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Virty [35]
3 years ago
8

X^2-18x+67=0 Solve the quadratic equation by completing the square.

Mathematics
1 answer:
Assoli18 [71]3 years ago
5 0

Answer:

x = 9 ± √14

Step-by-step explanation:

x² − 18x + 67 = 0

Move the constant to the other side:

x² − 18x = -67

Take half of -18, square it, and add to both sides.

(-18/2)² = (-9)² = 81

x² − 18x + 81 = -67 + 81

x² − 18x + 81 = 14

Factor the perfect square:

(x − 9)² = 14

Solve for x:

x − 9 = ±√14

x = 9 ± √14

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What shapes can you obtain by taking a cross section of a cone?
SashulF [63]
You can get a circle by cutting horizontally and a hyperbola by cutting vertically. You can also get an ellipse and a parabola by cutting at an angle depending on whether the cut comes out the other side or not. 

7 0
3 years ago
Please help with this problem ​
Luden [163]
<h3>2, 6, 10</h3>

Step-by-step explanation:

Tom = s

Nancy = r

s=r-2 = Tom=Nancy-2

This means that Tom has $2 less than Nancy as they stayed in the information they gave us. They want us to complete the graph.

Since Tom has $2 less than Nancy all we have to do is apply rule -2 to each number.

4-2=2

8-2=6

12-2=10

Therefore the numbers to add to the graph are 2, 6, and 10.

3 0
2 years ago
What values of a and b make this equation true?
Fynjy0 [20]

Answer:

a = -4

b=-29

Step-by-step explanation:

<h3>Complex number:</h3>

First write the radicals in simplest form.

i² = -1

\sf (4 + \sqrt{-49}) -2\left(\sqrt{(-4)^2}+\sqrt{-324}\right)=4 + \sqrt{49i^2} - 2\left(\\\sqrt{16}+\sqrt{324i^2}\right)

                                                          \sf =4 + \sqrt{7*7*i*i}-2\left(\sqrt{4*4}+\sqrt{18*18*i*i}\right)\\\\= 4 + 7i - 2(4 + 18i)\\\\= 4 + 7i - 2*4 - 2*18i\\\\= 4 + 7i -8-36i\\\\= 4 - 8 +7i - 36i\\\\= -4 - 29i

   \sf \boxed{a = -4 }\\\\\boxed{b=-29}

5 0
2 years ago
PLEASE HELP a right triangle is removed from a rectangle to create the shaded region shown below. Find the area of the shaded re
UNO [17]

Answer:

56m²

Step-by-step explanation:

First, find the area of the entire rectangle:

10 × 8 = 80

Then, find the area of the triangle:

1/2(6)(8) = 24

Finally, subtract the two areas to find the shaded area:

80 - 24 = 56

3 0
3 years ago
Solve each equation for given variable<br> -5i -15 = 15
Illusion [34]

Answer:

i= -6

Step-by-step explanation:

-5i-15=15

if we use inverse operation here, it would be -5i=30, so i= -6

5 0
3 years ago
Read 2 more answers
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