How many times does the graph of 4x = 32 - x2 cross the x-axis?
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what are the solutions to the equation?

The graph crosses the x-axis 2 times

The solutions are  x = -8  &  x = 4

Step-by-step explanation:

Qaudratics are in the form

Where a, b, c are constants

Now, let's arrange this equation in this form:

Where

a = 1

b = 4

c = -32

We need to know the discriminant to know nature of roots. The discriminant is:

If

Let's find value of Discriminant:

Certainly D > 0, so there are 2 distinct roots and cuts the x-axis twice.

We get the roots/solutions by factoring:

Thus,

The graph crosses the x-axis 2 times

The solutions are  x = -8  &  x = 4

34.5 cm

step-by-step explanation:

generally for a circular segment of angle, θ° and radius r

arc length

= (θ/360) x circumference

= (θ/360) x 2πr

in our case, θ = 60°, π=3.142 and r = 33 cm

substitute into above formula

arc length

= (60/360) x 2(3.142)( 33) = 34.5 cm

= 5

step-by-step explanation:

to find the 15th term substitute n = 15 into the nth term formula

= (- 3 × 15 ) + 50 = - 45 + 50 = 5