MATHEMATICS HIGH SCHOOL

A rhombus is a quadrilateral that has exactly one pair of parallel sides.
True or false

Answers

Answer 1

Answer:

Answer:

False

Step-by-step explanation:

Every rhombus has two diagonals connecting pairs of opposite vertices, and two pairs of parallel sides.

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Which long division problem can be used to prove the formula for factoring the difference of two perfect cubes?

Answers

Some of the possible options of the questions are;

A) $(a - b) | \overline {a^2 + a \cdot b + b^2}$

B) $(a + b) | \overline {a^2 - a \cdot b + b^2}$

C) $(a + b) | \overline {a^3 + 0 \cdot a \cdot b^2 + 0 \cdot a \cdot b^2 - b^3}$

D) $(a - b) | \overline {a^3 + 0 \cdot a \cdot b^2 + 0 \cdot a \cdot b^2 - b^3}$

The difference of two perfect cubes has a binomial factor and a trinomial factor

The option that gives the long division problem that can be used to prove the difference of two perfect cubes is option D

D) $\underline {(a - b) | \overline {a^3 + 0 \cdot a \cdot b^2 + 0 \cdot a \cdot b^2 - b^3}}$

Reason:

The formula for factoring the difference of twoperfect cubes is presented as follows;

a³ - b³ = (a - b)·(a² + a·b + b²)

Given that a factor of the difference of two cubes is (a - b), and that we

have; (a³ + 0·a·b² + 0·a²·b - b³) = (a³ - b³), both of which are present in

option D, by long division of option D, we have;

${} \hspace {33} a^2 + a \cdot b + b^2\n(a - b) | \overline {a^3 + 0 \cdot a \cdot b^2 + 0 \cdot a^2 \cdot b - b^3}\n{} \hspace {33} \underline{a^3 - a^2 \cdot b }\n{} \hspace {55} a^2 \cdot b + 0 \cdot a \cdot b^2 + 0 \cdot a \cdot b^2 - b^3\n {} \hspace {55} \underline{a^2 \cdot b - a \cdot b^2}\n{} \hspace {89} a \cdot b^2 + 0 \cdot a \cdot b^2 - b^3\n{} \hspace {89} \underline{a \cdot b^2 - b^3}\n{}\hspace {89} 0$

By the above long division, we have;

$(a - b) | \overline {a^3 + 0 \cdot a \cdot b^2 + 0 \cdot a \cdot b^2 - b^3}$ = a² + a·b + b²

Which gives;

$(a - b) | \overline {a^3 + 0 \cdot a \cdot b^2 + 0 \cdot a \cdot b^2 - b^3}$ = (a³ + 0·a·b² + 0·a·b² - b³)/(a - b)

We get;

(a³ + 0·a·b² + 0·a·b² - b³)/(a - b) = a² + a·b + b²

(a - b)·(a² + a·b + b²) = (a³ + 0·a·b² + 0·a·b² - b³) = (a³ - b³)

(a - b)·(a² + a·b + b²) = (a³ - b³)

(a³ - b³) = (a - b)·(a² + a·b + b²)

Therefore;

The long division problem that can be used to prove the formula for

factoring the difference of two perfect cubes is

$(a - b) | \overline {a^3 + 0 \cdot a \cdot b^2 + 0 \cdot a \cdot b^2 - b^3}$ , which is option D

D) $(a - b) | \overline {a^3 + 0 \cdot a \cdot b^2 + 0 \cdot a \cdot b^2 - b^3}$

Learn more here:

brainly.com/question/17022755

Answer:

The correct options, rearranged, are:

Options:

$A)(a^2+ab+b^2)/(a-b)\n\nB)(a^2-ab+b^2)/(a+b)\n\nC)(a^3+0a^2+0ab^2-b^3)/(a+b))\n\n D)(a^3+0a^2+0ab^2-b^3)/(a-b)$

And the asnwer is the last option (D).

Explanation:

You need to find which long division can be used to prove the formula for factoring the difference of two perfect cubes.

The difference of two perfect cubes may be represented by:

$a^3-b^3$

And it is, as a very well known special case:

$a^3-b^3=(a-b)(a^2+ab+b^2)$

Then, to prove, it you must divide the left side, $a^3-b^3$ , by the first factor of the right side, $a-b$

Note that, to preserve the places of each term, you can write:

$(a^3-b^3)=(a^3+0a^2+0ab^2-b^3)$

Then, you have:

$(a^3+0a^2+0ab^2-b^3)=(a-b)(a^2+ab+b^2)$

By the division property of equality, you can divide both sides by the same factor, which in this case will be the binomial, and you get:

$(a^3+0a^2+0ab^2-b^3)/(a-b)=(a^2+ab+b^2)$

That is the last option (D).

What's the answer too x+7/7x+35*x^2-3x-40/x-8

Answers

$(x+7)/(7x+35)\cdot(x^2-3x-40)/(x-8)=(*)\n\nx^2-3x-40=0\na=1;\ b=-3;\ c=-40\n\Delta=b^2-4ac;\ x_1=(-b-\sqrt\Delta)/(2a);\ x_2=(-b+\sqrt\Delta)/(2a)\n\n\Delta=(-3)^2-4\cdot1\cdot(-40)=9+160=169;\ \sqrt\Delta=√(169)=13\n\nx_1=(3-13)/(2\cdot1)=(-10)/(2)=-5;\ x_2=(3+13)/(2\cdot1)=(16)/(2)=8\n\nx^2-3x-40=(x+5)(x-8)\n\n(*)=(x+7)/(7(x+5))\cdot((x+5)(x-8))/(x-8)=(x+7)/(7)=(x)/(7)+(7)/(7)=(1)/(7)x+1\n\nD:x\neq-5\ \wedge\ x\neq8$

Help please just type down the answer asap.

Answers

Answer:

Step-by-step explanation:

based off the others.

40
Just add 100 + 40 because each angle will always add back to 180

A driver starts his parked car and within 4.6 seconds, reaches a velocity of 15.0 m/s. What is his acceleration?

Answers

Answer:

3.261

Step-by-step explanation:

Acceleration is velocity/time

15/4.6=3.261

Find the measures of 1 and 2

Answers

Answer:

1 ) ∠1 = 105 ∠2 = 75

2) ∠1 = 50 ∠2 = 50

Step-by-step explanation:

An adult elephant eats about 300 pounds of food each day. Write an expression to represent the number of pounds of food a heard of 12 elephants eats in 5 days.