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Kay [80]
2 years ago
6

Do you agree with the statement that " cubic functions must have at least 1 x-intercept but not more than 3, whereas quadratic f

unctions may or may not have x-intercepts
Mathematics
1 answer:
vladimir2022 [97]2 years ago
3 0

Answer:

Yes, I agree

Step-by-step explanation:

For the cubic function

A cubic function is represented as:

f(x)=ax^3+bx^2+cx+d

A cubic function may have 1, 2 or 3 x intercepts. This is shown below

For 3 x intercepts

y = x^3 - x

Equate y to 0

x^3 - x = 0

Expand

x(x^2 - 1) = 0

Express x^2 - 1 as difference of two squares

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

<em>x = 0 or 1 or -1</em>

For 2 x intercepts

y = x^3 - x

y  =(x-5)^2)(x+7)

Equate y to 0

(x-5)^2(x+7) = 0

Expand

(x-5)(x-5)(x+7) = 0

<em>x= 5 or x = -7</em>

For 1 x intercept

y = x^3

Equate y to 0

x^3 = 0

Take cube roots of both sides

x = 0

It has been shown above that a cubic function may have 1, 2 or 3.

So, I agree to the statement

For the quadratic function

A quadratic function will not have any x intercept when the function can not be factorized;

E.g.

y = x^2 + x + 17

<em>The above function has no x intercept.</em>

A quadratic function will have at least 1 x intercept when the function can be factorized;

E.g.

y = x^2- 6x + 9

Equate y to 0

x^2- 6x + 9 = 0

Expand

x^2 - 3x - 3x + 9 = 0

(x - 3)(x-3) = 0

x = 3

We've shown that a quadratic may have no x intercept, and it may also have x intercept(s)

Hence, I agree to both statement

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Answer:

C. \frac{27}{225}=\frac{b}{100}

Step-by-step explanation:

To find the number of black ribbons one would have subtract the amount of red ribbons from the total number of ribbons. Then one would have to express it as a proportion. Part over whole equals percent over 100. The number of black ribbons over total ribbons equals "b" over 100.

8 0
3 years ago
Which expression is equivalent to negative 32 5/3?
Sloan [31]
Im confused. Its not equal to any of the choices

Unless C  is the cube root of 32^5.

 [t3] \sqrt[n]{x} [32^5]
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3 years ago
The slope of the line below is -4. Which of the following is the point-slope
vodka [1.7K]

Answer:

y+2= -4(x-8)

Step-by-step explanation:

6 0
2 years ago
The manager of a store orders model railroad sets that cost $390 and sells them for $429. What is the mark-up, as a percentage?
Katarina [22]

Answer:

10%

Step-by-step explanation:

We have been given that the manager of a store orders model railroad sets that cost $390 and sells them for $429.  

We will use markup % formula for our given problem.

\text{Markup percentage}=\frac{\text{Selling price- Cost}}{\text{Cost}}\times 100

\text{Markup percentage}=\frac{429-390}{390}\times 100

\text{Markup percentage}=\frac{39}{390}\times 100

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\text{Markup percentage}=10

Therefore, markup is 10% of cost.

4 0
3 years ago
Solve this question
Art [367]
50 Dollars For The Member-Ship

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