Call the numbers x and y. According to the first sentence, x + y = 67. According to the second sentence, x = y + 5. You can combine these two equations to find the values of these variables:
x + y = 67
(y + 5) + y= 67
2y = 62
y = 31
You can use this to find x by plugging in y to either original equation:
x = y + 5
x = 31 + 5
x = 36
Answer:
1.5 seconds
Step-by-step explanation:
Since f(x) represents the distance from the ground to the rock (in feet), we just need to find the values of x for which f(x) = 340. Substituting f(x) = 340 into f(x) = -16x² - 4x + 382 gives us:
340 = -16x² - 4x + 382
0 = -16x² - 4x + 42 (Subtract 340 from both sides)
16x² + 4x - 42 = 0 (Multiply entire equation by -1, "flip" equation)
8x² + 2x - 21 = 0 (Divide entire equation by 2)
(4x + 7)(2x - 3) = 0 (Factor LHS)
4x + 7 = 0 or 2x - 3 = 0 (Zero Product Property)
4x = -7 or 2x = 3 (Subtract -7 and add 3 from/to both sides, respectively)
or 
x = -1.75 is an extraneous solution because in the context of the question, you can't have negative seconds so therefore, the final answer is 1.5 seconds.
Hope this helps!
One bag of popcorn would cost $6.50
To solve this, we can set up equations:
28p+40c=$282
17p+20c=$160.50
To solve this system, we would need to make either the candy bars the same or the bags of popcorn the same. Since we are solving for bags of popcorn, we will make the candy bars the same:
20(28p+40c=$282)
40(17p+20c=$160.50)
Which would give you:
560p+800c=$5,640
680p+800c=$6,420
Subtract them:
(680p+800c=$6,420)
-(560p+800c=$5,640)
_________________
120p=$780
Now divide by 120 to get the price of one bag of popcorn:
120p=$780
_________
120
p=$6.50
Answer:
2
Step-by-step explanation:
he value of K would be 2 because the function f(x) is the equation of a line. K is represented as the y-intercept. When a line is shifted down 2 units, the y-intercept also gets shifted down 2 units. In f(x) the y-intercept is zero. So the difference would be 2 units