All categories

3 years ago

Solve the equation by completing the square. x^2 -2x = 15

Mathematics

1 answer:

dlinn [17]3 years ago

5 0

Answer:

x = -3 or x = 5

Step-by-step explanation:

Solve: x^2 -2x = 15

x^2 - 2x - 15 = 0

Use the Diamond method of factoring

-15 = 3* -5 and 3 - 5 = -2 so...

x^2 - 2x - 15 = x^2 - 5x + 3x - 15

x^2 - 2x - 15 = x *(x - 5) + 3*(x - 5)

x^2 - 2x - 15 = (x + 3)*(x - 5)

x^2 - 2x - 15 = (x + 3)*(x - 5) = 0

solve (x + 3 ) = 0 and (x - 5) = 0

x = -3 or x = 5

You might be interested in

Definition:A sailboat set a course of N 25° E from a small port along a shoreline that runs north and south. Sometime later the

kicyunya [14]

Answer:

S 75°E

S 55°E

Step-by-step explanation:

Take the law if sines of a triangle:

$\frac{a}{sinA} = \frac{b}{sinB} = \frac{c}{sinC}$

Where,

a = 28 miles

B = 25°

b = 12 miles

First solve for A, using the law of sines:

$\frac{a}{sinA} = \frac{b}{sinB}$

$\frac{28}{sinA} = \frac{12}{sin25}$

Cross multiply:

$28 sin25 = 12 sinA$

$11.83 = 12 sinA$

$Sin A = \frac{11.83}{12}$

$Sin A = 0.986$

$A = sin^-^1(0.986)$

$A = 80.44 degrees$

Since A = 80.44° find A supplement, A`:

A` = 180 - 80.44

A` = 99.56°

If A` + B < 180°, find C.

Thus,

A` + B = 99.56 + 25 = 124.56

We can see that A` + B < 180

Find C:

C = 180 - (80.44+25) = 74.56° ≈ 75°

C` = 180 - (99.56+25) = 55.44° ≈ 55°

Rewrite in bearing form:

S 75°E

S 55°E

5 0

2 years ago

Place ( ) symbols in this problem to make a true statement: 4 + 5 × 2 = 18

yanalaym [24]

Answer:

(4+5)*2

Hope this was helpful have a beautiful day!

5 0

2 years ago

Read 2 more answers

Please help!! Explain how you got the answer!

mash [69]

multiply 3.5 x 3 = 10.5

add -5 +-10 = -15

so you have 10.5 x 10^15

then you need to move the decimal point 1 place to the left to get 1.05

since you move the decimal point 1 place to the left you add 1 to the -15 to get -14

so answer = 1.05 x 10^-14

8 0

3 years ago

Solve V = 1/3(3.14)r^2h for h

Ber [7]

V = 1/3(3.14)r^2h
=1.046r^2h

Solving for V

7 0

3 years ago

Read 2 more answers

With reference to the figure, sin X equals? 1.) 0.250 2.)0.447 3.)0.894 4.)1

Flura [38]

Answer:

3.) 0.894

Step-by-step explanation:

✔️First, find BD using Pythagorean Theorem:

BD² = BC² - DC²

BC = 17.89

DC = 16

Plug in the values

BD² = 17.89² - 16²

BD² = 64.0521

BD = √64.0521

BD = 8.0 (nearest tenth)

✔️Next, find AD using the right triangle altitude theorem:

BD = √(AD*DC)

Plug in the values into the equation

8 = √(AD*16)

Square both sides

8² = AD*16

64 = AD*16

Divide both sides by 16

4 = AD

AD = 4

✔️Find AB using Pythagorean Theorem:

AB = √(BD² + AD²)

AB = √(8² + 4²)

AB = √(64 + 16)

AB = √(80)

AB = 8.9 (nearest tenth)

✔️Find sin x using trigonometric ratio formula:

Reference angle = x

Opposite side = BD = 8

Hypotenuse = AB = 8.944

Thus:

$sin(x) = \frac{opp}{hyp} = \frac{8}{8.944} = 0.894$ (nearest thousandth)

6 0

3 years ago