Checking for extraneous solutions

Mathematics

1 answer:

jarptica [38.1K]3 years ago

8 0

There is no restriction on the domain because there is a cube root for all real values positive or negative. So you can solve this as there are no extraneous solutions...

Cube both sides...

2x-4=-8

2x=-4

x=-2

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A lizard needs to stay a safe distance from a cactus. The diameter of the cactus is 12 inches. If the lizard is 8 inches from a

frez [133]

We will use the Pythagorean theorem:
8² + 12² = c²
64 + 144 = c²
c = √208 ≈ 14.42
14.42 - 12 = 2.42 in
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3 years ago

x - 2y = 3 5x + 3y = 2 The lines whose equations are shown intersect at which point? (1, -1) (-1, 1) (0, 3/2)

gtnhenbr [62]

I would solve the first equation for x and then sub that value into x in the second equation. That's the easiest way. x - 2y = 3 solved for x is x = 2y+3. Now sub that in for x in the second equation: 5(2y+3)+3y=2 and 10y + 15 + 3y = 2. 13y = -13, and y = -1. Now sub that y value into either equation to solve for x: x = 2(-1) + 3 gives us an x value of x = 1. Therefore, your solution to this system is (1, -1), first choice above.

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3 years ago

One ticket to a ride of the merry-go-round at the Sunday Fair costs $2.

sammy [17]

Considering the definition of an inequality, the maximum number of tickets that they can buy is 10.

<h3>Definition of inequality</h3>

An inequality is the existing inequality between two algebraic expressions, connected through the signs:

greater than >.
less than <.
less than or equal to ≤.
greater than or equal to ≥.

An inequality contains one or more unknown values called unknowns, in addition to certain known data.

Solving an inequality consists of finding all the values of the unknown for which the inequality relation holds.

<h3>Maximum number of tickets that they can buy</h3>

In this case, you know that

One ticket to a ride of the merry-go-round at the Sunday Fair costs $2.
Jenny and her friends have $36 with them.
After buying tickets to the merry-go-round, they want to be left with no less than $15.

So, they want to spend on the purchase of tickets for the merry-go-round a value less than or equal to $36 - $15= $21.

Being "x" the maximum number of tickets that they can buy, the inequality that expresses the previous relationship is

2x≤ 21

Solving:

x≤ 21÷2

Then, the maximum number of tickets that they can buy is 10.

Learn more about inequality:

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