All categories

3 years ago

Write the equation of the parabola in vertex form.Vertex: (−4,6); Point: (−2,−2)

Mathematics

1 answer:

gtnhenbr [62]3 years ago

5 0

Answer:

y = - 2(x + 4)² + 6

Step-by-step explanation:

The equation of a parabola in vertex form is

y = a(x - h)² + k

where (h, k) are the coordinates of the vertex and a is a multiplier

Here (h, k ) = (- 4, 6 ) , thus

y = a(x - (- 4) )² + 6 , that is

y = a(x + 4)² + 6

To find a substitute (- 2, - 2) into the equation

- 2 = a(- 2 + 4)² + 6 ( subtract 6 from both sides )

- 8 = a(2)² = 4a ( divide both sides by 4 )

- 2 = a , thus

y = - 2(x + 4)² + 6 ← equation in vertex form

You might be interested in

Armando took his dog, Tasha, to the vet. Tasha was placed on the scale and weighed 45.72 pounds. The veterinarian told Armando t

belka [17]

Answer: 17 pounds

Step-by-step explanation:

6 0

3 years ago

The polynomial of degree 4, P ( x ) has a root of multiplicity 2 at x = 4 and roots of multiplicity 1 at x = 0 and x = − 4 . It

Annette [7]

Answer: P(x) = {(x-4)^2} (x) (x+4)

Step-by-step explanation:

Let's start with the multiplicity of 2;

At multiplicity of 2; x=4.

Therefore, x - 4 is a factor of the function P(x).

Since it has a multiplicity of 2, we will rewrite the factor as (x-4)^2

Now for the multiplicity of 1.

At this multiplicity of 1, x= 0 and - 4.

Therefore, the factors are x-0 and x+4

Since multiplicity of 1, the factors remain as they are without any additional root on top.

Therefore, the factors of the polynomial p(x) are (x-4)^2 and x and x+4.

And solution of P(x) in factor form will be: P(x) = {(x-4)^2} (x) (x+4)

7 0

3 years ago

1. Evaluate the expression if y = 5 and z = 0

natta225 [31]

Answer:

1. 0

2. -1

3. $120

4. $653.25

5. 4ab + 7a - 2b

Step-by-step explanation:

1. y = 5, z = 0

2z/y = ?

You'll need to substitute the values of y and z in the expression

2z/y

Becomes

2 * 0 / 5

= 0

So, 2z/y equals 0

......................................................................................................................

2. x = 0, y = -1 z = 7

xz - y²

Substituting the values of x, y and z in the above algebraic expression

xz - y²

Becomes

0*7 - (-1²)

0 - 1

-1

So, xz - y² equals -1

......................................................................................................................

3. The question falls under SIMPLE INTEREST

The formula is

I = (PRT)/100

Where I represents Interest

P = Principal (Amount Invested)

R = Rate of Interest

T = Time (in years)

From the question,

The interest is unknown ----------------- (To be calculated)

P equals $600

R = 2%

T = 10 years

Substitute these values in the formula above

I = (PRT)/100

Becomes

I = (600 * 2 * 10) / 100

I = 12000/100

I = 120

Result: The interest is $120

......................................................................................................................

The formula is

I = (PRT)/100

Where I represents Interest

P = Principal (Amount Invested)

R = Rate of Interest

T = Time (in years)

From the question,

The interest is unknown ----------------- (To be calculated)

P equals $13000

R = 6.7%

T = 9 months

Remember that time has to be in years

So, 9 months must be converted to year(s)

If 12 months makes a years

Then 9 months would be 9/12 years

So, T = 9/12 years

T = 0.75 years

Substitute these values in the formula above

I = (PRT)/100

I = (13000 * 6.7 * 0.75) / 100

I = 65325/100

I = 653.25

Result: The interest is $653.25

5. Simplify 4ab - 3bc + 7a - 2b + 3bc

4ab - 3bc + 7a - 2b + 3bc---------------------- Collect like terms

4ab + 7a - 2b + 3bc - 3bc

4ab + 7a - 2b

6 0

3 years ago

mr. walker works as a salesperson at an electronics store. her earns $600 a week, plus $50 for a every computer he sells. write

harkovskaia [24]

Answer:

The number of computer must Mr. walker sale that week to earn at least $ 1250 is 13 .

Step-by-step explanation:

Given as :

The earning of Mr . walker = $ 600 per week + $ 50 for every computer he sell

Let The number of computer does he must sell to earn $ 1250 for the week = n computers

Now, According to question

$ 600 per week + $ 50 × number of computer he sale = total earning that week

Or, $ 600 per week + $ 50 × number of computer he sale = $ 1250

Or, $ 600 per week + $ 50 × n = $ 1250

or, $ 50 × n = $ 1250 - $ 600

Or, $ 50 × n = $ 650

∴ n = $\frac{650}{50}$

I.e n = 13

So, number of computer must he sale to earn $ 1250 = n = 13

Hence The number of computer must Mr. walker sale that week to earn at least $ 1250 is 13 . Answer

3 0

3 years ago

What are the odds in russian roulette?

algol13

Answer:

about 66.5%

Step-by-step explanation:

There are two rounds, and six locations. There is a one in three chance that you will die. This probability does not change with any number of spins. There is a 66.7% chance (4/6) that you will live.

3 0

3 years ago