In order to begin we must start off with the formula for the area of a triangle, which is a=1/2b(h) where a is area, b is base, and h is height.
In this scenario, we know that the area is 45cm^2 and the base is 2h+12 (since it is twice it’s height plus twelve). We can plug this into the area equation and then proceed to solve out accordingly.
a=1/2b(h)
45=1/2(2h+12)(h)
90=(2h+12)(h)
90=2h^2 + 12h
0= 2h^2 + 12h - 90
Simplify by dividing the two out.
h^2 + 6h - 45 = 0.
Now plug into the quadratic formula (with a=1, b=6, and c=-45) as shown in the image below.
After plugging the equation in and solving, we come to the idea that h is roughly equal to 4.34. We can now plug this back into the triangle area formula to solve out for b.
a=1/2b(h)
45=1/2(2h + 12)(h)
45=1/2(20.69)(4.34)
45=45.
In conclusion;
The height is ≈ 4.34
The base is ≈ 8.68
Hope this helps :)
Company A: 120 + 0.50x
Company B: 60 + 0.60x
Company A = Company B (solve for x)
(Here, x = miles)
120 + 0.50x = 60 + 0.60x
120 - 60 = 0.60x - 0.50x
60 = 0.10x
600 = x
Answer: 9. x=-3/2 10. x=2
x= 5/2 x=5/3
Step-by-step explanation:
9. Factor the equation:
How: put 4x^2 in the bottom left box and -15 in the upper right box.
then multiply 4x^2 x -15 = -60x^2 and put your answer in the top center box of the diamond.
Put the -4x from the equation in the bottom box. Then list out factors that multiply to the top box (-60x^2) and add to the bottom box (-4x) The two factors are -10 and 6
-10 x 6 = -60
-10 + 6 = -4
Put -12x and -5x in the remaining white boxes and find what numbers multiply to each.
I attached a picture. The colored dots correspond with each other.
Eg: Orange dot x orange dot = number in white square
Now you get the two factors (2x+3)(2x-5)
Set both of these equal to 0 and solve
0=2x+3 0=2x-5
x= -3/2 x= 5/2
Do the same for the other problem
It could be 10000,9800,or 9710
