Given that cos (x) = k
what does cos (2x) = ?

Thanks in advance :)

To rationalize essentially means to get rid of the radical.

The trick to all of these it to multiply the top and bottom by a radical that will turn the radical you have into the square root of a perfect square.

Part a: [tex]\dfrac{1}{2\sqrt{5}}[/tex]

One approach that will always work, but not be the smallest radical, is to just multiply by the radical that is already there.

In the case of [tex]\dfrac{1}{2\sqrt{5}}[/tex], you can multiply the top and bottom by [tex]\sqrt{5}[/tex], so you'll really do this:

     [tex]\dfrac{1}{2\sqrt{5}}\cdot\dfrac{\sqrt{5}}{\sqrt{5}} = \dfrac{1\cdot\sqrt{5}}{2\sqrt{5}\sqrt{5}}[/tex]

But in the bottom, [tex]\sqrt{5}\cdot\sqrt{5} = \sqrt{25}=5[/tex], so your work finishes out like this:

    [tex]\dfrac{1\cdot\sqrt{5}}{2\sqrt{5}\sqrt{5}} = \dfrac{\sqrt{5}}{2\sqrt{25}} = \dfrac{\sqrt{5}}{2\cdot5} = \dfrac{\sqrt{5}}{10}[/tex]

Part b: [tex]\dfrac{4}{5\sqrt{2}}[/tex]

In the case of [tex]\dfrac{4}{5\sqrt{2}}[/tex], you can multiply the top and bottom by [tex]\sqrt{2}[/tex], so you'll really do this:

     [tex]\dfrac{4}{5\sqrt{2}}\cdot\dfrac{\sqrt{2}}{\sqrt{2}}[/tex]

But in the bottom, [tex]\sqrt{2}\cdot\sqrt{2} = \sqrt{4}=2[/tex], so your work finishes out like this:

    [tex]\dfrac{4}{5\sqrt{2}}\cdot\dfrac{\sqrt{2}}{\sqrt{2}} = \dfrac{4\sqrt{2}}{5\sqrt{4}}=\dfrac{4\sqrt{2}}{5\cdot{2}}=\dfrac{4\sqrt{2}}{10}[/tex]

Sometimes the fraction can be reduced, so this should be reduced to [tex]\dfrac{2\sqrt{2}}{5}[/tex].

Looking at all the others, they'll follow this same approach and they will all reduce at the end.

Here's part c, for one more example.

Part c: [tex]\dfrac{3}{3\sqrt{2}}[/tex]

In the case of [tex]\dfrac{3}{3\sqrt{2}}[/tex], you can multiply the top and bottom by [tex]\sqrt{2}[/tex], but you should also reduce the initial fraction first.

     [tex]\dfrac{3}{3\sqrt{2}} = \dfrac{1}{1\cdot\sqrt{2}} = \dfrac{1}{\sqrt{2}}[/tex]

And now proceed with rationalizing:

    [tex]\dfrac{1}{\sqrt{2}} \cdot\dfrac{\sqrt{2}}{\sqrt{2}}[/tex]

But in the bottom, [tex]\sqrt{2}\cdot\sqrt{2} = \sqrt{4}=2[/tex], so your work finishes out like this:

    [tex]\dfrac{1}{\sqrt{2}}\cdot\dfrac{\sqrt{2}}{\sqrt{2}} = \dfrac{1\cdot\sqrt{2}}{\sqrt{4}}=\dfrac{\sqrt{2}}{{2}}[/tex]

And you're done.

Hopefully that helps you finish the rest of those.

To check your answers, here is the answer key for the rest:

part d:[tex]\dfrac{2\sqrt{6}}{5}[/tex]

part e:[tex]\dfrac{4\sqrt{2}}{3}[/tex]

part f:[tex]\dfrac{4\sqrt{5}}{7}[/tex]

part g:[tex]\dfrac{5\sqrt{10}}{3}[/tex]

part d:[tex]\dfrac{5\sqrt{2}}{3}[/tex]

Answer:

Step-by-step explanation:

(a) 1/(2 sqrt5) x (sqrt 5)/(sqrt5) = (sqrt 5)/10

(b) 4/(5bsqrt2) x (sqrt2)/(sqrt2) = (4sqrt2)/10 = (2sqrt2)/5

(c) 3/(3 sqrt2) x (sqrt2)/(sqrt2) =(sqrt2)/2

(d) 12 /(5 sqrt6) x (sqrt6)/(sqrt6) = (12sqrt6)/30 = (2sqrt6)5

(e) 8/(3 sqrt2) x (sqrt2)/(sqrt2) = (8 sqrt2)/6 = (4 sqrt2)/3

(f) 20/(7 sqrt5) x (sqrt5)/(sqrt5) = (20 sqrt5)/35 = (4 sqrt5)/7

(g) 50/(3 sqrt10) x (sqrt10)(sqrt10) = (50 sqrt10)/30 = (5sqrt10)/3

(h) 10/(3 sqrt2) x (sqrt2)/(sqrt2) = (10 sqrt2)6 = (5 sqrt2)/3

Answer:

y = -x

Step-by-step explanation:

Slope-intercept form looks like this: y = mx + b, with m being the slope or rate of change and b being the y-intercept. We already know the rate of change, so we can put -1 as m: y = -1x + b. To find our y-intercept, we can plug the point (3, -3) into the equation and solve for b:

-3 = -1(3) + b

-3 = -3 + b

b = 0

So we have y = -1x + 0. This can be simplified to y = -x.

Answer:

C is the answer

Step-by-step explanation:

Because he have most tresures.

Answer: deep diving dan

Step-by-step explanation: he dived 26 times and found 104 treasure boxes

Answer:

w = 4

Step-by-step explanation:

6w+2=9w+14

9w-6w=14-2

3w=12

w=12/3

w=4

Answer:32.5

Step-by-step explanation: i used a calculator

Answer:

$162.50

Step-by-step explanation:

Answer:

10

Step-by-step explanation:

Answer: Its 10, so plot it on 10 in the number line

Step-by-step explanation: Since the subtraction signs cancel out, they make a addition sign. Henceforth its " 3+5+2" which would mean the sum is 10.

Answer:4

Step-by-step explanation:

Answer:

(a) SSS

................................

Answer:

x=5

Explanation:

y∝1x∴y=k⋅1x∴x⋅y=k;

When x=4;y=10∴4⋅10=kork=40.

So variation equation is x⋅y=40

When y=8;x=408=5∴x=5 [Ans]

Step-by-step explanation:

not surre

Answer:

6.67

Step-by-step explanation:

10=4

y=6

10×4/6

Answer:

74 + 43[tex]\sqrt{3}[/tex]

Step-by-step explanation:

For this problem, let's say side x is 2 + [tex]5\sqrt{3}[/tex] and side y is 7 + [tex]4\sqrt{3}[/tex].

To find the area of a rectangle, you need to multiply both height and width, and in this case, x and y.

(x)(y) = 14 + 8[tex]\sqrt{3}[/tex] + 35[tex]\sqrt{3}[/tex] + 60

= 74 + 43[tex]\sqrt{3}[/tex]

Answer:

divide 8/3

8/3 = 2

and for -11/3 it = -4 because it would originally = to  -3.66666666667 and u have to round it.

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for the second picture

make it into an improper fraction

-2 1/2 = -5/2

and for 6 1/2 it = to 13/2

now, to plot it on the line you have to divide

divide -5/2 = -2.5

and divide 13/2 = 6.5

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Hope this helps!

Answer:

ABCD dilates in a scale of 1/3 by the center of A followed by a reflection of C.

AD/AD = 1/3

Step-by-step explanation:

Answer:

Y=-3

You see y=-3 does pass through 2,3 and is also parallel to y=6

Answer:

D) 6.48 x 10⁻³

Step-by-step explanation:

to get an exponent of -3 means you move the decimal point three spaces to the right

2) 8,300,000

3) 970,000

4) 5.01 x 10⁻²  (picture)         5.01 x 10⁻¹ (question)

5) 0.000499

Answer:

3c-2

Step-by-step explanation:

Hope it helps!!!!!!!

Answer:

dont understand

Step-by-step explanation:

Answer:

just rearrange the equation. I did the first one. Do the same for the rest.

2x - 3y = 9

-3y = -2x + 9

y = -2/-3x + 9/-3

y = 2/3x - 3

Step-by-step explanation:

Answer:

Step-by-step explanation:

9th square number = 81

5th square number=25

81-25=56

56 is a multiple of 8 as 8 x 7=56

Answer:

Mean = 9

Step-by-step explanation:

The mean is the average of a data set.  Given the values, 2, 9, 10, 12, 12:

Add all the numbers in the data set, and divide its sum by the number of items in the set:

Mean = [tex]\frac{2+9+10+12+12}{5}[/tex] =  [tex]\frac{45}{5}[/tex] = 9

Therefore, the mean of the given data set is 9.

Answer:

Isolate the variable by dividing each side by factors that don't contain the variable.

Inequality Form:

x < 1

Interval Notation:

( − ∞, 1)

Answer:

(x+3)(x-3)

Step-by-step explanation:

We know that [tex](a+b)(a-b)=a^2+b^2\\[/tex]

So, here we have x² and 9, which can be written as 3².

Therefore, we can have x=a and 3=b

So we get

(x+3)(x-3)

To check that we are correct, we can expand the brackets:

x²-3x+3x-9

=x²-9

Answer:

=2x+4

Step-by-step explanation:

Let's simplify step-by-step.

5x+4−3x

=5x+4+−3x

Combine Like Terms:

=5x+4+−3x

=(5x+−3x)+(4)

=2x+4

Answer:

2x+4...

Step-by-step explanation:

Hopefully it helps

Answer:

hannah is paying 60 cents per pound or dried fruit

Step-by-step explanation:

1.5÷2.5=0.6

Answer:

The first numbers in the sets are input and the second numbers are outputs.

1. {(1, 1), (2, 3), (3,5)}

2. {(6,2), (5, 3), (4,8)}​

Answer:

11,765

Step-by-step explanation: 1 word make up 0,024 minute so 500 words 500.0,024 = 11,765 minutes

Answer:

3x + y = 15

Step-by-step explanation:

y/3 + x = 5

You can first move the x and y variable around so it fits the standard linear equation format.

x + y/3 = 5

In order to make it look more like the standard format, you can multiply both sides of the equation by 3 to get rid of the 3 in the denominator of the y variable.  It would look like this:

3 ( x +y/3) = 3 ( 5 )

When you multiply this out, you get this:

3x + y = 15