MATHEMATICS HIGH SCHOOL

Y = 10 + 16x − x^2y = 3x + 50
If (x1, y1) and (x2, y2) are distinct solutions to the system of equations shown above, what is the sum of the y1 and y2?

Answers

Answer 1

Answer:

Solving the system we can see that the sum of the y-values of the two solutions is 139.

How to get the sum of y₁ and y₂?

Let's solve the system of equations.

y = 10 + 16x − x²

y = 3x + 50

We can write this as a single quadratic equation:

10 + 16x - x² = 3x + 50

10 + 16x - x² - 3x - 50 = 0

-x² + 13x - 40 = 0

Using the quadratic formula we will get the two solutions for x:

$x = (-13 \pm √(13^2 - 4*-1*-40) )/(-2) \n\nx = (-13 \pm 3 )/(-2)$

So the two solutions are:

x = (-13 + 3)/-2 = 5

x = (-13 - 3)/-2 = 8

Evaluating the linear equation in these two values we will get y1 and y2.

if x = 5

y₁ = 3*5 + 50 = 65

if x= 8

y₂ = 3*8 + 50 = 74

The sum is:

65 + 74 =139

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Answer 2

Answer:

Final answer:

The distinct solutions to the system of equations are (5, 65) and (8, 74), and the sum of the y-values is 139.

Explanation:

To find the sum of y-values of the distinct solutions to this system of equations, first, you need to set the two equations equal to each other to find the x-values of the solutions:

10 + 16x − x^2 = 3x + 50.

Then, solve the resulting equation for x:

x^2 - 13x + 40 = 0.

This is a quadratic equation, and it can be solved either by factoring or using the quadratic formula. The solutions for x result in:

x = 5 and x = 8.

These are the two distinct x-values for the intersections of the graphs of the two equations. To find the corresponding y-values, plug these x-values into either of the original equations. We'll use the simpler equation, y = 3x + 50:

For x = 5, y = 65 and for x = 8, y = 74.

Therefore, the distinct solutions to the system of equations are (5, 65) and (8, 74). Finally, the sum of y1 and y2 is 65 + 74 = 139.

Learn more about System of Equations here:

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What is 23.791 rounded to the nearest tenth?

Answers

The nearest tenth would be the first decimal place, so the answer would be 23.8

What polynomial identity will prove that 49 = (2+5)^2? (A. Difference of Squares; B. Difference of Cubes; C. Sum of Cubes; D. Square of a Binomial)

Answers

Answer:

Option D is correct.

Square of binomials.

Step-by-step explanation:

Prove that: $49 = (2+5)^2$

Square of binomials states that the square of a binomial is always a trinomial.

Also, it will be helpful to memorize these patterns for writing squares of binomials as trinomials.

$(a+b)^2 = a^2+2ab+b^2$

Take RHS

$(2+5)^2$

Apply the square of binomial, we have;

$(2+5)^2 = 2^2+2 \cdot 2 \cdot 5 +5^2$

= 4 + 20 + 25 = 24 + 25 = 49 = LHS proved.

Therefore, Square of binomials identity will prove that $49 = (2+5)^2$

Hi,

(a+b)² = a²+2ab+b²

For a = 2 and b = 5

(2+5)² = 2²+2(2)(5)+5²
(2+5)² = 4+20+25
(2+5)² = 49

Answer:

D. Square of a Binomial

Give the slope and y-intercept ofthe line.
slope = [?], y-intercept = [ ]
Enter the number that belongs in the green box.
Enter

Answers

Answer:

Slope = 2, y-intercept = 3

Step-by-step explanation:

I will be calculating the slope of the line using these two points: (-1, 1) and (0, 3)

Slope = $(rise)/(run)$

= $(3-1)/(0-(-1))$

= $(3-1)/(0+1)$

= 2

Based on the graph, the y-intercept is 3.

Find the product. -mnp(3m - 5n + 7p)

Answers

- mnp ( 3 m - 5 n + 7 p )

= -mnp * 3 + 5mn² - 7 mnp²

=> - 3 m²np + 5 mn² - 7 mnp²

hope this helps!

Answer:

- 3 m²np + 5 mn² - 7 mnp²

Step-by-step explanation:

Kenya has 2 hours to make a 104 mile road trip. What rate must she average to make the trip in 2 hours?51 mph

52 mph

53 mph

54 mph

Answers

104/2 = 52
answer is 52 mph
hope it helps

What are the roots of the equation x^2+4x-16=0

Answers

$x^2+4x+16=0 \n \n \Delta=b^2-4ac \n \Delta=4^2-4*1*16 \n \Delta = 16-64 \n \Delta=-48 \n \Delta \ \textless \ 0 =\ \textgreater \ \text{we don't have REAL solutions} \n \n \text{but it can solve with the multitude of complex numbers }\mathbb{C}$