d=18+34 d=22t system of equations

Answer:  see proof below

Step-by-step explanation:

Use the following Sum to Product Identities:

sin (A) - sin (B) = 2 cos (A+B)/2 · sin (A-B)/2

sin (A) + sin (B) = 2 sin (A+B)/2 · cos (A-B)/2

Given:  sin Ф = k sin β      -->   (sin Ф)/(sin β) = k

Proof RHS → LHS

[tex]\text{RHS:}\qquad \qquad \qquad \dfrac{k-1}{k+1}\tan\dfrac{\theta+\beta}{2}[/tex]

[tex]\text{Given:}\qquad \qquad \dfrac{\frac{\sin \theta}{\sin \beta}-1}{\frac{\sin \theta}{\sin \beta}+1}}\cdot \tan\dfrac{\theta +\beta}{2}[/tex]

[tex]\text{Simplify:}\qquad \qquad \dfrac{\frac{\sin \theta}{\sin \beta}-\frac{\sin \beta}{\sin \beta}}{\frac{\sin \theta}{\sin \beta}+\frac{\sin \beta}{\sin \beta}}}\cdot \tan\dfrac{\theta +\beta}{2}\\\\\\.\qquad \qquad \qquad = \dfrac{\sin \theta -\sin \beta}{\sin \theta +\sin \beta}\cdot \tan\dfrac{\theta +\beta}{2}[/tex]

[tex]\text{Product to Sum:}\qquad \quad \dfrac{2\cos \frac{\theta+\beta}{2}\cdot \sin \frac{\theta-\beta}{2}}{2\sin \frac{\theta+\beta}{2}\cdot \cos \frac{\theta-\beta}{2}}\cdot \tan\dfrac{\theta +\beta}{2}[/tex]

[tex]\text{Expand:}\qquad \qquad \dfrac{2\cos \frac{\theta+\beta}{2}\cdot \sin \frac{\theta-\beta}{2}}{2\sin \frac{\theta+\beta}{2}\cdot \cos \frac{\theta-\beta}{2}}\cdot \dfrac{\sin\frac{\theta +\beta}{2}}{\cos \frac{\theta +\beta}{2}}[/tex]

[tex]\text{Simplify:}\qquad \qquad \quad \quad \dfrac{\sin \frac{\theta +\beta}{2}}{\cos \frac{\theta+ \beta}{2}}\\\\\\.\qquad \qquad \qquad \quad =\tan\dfrac{\theta +\beta}{2}[/tex]

 [tex]\text{LHS = RHS:}\quad \tan\dfrac{\theta +\beta}{2}=\tan\dfrac{\theta +\beta}{2}\quad \checkmark[/tex]

Answer:

Step-by-step explanation:

In this problem. we are required to solve for the diameter of a circle.

Given data

circumference of circle c= 7.54mm

we know that the expression for the circumference is given as

c= 2πr

We can substitute our given data to solve for r

7.54= 2*3.142*r

7.54=6.284*r

divide both sides by 6.284 we have

r= 7.54/6.284

r= 1.199

diameter = 2*r

diameter= 1.199*2

diameter= 2.399

to  the nearest tenth

diameter= 2.40mm

Answer:

13

Step-by-step explanation:

12y = 156

y = 156 ÷ 12

y = 13

Answer:

yes it is a function

Step-by-step explanation:

if you put three lines on the line of the line passes more than 1 it is not a function

Answer:

The simplified answer is -2n+6

Step-by-step explanation:

All you have to do is simplify terms. -7n and 5n are terms you can combine, giving you -2n and +6 cant be simplified

Answer:

$16.56

Step-by-step explanation:

Answer:

Carlos should get back $16.56

I hope this helps you

Answer:

2x² + 5x - 4y - 7

Step-by-step explanation:

combine the like terms -6y and 2y

2x² + 5x - 6y + 2y - 7

2x² + 5x - 4y - 7

Answer:

16

Step-by-step explanation:

(75/100)*x=12

75x=12*100

75x=1200

x=1200/75

x=16

Answer:

16

Step-by-step explanation:

divide 75 by 100

multiply 12 by 100

which is 1200

divide 1200 by 75

and your answer is 16

Answer:

(7+x)-5=42

Step-by-step explanation:

Follow me for more answers If you like my way of solving

Answer: GIVE MEEEE BRAINLIEST PLEASE

(−1)2−2+(−3)2+(−4)2

=24

Step-by-step explanation:

(−1)2−2+(−3)2+(−4)2

=24

Answer:

205 : 41

or 41 cinnamon bars

Answer:

3

Step-by-step explanation:

So we have the function:

[tex]f(x)=3x^2+2x-5[/tex]

To evaluate the value of f(-2), substitute -2 for x. Thus:

[tex]f(-2)=3(-2)^2+2(-2)-5[/tex]

Square first:

[tex]f(-2)=3(4)+2(-2)-5[/tex]

Multiply:

[tex]f(-2)=12-4-5[/tex]

Now, subtract:

[tex]f(-2)=8-5=3[/tex]

So:

[tex]f(-2)=3[/tex]

And we're done!

Answer:

Red balls =  84     Blue balls =  140

Step-by-step explanation:

Ok so there are 225 marbles

And ratio here is Red : Blue = 3 : 5

So Red marbles = 3x whereas Blue marbles = 5x

Therefore,

3x + 5x = 225

8x = 225

x = 28.125 = 28

Red balls = 28*3 = 84     Blue balls = 28*5 = 140

(Pls check whether total no of balls is 224)

one ans six are infinite

Answer:

Domain = [0, ∞).

Step-by-step explanation:

he profit, in dollars, when the company sells x shirts can be found using the function

[tex]f(x)=8x-40[/tex]

For x=0,

[tex]f(0)=8(0)-40=-40[/tex]

It means, if company sells 0 shirts, then company makes loss (because of negative sign) of $40.

For x=5,

[tex]f(5)=8(5)-40=0[/tex]

It means, if company sells 5 shirts, then company makes profit of $0 means no loss no profit.

For x=10,

[tex]f(10)=8(10)-40=40[/tex]

It means, if company sells 10 shirts, then company makes profit of $40.

Domain is the set of input values.

We know that number of shirts can not be negative, therefore the value of x is always greater than or equal to 0.

Domain = [0, ∞).

Therefore, the domain for the function is [0, ∞).

Answer:

The answer is 0.8-0.3=0.5.

Answer:

Step-by-step explanation:

y = 6x − 4

y = 5x − 3

A: chose a value for x(input) and get the out put (y) because the equation already in the slope intercept mode:y=mx+b

x                   y=6x-4                  y=5x-3

1                    y=2                        y=2

2                    y=8                        y=7

0                     -4                            -3

slope  :

y=6x-4    slope is 6            y intercept(0,-4)

y=5x-3      slope is 5          y intercept (0,-3)

solution of the pair of equation is  the point of intersection :

6x-4=5x-3

6x-5x=-3+4

x=1   and y=6x-4   ⇒ y=6-4=2

Answer:

x = 3

Step-by-step explanation:

Step 1:

6x + 5 = 23

Step 2:

6x = 18

Answer:

x = 3

Hope This Helps :)

Step-by-step explanation:

thats what I got hope this helped you out

Answer:

BC = 26

Step-by-step explanation:

Given that:

B is the midpoint of AC

Then AC = AB + BC

AC = 8x - 20 and AB = 3x - 1

Then,

8x - 20 = (3x - 1) + BC

8x - 20 - (3x - 1) = BC

8x - 20 - 3x + 1 = BC

5x - 19 = BC

But AB = BC

5x - 19 = 3x - 1

5x - 3x = - 1 + 19

2x = 18

x = 9

Hence,

Since BC = AB = 3x - 1

3(9) - 1

27 - 1

= 26

Answer:

a = 5.333..  or 5 1/3

Step-by-step explanation:

I am not sure what your question is but it looks like you need to solve for  a.

Based on that fact:

6a - 10 = 12 - 6 +  3a      you multiply -1  by each term in the parenthesis

Then it is simple algebra

6a -10          =        6+ 3a

     +10               + 10                   add 10 to both sides

6a                =  16  + 3a

-3a                         -3a                 add  -3a to both sides

3a  = 16                     Divide both sides by 3

a = 5.3333

Answer:

The answer is 10

Step-by-step explanation:

Answer:

Answer is 10!

Step-by-step explanation:

Answer:

x+8 i used mathaway i recommend it for math

[tex]5x - 4x + 8\\x + 8\\\\ahi queda creo \\pero si esque te confundiste y pusiste "-" en vez de poner "=" seria:\\5x = 4x + 8\\x = 8\\xd 7w7[/tex]

Answer:

PR=71

Step-by-step explanation:

visualize:

P                Q               R

O-------------O-------------O

       13               58

so if PQ + QR = PR, than 13+58=PR

13+58=71

PR=71

The value of the segment PR will be 71.

A line segment in geometry is a section of a line that has two clearly defined endpoints and contains every point on the line that lies within its confines.

Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

Given that the value of the segment Qr=58 and pq=13. The value of segment PR will be calculated as below:-

PR = QR + PQ

PR  = 13 + 58

PR = 71

Therefore, the value of the segment PR will be 71.

To know more about a line segment follow

https://brainly.com/question/18315903

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Answer:

distributive property of multiplication over addition

Step-by-step explanation:

hope this helps! :)

Answer:

Pemdas

Step-by-step explanation:

parenthesis

exponents

multiplication

division

addition

subtraction