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Kryger [21]
2 years ago
7

Using the Factor Theorem, which of the polynomial functions has the zeros 2, radical 3 , and negative radical 3 ? f (x) = x3 – 2

x2 – 3x + 6 f (x)= x3 – 2x2 + 3x + 6 f (x) = x3 + 2x2 – 3x + 6 f (x) = x3 + 2x2 – 3x – 6
Mathematics
1 answer:
Basile [38]2 years ago
3 0

Answer:

A

f(x) = x^3 - 2x^2 -3x + 6

Step-by-step explanation:

According to the Factor Theorem, if (<em>x</em> - <em>k</em>) is a factor of a polynomial P(x), then P(k) must equal zero.

We are given that a polynomial function has the zeros 2, √3, and -√3. So, we can let <em>k</em> = 2, √3, -√3.

So, according to the Factor Theorem, P(2), P(√3) and P(-√3) must equal 0.

Testing each choice, we can see that only A is true:

\displaystyle f(x) = x^3 - 2x^2 - 3x + 6

Testing all three values yields that:

\displaystyle \begin{aligned} f(2) &= (2)^3 - 2(2)^2 -3(2) + 6 \\ &= (8) - (8) -(6) + (6) \\ &= 0\stackrel{\checkmark}{=}0 \\ \displaystyle  f(\sqrt{3}) &= (\sqrt{3})^3 - 2(\sqrt{3})^2 - 3(\sqrt{3}) + 6 \\ &=(3\sqrt{3}) -(6)-(3\sqrt{3}) + 6 \\ &= 0\stackrel{\checkmark}{=}0 \\ f(-\sqrt{3}) &= (-\sqrt{3})^3 - 2(-\sqrt{3})^2 - 3(-\sqrt{3}) + 6 \\ &=(-3\sqrt{3}) -(6)+(3\sqrt{3}) + 6 \\ &= 0\stackrel{\checkmark}{=}0   \end{aligned}

Hence, our answer is A.

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The cost to rent a car at one agency is $24.50 per day plus an additional $15.99 fee for insurance. At a different agency, the c
Lena [83]

Answer:

d=4

Step-by-step explanation:

Agency 1:

Total cost of renting a car=24.50d + 15.99

Agency 2:

Total cost of renting a car=27.50d + 3.99

Where, d=No. of days of renting the car

Which equation could be used to find the number of days, d, at which the rental fee is the same for both agencies?

The equation is by equating agency 1 and agency 2 equation

24.50d + 15.99 = 27.50d + 3.99

Collect like terms

24.50d - 27.50d = 3.99 - 15.99

-3d = -12

Divide both sides by -3

d= -12 / -3

=4

d=4

Check

Agency 1:

24.50d + 15.99

= 24.50(4) + 15.99

= 98 + 15.99

= 113.99

Agency 2:

27.50d + 3.99

= 27.50(4) + 3.99

= 110 + 3.99

= 133.99

3 0
3 years ago
if you make $2710.00 a month and must spend 89% of that on recurring and variable expenses, how much money can you potentially s
Setler [38]

Answer:

  $3577.20

Step-by-step explanation:

You can save 11% of your income each month, so in 12 months, you can save ...

  12×0.11×$2710 = $3577.20

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What is the mode(s) of this data?
Neko [114]

Answer:

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Step-by-step explanation:

Mode= the most common number

7 0
2 years ago
Suppose the base of the prism was a rectangle of sides I and w. Type a formula for the volume of the prism using i, w and h
tester [92]

Answer: V = l  w  h

Step-by-step explanation:

Hi, to answer this question we have to apply the formula for the volume of a rectangular prism.

Volume of a rectangular prism (V) = Length x Width x Height

Replacing with the values given:

V = l w h

All values are multiplied (didn’t use x as a multiplication symbol to avoid confusion)  

Feel free to ask for more if needed or if you did not understand something.

7 0
3 years ago
Write each expression as a single natural logarithm. ln 3+ ln 4
Oduvanchick [21]

Expression as a single natural logarithm is 2.48490664979.

<h3>What is natural logarithm?</h3>

ln 3+ ln 4

ln (3×4)

ln(12) =2.48490664979

The inverse of an exponential function, the natural log is the logarithm to the base of the number e. Natural logarithms are unique varieties of logarithms that are employed in the treatment of time and growth-related issues.

The distinction between log and ln is that log is expressed in terms of base 10, while ln is expressed in terms of base e. As an illustration, log of base 2 is denoted by log2 and log of base e by loge = ln (natural log).

To learn more about natural logarithm from the given link:

brainly.com/question/20785664

#SPJ4

5 0
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