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bogdanovich [222]
2 years ago
11

Four Questions, 60 points & Brainliest! (Please show all steps)

Mathematics
1 answer:
pogonyaev2 years ago
4 0

Answer:

a) -2, 1 and 2

b) 4

Step-by-step explanation:

The given equation is:

g(x) = (x + 2)(x - 1)(x - 2)

Part a1 and a2) Finding zeros of the function

By zeroes of the function we mean the points the graph where the value of the function is zero. In order to find the zeroes of the function we equate the  function equation to zero and find the corresponding values of x. This is shown below:

0 = (x + 2)(x - 1)(x - 2)

According to the zero product property, we can write:

x + 2 = 0     ⇒     x = -2

x - 1 = 0      ⇒     x = 1

x - 2 = 0     ⇒     x = 2

Therefore, the zeroes of the given function are -2, 1 and 2. In ordered pairs we can write these as (-2, 0), (1, 0) and (2, 0)

Part b1 and b2) y-intercept of the function

y-intercept is the point on the graph where the function crosses the y-axis. Since on y-axis, the value of x coordinate is zero, in order to find the y-intercept we simply substitute zero for all occurrences of x. This is shown below:

g(0) = (0 + 2)(0 - 1)(0 - 2)

g(0) = 2(-1)(-2)

g(0) = 4

Thus, the y-intercept of the function is 4, which in ordered pair can be written as (0, 4)

Part c) End behavior of the graph

End behavior of the graph depends on:

  • Sign of the leading coefficient
  • Degree of the function

Degree of the function is 3 i.e. odd and sign of leading coefficient is positive. This means the end behavior of the graph will be:

  • Rising towards Right end
  • Falling towards Left end

Part d) Graph of polynomial

Based on all the above discussion, a graph of the function can be plotted. The graph is attached below.

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Lemur [1.5K]

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Solve for x<br> A) 36<br> B) 54<br> C) 72<br> D) 84 <br> Ayo help a girl out
kykrilka [37]

Answer:

72°

Step-by-step explanation:

This is called an isosceles triangle. This means that the 2 angles related to the equal sides, are also equal. Hence, the answer is 72°

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The radius of the cone is 7 in and y = 25 in. What is the volume of the cone in terms of π? A cone with a right triangle formed
Lady bird [3.3K]

Answer:

142.1π in³

Step-by-step explanation:

Given that:

The radius (r) =  7 in

The slant height (y) = 25 in

Then the height (x) can be determined by using the Pythagoras rule:

y² = x² + r²

25² = x² + 7²

125 = x² + 49

125 - 49 = x²

x² = 76

x = √76

x = 8.7

The formula for the volume of a cone is;

= 1/3 πr²h

where;

height(h) is calculated as "x" from above = 8.7

Then;

= 1/3 × π × (7 in)² × 8.7 in

= 142.1π in³

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ludmilkaskok [199]
I will help you because I need points like the answers for 4 huhg
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What are the sine and cosine ratios for a 30°–60°–90° triangle with a hypotenuse of 6, when θ = 60°?
Margaret [11]

Answer:

There are two ways to do this problem algebraically or trigonometrically.

Algebraically/geometrically

The ratios of the sides of a 30/60/90 tri. are x, x√3, 2x (short leg, long leg, hyp). Therefore, if the long leg is 6 'units'. then 6 = x√3. x = 6√3.

The hyp is 2x then the hypotenuse is 2(6√3) = 12√3, rationalizing is 12√3/3 = 4√3

Using Trig.

We can use sinx = y/r = opp/hyp. The long leg of 6 is opposite 60 degrees (pi/3).

Therefore, sin(pi/3) = 6/r =

r = 6/sin(pi/3) = 6/(√3/2) = 12/√3, when you rationalize you get 12√3/3 = 4√3

4 0
2 years ago
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