Use the order of operations to find the value of the following expression. (4-9)(-4-1)

1 answer:

3 0

Answer is 25

Step by step.

We know PEMDAS is the order of operations, so Parentheses is first.

(4-9) (-4-1)
(-5) (-5)

Now multiply (-5)(-5)

Answer is 25

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The sum of two numbers is 18. Twice the first number (x) minus the second number (y) is 6. Find the two numbers

ki77a [65]

Answer:

8 and 10

Step-by-step explanation:

Set the first number as x, the second as y

x+y=18

2x-y=6

This is an binary system of first order equations

3x=24

x=8

y=10

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Suppose cos(x)= -1/3, where π/2 ≤ x ≤ π. What is the value of tan(2x). EDGE

AVprozaik [17]

Answer:

Step-by-step explanation:

We are given that:

$\displaystyle \cos x = -\frac{1}{3}\text{ where } \pi /2 \leq x \leq \pi$

And we want to find the value of tan(2<em>x</em>).

Note that since <em>x</em> is between π/2 and π, it is in QII.

In QII, cosine and tangent are negative and only sine is positive.

We can rewrite our expression as:

$\displaystyle \tan(2x)=\frac{\sin(2x)}{\cos(2x)}$

Using double angle identities:

$\displaystyle \tan(2x)=\frac{2\sin x\cos x}{\cos^2 x-\sin^2 x}$

Since cosine relates the ratio of the adjacent side to the hypotenuse and we are given that cos(<em>x</em>) = -1/3, this means that our adjacent side is one and our hypotenuse is three (we can ignore the negative). Using this information, find the opposite side:

$\displaystyle o=\sqrt{3^2-1^2}=\sqrt{8}=2\sqrt{2}$

So, our adjacent side is 1, our opposite side is 2√2, and our hypotenuse is 3.

From the above information, substitute in appropriate values. And since <em>x</em> is in QII, cosine and tangent will be negative while sine will be positive. Hence: