# Parabola a can be represented using the equation (x+3)^2=y

## Answers

answer: l

step-by-step explanation:

The Amount after 4 years is $2430 .

Step-by-step explanation:

Given as :

The principal amount investment = p = $2000

The rate of interest applied = r = 5%

The time for investment = t years

Let The Amount after t years = $A

From Compound Interest method

Amount = Principal × [tex](1+\dfrac{\textrm rate}{100})^{\textrm time}[/tex]

Or, A = p × [tex](1+\dfrac{\textrm r}{100})^{\textrm t}[/tex]

Or, A = $2000 × [tex](1+\dfrac{\textrm 5}{100})^{\textrm t}[/tex]

Or, A = $2000 × [tex](1.05)^{\textrm t}[/tex]

So, The Amount after t years = A = $2000 × [tex](1.05)^{\textrm t}[/tex]

B) The principal amount investment = p = $2000

The rate of interest applied = r = 5%

The time for investment = t = 4 years

Let The Amount after t years = $A

From Compound Interest method

Amount = Principal × [tex](1+\dfrac{\textrm rate}{100})^{\textrm time}[/tex]

Or, A = p × [tex](1+\dfrac{\textrm r}{100})^{\textrm t}[/tex]

Or, A = $2000 × [tex](1+\frac{5}{100})^{4}[/tex]

Or, A = $2000 × [tex](1.05)^{4}[/tex]

i.e A = $2000 × 1.215

Or, A = $2430

So, The Amount after 4 years = A = $2430

Hence, The Amount after 4 years is $2430 . Answer

The answer is C

Step-by-step explanation:

I just took the test and sacrificed an answer for you. Your welcome :D

The situation of balloon B

Step-by-step explanation:

Balloon A is released 5 feet above the ground and our ground level be 0 feet. Let k be the rate at which it rises and t the time it takes to rise. Its height y, above the ground after time x is y = kt + 5

For Balloon B since it is released at ground level at which ground level is taken as 0 feet, let t be the time it takes to rise above the ground and k the rate at which it rises above the ground. Its height y above the ground after tie x is y = kt

Since the expression for Balloon B is y = kt and the expression for Balloon A is y = kt + 5, only the situation of Balloon B can be expressed in the form y = kx.

This is because the rate of rise of Balloon B follows a direct proportionality while the rate of rise of Balloon follow a joint proportionality since it starts from a point other than ground level.

The vertex of the parabola is at the solution of (x+ 3) = 0 which is -3. The y intercept of the line is (0,9)

The answer would be:

C: Isabel is incorrect because the point of intersection between Line B and Parabola A that can be determined is the y-intercept of the functions, not necessarily the vertex.

Parabola a: y = (x+3)²

line b: y = mx + 9

y = (x+3)² → (x+3)(x+3) = x² + 3x + 3x + 9 = x² + 6x + 9

y = y

mx + 9 = x² + 6x + 9 ; assume that m = 1

x + 9 = x² + 6x + 9

9 = x² + 6x - x + 9

9 - 9 = x² + 5x

0 = x² + 5x

x = -b + √(b²) - 4ac / 2a

x = [-5 + √25 - 4(1)(0)] /2(1)

x = (- 5 + √25)/2 = -5 + 5 / 2 = 0/2 = 0

x = (-5 - √25)/2 = -5 -5 /2 = -10/2 = -5

x = 0 ; y = x² + 6x + 9 → y = 0² + 6(0) + 9 → y = 9 → (0,9)

x = -5 ; y = x² + 6x + 9 → y = (-5)² + 6(-5) + 9 → y = 25 - 30 + 9 → y = 4 → (-5,4)

the points of intersection are (0,9) and (-5,4)

Parabola equation: (x+3)² = y

The vertex of parabola is given when the expression inside the bracket = 0

Vertex of parabola ⇒ x + 3 = 0

Vertex of parabola ⇒ x = -3

The y-intercept of parabola is when x = 0

(0 + 3)² = 3² = 9

The coordinate of y-intercept of parabola is (0, 9)

The y-intercept of the straight line is when x = 0

y = m(0) + 9

y = 9

The coordinate of y-intercept of the straight line is (0, 9)

The parabola and the straight line has the point of intersection at (0, 9) but this point is not the vertex of the parabola. We showed earlier that the vertex of parabola is at x = -3, not at x = 0

Correct

Isabel is incorrect because the point of intersection between Line B and Parabola A that can be determined is the y-intercept of the functions, not necessarily the vertex.

The 1st choice is the correct one.

Isabel is correct because the y-intercept of Line B is (0, 9) and the value of y when x = 0 in Parabola A is 9.

[tex]Parabola a can be represented using the equation (x + 3)2 = y, while line b can be represented using[/tex]

The answer is the third option.

the third option: Isabel is incorrect because the point of intersection between Line B and Parabola A that can be determined is the y-intercept of the functions, not necessarily the vertex.

Explanation:

1) The given equation of the parabola is y = (x + 3)², so that is in its vertex form: y = (x - h)² + k, where the vertex is (h,k).

Hence, the vertex of the parabola is the point ( -3,0).

2) The given equation of the line given is y = mx + 9, so that is the slope-intercept form, where the slope is m and the y-intercept is 9.

Hence, the y-intercept of the line is 9, that is the point (0,9).

3) The y-intercept of the parabola is determined doing x = 0 in its equation: => y = (0 + 3)² = 3² = 9. That is the point (0,9).

4) As you see, the point (0,9) is necessarily a solution of the system, but not the vertex of the parabola, (-3,0). The line might intercept or not the parabola at the vertex (-3,0) depending of the slope m.

10000

step-by-step explanation: divide by 2,

i dont know men

step-by-step explanation: