HELP ONLY WITH PART A I ALREADY DID PART B INSTRUCTIONS ARE IN PICTURE

Answer:

Part A

The equation of the parabola in standard form is f(x) = 0.5·x² + x - 7.5

Part B

The equation of the parabola in factored form is f(x) = 0.5·(x + 5)·(x - 3)

Step-by-step explanation:

The coordinates of the vertex of the parabola, (h, k) = (-1, -8)

The zeros of the parabola = -5, 3

Part A

The quadratic equation representing the parabola can be written as follows;

y = a·(x - h)² + k

The standard form of the equation is f(x) = a·x² + b·x + c

k = c - b²/(4·a)

h = -b/(2·a)

c = k + a·h² = -8 + a

From the zeros of the parabola, we have;

f(-5) = a × (-5)² + b×(-5) + c = 25·a - 5·b + c = 0

f(3) = a × (3)² + b×(3) + c = 9·a + 3·b + c = 0

Therefore, we have;

25·a - 5·b + c = 0...(1)

9·a + 3·b + c = 0...(2)

From which we have;

25·a - 5·b + c = 25·a - 5·b - 8 + a = 26·a - 5·b - 8 = 0

9·a + 3·b + c = 9·a + 3·b - 8 + a = 10·a + 3·b - 8 = 0

We then have;

26·a - 5·b = 8...(3)

10·a + 3·b = 8...(4)

Making 'b', the subject of both equations (3) and (4), equating the values, we find the value of 'a' as follows;

From equation (3), we have;

26·a - 5·b = 8

∴ b = (26·a - 8)/5

From equation (4), we have;

10·a + 3·b = 8

∴ b = (8 - 10·a)/3

From b = b, by transitive property, we have;

(26·a - 8)/5 = (8 - 10·a)/3

3 × (26·a - 8) = 5 × (8 - 10·a)

78·a - 24 = 40 - 50·a

∴ 128·a = 64

a = 64/128 = 1/2 = 0.5

a = 0.5

∴ b = (26·a - 8)/5 = (26 × 0.5  - 8)/5 = (13 - 8)/5 = 1

b = 1

c = -8 + a

∴ c = -8 + 0.5 = -7.5

c = -7.5

The equation of the parabola in standard form is therefore presented as follows;

f(x) = 0.5·x² + x - 7.5

Part B

The equation of the parabola in factored form is given as follows;

With the aid of a graphing calculator, we have;

f(x) = 0.5·x² + x - 7.5 = 0.5×(x² + 2·x - 15) = 0.5·(x + 5)·(x - 3)

The equation of the parabola in factored form is f(x) = 0.5·(x + 5)·(x - 3)

Answer:

35

Step-by-step explanation:

Answer:

The answer is 35

Step-by-step explanation:

all i did was multiply 5% by 700

Answer:

I think the answer is B

Step-by-step explanation:

Sorry if it's wrong

Answer: i think its b

Step-by-step explanation:

Answer:

$8.75

Step-by-step explanation:

I HOPE THIS HELPS YOU OUT WITH YOUR QUESTION! PLZ LET ME KNOW IF IT DID! IT MAKES ME FEEL GOOD THAT SOMEONE APPRECIATES IT! ANYWAY, IF YOU HAVE A FEW MINUTES PLZ GOT TO MY PROFILE AND THANK MY ANSWERS (THE MORE THE MERRIER)

Answer:

[tex]x = 64 + 45 \\ x = 109[/tex]

Answer:

∠A = 60°

∠B = 42°

∠C = 78°

Step-by-step explanation:

∵ In a triangle, sum of all the three interior angles is 180°

∴ m∠A + m∠B + m∠C = 180°

∴ (4x)° + (3x - 3)° + (5x + 3)° = 180°

∴ (4x + 3x - 3 + 5x + 3)° = 180°

∴ (12x)° = 180°

∴ 12x = 180

∴ x = 180/12

∴ x = 15

∠A = (4x)° = (4× 15)° = 60°

∠B = (3x-3)° = (3× 15-3)° =(45-3)°= 42°

∠C = (5x+3)° = (5× 15 + 3)° =(75 + 3)°= 78°

Answer:

1/2m - 4

Step-by-step explanation:

Answer:

a

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:

Richie should add the number 36 to both sides.

Step-by-step explanation:

To complete the square, you need to divide b by 2, square it, then add it to both sides. In this case, you'd do this:

12/2=6

6^2=36

Answer: The second one, 10 rolls for $12. 1.29 (Rounded)

Step-by-step explanation:

14/18 is 1.29 (Rounded)

10/12 is 1.20.

The unit rate is cheaper, therefore making it the better buy

Answer:

do you need an equation? if so it would be 2x+40

Step-by-step explanation:

Let's solve for i.

54−(

1

7

y)(i)=9x−4

Step 1: Add -54 to both sides.

−1

7

iy+54+−54=9x−4+−54

−1

7

iy=9x−58

Step 2: Divide both sides by (-y)/7.

−1

7

iy−y7=

9x−58−y7i=

−63x+405y

Answer:i=

−63x+406y

Answer:

You were correct.

Step-by-step explanation:

If the input to the function y = 4x - 3 is 2 Then

y = 4 * 2 - 3

= 8 - 3

= 5

Hope it helps :)

Answer:

[tex]\sqrt{149}[/tex]

Step-by-step explanation:

The third side of a triangle can be any value in the range of -

1 ≤ a < 17.

Given are two sides of a triangle as b = 7m and c = 10m.

The sum of two sides of a triangle is always greater than the third side. Mathematically -

a < {b + c}

a < {7 + 10}

a < 17

a ∈ [1, 16]

Therefore, the third side of a triangle can be any value in the range of -

1 ≤ a < 17.

To solve more questions on triangles, visit the link below -

https://brainly.com/question/12538366

#SPJ2

Answer:

242

First is 9 times 10 which is 90, then 4 times 8 is 32 divided by 2 which is 16 times 2 since there are two, 32 again. 8 times 10 is 80. 4 times 10 is 40.

90 + 32 + 80 + 40 = 242

Step-by-step explanation:

Answer:

$200

Step-by-step explanation:

Hey There!

So first we want to find the price of each pound of banana

To do this we divide the cost by amount of bananas bought

86/43=2

so each pound of bananas cost $2

now we just multiply 2 and 100

2x100=200

so 100 pounds of bananas would cost $200

hope this helps :)

Answer:

50

Step-by-step explanation:

Calculate how much 1lbs of bananas cost by dividing 86 by 43. getting you 2. That means each lbs of bananas is $2. Then divide $100 by $2 getting you 50 because you have $100. So you can get 50lbs of bananas with $100.

Answer:

1/3x + 1/2

Step-by-step explanation:

combine like terms 1/3x plus 2/3x equals 3/3x - 2/3x = 1/3x

and 3/4-1/4 = 2/4.

Answer:

1/3x+1/2

Step-by-step explanation:

1/3x+2/3x-2/3x+3/4-1/4      eliminated +2/3x-2/3x

1/3x+3/4-1/4

1/3x+2/4    simplify 2/4 to 1/2

1/3x+1/2

Answer:

[tex]0.3 m = 12[/tex]

Step-by-step explanation:

See comment for complete question

Given

30% in 12 minutes

Required

Time to complete the homework

From the question: m represents the required minutes

This implies that:

[tex]30\% * m = 12[/tex]

Convert to decimal

[tex]0.30 * m = 12[/tex]

[tex]0.3 m = 12[/tex]

Hence:

The equation is: [tex]0.3 m = 12[/tex]

Answer:

320 i think lol

Step-by-step explanation:

Answer:

3.56

Step-by-step explanation:

Answer:

I think it is 73

Step-by-step explanation:

Because i tryed all of the other numbers and they didnt work

HOPE THIS HELP !!!!!!!!!!!!!!!! :)

Answer:

so you answered your own question?

Answer:

One hour’s sleep before midnight is worth three after.

Answer: You may laugh or whatever but for that london one

Step-by-step explanation:

A beautiful city of night.

Answer: 72.5

Step-by-step explanation:

The average of 2 points is the midpoint so if I add 70 and 75 to get 145 and divide by the number of numbers which is 2 I get 72.5

Answer:

x > -1

Step-by-step explanation:

Open circle so the sign is not inclusive. The point is at -1 and goes to the right so it is more than.

Answer:

2/4=4/8

Step-by-step explanation:

you do 2×2=4 and 4×2=8. You multiply both denominators by 2.

Answer:

its B

Step-by-step explanation: