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2 years ago

The solution set of x^2+12=21

Mathematics

1 answer:

Free_Kalibri [48]2 years ago

5 0

The solution set of the equation is: x = -3, x = 3.

<h3>How to Find the Solutions to an Equation?</h3>

Given the equation, x² + 12 = 21, the solution set is the possible value of x that will make the equation true. To find the values of x, do the following as shown below:

x² + 12 = 21

Subtract 21 from both sides of the equation

x² + 12 - 21 = 21 - 21

x² + 12 - 21 = 0

x² - 9 = 0

Find the difference of the two squares

(x + 3)(x - 3) = 0

x = -3

x = 3

Therefore, the solution set of the equation is: x = -3, x = 3.

Learn more about solution set of equations on:

brainly.com/question/13729904

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Three consecutive even integers have a sum of 24. Find the integers

strojnjashka [21]

Even integers have the form 2k so three consecutive even integers will be 2k,2(k+1),2(k+2)
so there sum will be
2k+2(k+1)+2(k+2)=24
simplifying
2k+2k+2+2k+4=24
adding like terms
6k+6=24
6k=18
k=3
so the three consecutive even integers are
2(3),2(3+1),2(3+2)
6,8,10

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3 years ago

What is the solution to the system of the linear equations

mote1985 [20]

The solution to this system of linear equations would be (0,2), since you look at the point of intersection. Where the two lines intersect, you look at the corresponding x and y values. Hence, the solution is (0,2). I hope you understand.
Thank you,
kaloliavivek

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3 years ago

Slope intercept from two points<br> (3,-8) and (6,-4)

sukhopar [10]

Answer:

(3,4)

Step-by-step explanation:

(6-3)(-4(--)+3)

5 0

4 years ago

Rita is spending more time at home to study and practice math. Her efforts are finally paying off. On her first assessment she s

kogti [31]

Hey, looks like when she doesn't study, she ALWAYS fails. Don't mean to insult though.

Let's see the difference between the three numbers. 63-58=5. 68-63=5.

We know the difference between each assessment she scores is 5 now!!

Let's put it to use.

Although you don't have multiple choice answers...

after 4 assessments(not including first 3), her score will be above 85!!

Including the first 3 assessments, her score would be above 85 after 7 assessments!!

anyways, I hope this helps!!

3 0

4 years ago

Read 2 more answers

Consider points A(1, 6) and B(8, 8). Find point C on the x-axis so AC +BC is a minimum.

Kay [80]

Answer:

The coordinates of the point C that minimizes AC + BC are (-20, 0) or (4, 0)

Step-by-step explanation:

The given coordinates of the points A and B are A(1, 6) and B(8, 8)

The location of the point C = The x-axis

Therefore;

The coordinates of the point C = (x, 0)

The length of the segment AC = √((1 - x)² + (6 - 0)²) = √((1 - x)² + 6²)

The length of the segment BC = √((8 - x)² + (8 - 0)²) = √((8 - x)² + 8²)

At minimum distance of AC + BC, we have;

d(√((1 - x)² + 6²) +√((8 - x)² + 8²))/dx = 0 = (1 - x) × 2 × (0.5 - 1)× (√((1 - x)² + 6²)^(0.5 - 1) + (8 - x) × 2 × (0.5 - 1)× √((8 - x)² + 8²)^(0.5 - 1)

∴ d(√((1 - x)² + 6²) +√((8 - x)² + 8²))/dx = 0 = -(1 - x)/√((1 - x)² + 6²) - (8 - x)/√((8 - x)² + 8²)

-(1 - x)/√((1 - x)² + 6²) = (8 - x)/√((8 - x)² + 8²)

(8 - x)·√((1 - x)² + 6²) = -(1 - x)·√((8 - x)² + 8²)

Squaring both sides gives;

(8 - x)²·((1 - x)² + 6²) = (1 - x)²·((8 - x)² + 8²)

Expanding, using an online tool, we get;

x⁴ - 18·x³ + 133·x² -720·x + 2368 = x⁴ - 18·x³ + 161·x² - 272·x + 128

Which gives;

(161 - 133)·x² - (272 - 720)·x + 128 - 2368 = 28·x² + 448·x - 2240 = 0

Dividing by 28 gives;

x² + 16·x - 80 = 0

(x + 20)·(x - 4) = 0

Therefore, x = -20 or x = 4

The coordinates of the point C that minimizes AC + BC are (-20, 0) or (4, 0)

4 0

3 years ago