Answer:
200
Step-by-step explanation:
this is a 3-4-5 triangle so since 120/3 and 160/4 = 40 which are the two sides the ladder is 5*40=200
Answer:
I'm pretty sure it would cost $11.25 since 6 cookies would be $2.25 if you divide the amount for a dozen in half. I hope it was right!
Step-by-step explanation:
Extraneous solutions, is answers that we get because of squaring both sides of the radical equation, but in reality, they are not going to be the solutions of the given equation.
(√(4x+41))²=(x+5)²
4x+41=x²+10x+25
x²+6x-16=0
(x-2)(x+8)=0
x1=2 , x2=-8,
And now we must to check them by substitution into initial equation
√(4x+41)=x+5
1) x=2, √(4*2+41)=2+5, √49=7, 7=7 true
2) x=-8, √(4*(-8)+41)=-8+5, √9 =-3 false,
so an extraneous solution x=-8
Speed of the car is 45 km/h
Step-by-step explanation:
- Step 1: Find the distance traveled by the car in the first case.
Given that the speed of the car = 10 (t + 3) km/h
Time taken = 4 (t + 3) hours
Distance = Speed × Time
= 10 (t + 3) × 4 (t + 3) = 40(t + 3)² km
- Step 2: Equate the distance of 810 km with the distance that has been calculated above, since both are the same.
⇒ 810 = 40 (t + 3)²
⇒ (t + 3)² = 81/4
⇒ t + 3 = √81/4 = 9/2
⇒ t = 9/2 - 3 = 3/2 = 1.5
- Step 3: Find the speed of the car.
Speed = 10 (1.5 + 3) = 10 × 4.5 = 45 km/h
Answer:
Diane has a booth at the state fair that sells bags of popcorn she has found that her daily costs are approximated by the function c(x) =x squared -20x+150
a) How many bags of popcorn must Diane sell to minimize her cost?
b) What is Diane’s minimum cost?
a) 10
b) 50
Step-by-step explanation:
According to the quadratic equation given in the question ,
the cost will be minimum at
comparing x^{2} -20x+150[/tex] with the standard quadratic equation
we get
a= 1, b = -20, c=150
now
Hence to minimize her cost, she must sell
a) x= 10 popcorns
and her minimum cost is
b)