I have been working on these for days. I appreciate all the help given!?

Question

1). Find the x- intercepts. y=x^2+3x-10


2). The height in feet of an object after t seconds is given by the function h= -16t^2+20t+6. How long will it take the object to hit the ground? Round answer to the nearest thousandth.


3). Multiply 5x-46/x^2-7x times 2x/9-x


4) factor completely ax-ay+x^2-xy


5) write in simplest form x^2 +18+80/x^2-64

Answer 1

1. x intercept means that y=0
0=x^2+3x-10
0=(x+5)(x-2)
x=-5 or x=2

2. object hits the groun means h=0
solve 0=-16t^2+20t+6
whis is equivallent to 0=8t^2-10t-3
factorize the right side:
8t^2+2t-12t-3
2t(4t+1)-3(4t+1)
(2t-3)(4t+1)=0
2t-3=0 or 4t+1=0
2t=3 or 4t=-1
t=3/2

answer after 1.5 seconds.

3. (2x(5x-46))/(x(x-7)(9-x))
x will simplify:
(2(5x-46)/(x-7)(9-x)
(2(5x-46))/(-(x-7)(x-9))
(-2(5x-46))/((x-7)(x-9))

This is the answer when the first numerator is 5x-46. some posters change it into 45. Looks like you made a mistake. I will leave this answer which is correct to the question you posted. If you made a mistake check the answer below mine.

4. ax-ay+x^2-xy
look at the first two terms: common factor is a
two last terms: x
a(x-y)+x(x-y)
(a+x)(x-y)

5. factorize denominator and numerator
Num: (x+8)(x+10)
Den: (x-8)(x+8)
x+8 will "cancel"
what is left is: (x+10)/(x-8)

I see rockstarmonkey knows how to copy and paste from other answers!!!!!

Answer 2

1) y = x^2 + 3x - 10

To find the x-intercepts, make y = 0. (Similarly, if you wanted to find the y-intercept, make x = 0).

0 = x^2 + 3x - 10

Factor the quadratic.

0 = (x + 5)(x - 2)

Equate each factor to 0; x + 5 = 0, x - 2 = 0. This implies
x = 5 or 2. x = {5, 2}.
Therefore, your x-intercepts are 5 and 2.

3) (5x - 45)/(x^2 - 7x) times 2x/(9 - x)

First, factor everything.

( 5(x - 9)/[x(x - 7)] ) ( 2x/(9 - x) )

Apply the "negative one technique" on 9 - x; this means factoring out a (-1) in order to swap the difference of terms.

( 5(x - 9)/[x(x - 7)] ) (2x/ [(-1)(x - 9)] )

Now, we can cancel terms diagonally. Note that (x - 9) cancels out, because it appears on the top of one fraction and the bottom of the other. Also, the x cancels out in both fractions for the same reason. That leaves us with

( 5/(x - 7) ) (2/(-1) )

Which we multiply normally.

5/(x - 7) (-2)

(-10)/(x - 7)

4) ax - ay + x^2 - xy

To factor this, you group them. Factor the first two terms and the last two.

a(x - y) + x(x - y)

Now, factor (x - y) out of these two terms.

(x - y)(a + x)

5) (x^2 + 18x + 80)/(x^2 - 64)

Factor each quadratic. Note that the bottom factors as a difference of squares.

[(x + 8)(x + 10)] / [(x - 8)(x + 8)]

Cancel the common factor of (x + 8).

(x + 10)/(x - 8)

Answer 3

y = x² + 3x - 10

Find the sum of the middle term

multiply the first term 1 times the last term 10 euals 10 and factor

factors of 10 = 1, 2, 5, 10

+ 5 - 2 satisfy the sum of the middle term

insert + 5x and - 2x into the equation

y = x² + 3x - 10

y = x² + 5x - 2x - 10

y = x(x + 5) - 2(x + 5)

y = (x - 2)(x + 5)

- - - - - - - - - - -s-

Answer 4

1) y=x^2+3x-10

At x-intercept, y=0.
Therefore,
x^2+3x-10=0
or, x^2+5x-2x-10=0
or, x(x+5)-2(x+5)=0
or, (x+5)(x-2)=0

Either,
x+5=0
or, x= -5

or, x-2=0
or, x=2

2) h= -16t^2+20t+6

At ground level, h=0
Therefore,
-16t^2+20t+6 =0
or, 16t^2-20t-6=0
or, 8t^2-10t-3=0
or, 8t^2-12t+2t-3=0
or, 4t(2t-3)+1(2t-3)=0
or, (2t-3)(4t+1)=0

Either,
2t-3=0
or, 2t=3
or, t=3/2 or 1.5 seconds

Or,
4t+1=0
or, 4t= -1
or, t = -1/4
As t cannot be negative, do not take this value of t.

3) (5x-45)/(x^2-7x)*(2x)/(9-x)
=(5(x-9))/(x(x-7))*(2x)/(9-x)
=(-5(9-x))/(x-7))*(2)/(9-x)
= -10/(x-7)

4)ax-ay+x^2-xy

=a(x-y)+x(x-y)
=(x-y)(a+x)

5) (x^2+18x+80)/(x^2-64)

=(x^2+10x+8x+80)/(x^2-8^2)
=(x(x+10)+8(x+10))/((x+8)(x-8))
=((x+10)(x+8)/((x+8)(x-8))
=(x+10)/(x-8)

Answer 5

here is what i got when i caculated this equation in my mind (formula)

1. x intercept means that y=0
0=x^2+3x-10
0=(x+5)(x-2)
x=-5 or x=2

4. ax-ay+x^2-xy
look at the first two terms: common factor is a
two last terms: x
a(x-y)+x(x-y)
(a+x)(x

hope this helps you out! best of wishes!