1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
nevsk [136]
3 years ago
12

Square Root

Mathematics
2 answers:
lawyer [7]3 years ago
8 0

Answer:

1. Perfect square trinomial on left sides is (x+\frac{1}{4})^2=\frac{4}{9}.

2. The equation after applying the square root property of equality is x+\frac{1}{4}=\pm \frac{2}{3}.

Step-by-step explanation:

The given equation is

x^2+\frac{1}{2}x+\frac{1}{16}=\frac{4}{9}

It can be written as

x^2+\frac{1}{2}x+(\frac{1}{4})^2=\frac{4}{9}

Factor the perfect-square trinomial on the left side of the equation.

x^2+2(\frac{1}{4})x+(\frac{1}{4})^2=\frac{4}{9}

(x+\frac{1}{4})^2=\frac{4}{9}        [\because (a+b)^2=a^2+2ab+b^2]

Therefore the required equation is

(x+\frac{1}{4})^2=\frac{4}{9}

Taking square root both the sides.

\sqrt{(x+\frac{1}{4})^2}=\pm\sqrt{\frac{4}{9}}

x+\frac{1}{4}=\pm \frac{2}{3}

Therefore the equation after applying the square root property of equality is x+\frac{1}{4}=\pm \frac{2}{3}.

Oxana [17]3 years ago
5 0

Answer:

1).(x+\frac{1}{4})^{2}=\frac{4}{9}

2).x+\frac{1}{4}=\pm \frac{2}{3}

Step-by-step explanation:

Here the given equation is x^{2}+\frac{1}{2}x+\frac{1}{16}=\frac{4}{9}

We have to factor the perfect square trinomial on the left side of the equation

So left side of the equation is x^{2}+\frac{1}{2}x+\frac{1}{16}

= x^{2}+2\times \frac{1}{4}x+(\frac{1}{4})^{2}

=(x+\frac{1}{4})^{2}    since [(a+b)²= a²+b²+2ab]

Therefore the factorial form of the equation will be

(x+\frac{1}{4})^{2}=\frac{4}{9}

Now we have to solve the equation by applying square root property

\sqrt{(x+\frac{1}{4})^{2}}=\sqrt{\frac{4}{9}}

x+\frac{1}{4}=\pm \frac{2}{3}

You might be interested in
1/2(4x+10)=2 i need to get x
kari74 [83]
First you need to distribute the 1/2 by the numbers in the parentheses
1/2•4x and 1/2•10 which equals
2x+5=10

next, you will need to get the 2x by itself so you would do
2x+5=10
-5=-5
2x=5

finally, you divide the 2 by the 5 so you can get the x by itself
2x divided by 5

the answer is: x=2.5
8 0
2 years ago
Which graph represents the following system of inequalities.
Marta_Voda [28]

Answer: Graph C is correct

Step-by-step explanation:

The region below the dashed red line is y < 4/3x +2

The region below the solid purple line is y ≤ -1

The region below and left of the solid green line is y ≤ -3x

4 0
3 years ago
Hello if you could help me that would be great
tankabanditka [31]

2.74x=58.19

x=21.2372

He only has enough lunch money for 21 full days.

3 0
3 years ago
A map has a scale of 1cm:20 km two cities are 2.5 cm apart on the map to the nearest tenth of a kilometer what is the actual dis
Aleksandr-060686 [28]

Answer: 50 km

Step-by-step explanation: So the map has a scale of 1 cm: 20 km. Next, you look at how far they are apart and see if the scale and the distance on the map are the same measurement. In this case, they are both centimeters so they stay the same. Then, all you do is multiple the real size, 20 km, by  

2.5 /1 . Then, 20 x 2.5=50. So the answer is 50 km

6 0
3 years ago
The numbers 1 through 12 are written on 12 slips of paper, with a different number on each paper slip, and placed in a bag. One
Naddik [55]
If you're asking for the number of digits smaller than 13 in the bag:12
8 0
3 years ago
Other questions:
  • Alaska has a land area of about 1,700,000 square kilometers Florida has a land area 1/10 the size of Alaska.what is the land are
    6·2 answers
  • Factor 2x2 − 24x + 72.
    6·1 answer
  • Whats the difference between adding me on ig <br><br> answer papi_lopez_4k<br> help me reach 100
    5·2 answers
  • Xy-11=5 is this a direct variation
    5·2 answers
  • A basket contains 6 oranges and 4 tangerines. a sample of 3 is drawn. find the probability that they are all oranges
    15·1 answer
  • Isabel Moreno<br> Simplify: (5p? +7 – 3p' – 5p)+(-7p* – 3p²-9-5p)
    10·1 answer
  • Mr. Jerome has an outstanding balance of $12000 on his credit card. The interest rate on the card is 12% he intends to pay off
    6·2 answers
  • X
    9·1 answer
  • What is the slope of the two points (-6,3) (12,6)
    13·1 answer
  • A store buys 13 sweaters for $52 and sells them for $377. How much profit does the store make per sweater?
    11·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!