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Mathematics

1 answer:

Leto [7]2 years ago

6 0

In this triangle
ab and cb are the same length

a^2 + b^2 = c^2

Have you used this befor

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Pls help, thank you

Lemur [1.5K]

Answer:

y = -3x² + 7x - 9

Step-by-step explanation:

Given quadratic function:

y = ax² + bx + c

Points on the graph:

(-2,-35), (1,-5), (3,- 15)

Substitute values of x and y and solve the system of equations:

-35 = a(-2)² + b(-2) + c ⇒ -35 = 4a - 2b + c ⇔ eq 1
-5 = a(1)² + b(1) + c ⇒ -5 = a + b + c ⇔ eq 2
-15 = a(3)² + b(3) + c ⇒ -15 = 9a + 3b + c ⇔ eq 3

Subtract eq 2 from eq 1:

-35 - (-5) = 4a - 2b + c - a - b - c
-30 = 3a - 3b
b = a + 10 ⇔ eq 4

Subtract eq 2 from eq 3:

-15 - (-5) = 9a + 3b + c - a - b - c
-10 = 8a + 2b
b = -4a - 5 ⇔ eq 5

Compare eq 4 and eq 5, solve for a:

a + 10 = -4a - 5
a + 4a = -5 - 10
5a = -15
a = -3

Find the value of b using eq 4:

b = -3 + 10
b = 7

Find the value of c using eq 2:

-5 = -3 + 7 + c
c = -5 - 4
c = -9

We now have a, b and c:, the function is:

y = -3x² + 7x - 9

8 0

3 years ago

Read 2 more answers

I need help it’s a quiz

solmaris [256]

Answer:

Question 6: 26 crowns plus 15 ribbons.

Question 7: 10 footballs plus 42 basketballs.

Step-by-step explanation:

Question 6 explanation: Since the expression is 22 crowns plus 13 ribbons plus 2 ribbons plus 4 crowns, you can think of the different items as variables in an equation. Picture crowns are the variable $x$ , and ribbons as the variable $y$ , this will help you solve the equation in an easier way that allows you to comprehend each step better. The equation will now be $22x+13y+2y+4x$ , in order to find how many $x$ (crowns) and $y$ (ribbons) you have, you need to combine like terms in the expression. In other words, add the terms with the variable $x$ together, and add the terms with the variable $y$ together. Simplified, the equation will be $26x+15y$ . Since the variables $x$ and $y$ were used to represent crowns and ribbons respectively, that means the correct answer is 26 crowns plus 15 ribbons.

Question 7 explanation: You can use the same method as you did in question 6, think of footballs and basketballs as the variables $x$ and $y$ respectively. The equation will be $16x+38y-6x+4y$ = $10x+42y$ . Since the variable $x$ was used to represent footballs and the variable $y$ was used to represent basketballs, that means the correct answer would be 10 footballs plus 42 basketballs.