All categories

2 years ago

Which polynomial identity will prove that 117 = 125 − 8?

Mathematics

2 answers:

Levart [38]2 years ago

7 0

The answer is Sum of cubes :)

777dan777 [17]2 years ago

4 0

Answer:

Difference of cubes.

Step-by-step explanation:

We are asked to find the identify that will prove that $117=125-8$ .

Polynomial identities are equations that are true and have general applications in our algebra work.

We can see that 125 equals $5^3$ and 8 equals $2^3$ . So polynomial identity used in our given problem is difference of cubes.

Difference of cubes: $a^3-b^3=(a-b)(a^2+ab+b^2)$

Let us prove that 117=125-8.

We can write right hand side of our given equation as:

$5^3-2^3=(5-2)(5^2+5\times 2+2^2)$

$125-8=(3)(25+10+4)$

$117=(3)(39)$

$117=117$

We can see that left hand side of our equation is equal to right hand side of equation. Hence, proved that difference of cubes will prove our equation equal.

You might be interested in

Please answer correctly !!!!! Will mark Brianliest !!!!!!!!!!!!!!

AlexFokin [52]

Answer:

AE = 60 units

Step-by-step explanation:

GE is one third the length of AE so...

GE = 1/3(AE)

20 = 1/3x

3(20) = (1/3x)3/1

60 = x

x = 60

AE = 60 units

7 0

2 years ago

PLEASE ANSWER OFFERING BRAINLEST

jonny [76]

we can establish a ratio since triangle MNQ is equal to Triangle MLP.

your answer is B 9 inches

6 0

2 years ago

1) Determine the discriminant of the 2nd degree equation below:

Aleksandr-060686 [28]

$\LARGE{ \boxed{ \mathbb{ \color{purple}{SOLUTION:}}}}$

We have, Discriminant formula for finding roots:

$\large{ \boxed{ \rm{x = \frac{ - b \pm \: \sqrt{ {b}^{2} - 4ac} }{2a} }}}$

Here,

x is the root of the equation.
a is the coefficient of x^2
b is the coefficient of x
c is the constant term

1) Given,

3x^2 - 2x - 1

Finding the discriminant,

➝ D = b^2 - 4ac

➝ D = (-2)^2 - 4 × 3 × (-1)

➝ D = 4 - (-12)

➝ D = 4 + 12

➝ D = 16

2) Solving by using Bhaskar formula,

❒ p(x) = x^2 + 5x + 6 = 0

$\large{ \rm{ \longrightarrow \: x = \dfrac{ - 5\pm \sqrt{( - 5) {}^{2} - 4 \times 1 \times 6 }} {2 \times 1}}}$

$\large{ \rm{ \longrightarrow \: x = \dfrac{ - 5 \pm \sqrt{25 - 24} }{2 \times 1} }}$

$\large{ \rm{ \longrightarrow \: x = \dfrac{ - 5 \pm 1}{2} }}$

So here,

$\large{\boxed{ \rm{ \longrightarrow \: x = - 2 \: or - 3}}}$

❒ p(x) = x^2 + 2x + 1 = 0

$\large{ \rm{ \longrightarrow \: x = \dfrac{ - 2 \pm \sqrt{ {2}^{2} - 4 \times 1 \times 1} }{2 \times 1} }}$

$\large{ \rm{ \longrightarrow \: x = \dfrac{ - 2 \pm \sqrt{4 - 4} }{2} }}$

$\large{ \rm{ \longrightarrow \: x = \dfrac{ - 2 \pm 0}{2} }}$

So here,

$\large{\boxed{ \rm{ \longrightarrow \: x = - 1 \: or \: - 1}}}$

❒ p(x) = x^2 - x - 20 = 0

$\large{ \rm{ \longrightarrow \: x = \dfrac{ - ( - 1) \pm \sqrt{( - 1) {}^{2} - 4 \times 1 \times ( - 20) } }{2 \times 1} }}$

$\large{ \rm{ \longrightarrow \: x = \dfrac{ 1 \pm \sqrt{1 + 80} }{2} }}$

$\large{ \rm{ \longrightarrow \: x = \dfrac{1 \pm 9}{2} }}$

So here,

$\large{\boxed{ \rm{ \longrightarrow \: x = 5 \: or \: - 4}}}$

❒ p(x) = x^2 - 3x - 4 = 0

$\large{ \rm{ \longrightarrow \: x = \dfrac{ - ( - 3) \pm \sqrt{( - 3) {}^{2} - 4 \times 1 \times ( - 4) } }{2 \times 1} }}$

$\large{ \rm{ \longrightarrow \: x = \dfrac{3 \pm \sqrt{9 + 16} }{2 \times 1} }}$

$\large{ \rm{ \longrightarrow \: x = \dfrac{3 \pm 5}{2} }}$

So here,

$\large{\boxed{ \rm{ \longrightarrow \: x = 4 \: or \: - 1}}}$

<u>━━━━━━━━━━━━━━━━━━━━</u>

5 0

2 years ago

Read 2 more answers

4/ PLEASE HELP ME ON THIS. ASAP

rewona [7]

Answer: a,b,d,e are all right beacuse they all relate to the question

Step-by-step explanation:

c how ever is no shown on the graph and is therefor wrong

4 0

2 years ago

4z - 8 = 20<br> Step by step

AysviL [449]

Answer:

z = 7

Step-by-step explanation:

4z - 8 = 20

Add 8 to each side

4z - 8+8 = 20+8

4z = 28

Divide each side by 4

4z/4 = 28/4

z = 7

5 0

2 years ago