Answer:
A parabola opens downward with vertex at (1,20)
Step-by-step explanation:
The function that models the height of bag of candies is
The graph of this function is a parabola that opens downward.
To find the maximum height of the candy bag, we complete the squares to obtain the vertex form of the function.
Factor -16 to get;
Add and subtract the square of half the coefficient of t.
Factor the perfect square trinomial:
The vertex is (1,20)
This means the maximum height after 1 second is 20 feet.
Answer:
x = 8
Step-by-step explanation:
The sum of two interior angles in a triangle is equal to the exterior angle that's supplementary to the third interior angle:
7x + 6 + 22 = 9x + 12 add like terms
7x + 28 = 9x + 12 export like terms to the same side of the equation
28 - 12 = 9x - 7x
16 = 2x divide both sides by 2
8 = x
Answer:
c = 42.5
Step-by-step explanation:
The legs of the triangle are a and b and the hypotenuse is c
Let a be the shorter leg
The hypotenuse is 5 more than the longest leg
c = b+5
The shortest leg is 20
a = 20
We can use the Pythagorean theorem
a^2 +b^2 = c^2
Substituting in what we know from above
20 ^2 + b^2 = (b+5)^2
FOIL (b+5)^2 = b^2 +5b+5b +25 = b^2+10b+25
400 + b^2 = b^2+10b+25
Subtract b^2 from both sides
400+b&2-b^2 = b^2 -b^2 +10b+25
400 = 10b+25
Subtract 25 from both sides
400-25 = 10b+25-25
375 = 10b
Divide by 10
375/10 = 10b/10
37.5 = b
But we want to find c
c=b+5
c = 37.5+5
c = 42.5
Answer:Let the number be x, then (x - 9)^2 = x - 3
x^2 - 18x + 81 = x - 3
x^2 - 19x + 84 = 0
(x - 12)(x - 7) = 0
x = 12 or 7
Step-by-step explanation:
Answer:
the first one is 13 and the second is 22
