i need help with some pre calc. plz?

Question

6. a triangle with an area of 16 has a base of (x+1) and a height of (x-13) fine the value of x along with the base and the height of the triangle.



1. between what two consecutive intergers is the value of log 66
2



7. express (6-3i)^2 in a+bi form.


2. which equation represents a circle with a center of (2,-3) and a radius of 6

Answer 1

6.

A = 1/2bh
16 = 1/2(x + 1)(x - 13) = 1/2(x² -12x -13) = 1/2x² - 6x - 13/2
32 = x² - 12x - 13
0 = x² - 12x - 45
0 = (x - 15)(x + 3)

Throw out -3, so x = 15, the base is 16 and the height is 2.

2)

log 66 is between 1 and 2, because it's bigger than 10 (log 10 = 1) and less than 100 (log 100 = 2).

3)

(6 - 3i)² = 36 - 36i + 9i² = 36 - 36i - 9 = 27 - 36i

4)

(x - h)² + (y - k)² = r²
(x - 2)² + (y + 3)² = 6²

or in "standard form":

x² - 2x + 4 + y² + 6x + 9 = 36
x² - 2x + y² + 6x - 23 = 0

Answer 2

6. a triangle with an area of 16 has a base of (x+1) and a height of (x-13) fine the value of x along with the base and the height of the triangle
A=16=.5bh=.5(x+1)(x-13)
32=x^2-12x-13
x^2-12x-45=0
(x-15)(x+3)
only x-15=0
x=15 has physical meaning
so x=15
b=x+1=16
h=x-13=2

1. between what two consecutive intergers is the value of log 66
log 10=1
log 100=2
66 is between 10 & 100, so log 66 is between 1 & 2.



7. express (6-3i)^2 in a+bi form.
36-2*3*6i+9i^2
36-9-36i
25-36i


2. which equation represents a circle with a center of (2,-3) and a radius of 6

(x-2)^2+(y+3)^2=36

Answer 3

6. you just need to set up an equation and solve for x. area of a triangle = 1/2 base * height so...

16 = ((x+1)/2) * (x-13)
simplify this function by multiplying each side by 2.
32 = (x + 1) * 2(x-13)
you should be able to solve from here

Answer 4

Area Triangle = a base x height
Area triangle = (x + 1)(x -13)
X' = -1
x" = 13
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Answer 5

6.)
A = (1/2)bh
16 = (1/2)(x + 1)(x - 13)
32 = x^2 - 13x + x - 13
x^2 - 12x - 45 = 0
(x - 15)(x + 3) = 0
x = 15 or -3

Since you can't have a negative length

ANS : 16in base and 2 in height.

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1.) log(66) = 1.82
ANS : 1 and 2

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7.)
(6 - 3i)^2
(6 - 3i)(6 - 3i)
36 - 18i - 18i + 9i^2
36 - 36i + 9(-1)
36 - 36i - 9
27 - 36i

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2.)
(x - 2)^2 + (y - (-3))^2 = 6^2
(x - 2)^2 + (y + 3)^2 = 36