Recall that A = 1/2bh.
We are given that h = 4+2b
So, putting it all together:
168 = 1/2 b(4+2b)
168 = 1/2(4b + 2b^2)
168 = 2b + b^2
b^2 + 2b - 168 = 0.
Something that multiplies to -168 and adds to 2? There's a trick to this.
Notice 13^2 = 169. So, it's more than likely in the middle of the two numbers we're trying to find. So let's try 12 and 14. Yep. 12 x 14 = 168. So this factors into (b+14)(b-12) So b = -14 or b =12. Is it possible to have a negative length on a base? No. So 12 must be our answer.
Let's check this. If 12 is our base, then according to our problem, 2*12 + 4 would be our height... or 28. so what is 12 * 28 /2?
196. Check.
Hope this helped!
Answer:
x=4
Step-by-step explanation:
7x - 9 = 19
add 9 to both sides
7x = 28
divide by 7
x = 4
Answer:
f^-1(x) = (x -2)/3
Step-by-step explanation:
To find the inverse function, swap x and y, then solve for y.
y = 3x +2 . . . . given function
x = 3y +2 . . . . inverse relation
x -2 = 3y . . . . subtract 2
(x -2)/3 = y . . . divide by 3
f^-1(x) = (x -2)/3 . . . . in functional form
Answer:
RS = 2
Step-by-step explanation:
Points R, S, and T are collinear, and S is between R and T, in addition, RS = 2x-4, ST = 3x+2, and RT = 13. Find the value of RS
Hence:
RS + ST = RT
2x - 4 + 3x + 2 = 13
2x + 3x - 4 + 2 = 13
5x - 2 = 13
5x = 13 + 2
5x = 15
x = 15/5
x = 3
To find the value of RS
RS = 2x-4
RS = 2 × 3 - 4
RS = 6 - 4
RS = 2
Answer:
y = 8x + 50
Step-by-step explanation:
Use (0,50) and (10,130)
Slope: m = (130-50)/(10-0) = 8
Y-intercept is 50
y = 8x + 50
