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Andreas93 [3]
3 years ago
7

Which point is an x-intercept Og the quadratic function f(x) = (x-4)(x+2)?

Mathematics
2 answers:
user100 [1]3 years ago
8 0
<span>(-6,0) would be correct </span>
worty [1.4K]3 years ago
3 0
Hi there!

To find the x-intercept of the function we need to calculate f(x) = 0.

(x - 4)(x + 2) = 0

Rule AB = 0, gives A = 0 or B = 0.
x - 4 = 0 \: \: \: or \: \: \: x + 2 = 0

Add 4 to both sides or subtract 2 from both sides.
x = 4 \: \: \: \: \: \: \: \: \: \: or \: \: \: x = - 2

Hence, the solutions are:
(4, 0) & (-2, 0)
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A grasshopper jumps straight up from the ground with an initial vertical velocity of 8 feet per second. After how many seconds w
vlabodo [156]

Answer:

Problem 1 : After 0.25 s

Problem 2 : The squirrel doesn't reach the ground before the nut

Step-by-step explanation:

Problem 1

This is a standard physics problem

The equation that defines the movement of the grasshopper given the initial velocity, and the acceleration is the following

Distance =  Do + Vo*t + 0.5*a*t^2

Where

Do is the initial distance.

(Do = 0, because the grasshopper is on the ground and we choose the reference system there)

Vo is the initial velocity = 8 feet/sec

a is the acceleration that is exerted on the body (in this case a = g = -9.8 m/s^2 = - 32.174 feet per second per second.)

t is the time

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Distance =  Do + Vo*t + 0.5*a*t^2

(1 foot)=  (0)+ (8 feet/s)*t + 0.5*(-32.174 feet/s^2)*t^2

Solving this equation, we get that

t = 0.25 s

Problem 2

This problem is similar to the previous one

We apply the same formula

D =  Do + Vo*t + 0.5*a*t^2

But in this case, we are going in the opposite direction, and we have an initial distance.

Do = 27 feet

Vo is the initial velocity of the nut = -6 feet/s

D = 0  (Ground)

We substitute in the equation, and solve for t (time)

(0) =  (27) + (-6 feet/s)*t + 0.5*(-32 feet/s^2)*t^2

t = 1.125 s  <  2s

The nut reaches ground in 1.125 s, so the squirrel doesn't reach the ground before the nut

4 0
3 years ago
PLEASE HELP ME OUT!!
andrey2020 [161]
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A <<<<< answer
8 0
3 years ago
Hello, could you please explain this to me?
Viefleur [7K]

Find the value of r(q(4)), so first you need to find the value of q(4).

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r(q(4)) = 2(-9)² + 1

r(q(4)) = 2(81) + 1

r(q(4)) = 163           163 is the value of r(q(4))

5 0
3 years ago
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