All categories

3 years ago

Solve the equation z^2 + 3z - 18 = 0

Mathematics

1 answer:

maksim [4K]3 years ago

7 0

This is a quadratic equation. You have to factor it.

You have to find two numbers that meet the following requirement:

-When multiplied, is equal to -18.

-When added, is equal to 3.

The two numbers are 6 and -3.

Now factor it:

(x + 6)(x - 3)

So x = -6 or x = 3

You might be interested in

Find the average montly loss of a conpany with a loss of 36,000 for one year. What's the equation?

algol13

36,00÷ 12= 3,000 so that would be the average monthly loss.

5 0

3 years ago

Expand the binomial<br> <img src="https://tex.z-dn.net/?f=%28x-%5Cfrac%7B2%7D%7B5%7D%29%5E%7B2%7D" id="TexFormula1" title="(x-\f

kkurt [141]

Answer:

$(x- \frac{2}{5})^{2} = x^2 -\frac{4}{5}x + \frac{4}{25}$

Step-by-step explanation:

You have two methods to expand this binomial.

Method 1

If you have the expression:

$(x- \frac{2}{5})^{2}$

You can write the expression it in the following way:

$(x-\frac{2}{5})^{2}=(x-\frac{2}{5})(x-\frac{2}{5})$

Then, apply the distributive property:

$(x-\frac{2}{5})(x-\frac{2}{5}) = x^2 -\frac{2}{5}x -\frac{2}{5}x+ (\frac{2}{5})\frac{2}{5}$

Simplify the expression:

$(x-\frac{2}{5})^2= x^2 -\frac{4}{5}x+ (\frac{4}{25})$

---------------------------------------------------------------------------------------

Method 2

For any expression of the form:

$(a-b)^2$

Its expanded form will be:

$(a-b)^2= a^2 -2ab + b^2$

$a = x$

$b =\frac{2}{5}$

$(x- \frac{2}{5})^{2} = x^2 - 2x\frac{2}{5} + (\frac{2}{5})^2$

$(x- \frac{2}{5})^{2} = x^2 -\frac{4}{5}x + \frac{4}{25}$

3 0

3 years ago

Show that 551 is a rational by writing it in the form a/b, where a and b are integers

igor_vitrenko [27]

Answer:

551/1

Step-by-step explanation:

$551 = \dfrac{551}{1}$

Any integer can be written as a rational number with a denominator of 1.

3 0

3 years ago

-a^2+46a-480=0<br> a - ?

sattari [20]

a = 30
a = 16

-a² + 46a -480 = 0

(-a + 30) (a -16) = 0
(-a)(a) + (-a)(-16) + 30(a) + 30(-16) = 0
-a² + 16a + 30a -480 = 0
-a² + 46a - 480 = 0

(-a + 30) = 0 ; (a - 16) = 0
-a = -30 ; a = 16
a = 30

To check:
a = 30
-(30)² + 46(30) - 480 = 0
-900 + 1380 - 480 = 0
480 - 480 = 0
0 = 0

a = 16
-(16)² + 46(16) - 480 = 0
-256 + 736 - 480 = 0
480 - 480 = 0
0 = 0

5 0

3 years ago

Read 2 more answers

ABC is formed by two tangents intersecting outside of a circle. If minor arc AC = 98°, what is the measure of ∠ABC?

gregori [183]

It's 82 degrees. Subtract your minor arc (98) by 360 to get your major arc, which is 262. Then, subtract 98 (minor arc) from 262 (major arc), which gives you 164. Finally, divide 164 by 2 to get angle ABC.

8 0

3 years ago

Read 2 more answers

Solve the equation z^2 + 3z - 18 = 0​

Solve the equation z^2 + 3z - 18 = 0