of the events from multiple pathways. If you want that only one of the events happens, you will use the addition rule. The multiplication rule calculates the probability that both of two events will occur.
First, there are two possibilities for winning exactly one match:
1. To win the first match and lose the second one.
2. To lose the first match and win the second one.

9% = 0.09 is the probability of winning. The probability of losing is 1-0.09 = 0.91. To calculate the probability of winning the first match and losing the second one and vice versa, we will use the multiplication rule:
1. 0.09 × 0.91 = 0.0819
2. 0.91 × 0.09 = 0.0819

We want to either one of these events to happen, so using the addition rule, we have:
0.0819 + 0.0819 = 0.1638

In 10,000 matches:
0.1638 × 10,000 = 1,638

What is x^2 + 3x - 10 =0

Answers

$x^2 + 3x - 10 = 0 \n \n (x - 2)(x + 5) = 0 \n \n x = 2, -5 \n \n$

The final result is: x = 2, -5.

(x - 5)(x + 2) = 0

Set both factors equal to 0
x - 5 = 0
x + 2 = 0

Solve for x and the answer is
x = 5
x = -2

Determine whether (5,6) is the solution for y=x+1

Answers

$(5,6)$

$x=5 \n y=6$

$y=x+1$

$(6)=(5)+1$

$6=6$

$true$

Has your class not learned how to check an answer to see if it's correct ? ! ?

Your equation is [ y = x + 1 ].
You want to know whether (5, 6) is A solution to the equation.

When you write (5, 6), that means "x=5 and y=6".
So put those numbers into the equation in place of 'x' and 'y'
and see if the equation is true after you do that.

(y) = (x) + 1

(6) = (5) + 1

Do you see 5+1 on the right side. That's 6.
So the equation says " 6 = 6 " . . . a true statement.
So (5, 6) is a solution of the equation.

It's not THE solution. There are an infinite number of solutions
to that equation. (5, 6) is one of them.

For the function f(x)=x^2-12 find (f^-1)(4)