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3 years ago

Given the binomials (x-1), (x-3), (x+3), (x+5), which one is the factor of f(x) = x^3 + 6x^2 + 12x +35?

1 answer:

4 0

The given polynomial is
f(x) = x³ + 6x² + 12x + 35

According to the Remainder Theorem, if x = a is a zero, then
f(a) = 0, and (x-a) is a factor.

Test (x-1):
f(1) = 1 + 6 +12 + 35 = 54
Not a factor.

Test (x-3):
f(3) = 3³ +6*3² + 12*3 + 35 = 152
Not a factor.

Test (x+3):
f(-3) = (-3)³ + 6*(-3)² + 12*(-3) + 35 = 26
Not a factor.

Test (x+5):
(-5)³ + 6*(-5)² + 12*(-5) + 35 = 0
It is a factor.

Answer: (x+5) is a factor.

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Polygon CCC has an area of 404040 square units. K 2ennan drew a scaled version of Polygon CCC using a scale factor of \dfrac12 1

nikdorinn [45]

Answer:

Area of polygon D = 10 square units

Step-by-step explanation:

Given:

Polygon C has an area of 40 square units.

It is scaled with a scale factor of $\frac{1}2$ to form a new polygon D.

To find:

The area of polygon D = ?

Solution:

When any polygon is scaled to half, then all the sides of new polygon are half of the original polygon.

And the area becomes one-fourth of the original polygon.

Let us consider this by taking examples:

First of all, let us consider a right angled triangle with sides 6, 8 and 10 units.

Area of a right angled triangle is given by:

$A = \dfrac{1}{2} \times Base \times Height\\\Rightarrow A = \dfrac{1}{2} \times 6 \times 8 = 24\ sq\ units$

If scaled with a factor $\frac{1}{2}$ , the sides will be 3, 4 and 5.

New area, A':

$A' =\dfrac{1}{2} \times 3 \times 4 = 6\ sq\ units = \dfrac{1}4\times A$

i.e. Area becomes one fourth.

Let us consider a rectangle now.

Sides be 8 and 10 units.

Area of a rectangle, A = $Length \times Width$ = 8 $\times$ 10 = 80 sq units.

Now after scaling, the sides will be 4 and 5 units.

New Area, A' = 4 $\times$ 5 =20 sq units

So, $\bold{A' = \frac{1}4 \times A}$

Now, we can apply the same in the given question.

$\therefore$ Area of polygon D = $\bold{\frac{1}{4}}$ $\times$ Area of polygon C

Area of polygon D = $\bold{\frac{1}{4}}$ $\times$ 40 = 10 sq units

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3 years ago

Sin(5x 3 + 20) = cos(2x 3 + 14)

Ronch [10]

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3 years ago

The cube of the sum of a number and 3.

Verdich [7]

The answer is 3! You got this!

3 0

2 years ago

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artcher [175]

Answer:

m∠ADB = 59°

Step-by-step explanation:

I've provided my work which also includes how I check my answers by using the information given! Hope this helps!!! If you have any questions, I can try to help.

6 0

3 years ago

Can someone solve this for me please.

nika2105 [10]

Answer:

The value of PR is 21 ft.

Step-by-step explanation:

We know that:

3(PQ + QT + TP) = PR + RS + SP
PQ = 7 ft.
QT = 4 ft
RS = 12 ft.

Work:

3(PQ + QT + TP) = PR + RS + SP
=> 3(7 + 4 + TP) = PR + 12 + SP
=> 21 + 12 + 3TP = PR + 12 + SP
=> 21 + 3TP = PR + SP
=> 21 + SP = PR + SP [3TP = SP]
=> 21 = PR

Hence, the value of PR is 21 ft.

Hoped this helped.

$BrainiacUser1357$

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2 years ago