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skelet666 [1.2K]
3 years ago
8

the area of a rectangular patio is represented by the expression 6x^2+13-5. the width of the patio is (3x-1) write an expression

to represent the length of the patio in terms of x
Mathematics
1 answer:
jok3333 [9.3K]3 years ago
6 0

<span>I think you meant 6x²+13x-5 so first thing we have to do is factor it which is really quite tricky with this kind of trinomial so first take ac which is 6 times -5 so -30 now figure out factors of -30 that will add up to 13 how about 15 and -2 now that we have the factors write the equation again</span>

<span /><span> 6x²+15x-2x-5  </span>split the equation in half<span />

<span>6x²+15x   -2x-5 so out of the first equation we can pull a 3x out</span>

<span>3x(2x+5) and out of the second we can pull a negative 1</span>

<span>3x(2x+5) -1(2x+5) rewrite it</span>

<span>(3x-1)(2x+5) so the 3x-1 is the factor we already had so the other side is (2x+5)</span>

<span>
</span>

<span><u>HOPE THIS HELPS!!!</u></span>

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3 years ago
What is the following quotient?
seropon [69]

Answer:  Choice B) \frac{5\sqrt{11}+5\sqrt{3}}{8}\\\\

==========================================

Work Shown:

\frac{5}{\sqrt{11}-\sqrt{3}}\\\\\\\frac{5(\sqrt{11}+\sqrt{3})}{(\sqrt{11}-\sqrt{3})(\sqrt{11}+\sqrt{3})}\\\\\\\frac{5\sqrt{11}+5\sqrt{3}}{(\sqrt{11})^2-(\sqrt{3})^2}\\\\\\\frac{5\sqrt{11}+5\sqrt{3}}{11-3}\\\\\\\frac{5\sqrt{11}+5\sqrt{3}}{8}\\\\\\

This shows why choice B is the answer.

---------------

Explanation:

  • In the second step, I multiplied top and bottom by (\sqrt{11}+\sqrt{3})
  • This is so we can apply the difference of squares rule in step 3. The difference of squares rule is (x-y)(x+y) = x^2-y^2.
  • In step 4, the square roots cancel out with the squaring operation. The two operations are inverses of one another, which is why they cancel.

So in general, if the denominator is \sqrt{a}-\sqrt{b} and you want to rationalize the denominator, then you should multiply top and bottom by \sqrt{a}+\sqrt{b}. The same applies in reverse as well.

This leads to the denominator becoming (\sqrt{a}-\sqrt{b})(\sqrt{a}+\sqrt{b}) = (\sqrt{a})^2-(\sqrt{b})^2 = a-b

Keep in mind that a \ge 0 and b \ge 0

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2 years ago
Ricardo deposits $30 and it increases by 15% each month how much money will he have in 6 months and what is the linear equation
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Answer: 207$ I think..

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3 years ago
Alison’s age is 12 more than half of Sam’s age. Using S to represent Sam’s age, write an expression that represents Alison’s age
UNO [17]

Answer: the answer is C

Step-by-step explanation:

6 0
3 years ago
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Lines LaTeX: CEC E and LaTeX: ADA D intersect at LaTeX: BB.
Goshia [24]

Answer:

✔️The measure of angle <CBA is equal to the measure of angle <DBE.

✔️The measure of angle CBD is equal to the measure of angle ABE.

✔️The sum of the measures of angles CBD and CBA is 180 degrees.

Step-by-step explanation:

Vertical angles are formed when two straight lines intersect each other at a certain point. The diagram given is a typical example. This, vertical opposite angles formed are said to be congruent, that is their measures are equal to each other.

The following statements are true of the given diagram:

✔️The measure of angle <CBA is equal to the measure of angle <DBE.

(<CBA and ,<DBE are vertically opposite angles)

✔️The measure of angle CBD is equal to the measure of angle ABE.

(They are both vertically opposite angles)

✔️The sum of the measures of angles CBD and CBA is 180 degrees.

(<CBA and <CBD are supplementary angles)

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