Answer:
K = -1 or -2
Step-by-step explanation:
Given the equation of parabola is, y = 0.5(x-3)(x+k).
Finding y-intercept, put x=0 and solve for y :-
y = 0.5(0-3)(0+k)
y = 0.5(-3)(k)
y = -1.5k
Finding x-intercepts, put y=0 and solve for x :-
0 = 0.5(x-3)(x+k)
(x-3)(x+k) = 0
x = 3 OR x = -k
So, the coordinates of triangle ABC are:-
A(0, -1.5k), B(3, 0), and C(-k, 0)
Assuming origin O(0,0), find the area of triangle ABC:-
Area = (1/2) * BC * OA
Area = (1/2) * (k+3) * (1.5k)
But given the area is 1.5 square units.
So, (1/2) * (-k-3) * (1.5k) = 1.5
(1/2) * (-k-3) * (k) = 1
k(-k-3) = 2
-k² -3k -2 = 0
k² +3k +2 = 0
k² +2k +k +2 = 0
(k+2)(k+1) = 0
So, k = -1 or k = -2
Step-by-step explanation:
Hey there!
Given;
-8x= -32
~ Divide both sides by"-8".
(-8x)/-8 = (-32)/-(8)
Or, X= 4.
Therefore, the value of x must be 4.
<u>Check</u><u>:</u>
-8*4 = -32
-32 = -32 (True)
<em><u>Hope</u></em><em><u> it</u></em><em><u> helps</u></em><em><u>.</u></em><em><u>.</u></em><em><u>.</u></em>
30+2x=3x+5
x=25
edit: sorry for the wrong answer. i messed up
Answer:
A. $301
B. $721
Step-by-step explanation:
Let $x be the amount of money they raised.
Rowena tried to put the $1 bills into two equal piles and found one left over at the end, then
Polly tried to put the $1 bills into three equal piles and found one left over at the end, then
Frustrated, they tried 4, 5, and 6 equal piles and each time had $1 left over, then
Finally Rowena put all the bills evenly into 7 equal piles, and none were left over, then
This means is divisible by 2, 3, 4, 5 and 6 without remainder, so
Hence,
The smallest amount of money they could have raised is $301, because
is divisible by 7.
Now, the number should be divisible by 7 and must be greater than 500.
So,
When n = 9,
is not divisible by 7.
When n = 10,
is not divisible by 7.
When n = 11,
is not divisible by 7.
When n = 12,
is divisible by 7.
B. The least amount of money they could have raised is $721