Graph each pair of ordered pairs. Then find the distance between the points. Round to the nearest tenth if necessary.

1. (4, 3), (1, –1)

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:

$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:

3

Step-by-step explanation:

Answer:

3

Step-by-step explanation:

yes

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.

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:

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

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:

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:

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:

study lol

Step-by-step explanation:

Answer:

87  ?

Step-by-step explanation:

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:

x = 10.

Step-by-step explanation:

x + (-8) = 2.

First, isolate x by adding 8 to both sides.

x = 8 + 2.

Next, solve.

x = 10.

Finally, you can come to the conclusion that x = 10. Always plug in your answer to make sure it works.

10 - 8 = 2.

2 = 2.

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:

4ln x +ln 3-lnx

4ln x -ln x+ln3

3ln x+ln 3

ln(3x+3)is equivalent.

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

Answer:                         t=33

Step-by-step explanation:

Answer:

t = 33

Step-by-step explanation:

t/3 = 11

t = 11 × 3

t = 33

Answer:

I hope if one of these help.

Step-by-step explanation:

(4 - 3i) + (2 + i )(5 - 2i)

=16 - 2i

If you simplify your answer will be: 16−2i

1) (3+2i)-(1-6i)

2) 4i+3-6+i-1

3) 5i(3-2i)

4) (5+3i)(2-3i)

5) (2+i)(2-i)

1) (3 + 2i) - (1 - 6i)

 3 + 2i - 1 + 6i

 2 + 8i

2) 4i + 3 - 6 + i - 1

  5i - 3 - 1

  5i - 4

3) 5i ( 3 - 2i )

  15i - 10i^2

  15i - 10 ( -1 )

  15i + 10

4) ( 5 + 3i ) ( 2 - 3i )

  10 - 15i + 6i - 9i^2

  10 - 9i - 9i^2

  10 - 9i - 9 ( -1 )

  10 - 9i + 9

 - 9i + 19

5) ( 2 + i ) ( 2 - i )

   4  - 2i + 2i - i^2

   4 - i^2

   4 - (-1)

   5

1) 2 + 8i

2) -4 + 5i

3) 10 + 15i

4) 19 - 9i

5) 5

The operations with imaginary numbers are equal to those of the real numbers considering i as a variable, but with a property that allows to simplify the expression more, that is that i squared equals -1. Taking this property into account, we solve the expressions like this:

1) (3 + 2i) - (1-6i) = 3 + 2i - 1 + 6i = 2 + 8i

2) 4i + 3-6 + i-1 = 5i - 4 = -4 + 5i

3) 5i (3-2i) = 5i*3 - 5i*2i = 15i - 10i^2 = 15i - 10(-1) = 15i + 10 = 10 + 15i

4) (5 + 3i) (2-3i) = 5*2 - 5 3i + 3i*2 - 3*3i^2 = 10 - 15i + 6i - 9i^2 = 10 - 9i - 9(-1) = 10 - 9i + 9 = 19 - 9i

5) (2 + i) (2-i) = 2*2 - 2*i + 2*i - i^2 = 4 - 2i + 2i - (-1) = 4 + 1 = 5

I hope one of these help:)

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:

Pi ~ 3.14

That is probably the best measure.

Step-by-step explanation:

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:

-3

Step-by-step explanation:

you can tell that the awnser is negative because the coordinates of Y go down from 3 to 0.