Algebra help please asap thanks?

Question

1. Solve the formula for the given letter. Assume all variable represent non negative numbers. E=kc^2, for c

2. Y^2 – 14y +49 =1 what are the exact solutions? Y=

3. Find the vertex, the line of symmetry, the max or minimum value of the quadratic function

F(x)= -2x^2 +2x +1

The x coordinate=

The y coordinate=

The x symmetry=

The y symmetry =

4. The width of a triangle is 3 ft less than the length. The area is 4ft. the length is the width is

5.a student open a mathematic book to two facing pages. The product of the page number is 210. Find the page numbers. The first page is the second page is

6. give an exact and approximate solution to three decimal places. (x-9)^2=16 what are the exact solutions? X=

Answer 1

qn 1 : c= square root of E/k

qn 2 :  assuming Y is same as y , Y = 6 or 8

qn 5 : pages 14 and 15

qn 6 : 5.000 and/or 13.000

Answer 2

1.

E=kc^2

(Divide by k)

E/k = c^2

(take the square root)

+- sqrt (E/k) = c

2. Y^2 – 14y +49 =1

y^2 - 7y - 7y + 49 = 0

(y^2 - 7y) - (7y - 49) = 0

y(y - 7) - y(y - 7) = 0

(y - 7)(y - 7) = 0

y - 7 = 0

y = 7

3.

Use Completing the Square to put in general form.

F(x) = a(x - h)^2 + k

where (h, k) is the vertex

the max/min value is k

the line of symmetry is x = h

F(x)= -2x^2 +2x +1

= -2(x^2 - x) + 1

= -2(x^2 - x + 1/4) - (-2)(1/4) + 1

= -2(x - 1/2)^2 + (1/2) + 1

= -2(x - 1/2)^2 + (3/2)

Vertex is (1/2, 3/2)

Max value is 3/2

line of symmetry: x = 1/2

4.

Length = x

width = x - 3

area:

(x)(x - 3) = 4

x^2 - 3x - 4 = 0

(x - 4)(x + 1) = 0

x = 4 or -1

since length can't be negative, the length is 4 ft

and the width is (4 - 3) or 1 ft.

5.

The page numbers are x and x + 1.  (because if the first page is 3, the second page is one more, or 4.)

(x)(x + 1) = 210

x^2 + x - 210 = 0

(x + 15)(x - 14) = 0

x = -15 or 14

Since can't have a neg page number...

first page is 14, second page is 14 + 1 or 15.

6.

(x - 9)^2 = 16

x - 9 = +- 4

x = 9 +- 4

x = 13 and 5