All categories

3 years ago

When solving an equation in the form by taking square roots, how many solutions will there be?

Mathematics

2 answers:

harina [27]3 years ago

6 0

Answer:

Two

Step-by-step explanation:

When you solving square equation, you will have two solutions.

Here we are given $ax^2 = c$

We have to solve for x.

Divide both sides by a, we get

$\frac{ax^2}{a} = \frac{a}{c}$

Simplifying, we get

$x^2 = \frac{a}{c}$

In order to find the value of x, we need to get rid of square on the left side, so we need to take the square root on both sides, we get

$\sqrt{x^2} = \sqrt{\frac{a}{c} }$

x = ± $\sqrt{\frac{a}{c} }$

So you will have a positive number and a negative number.

Therefore, there are two solutions.

ss7ja [257]3 years ago

3 0

Normally two. However, one is often extraneous.

You might be interested in

What is −13+2z=−56 Thanks

Zinaida [17]

<h3>Original Equation:</h3>

$-\frac{1}{3}+2z=-\frac{5}{6}$

<h3>Steps:</h3>

<em>*To solve for a variable, isolate the desired variable onto one side.</em>

Firstly, we want to add 1/3 to each side however -5/6 and 1/3 do not share the same denominator, and we want them to have that and we can do that by finding the LCD, or lowest common denominator. To find the LCD, list the multiples of 6 and 3 and the lowest multiple that they share is their LCD. In this case, their LCD is 6. Multiply -1/3 by 2/2:

$-\frac{1}{3}\times \frac{2}{2}=-\frac{2}{6}\\\\-\frac{2}{6}+2z=-\frac{5}{6}$

Now that we have common denominators, add both sides by 2/6:

$2z=-\frac{3}{6}\\\\2z=-\frac{1}{2}$

Next, you want to cancel out 2 to isolate z. Usually, one would divide both sides by 2, however remember that <u>dividing by a number is the same as multiplying by it's reciprocal.</u> To find a number's reciprocal, flip the numerator and denominator around. In this case, since 2 is a <em>whole number</em> this means that the denominator is 1. In this case: 2/1 would become 1/2. Multiply both sides by 1/2:

$\frac{1}{2}\times 2z= -\frac{1}{2}\times \frac{1}{2}\\\\z=-\frac{1}{4}$

<h3>Final Answer:</h3>

<u>Your final answer is z = -1/4.</u>

7 0

3 years ago

Ralph buys a desk that regularly sells for $250 and a desk chair that regularly sells for $145. both items are on sale at 15% of

Lunna [17]

C) (0.85 + x/100)(250+145) does not give the correct answer.

Explanation
A) works; adding the two costs together is 250+145=395. We multiply this by 0.85 because 100%-15%=85%=0.85. We also have x% tax, which is represented by x/100, added to 100% of the value, or 1.00. Altogether this gives us
395(0.85)(1+x/100) = 395(0.85 + (0.85x/100)) = 395(0.85) + 395(0.85x/100)
= 395(0.85) + 395(0.0085x)
B) works; we have 250+145 for the original price; we have 85% = 0.85 of the value; we also have 100% + x%, which is (100+x)/100.
C) does not work; (0.85+x/100)(395) does not take into consideration that you are finding the tax after taking the 85%. This will simplify out to
0.85*395 + (x/100)(395) = 335.75 + 395x/100 = 335.75 + 3.95x, which is too much.
D) works; simplifying the expression from A, we have 395(0.85) + 395(0.0085x) = 335.75 + 3.3575x.

6 0

3 years ago

HELP PLEASE!!!

Thepotemich [5.8K]

The answer is: 7/7

hope this helps :))

8 0

2 years ago

What is the solution set of {x | x < -5} ∩ {x | x > 5}?

777dan777 [17]

This symbol "∩" means intersection of both sets or what do both sets contain that are the same..

First set contains all numbers less than -5 and the other set contains all numbers greater than 5 so the sets don't overlap at all.

The solution set is empty ∅

7 0

3 years ago

9. How many planes are shown in the figure?

Paraphin [41]

<h3>9)</h3><h3>5 planes</h3>

<h3>10)</h3><h3>2 planes</h3>

<h3>12)</h3><h3>Yes , they belong to plane (w)</h3>

3 0

1 year ago