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Leto [7]
2 years ago
5

If f is a polynomial function and xminus−5 is a factor of​ f, then ​f(5)equals=​_______.

Mathematics
2 answers:
sp2606 [1]2 years ago
8 0

if (x - 5 ) is a factor of f(x ) then x = 5 is a root of f(x) and f(5) = 0


gogolik [260]2 years ago
5 0

Answer:

f(5) = 0

Step-by-step explanation:

A function f can be simplified by it's roots.

For example, a second order function expressed by the following equation:

ax^{2} + bx + c, a\neq0.

Can be expressed in function of it's roots x_{1}, x_{2} such that ax^{2} + bx + c = (x - x_{1})*(x - x_{2}).

Is x-5 is a factor of f, this means that f can be expressed in function of x - 5, that is, x = 5 is a root of the equation.

This means that:

f(5) = 0

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3 years ago
The function f(x) = (x - 4)(x - 2) is shown.
agasfer [191]

Answer:

all real numbers greater than or equal to -1

Step-by-step explanation:

In order to solve this problem we need to know the vertex and the direction its pointing.

First we expand,

x^2-6x+8

To find the x value of the vertex we use this formula (-b/2a).

-(-6)/2(1) = 3

Now we plug 3 in the equation to get the y value,

(3)^2 - 6(3) + 8 = 9 - 18 + 8 = -1

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We know the graph points up because x^2 is positive

The vertex is the lowest point, so we now know that -1 is the starting range and if the graph is pointing up, that means all values greater than -1.

This leads to our answer all real numbers greater than or equal to -1.

6 0
3 years ago
I need help with this pls use 3.14 with or the formula with area
Leni [432]
Rectangle:
A=l(w)

A=12(6)

A=72cm^2

Semicircle:
r=6/2

r=3

A=(3.14(r)^2(1/2)

A=3.14(3)^2(1/2)

A=3.14(9)(1/2)

A=14.13cm^2

A=14.1cm^2

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2 years ago
Country days scholarship rounds receive a gift of $135000. The money is invested in stock, bonds, and CDs. CDs pay 2.75% interes
Vsevolod [243]

Answer:

  • CDs — $10,000
  • bonds — $80,000
  • stocks — $45,000

Step-by-step explanation:

Let the variables c, b, s represent the dollar amounts invested in CDs, stocks, and bonds, respectively. Then the problem statement gives us 3 relations between these 3 variables:

  c + b + s = 135000 . . . . . . . . . . . . . . . . . total invested

  0.0275c +.045b +0.104s = 8555 . . . . . total income earned

  -c + b = 70000 . . . . . . . . . . . . . . . . . . . . . 70,000 more was in bonds than CDs

Using the third equation to write an expression for b, we can substitute into the other two equations.

  b = 70000 +c . . . . . . . . . . . . . . . . expression we can substitute for b

  c + (70000 +c) +s = 135000 . . . . substitute for b in the first equation

  2c +s = 65000 . . . . . . . . . . . . . . . . [eq4] simplify

  .0275c +.045(70000 +c) +.104s = 8555 . . . . . substitute for b in 2nd eqn

  .0725c +.104s = 5405 . . . . . . . . . . [eq5] simplify

Using [eq4], we can write an expression for s that can be substituted into [eq5].

  s = 65000 -2c . . . . . . . expression we can substitute for s

  0.0725c +0.104(65000 -2c) = 5405

  -0.1355c = -1355 . . . . . . . . . . . . . . . . . . . . subtract 6760, simplify

  c = 1355/.1355 = 10,000

  s = 65000 -2×10000 = 45,000

  b = 70000 +10000 = 80,000

The amounts invested in stocks, bonds, and CDs were $45,000, $80,000, and $10,000, respectively.

_____

Alternatively, you can reduce the augmented matrix for this problem to row-echelon form using any of several calculators or on-line sites. That matrix is ...

\left[\begin{array}{ccc|c}1&1&1&135000\\0.0275&0.045&0.104&8555\\-1&1&0&70000\end{array}\right]

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