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Solve x2-8x=3 by completing the square. which is the solution set of the equation

Mazyrski [523]

we have

$x^{2}-8x=3$

Complete the square. Remember to balance the equation by adding the same constants to each side

$x^{2}-8x+16=3+16$

$x^{2}-8x+16=19$

Rewrite as perfect squares

$(x-4)^{2}=19$

$(x-4)^{2}=19\\ (x-4)=(+/-)\sqrt{19} \\ \\ x1=4+\sqrt{19} =8.359\\ x2=4-\sqrt{19} =-0.359$

therefore

the answer is

$x1=4+\sqrt{19} =8.359\\x2=4-\sqrt{19} =-0.359$

5 0

3 years ago

Read 2 more answers

What perfect square that is between 1 and 100 has 27 as one of its factors?

astra-53 [7]

Answer:

81

Step-by-step explanation:

Its a perfect square and 27*3=81

6 0

3 years ago

William works at a nearby electronics store. He makes a commission of 6% percent on everything he sells. If he sells a computer

Naddika [18.5K]

Commission earned by William is $ 45.84

<h3><u>Solution:</u></h3>

Given that,

William makes a commission of 6% percent on everything he sells

He sells a computer for $764.00

<em><u>To find: Commission amount of William</u></em>

Given that he makes a commission of 6 % on everything he sells. So he has received a commission of 6 % of $ 764.00

Commission amount of William = 6 % of $ 764.00

a % of b can be written in fraction as $\frac{a}{100} \times b$

$6 \% \text { of } 764=\frac{6}{100} \times 764=0.06 \times 764=45.84$

Thus commission earned by William is $ 45.84

8 0

2 years ago

Triangle EFG is dilated by a scale factor of 3 centered at (0, 1) to create triangle E'F'G'. Which statement is true about the d

lesya [120]

Answer:

segment EH and segment E prime H prime both pass through the center of dilation.

Step-by-step explanation:

Center of dilation is point (0.1), same as H. Both, E(0,5) and H(0,1) are placed over y-axis, then E' and H' are also located at y-axis.

After dilation, H' is placed at (0,1) because it coincides with the center of dilation

Distance between E and center of dilation is 4 units, then E' should be at 4*3=12 units from the center of dilation and over y-axis. Therefore, E' is placed at (0, 13)

So, segment E'H' goes from (0,1) to (0,13), and pass through the center of dilation, like segment EH.

4 0

2 years ago

What is the solution to the system? 1. x-y + 2 z = -7<br> 2. y + z =1<br> 3. x-2 y - 3 z = 0

kvv77 [185]

You'd find this problem easier to understand and do if you'd please list the defining equations vertically and line up variables:

1. x - 1y + 2 z = -7

2. y + 1z = 1

3. x - 2 y - 3 z = 0 Now eliminate the line numbers:

x - 1y + 2 z = -7

1y + 1 z = 1

x - 2 y - 3 z = 0

Let's use the elimination method to eliminate variable z: Seeing that z = 1 - y, we transform the first equation into 1x - 1y + 2(1-y) = -7

and the third into x - 2y - 3(1-y) = 0.

Simplifying 1x - 1y + 2(1-y) = -7

and x - 2y - 3(1-y) = 0,

we get

1x - 2y - 3 + 3y) = 0 and 1x - 1y + 2 - 2y = -7

which in turn simplify to

1x + y = 3 and 1x - 3y = -9

Having eliminated the variable z, we now focus on eliminating x. Mult. the 1st equation by -1, obtaining -1x - 1y = -3. Add this result to 1x - 3y = -9:

0 - 4y = -12, which tells us that y = 3. Subbing 3 for y in 1x + 1y = 3 tells us that x = 0.

All we have left to determine is the vaue of z.

Borrowing Equation 3, from above, we get x - 2 y - 3 z = 0, and into this equation we substitute x = 0 and y = 3: 0 -2(3) - 3z = 0.

Thus, -3z = 6, and z = -2.

The solution set is (0, 3, -2). You should check this by substitution.

3 0

3 years ago