Write log1/4(1/64)=3 in exponential form

Answer:

step 1: =4% of £500

=20

=20 × 5 years

= 100

= £500 + £100

=£600 ....therefore Rob will have £600 in his bank account after years.

Answer:

[tex]\cot(x)+\cot(\frac{\pi}{2}-x)[/tex]

[tex]\cot(x)+\tan(x)[/tex]

[tex]\frac{\cos(x)}{\sin(x)}+\frac{\sin(x)}{\cos(x)}[/tex]

[tex]\frac{1}{\sin(x)}(\cos(x)+\sin(x)\frac{\sin(x)}{\cos(x)})[/tex]

[tex]\csc(x)(\cos(x)+\sin(x)\frac{\sin(x)}{\cos(x)})[/tex]

[tex]\csc(x)[\frac{\cos(x)\cos(x)}{\cos(x)}+\sin(x)\frac{sin(x)}{\cos(x)}][/tex]

[tex]\csc(x)[\frac{\cos(x)\cos(x)+\sin(x)\sin(x)}{\cos(x)}][/tex]

[tex]\csc(x)[\frac{\cos^2(x)+\sin^2(x)}{\cos(x)}][/tex]

[tex]\csc(x)[\frac{1}{\cos(x)}][/tex]

[tex]\csc(x)[\sec(x)][/tex]

[tex]\csc(x)[\csc(\frac{\pi}{2}-x)][/tex]

[tex]\csc(x)\csc(\frac{\pi}{2}-x)[/tex]

Step-by-step explanation:

I'm going to use [tex]x[/tex] instead of [tex]\theta[/tex] because it is less characters for me to type.

I'm going to start with the left hand side and see if I can turn it into the right hand side.

[tex]\cot(x)+\cot(\frac{\pi}{2}-x)[/tex]

I'm going to use a cofunction identity for the 2nd term.

This is the identity: [tex]\tan(x)=\cot(\frac{\pi}{2}-x)[/tex] I'm going to use there.

[tex]\cot(x)+\tan(x)[/tex]

I'm going to rewrite this in terms of [tex]\sin(x)[/tex] and [tex]\cos(x)[/tex] because I prefer to work in those terms. My objective here is to some how write this sum as a product.

I'm going to first use these quotient identities: [tex]\frac{\cos(x)}{\sin(x)}=\cot(x)[/tex] and [tex]\frac{\sin(x)}{\cos(x)}=\tan(x)[/tex]

So we have:

[tex]\frac{\cos(x)}{\sin(x)}+\frac{\sin(x)}{\cos(x)}[/tex]

I'm going to factor out [tex]\frac{1}{\sin(x)}[/tex] because if I do that I will have the [tex]\csc(x)[/tex] factor I see on the right by the reciprocal identity:

[tex]\csc(x)=\frac{1}{\sin(x)}[/tex]

[tex]\frac{1}{\sin(x)}(\cos(x)+\sin(x)\frac{\sin(x)}{\cos(x)})[/tex]

[tex]\csc(x)(\cos(x)+\sin(x)\frac{\sin(x)}{\cos(x)})[/tex]

Now I need to somehow show right right factor of this is equal to the right factor of the right hand side.

That is, I need to show [tex]\cos(x)+\sin(x)\frac{\sin(x)}{\cos(x)}[/tex] is equal to [tex]\csc(\frac{\pi}{2}-x)[/tex].

So since I want one term I'm going to write as a single fraction first:

[tex]\cos(x)+\sin(x)\frac{\sin(x)}{\cos(x)}[/tex]

Find a common denominator which is [tex]\cos(x)[/tex]:

[tex]\frac{\cos(x)\cos(x)}{\cos(x)}+\sin(x)\frac{sin(x)}{\cos(x)}[/tex]

[tex]\frac{\cos(x)\cos(x)+\sin(x)\sin(x)}{\cos(x)}[/tex]

[tex]\frac{\cos^2(x)+\sin^2(x)}{\cos(x)}[/tex]

By  the Pythagorean Identity [tex]\cos^2(x)+\sin^2(x)=1[/tex] I can rewrite the top as 1:

[tex]\frac{1}{\cos(x)}[/tex]

By the quotient identity [tex]\sec(x)=\frac{1}{\cos(x)}[/tex], I can rewrite this as:

[tex]\sec(x)[/tex]

By the cofunction identity [tex]\sec(x)=\csc(x)=(\frac{\pi}{2}-x)[/tex], we have the second factor of the right hand side:

[tex]\csc(\frac{\pi}{2}-x)[/tex]

Let's just do it all together without all the words now:

[tex]\cot(x)+\cot(\frac{\pi}{2}-x)[/tex]

[tex]\cot(x)+\tan(x)[/tex]

[tex]\frac{\cos(x)}{\sin(x)}+\frac{\sin(x)}{\cos(x)}[/tex]

[tex]\frac{1}{\sin(x)}(\cos(x)+\sin(x)\frac{\sin(x)}{\cos(x)})[/tex]

[tex]\csc(x)(\cos(x)+\sin(x)\frac{\sin(x)}{\cos(x)})[/tex]

[tex]\csc(x)[\frac{\cos(x)\cos(x)}{\cos(x)}+\sin(x)\frac{sin(x)}{\cos(x)}][/tex]

[tex]\csc(x)[\frac{\cos(x)\cos(x)+\sin(x)\sin(x)}{\cos(x)}][/tex]

[tex]\csc(x)[\frac{\cos^2(x)+\sin^2(x)}{\cos(x)}][/tex]

[tex]\csc(x)[\frac{1}{\cos(x)}][/tex]

[tex]\csc(x)[\sec(x)][/tex]

[tex]\csc(x)[\csc(\frac{\pi}{2}-x)][/tex]

[tex]\csc(x)\csc(\frac{\pi}{2}-x)[/tex]

Answer:

For zero number the cost is zero and the rate of change is 25.

This is the indication of the proportional relationship

The equation is:

where y - cost, x - number of pairs of shoes, 25 - constant of proportionality

Answer:

87  ?

Step-by-step explanation:

Answer:

A. 80

Step-by-step explanation:

T° = H°

if you rotated the first shape to match the second one, H° would fall on T°

Answer:

I think that the ratio would be 12:11

Step-by-step explanation:

Because if you multiply 3 and 9 then you do 12:11

Step-by-step explanation:

A number,c times two equal forty.

Answer:

The following statement means that the cost of 2 months' worth of gigabytes costs $40.

Step-by-step explanation:

Go shop Quelenasboutique on Esty!

Answer : $36

Explanation:

To find the sale price we can set up a proportion. 25/100 = x/48. We keep the 100 and 48 both on the bottom of the fraction since they represent the "whole". x represents the discount off the full price of the dress. To solve this proportion, we cross multiply, yielding 48 * 25 = 100x. Alternatively, if you notice that 25/100 simplifies to 1/4, we can use 1/4 in our proportion instead of 25/100, thus, 1/4 = x/48. Then, cross multiplying, we get 48 = 4x, so x = 12. Then we subtract this discount from the original price yielding 48 – 12 = 36; thus, she paid $36 for the dress.

25% = 25/100

25100=x48

14=x48

(1) * (48) = (4) * (x)

48 = 4x

(48)/4 = (4x)/4

12 = x

The discount is $12.

$48 – $12 = $36

Answer:

https://www.mrelisara.com/uploads/5/8/7/3/58736993/chapter_2_review_ws_answers.pdfStep-by-step explanation:

Answer:

b= 64 m

Step-by-step explanation:

[tex]b^{2}[/tex] + [tex]48^{2}[/tex] = [tex]80^{2}[/tex]

[tex]b^{2}[/tex] = [tex]80^{2}[/tex] - [tex]48^{2}[/tex]

[tex]b[/tex] = [tex]\sqrt{80^{2}-48^{2} }[/tex]

 = [tex]64[/tex] m

Answer:

is it math

Step-by-step explanation:

omg I really really really hate math

1. x + 6 = 8

8 - 6 = 2

x = 2

2. 12 + y = 21

21 - 12 = 9

x = 9

3. h - 7 = 13

13 - 7 = 6

x = 6

4. 35 = 50 - 15

p = 50

5. 17 = 8 + 9

e = 8

6. 0 + 10 = 10

k = 10

Hope this helps! Have a wonderful day!

Answer:

212.5

Step-by-step explanation:

For triangles, A = (bh)/2

You can do 15+25 to find the base, which is 40. From here do 17*40/2. You get 340. However, you need to remove the right triangle on the left side.

Again do 17*15/2, which you get 127.5.

From here subtract 127.5 from 340 and get 212.5

Answer:

Step-by-step explanation:

Answer:

not 35

Step-by-step explanation:

it 18

Answer:

Original coordinates of F is (2,1)

Step-by-step explanation:

when DEFG is dilated by a scale factor of 1/2 with a dilation center of (0, 0), coordinates of point F' will be

( 2 x 1/2, 1 x 1/2 ) = ( 1, 1/2 )

Answer:

48.1 cubic meters or 48100000 cubic centimeters

Step-by-step explanation:

Firstly we need to find the radius.To find that we divide the diameter by two.3.5÷2=1.75

Volume of Cylinder=Pi×radius squared×height

Lastly 3.14×1.75×1.75×5=48.1

I hope this helps you in any way:)

Answer:

$7,359.65

Step-by-step explanation:

The computation of the amount that to be deposited is shown below:

Here we have to calculate the present value

As we know that

Present value = future value ÷(1+ rate of interest)^years

where,

rate of interest = 12.2% ÷ 4 = 3.05%

And, the years is = 5 × 4 = 20

Now the present value is

= $13,422 ÷ (1+ 3.05%)^20

= $7,359.65

Answer: The measurement of angle B is 50 degrees

Step-by-step explanation: we know all triangles add up to 180 degrees so substitute 40 with a degrees and solve

Step-by-step explanation:

According to the Triangle Sum Theorem, all angles in triangle are sum of 180⁰. This means that m<a + m<b + m<c = 180⁰. You will first solve for a.

m<a + m<b + m<c = 180⁰

2a⁰ + a + 10⁰ + a⁰ = 180⁰ combine like terms.

2a⁰ + a + a⁰ + 10⁰ = 180⁰

4a⁰ + 10⁰ = 180⁰ subtract 10 from both sides.

4a⁰ + 10⁰ - 10⁰ = 180⁰ - 10⁰

4a⁰ = 170⁰ Divide 4 from both sides.

4a⁰ / 4 = 170⁰ / 4

a = 42.5⁰

Now that you found a, plug 42.5⁰ in place of in all angles and solve.

m<a :-

2a⁰

2(42.5)⁰

85⁰

m<b :-

a + 10⁰

42.5⁰ + 10⁰

52.5⁰

m<c :-

a⁰

42.5⁰

m<a = 85⁰

m<b = 52.5⁰

m<c = 42.5⁰

Remember that all angle must sum up to 180⁰ in a triangle. So we will now add all of our angle to find it if it equals 180⁰.

m<a + m<b + m<c = 180⁰

85⁰ + 52.5⁰ + 42.5⁰ = 180⁰

180⁰ = 180⁰

Thus, m<b = 52.5⁰.

Hope this helps, thank you :) !!

Answer:

Step-by-step explanation:

this is the start of your mad algebra skilz.. it does take constant practice, like anything you want to get better at :)  keep trying

this is called  "Distribution" and is used often

3(-5[tex]y^{2}[/tex] -3)

-15[tex]y^{2}[/tex] +9

if you need more explanation just put your questions at the comments of this problem ... i'll see them   :)

Answer:

Germany - 90

Step-by-step explanation:

Here are the options to this question

Germany 90

Sweden   78

Japan       63

Canada    75

The appropriate answer should be a multiple of 2, 3, 5, 6, and 9. That is when the number is divided by 2, 3, 5, 6, and 9 it should have a remainder of zero.

90 / 2 = 45

90 / 3 = 30

90 / 5 = 18

90 / 6 = 15

90 / 9 = 10

Thus, the appropriate number is 90

When 78 is divided by 5 and 9, the remainder is not zero

When 63 is divided by 2, 5 and 6, the remainder is not zero

When 75 is divided by 2, 3, 6 and 9, the remainder is not zero

Volume of the single prism will be : 576 inches

In geometry a Rectangular prism is a polyhedron with two congruent and parallel bases. It has six faces and have twelve edges.

Volume of a Rectangular prism = L * B * H

                                                      = 24 * 6 * 24

                                                    = 3456 inch^3

Since , it consists of six identical Rectangular prisms

Volume of single prism will be  = 3456 / 6

                                                      576 inch^3

Learn more about  Rectangular Prism:

https://brainly.com/question/21308574?referrer=searchResults

#SPJ2

Answer:

r=C2

Step-by-step explanation:

C=2r is the equation to find circumference

She needs to work backwards in this case, so:

r=C2

r=The circumference she knows x 2 x 3.14(or 3.14159265359)

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I hope this helped!

Answer:

1. 151.29 in.²

2. 413 km²

3. 75 cm²

Step-by-step explanation:

1. 12.3 in. × 12.3 in. = 151.29 in.²

2. 17.5 km × 23.6 km = 413 km²

The third is a parallelogram. To find the area of a parallelogram you multiply the base and height.

3. 15 cm × 5 cm = 75 cm²

For further calculation steps, look at these images:

These images are about multiplication and the decimal numbers in the problems have been converted to fractions.