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4 years ago

Given a polynomial f(x), if (x − 4) is a factor, what else must be true? f(0) = 4 f(0) = −4 f(4) = 0 f(−4) = 0

Mathematics

2 answers:

I am Lyosha [343]4 years ago

8 0

Answer:

f(4) = 0

Step-by-step explanation:

daser333 [38]4 years ago

5 0

Question:

Given a polynomial f(x), if (x − 4) is a factor, what else must be true?

f(0) = 4
f(0) = −4
f(4) = 0
f(−4) = 0

_______________________________________

Solution:

f(x) is a polynomial.

(x - 4) is a polynomial of f(x).

By converse of factor theorem: If (x - a) is a factor of f(x), then, f(a) = 0.

On comparing (x - 4) with (x - a), we get,

a = 4

So,

f(a) = 0

=> f(4) = 0

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The blueprint scale is 1 inch : 9 feet if the gym's area is 60 square inches on the blueprint, what is the actual square footage

WITCHER [35]

Answer:

4860 ft^2

Step-by-step explanation:

9 feet is represented by 1 inch.

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● 81 => 1

So a 81 ft^2 square is represented by a 1 in^2 square (picture below)

■■■■■■■■■■■■■■■■■■■■■■■■■■

The gym's area in the blueprint is 60 in^2

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3 years ago

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Joe and Janna leave home at the same time, traveling in opposite directions. Joe drives 45 mph and Janna drives 40 mph. In how m

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3 years ago

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Find the equation for the circle with a diameter whose endpoints are (3,-1) and (-2,-1)

cricket20 [7]

Answer:

The equation for the circle is: $(x-\frac{1}{2} )^2 + y^2 = (\frac{5}{2} )^2$

Step-by-step explanation:

Here, let us assume the two end points of the diameter are:

P (3,-1) and Q (-2,-1)

Now, as we knew diameter is the chord that passer through the center of the circle.

⇒ Mid point of DIAMETER = Center coordinates of the Circle

Let us assume O(x,y) is the center of the line segment PQ.

So, by MID POINT FORMULA:

$(x,y)= (\frac{3 -2}{2} , \frac{-1-1}{2} ) =( \frac{1}{2},\frac{-2}{2}) \\\implies (x,y) =( 0.5 , -1)$

⇒ The center coordinates of the circle = O(0.5,-1) ...... (1)

Now, RADIUS = Half of DIAMETER

Using DISTANCE FORMULA:

$PQ = \sqrt{(3-(-2))^2 + (-1 - (-1))^2} = \sqrt{(5)^2 + 0} = 5$

So, Radius = 5/2 = 2.5 units

Now, the equation of circle with radius r and center coordinate ( h,k) is given as: $(x-h)^2 + (y-k)^2 = r^2$

Substitute r = 2.5 and (h,k) = (0.5,0) we get:

$(x-0.5)^2 + (y-0)^2 = (2.5)^2\\\implies (x-\frac{1}{2} )^2 + y^2 = (\frac{5}{2} )^2$

Hence the equation for the circle is: $(x-\frac{1}{2} )^2 + y^2 = (\frac{5}{2} )^2$

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Natasha2012 [34]

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3 years ago

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Ber [7]

X^3 - 21x = -20
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Factors of P (constant) 20 = 1, 2, 4, 5, 10, 20
-------------------------------
Factors of Q (leading Coefficient) = 1

Possible zeros (all + -) 1/1, 2/1, 4/1, 5/1, 10/1, 20/1

Of the choices given only the number 1 is a possible root.

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3 years ago

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