A package of 24 Oreo cookies cost $3.89. How much would 3 cookies cost? 5 cookies?

Write the equation of a quadratic function who has the vertex of (4,-7)

timama [110]

Given:

The vertex of a quadratic function is (4,-7).

To find:

The equation of the quadratic function.

Solution:

The vertex form of a quadratic function is:

$y=a(x-h)^2+k$ ...(i)

Where a is a constant and (h,k) is vertex.

The vertex is at point (4,-7).

Putting h=4 and k=-7 in (i), we get

$y=a(x-4)^2+(-7)$

$y=a(x-4)^2-7$

The required equation of the quadratic function is $y=a(x-4)^2-7$ where, a is a constant.

Putting a=1, we get

$y=(1)(x-4)^2-7$

$y=(x^2-8x+16)-7$ $[\because (a-b)^2=a^2-2ab+b^2]$

$y=x^2-8x+9$

Therefore, the required quadratic function is $y=x^2-8x+9$ .

6 0

2 years ago

In one area, the lowest angle of elevation of the sun in winter is 27.5°. Find the minimum distance x that a plant needing full

Alex73 [517]

Answer:

The minimum distance x that a plant needing full sun can be placed from a fence that is 5 feet high is 4.435 ft

Step-by-step explanation:

Here we have the lowest angle of elevation of the sun given as 27.5° and the height of the fence is 5 feet.

We will then find the position to place the plant where the suns rays can get to the base of the plant

Note that the fence is in between the sun and the plant, therefore we have

Height of fence = 5 ft.

Angle of location x from the fence = lowest angle of elevation of the sun, θ

This forms a right angled triangle with the fence as the height and the location of the plant as the base

Therefore, the length of the base is given as

Height × cos θ

= 5 ft × cos 27.5° = 4.435 ft

The plant should be placed at a location x = 4.435 ft from the fence.

8 0

3 years ago

Solve this PLZ!<br> 4 - 7 (v - 9) = -7 -6(v - 10)

Arisa [49]

I maybe wrong, but I think it is 14

Simplify both sides of the equation
(Do distributive property)
Add 6v to both sides
Subtract 67 from both sides
Divide both sides by -1

7 0

2 years ago

(x + 1)^2 = 3x – 1 solving Quadratics ?

Deffense [45]

Step-by-step explanation:

$(x + 1)^{2} = 3x - 1 \\ \\ \therefore \: {x }^{2} + 2x + 1 = 3x - 1 \\ \\ \therefore \: {x }^{2} + 2x + 1 - 3x + 1 = 0\\ \\ \therefore \: {x }^{2} + 2x - 3x + 1 - 1 = 0 \\ \\ \therefore \: {x }^{2} - x = 0 \\ \\ \therefore \: x(x - 1) = 0 \\ \\ \therefore \: x = 0 \: \: or \: \: x - 1 = 0 \\ \\ \therefore \: x = 0 \: \: or \: \: x = 1 \\ \\ \huge{ \red{ \boxed{\therefore \: x = \{0, \: \: 1 \}}}}$

5 0

3 years ago

Read 2 more answers

Your friend is trying to grow her hair as long as her cousin's hair. The table (attached) shows their hair lengths (in inches) i

astra-53 [7]

Answer:

a) y = 1/2x + 5/2

y = 2/5x + 29/5

b) hair will be 19 inches for both at 33 months

Step-by-step explanation:

a) rate of growth of friend's hair: (3, 4) (8, 6.5)

(6.5 - 4) ÷ (8 - 3) = 2.5/5 or 1/2

find the y-intercept of equation for growth of friend's hair:

y = mx + b

4 = 1/2(3) + b

4 = 3/2 + b

8/2 - 3/2 = b

5/2 = b

equation for growth of friend's hair:

y = 1/2x + 5/2

rate of growth of cousin's hair: (3, 7) (8, 9)

(9 - 7) ÷ (8 - 3) = 2/5

find the y-intercept of equation for growth of cousin's hair:

y = mx + b

9 = 2/5(8) + b

9 = 16/5 + b

45/5 - 16/5 = b

29/5 = b

equation for growth of cousin's hair:

y = 2/5x + 29/5

b) y = 1/2x + 5/2

y = 2/5x + 29/5

1/2x + 5/2 = 2/5x + 29/5

5/10x + 25/10 = 4/10x + 58/10

1/10x = 33/10

10x = 3300

x = 33

8 0

1 year ago