Answer:
<h3>
f(x) = - 4x² - 20x + 56 </h3>
Step-by-step explanation:
f(x) = a(x - x₁)(x - x₂) - factored form of the equation of the parabola with zeros x₁ and x₂
x-intercepts at (2,0) and (-7,0) means zeros: x₁=2 and x₂=-7
So:
f(x) = a(x - 2)(x + 7) - factored form of the equation of the parabola with x-intercepts at (2,0) and (-7,0)
The parabola passing through point (1, 32) means if x=1 then f(x)=32
Then:
32 = a(1 - 2)(1 + 7)
32 = a(-1)(8)
32 = - 8a
a = - 4
Therefore the equation of a parabola with x-intercepts at (2,0) and (-7,0) and which passes through the point (1,32):
<u> f(x) = -4(x - 2)(x + 7) </u>
Expanding to standard form:
f(x) = -4(x - 2)(x + 7)
f(x) = -4(x² + 7x - 2x - 14)
<u> f(x) = -4x² - 20x + 56 </u>
Answer:
(1,1) (2,2) (1,2) (1,5) (4,4) (4,5)
there are a lot more but those are some.
Step-by-step explanation:
Answer:
16. Adults = $12
17. 750 ml
18. $9
19. 96 students
20. 5/6x
Step-by-step explanation:
16.
A child pays = $9
Bus fee = 1/3 of $9
= 1/3× 9
= $3
Admission fee for a child= amount paid - bus fee
= $9 - $3
= $6
What was the admission fee for adults, if children get in for haprice
Children = 1/2 of adults
$6 = 1/2 × adults
Adults = 6÷ 1/2
= $12
Adults = $12
17.
Leaking rate = 10 ml per minutes
One and quarter of an hour
1 hour = 60 minutes
Quarter of an hour = 15 minutes
Total time = 75 minutes
Air lost in 75 minutes = 10 ml × 75
= 750 ml
18. 4 glasses for $3
1 dozen of glasses = 12
12 glasses = $x
4 = 3
12 = x
Cross product
4*x = 3*12
4x = 36
x = 36 / 4
= 9
x = $9
19.
Total students = x
1/2x = soccer
Rugby = 1/2 of 1/2x
= 1/2 * 1/2x
= 1/4x
24 = 1/4x
x = 24÷1/4
= 24 × 4/1
x = 96 students
20.
Total petrol = x
Petrol in the tank = 1/2x
Petrol used = 1/3 of 1/2x
= 1/3 × 1/2x
= 1/6x
Petrol remaining after the trip = x - 1/6x
= 6x-x/6
= 5/6x
Because two side lengths are identical it is an isosceles triangle and also at least one angle is less than 90 degrees so the answer would be an acute isosceles triangle.