Solve the simultaneous equations. You must show all your working to find x and y. 1/2x -3y = 9 5x y + y = 28

Answer: see proofs below

Step-by-step explanation:

Proofs are like a puzzle that you have to unravel.

You can manipulate the left side to get the right side (LHS → RHS)

                                                or

You can manipulate the right side to get the left side (RHS → LHS)

You will need to use Pythagorean Identities, Sum and Difference Identities, and/or Double Angle Identities when manipulating one of the sides.

Use the following Identities:

cos 2A = cos²A - sin²A

sin 2A = 2 cosA · sinA    Note that A can be substituted with 2A        

sin 3A = 3 sinA - 4sin³A

cos 3A = 4cos³A - 3cosA

***********************************************************************************

e) Prove: 4 sin A · cos³A - 4 cos A · sin³A = sin(4A)

LHS → RHS

Given:         4 sin A · cos³A - 4 cos A · sin³A

Factor:        4 sin A · cos x (cos²A - sin²A)

                  2(2 sin A · cos A)(cos²A - sin²A)

Double Angle Identity:  2(sin 2·A)(cos 2·A)

                                       2 sin (2A) · cos (2A)

Double Angle Identity:  sin (2·2A)

                                       sin 4A

Proven:  sin 4A = sin 4A   [tex]\checkmark[/tex]

*****************************************************************************************

f) Prove: 4 sin³A · cos 3A + 4 cos³A · sin 3A = 3 sin(4A)

LHS → RHS

Given:          4 sin³A · cos 3A + 4 cos³A · sin 3A

Triple Angle Identity:   4sin³A (4cos³A - 3 cosA) + 4cos³A (3sinA - 4sin³A)

Expand:      16sin³A · cos³A - 12sin³A · cosA + 12cos³A · sinA - 16sin³A · cos³A

Simplify:      12cos³A · sinA - 12sin³A · cosA

Expand:        6cos²A(2cosA · sinA) - 6sin²A(2cosA · sinA)

Double Angle Identity: 6cos²A(sin 2A) - 6sin²A(sin 2A)

Factor:       6sin 2A (cos²A - sin²A)

Double Angle Identity:  6sin 2A (cos 2A)

                                       3(2sin 2A · cos 2A)

Simplify:     3sin (2·2A)

                  3 sin 4A

Proven: 3sin 4A = 3sin4A   [tex]\checkmark[/tex]

Answer:

B. 13.8

Step-by-step explanation:

The five-number summary consists of five items which is usually displayed on a box plot, and can be represented in ascending order.

The five-number summary given: 3.5, 12, 19.1, 25.8, 31.8, represents the following in ascending order:

1. The minimum value = 3.5

2. First quartile (Q1) = 12

3. The median = 19.1

4. Third quartile (Q3) = 25.8

5. The maximum value = 31.8

The interquartile range = Q3 - Q1

Therefore, the interquartile range of the data = 25.8 - 12 = 13.8

Answer:

4 17/25  

Step-by-step explanation:

                                                              68

four and sixty-eight hundredths => 4 -------  or 4 34/50  or 4 17/25                    

                                                               100

Answer:

you would need to use decimals

Step-by-step explanation:

Answer:

∠RPS = 49º

Step-by-step explanation:

∠RPS + ∠QPR = 88º

(5x + 34) + (8x + 15) = 88

13x + 49 = 88

13x = 39

x = 3

plug x into equations:

∠RPS = 5(3) + 34

∠RPS = 15 + 34

∠RPS = 49º

check work:

∠QPR = 8(3) + 15

∠QPR = 24 + 15

∠QPR = 39

∠RPS + ∠QPR = 88º

49 + 39 = 88

Answer:

49

Step-by-step explanation:

(5x+34) + (8x+15)= 88

13x + 49 = 88

13x= 39

x=3

RPS= 5(3)+34

RPS= 15 +34

RPS= 49

Negative Correlation - These variables point towards the left making them negative.

Positive Correlation - These variables point towards the right making them positive.

No Correlation - These variables have the same x coordinates or same y coordinates.

Hope that helped!!! k

Answer:

6 hours

Step-by-step explanation:

We can use ratios to solve

10 hours           x hours

-------------- = -------------

15 logs            9 logs

Using cross products

90 = 15x

Divide by 15

90/15 = 15x/15

6 = x

6 hours

Answer:

Below

Step-by-step explanation:

Jovie has maintained the fire burning with 15 logs for 10 hours.

● 15 => 10

Let's find how many hours do 9 logs keep the fire burning.

Let x be that time

● 9 => x

■■■■■■■■■■■■■■■■■■■■■■■■■■

● 15 => 10

● 9 => x

● 15 * x = 9×10

● 15x = 90

● x = 90/15

● x = 6

So the time that the fire will keep burning is 6 hours.

Answer:

The average temperature per hour:

-2.5 °F

Step-by-step explanation:

(-12-48) / 24 =  -60/24

-60/24 = -2.5

In average decrease:

2.5°F

per hour

Answer:

x = 120 degrees

Step-by-step explanation:

Since the angle given is 30 and the four lengths given are equal corresponding the angles opposite to their given sides for the top left triangle and bottom right triangle, the corresponding angles are equal and also 30 degrees.  Since x is where the top left triangle is, we need an equation to relate x.  The sum of all the angles in the top left triangle is 180.  So, x + 30 + 30 = 180.

Therefore,

x = 180-30-30 = 120

Answer:

Step-by-step explanation:

There are two equal Angels in the triangle so!

X=180°- (30+30)°

=180-60

=120°

Answer:

it took him 3 hours to get to work

Step-by-step explanation:

For the first part of the trip, the executive covered a distance "d" in time 't" at 35 mph, therefore we can write that the time it took to get to the helicopter was:

[tex]t-\frac{d}{35}[/tex]

which if the distance is in miles, will render the time in hours.

We can write something similar for the second part of the trip", using the same "t" since it took the same time as for the first one, and using for distance 169.5 - d (since it is the distance to complete the total traveled distance :

[tex]t=\frac{169.5-d}{78}[/tex]

Now we equal those two equations because the time "t" is the same, and solve for "d":

[tex]\frac{d}{35} =\frac{169.5-d}{78} \\78\,d=35\,(169.5-d)\\78\,d=5932.5-35\,d\\(78+35)\,d=5932.5\\d=\frac{5932.5}{113} \\d=52.5[/tex]

Now, knowing the distance covered in the first trip, we can find the time of that first trip:

[tex]t=\frac{52.5}{35} =1.5\,\,hours[/tex]

Therefore, the time it took for thye total trip is: 1.5 h + 1.5 h = 3 hours

Answer:

[tex]y=-3x+7[/tex]

Step-by-step explanation:

This is asking you to provide the equation is slope-intercept form:

[tex]y=mx+b[/tex]

In this equation, m is the slope of the line and b is the y-intercept (where the x value is 0).

By looking at the graph, we can find the y-intercept:

[tex]y-intercept=7\\\\m=7[/tex]

To find the slope of the line, you can count how many spaces it takes to go from one point to another. To do this, it's best to find an even point (1,4) and make your way to (0,7).

The slope is represented by [tex]\frac{rise}{run}[/tex] , where the rise is the change in the y-axis and the run is the change in the x-axis.

From (1,4) , move up (rise) as many spaces as it takes to get to the y-axis level of "7", which is 3 spaces. From  here, move to the left (run) as many spaces as it takes to get to the x-axis level of "0", which is 1 space. Since you moved to the left, however, this means that the number will be a negative:

[tex]\frac{rise}{run}=\frac{3}{-1}=-\frac{3}{1}=-3[/tex]

The slope is -3.

Insert the information into the equation:

[tex]y=-3x+7[/tex]

:Done

Answer:

the desired equation is y = -3x + 7

Step-by-step explanation:

The y-intercept can be read directly from the graph:  (0, 7).  

Another point on the graph is (2, 1).

As we move from (0, 7) to (2, 1), we see x (the run) increasing by 2 and y (the rise) decreasing by 6.  Thus the slope of this line is m = rise/run = -6/2, or -3.

Start with the slope-intercept form of the equation of a straight line, which is y = mx + b.

Then 1 = (-3)(2) + b; find b:

1 = -6 + b, or b = 7

Then the desired equation is y = -3x + 7.

Answer: Rises to the left and falls to the right

Step-by-step explanation:

Use the degree and the leading coefficient to determine the behavior.

There is a good video called "Describing End Behavior Using Limit Notation" by Mario's Math Tutoring, and it helps to show you how to find the end behavior with limits.

Answer:

  {1, 3, 5, 7}

Step-by-step explanation:

There are four possibilities:

  AD = AB -BC -CD = 1 -2 -4 = -5

  AD = AB +BC -CD = 1 +2 -4 = -1

  AD = AB -BC +CD = 1 -2 +4 = 3

  AD = AB +BC +CD = 1 +2 +4 = 7

Possible lengths of AD are 1, 3, 5, 7.

__

The negative sign means the segment is added toward the left instead of toward the right. A final negative value means D is left of A, instead of to the right.

The required measure for the given case is mode. The correct option is (b).

In order to find the mean, first sum all the values of the data and count the number of data then divide them.

In order to find the median, first check whether the number of data is even or odd. For even number, the median is n/2 th element of the sample and for odd number the median is (n + 1)/2 th element.

The given problem deals with a sample of data.

In order find the correct answer, each option is analysed one by one as follows,

(a) The mean of a sample of data represents a standard value for the whole sample such that the individual values of the data may be more or less than it. but, it does not tell about the number of times a value is repeated.

(b)The median of a given sample can tell the middle most value of data when arranged in ascending order.

(c) The mode of a sample is about the times of occurrence of a single value in the whole sample.

As per the given question, to tell about the most frequently brand mode can be used.

Hence, the statistical measure that measures gives the most frequently mentioned brand is mode.

To know more about Mean click on,

https://brainly.com/question/22871228

#SPJ2

Answer: The same number of tickets was sold on the fourth day and tenth day.

Step-by-step explanation:

Given, T(d) is a function that relates the number of tickets sold for a movie to the number of days since the movie was  released.

The average rate of change in a function with respect to the independent variable gives the value of change in a particular period.

If average rate of change in T(d) for the interval d = 4 and d = 10 is  is 0 , that means nothing has been changed in the number of tickets sold on 4th day and 10th day after the film release.

Hence, the correct statement is "The same number of tickets was sold on the fourth day and tenth day."

The correct option is (A).The same number of tickets was sold on the fourth day and tenth day.

Given,

T(d) is a function that relates the number of tickets sold for a movie to the number of days since the movie was released.

The Average rate of change in T(d) for the interval  d = 4 and d = 10 is 0.

We have to find which statement is true.

Since the average rate of change in T(d) for the interval d = 4 and d = 10 is 0, it means nothing has been changed in the number of tickets sold on day 4 and day 10 after the film release.

Hence, the correct statement is The same number of tickets was sold on the fourth day and tenth day.

Thus The correct option is A.

For more details follow the link:

https://brainly.com/question/8011401

Answer:

18.

a) 6k + 2y

b) 2x^2 + 2x

c) 16h

19.  4.5 cm

20.

a) x > 4.5

b) x >= 32

Step-by-step explanation:

Answer:

[tex]$L=\frac{v^2}{2-2\cos(\theta)}$[/tex]

Step-by-step explanation:

Solve for [tex]L[/tex] in

[tex]$L-L \cos(\theta)=\frac{v^2}{2} \Longrightarrow L(1-\cos(\theta))=\frac{v^2}{2}$[/tex]

[tex]$L=\frac{v^2}{2(1-\cos(\theta))}=\frac{v^2}{2-2\cos(\theta)}$[/tex]

Answer:

m² + 9n² + 4m - 12n - 6mn + 4

Step-by-step explanation:

18b

(2+m-3n)² = (2+m-3n)(2+m-3n)

= 2*2 + 2*m + 2*-3n + m*2 + m*m + m*-3n - 3n*2 -3n*m - 3n*-3n

= 4 + 2m - 6n + 2m + m² - 3mn - 6n  - 3mn + 9n²

= m² + 9n² + 2m + 2m  - 6n - 6n - 3mn - 3mn + 4

= m² + 9n² + 4m - 12n - 6mn + 4

Answer:

(2+m-3n)(2+m-3n)

Step-by-step explanation:

Here's solution:

(2+m-3n)(2+m-3n)

4 + 2m - 6n + 2m + m^2 - 3mn - 6n - 3mn + 9n^2

4 + 4m - 12n + m^2 - 9mn + 9n^2

I hope this is right, I'm a bit tired.

Hope this helps, and have a good day :)!

Answer:

440 in²

Step-by-step explanation:

Answer:

(D) 440 in²

Step-by-step explanation:

We can find the surface area of this complex shape by breaking it down into two smaller shapes:

The base (with side lengths of 10, 10 and 2) and the top (with side lengths of 5, 5, and 8.)

Let's first find the surface area of the base.

The sides of the bass are [tex]10\cdot2 = 20[/tex] in², since there are 4 of these sides, the total side area here is [tex]20\cdot4 = 80[/tex] in².

The bottom of this prism has side lengths of 10 and 10, so [tex]10\cdot10=100[/tex].

There are two of these sides.

[tex]100\cdot2=200[/tex].

Let's add up the side lengths and the base lengths.

[tex]200+80=280[/tex]

We aren't done yet - if we see, the top part is taking away some of that surface area. To find how much it is taking away, we need to find the area of that side.

Note that the side on the base is the exact same as the top, who's side lengths are 5 and 5. So [tex]5\cdot5=25[/tex] in² are being taken away from the base, making it [tex]280-25 = 255[/tex]

Now let's find the surface area of the top.

The side, with lengths of 5 and 8, have a surface area of [tex]5\cdot8=40[/tex] in². Since there are 4 of these sides:

[tex]40\cdot4=160[/tex] in².

Now, the top of the box has side lengths of 5 and 5, so the surface area of that is [tex]5\cdot5 =25[/tex] in².

We don't want to find the area of the bottom of the top prism because that cuts into the base and technically is empty space = no surface area.

Let's add the top and the sides of the top box: [tex]160+25=185[/tex] in².

Finally, let's add the base and the top box surface areas together:

[tex]185 + 255 = 440[/tex]

So the total surface area of this design is 440 in².

Hope this helped (oh my god this took so long to write)

Answer:

Minimum candy Tyler gets = 32

Step-by-step explanation:

Given:

Number of candy in box = 50

Extra candy = 5

Find:

Minimum candy Tyler gets

Computation:

Assume.

Number of candy Tyler gets = x

Number of candy Jamie gets = x - 8

Total number of candy in box = 50 + 5 = 55

So,

Number of candy Tyler gets + Number of candy Jamie gets = Total number of candy in box

x + x - 8 = 55

2x = 63

x = 31.5

So,

Minimum candy Tyler gets = 32

Answer:

its

1/7

step by step

Answer:

The answer is H because there are 7 balls in total and two of which is red so the possiblity of getting the red ball is 2/7

Answer:

13

Step-by-step explanation:

23-(12+6)+8

23-18+8

31-18

13

answer is 13

Step-by-step explanation:

Using the BODMAS rule,bracket of division or multiplication, addition or subtraction.

This applies the rule:

therefore,

23- (12+6)+8 ,calculate within bracket first

=23-(18)+8

now remove the bracket,by multiply by the -1

=23-18+8

the start calculate from the left to right

=23-10

=13

therefore the answer is 13

Answer:

80

Step-by-step explanation:

0,   3,   8,   15,   24,  35,   48,   63,  80 which is the nth term

first step you have to find how many steps the sequence was going with.

examples= from 0 to 3 the steps were 3

                =from 3 to 8 the steps were 5

                = from 8 to 15 the steps were 7

you will recognize that the steps the sequence is going with is odd numbers.

so you will use the odd numbers until you find what you need. which leads you to 80 which is the nth number in the sequence.

Answer:

80

Step-by-step explanation:

Answer:

2/5 [tex]cm^2[/tex]

Step-by-step explanation:

To find the area of a rectangle do A = bh

When you substitute 4/6 for base and 3/5 for height  it will be A = 4/6 x 3/5

This means the area is 2/5

Answer:

2/5 cm^2

Step-by-step explanation:

The area of a rectangle is found by

A = l*w

A = 4/6 * 3/5

  Rewriting

  =4/5 * 3/6

   = 4/5 *1/2

  = 2/5 cm^2

Answer:

x>-9/20 or x > -0.45

Step-by-step explanation:

simplify both sides of the inequality:

-20x-10<-1

add 10 to both sides of the inequality:

-20x<9

divide both sides of the inequality by -20:

x>-9/20

divide to discover the decimal value:

-9/20= -0.45

HOPE THIS HELPS!!!:)

Answer:x<-0.5

Step-by-step explanation:

10-19x-1x<-1

1st step=subtract 1x from 19x which will give you 18x

equation after:10-18x<-1

2nd step:subtract 10 from each side to isolate variable

equation after:-18x=9

3rd step:divide by side by -18 to isolate the variable

equation after:x<-0.5

Answer:

Definitely the bottom left

Step-by-step explanation:

Answer:

x = 4, y = -3

Step-by-step explanation:

{2x - y = 11

{x + 3y = -5

You can use the substitution method by solving for x in the second equation:

x + 3y = -5

Subtract 3y from both sides:

x = -3y - 5

Now, substitute this value for x into the first equation:

2x - y = 11

2(-3y - 5) - y = 11

Distribute:

-6y - 10 - y = 11

Add 10 to both sides:

-6y - y = 21

Combine like terms:

-7y = 21

Divide both sides by -7:

y = -3

Next, substitute this value for x into the second equation:

x + 3y = -5

x + 3(-3) = -5

Multiply:

x - 9 = -5

Add 9 to both sides:

x = 4

Answer:

(7, 3)

Step-by-step explanation:

2x - y =11                         2x-y =11

-2(x+3y)= (-5)-2              -2x-6y= 10

Then you will cross out the x, and add.

-7y =21 divide 7

y=-21/7 or y=3

Then you plug in the y where the y is and solve

2x-(3) = 11

2x = 14

x=7

Answer:

X : -6, 3, 15, -12

Y : 11, 5, -3, 15

Step-by-step explanation:

Hey there!

To find the y values we need to plug the x values into th given equation,

y = -2/3x + 7

-6 ⇒ 11

15 ⇒ -3

Now we have a x value missing to that that we work backwards,

we plug in 15 for y in the given equation,

15 ⇒-12

Hope this helps :)

Step-by-step explanation:

[tex]y = - \frac{2}{3} x + 7[/tex]

Substituting the values of x into the expression we have

[tex]y = - \frac{2 }{3} ( - 6) + 7[/tex]

Make x the subject

[tex]5 = - \frac{2}{3} x + 7[/tex]

Multiply through by 3

15 = - 2x + 21

-2x = 15 - 21

- 2x = - 6

Divide both sides by - 2

[tex]y = - \frac{2}{3} (15) + 7[/tex]

y = - 10 + 7

[tex]15 = - \frac{2}{3} x + 7[/tex]

Multiply through by 3

45 = - 2x + 21

- 2x = 45 - 21

- 2x = 24

Divide both sides by - 2

Hope this helps you

Answer:

06:00 a.m.

Step-by-step explanation:

That very simble, from 0:00 to 11:59 you use am, from 12:00 to 23:59 you use p.m :)

Answer:

£17.50

Step-by-step explanation:

30 punnets /  £20

= 30 / 20

= 1.5

1 punnet costs £1.5

30 strawberries * (1/6 punnets)

= 30 * (1/6)

= 30/6

= 5

5 punnets were rotten.

5 rotten punnets * £1.5

= 5 * 1.5

= 7.5

Sandeep lost £7.5 in profits.

6/6 punnets - 1/6 rotten punnets

= 6/6 - 1/6

= 5/6

5/6 punnets are good

30 punnets * 5/6 good punnets

= 30 * 5/6

= 150/6

= 25

Sandeep has 25 punnets left to sell

25 punnets to sell *  £1.50

= 25 * 1.5

= 37.50

Sandeep will get £37.50 from selling the punnets.  However, you must take into account that he lost £20 when he bought the strawberies.  THat money while be added back with some extra money left over:

£37.50 - £20

= 37.50 - 20

= 17.50

Put all into 1 equation:

{[30 * (5/6)] * 1.50} - 20

= {(150/6) * 1.50} - 20

= {25 * 1.50} - 20

= 37.50 -20

= 17.50

Overall, Sandeep's actual profits are equal to 17.50

I hope this is correct!  Please tell me if the answer or info I gave was wrong!