a. How do you identify the boundary line?

Ages of swapna and suma are 33 and 7 years old respectively

If Swapna is 26 years older than her daughter Suma, then;

x = y + 26 ............... 1

6 years later:

Age of Swapna  = x + 6

Age of Suna = y + 6

If Swapna will be thrice as old as Suma, then;

x + 6  = 3(y + 6) ................. 2

Substitute equation 1 into 2:

y + 26 + 6 = 3y + 18

y + 32 = 3y + 18

-2y = -14

y = 7

Since x = y + 26

x = 26 + 7

x = 33

Hence ages of swapna and suma are 33 and 7 years old respectively

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x+y=0

Step-by-step explanation:

x= 1.75

y= -1.75

1 = Given

2 = Addition Property of Equality

3 = Division Property of Equality

Answer: The equation is not an identity

==========================================================

Explanation:

We'll expand out the right hand side to see if we can simplify it to the left hand side. The stuff on the left will stay the same for each step.

I'll use  c = a+b as a way to help distribute.

[tex]a^4 + b^4 = (a+b)(a^3 - a^2b-ab^2 + b^3)\\\\a^4 + b^4 = c(a^3 - a^2b-ab^2 + b^3)\\\\a^4 + b^4 = a^3c - a^2bc-ab^2c + b^3c\\\\a^4 + b^4 = a^3(c) - a^2b(c)-ab^2(c) + b^3(c)\\\\a^4 + b^4 = a^3(a+b) - a^2b(a+b)-ab^2(a+b) + b^3(a+b)\\\\a^4 + b^4 = a^4+a^3b - a^3b-a^2b^2-a^2b^2-ab^3 + ab^3+b^4\\\\a^4 + b^4 = a^4+(a^3b - a^3b)+(-a^2b^2-a^2b^2)+(-ab^3 + ab^3)+b^4\\\\a^4 + b^4 = a^4-2a^2b^2+b^4\\\\[/tex]

Unfortunately, we can't go any further. We have a^4 and b^4 on the right hand side, but we also have the term -2a^2b^2 that didn't cancel out. Therefore, the original equation is not an identity.

----------------

Here's another way you can see that we don't have an identity.

Let's say we fixed 'a' to be equal to 1.

That means the equation

[tex]a^4 + b^4 = (a+b)(a^3 - a^2b-ab^2 + b^3)[/tex]

would turn into

[tex]1^4 + b^4 = (1+b)(1^3 - 1^2b-1b^2 + b^3)[/tex]

and simplify to

[tex]1 + b^4 = (1+b)(1 - b-b^2 + b^3)[/tex]

Now replace b with x and you'll have the two equations to represent the left and right hand sides

[tex]y = 1+x^4\\y = (1+x)(1-x-x^2+x^3)[/tex]

which you can graph on the same xy axis. You should note that the two equations produce different curves. The curves would need to be identical if we wanted an identity to happen.

Side note: you can pick other values for 'a' instead of just 1.

Answer:  659

Step by step solution:

Answer:

659

Step-by-step explanation:

0659

8 5272

0

52

48

 47

 40

   72

   72

     0

Dividend:

5272

Divisor:

8

Quotient:

659

Remainder:

0

You may have to write this on paper because it might be hard for you to understand. I'm sorry if this isn't helping and it is very confusing, this is the only way that I could explain it. Thank you for the question and I hope you enjoy your answer :)

The cost of 35 pounds of oolong tea is $84.

An equation is used to show the relationship between two or more variables or numbers.

Given that oolong tea sells for $2.40 per pound.

There are 35 pounds of oolong tea available. Hence:

Cost of 35 pounds of oolong tea = $2.40 per pound * 35 pound

Cost = $84

Hence, the cost of 35 pounds of oolong tea is $84.

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Answer:

35 LB (THIS IS ACTUALLY CORRECT)

Step-by-step explanation:

First, you lay it down like this:

Since you're selling 35 pounds of oolong tea that sells for $2.40, you multiply both

2.4*35

=84

However, since you don't know how many pounds of black tea, you use x

Multiply like above

1.8*x

=1.8x

The total mixture is selling for $2.10

Total pounds: 35 + x (given above, or black + oolong tea

equation:

84 + 1.8x = 2.1(35+x)

84 + 1.8x = 73.5 + 2.1x (distributive property)

    - 1.8x             - 1.8x

84 + 0 = 73.5 + 0.3x

-73.5             -73.5

10.5 = 0.3x

3.5 = 0.1x

35 = x

Answer: x= -2, y= 3

Step-by-step explanation:

3x+5y=9

X-y=-5

Multiply bottom equation by 5

3x+5y=9

5x-5y=-25

3x + 5x=8x

5y-5y cancels out

9-25= -16

8x= -16

X= -2

Plug -2 back into equation of choice to find y

3(-2)+5y=9

-6+5y=9

Add -6 to both sides

-6+6 cancels

9+6=15

5y=15

Y=3

Step-by-step explanation:

Distributive property

Step-by-step explanation:

<B=180°-70°-50°=60°

hope this helps you.

Answer:

1200 units 30 times 40 is 1200

1200 sq units

hope this helps

Answer:

448000004.

Hope that helps. x

Answer:

448000004

Step-by-step explanation:

QUICK MATHS

Answer:

f(x)=125k(1.05)x

Step-by-step explanation:

ommg

ok so every year it increase by 5%, aka 105%

which is 125k*105/100x which is the first one f(x)=125k(1.05)x

if u are not sure than use cross of elinimation

cant be 2nd one cause its not correct

third one ur decreasing

fourth one is just like the 2nd one

Answer:

Bala Bala Bala Bala Bala

Step-by-step explanation:

what is the slope of the Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah answer is answer the question Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah

========================================================

Explanation:

Let x and y be two positive whole numbers. They may or may not be equal.

The first bag has the ratio of red to blue as 3:5, which scales up to 3x:5x after multiplying both parts by x. We have 3x red and 5x blue.

The second bag has the ratio 3:2 which scales up to 3y:2y. This bag has 3y red and 2y blue.

We can make a handy table to keep track of all the expressions

[tex]\begin{array}{|c|c|c|}\cline{1-3}\text{ } & \text{Red} & \text{Blue}\\ \cline{1-3}\text{bag 1} & 3x & 5x\\ \cline{1-3}\text{bag 2} & 3y & 2y\\ \cline{1-3}\end{array}[/tex]

Based on that, we can then say:

Effectively, I added down along each column of that table.

Divide the two expressions for R and B to lead to the fraction 11/9, which is directly from the ratio 11:9

So,

(total red)/(total blue) = 11/9

R/B = 11/9

(3x+3y)/(5x+2y) = 11/9

---------------------

Let's cross multiply and then solve for y

(3x+3y)/(5x+2y) = 11/9

9(3x+3y) = 11(5x+2y)

27x+27y = 55x+22y

27y-22y = 55x-27x

5y = 28x

y = 28x/5

y = (28/5)x

y = 5.6x

We'll keep this in mind for later.

---------------------

Now let:

Recall that we had 3x red and 5x blue for the first bag. That means we have 3x+5x = 8x marbles in the first bag. Therefore, F = 8x.

Also, we had 3y red and 2y blue for the second bag.

So we have S = 3y+2y = 5y

Then we can apply further substitution to say

S = 5y

S = 5(5.6x) .... plug in y = 5.6x

S = 28x

---------------------

In short,

for some positive whole number x. We don't have enough info to pin down what x is exactly; however, it doesn't really matter. This is because the x variable will cancel when dividing F over S

F/S = (8x)/(28x) = 8/28 = 2/7

The fraction 2/7 leads directly to the final answer of the ratio 2:7

In other words, the ratio 8x:28x simplifies fully to 2:7 after dividing both parts by 4x.

The ratio between the total marbles of the first bag and the second bag is 2:7.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

Example:

2x + 4 = 9 is an equation.

We have,

x marbles in the first bag.

red marbles = 3x

blue marbles = 5x

y marbles in the second bag.

red marbles = 3y

blue marbles = 2y

Now,

Total red marbles in both bags.

3x + 3y = 11 _____(1)

3x = 11 - 3y

x = (11 - 3y) / 3

Total blue marbles in both bags.

5x + 2y = 9 ______(2)

From (1) and (2) we get,

Multiply 2 in (1).

6x + 6y = 22

6y = 22 - 6x _____(3)

Multiply 3 in (2)

15x + 6y = 27 ______(4)

Putting (3) in (4)

15x + 22 - 6x = 27

9x = 27 - 22

9x = 5

x = 5/9

Now,

x = 5/9 in (3)

6y = 22 - 6(5/9)

6y = 22 - 10/3

6y = (66 - 10)/3

y = 56/18

y = 28/9

Now,

First bag.

Red marbles = 3x = 3 x 5/9 = 5/3

Blue marbles = 5x = 5 x 5/9 = 25/9

Total marbles = 5/3 + 25/9 = (15 + 25)/9 = 40/9

Second bag.

Red marbles = 3y = 3 x 28/9 = 28/3

Blue marbles = 2y = 2 x 28/9 = 56/9

Total marbles = 28/3 + 56/9 = (84 + 56)/9 = 140/9

Now,

The ratio between the total marbles of the first bag and the second bag.

= 40 :140

= 4:14

= 2:7

Thus,

The ratio is 2:7.

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Answer:

5,600 g of flour

10,000g of sugar

3,200g of ginger

4,400g of butter

Just have to multiply each ingredient by 40

Answer:

36 yards

Step-by-step explanation:

48 - 31 = 17

17 + 3 + 5 + 7 + 4 = 36

The total distance between  the ball and the goal line is 36 yards

In computing, data is information that has been translated into a form that is efficient for movement or processing.

Given:

Eagles have the ball 48 yards away from the goal line.

On the first play, the Eagles gain 31 yards on a pass toward the goal line. On the next four plays, the Eagles lose 3, 5, 7, and 4 yards.

After first day they have yards remaining

=48 - 31

= 17

Now, the total distance between  the ball and the goal line

=17 + 3 + 5 + 7 + 4

= 36

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Answer:

56

Step-by-step explanation:

Answer:

i think its 140 because u got to add all the sides in order to subtract from 180

i dont know  if its right but that is what i think UwU

Answer:

y =47.5.

Step-by-step explanation:

First eliminate the fractions by multiplying through by the LCM of 7 and 3 which is 21:

21* 6[y-2]/7-21*12 = 21*2[y-7]/3

18(y - 2) - 252 = 14(y - 7)

18y -36 - 252 = 14y - 98

18y - 14y = -98 + 36 + 252

4y = 190

y = 190/4

y = 47.5.

Answer:

49 square metres

Step-by-step explanation:

The area of a square is the length of the side times itself.

The area is 7 x 7 = 49

Answer:

  x = 10

Step-by-step explanation:

The diagonals of a rectangle are the same length. This means ...

  AC = BD

  x +6 = 2x -4

  10 = x . . . . . . . . add 4-x to both sides

The figure is a rectangle for x=10.

Answer:

(7,-2)

Step-by-step explanation:

Answer:

(7, - 2 )

Step-by-step explanation:

x - y = 9 ( add y to both sides )

x = y + 9 → (1)

2x + 5y = 4 → (2)

Substitute x = y + 9 into (2)

2(y + 9) + 5y = 4 ← distribute parenthesis and simplify left side

2y + 18 + 5y = 4

7y + 18 = 4 ( subtract 18 from both sides )

7y = - 14 ( divide both sides by 7 )

y = - 2

Substitute y = - 2 into (1)

x = - 2 + 9 = 7

solution is (7, - 2 )

Answer:

(4, -6)

Step-by-step explanation:

The rule for rotation around the origin 90 degrees clockwise is

Ro, 90: (x, y) --> (y, -x)

so (6, 4) --> (4, -6)

Answer:

x = 14

Step-by-step explanation:

21 ÷[tex]\frac{2}{3}[/tex] = 14

Answer:

x = 31 1/2

Step-by-step explanation:

- Isolate x by multiplying 2/3 on each side, cancelling out the one of its original placement

- You can't divide by a fraction, so KCF (Keep Change Flip):

      x = 21 * 3/2

      = 63/2 or 31 1/2

[tex]\huge \rm༆ Answer ༄[/tex]

The equivalent expression is ~

Refer to attachment for solution ~

For x such that 0 < x < [tex]\frac{\pi}{2}[/tex], the mathematical expression is:

[tex]\frac{\sqrt{1 \;-cos^2x} }{sinx} + \frac{\sqrt{1 \;-sin^2x} }{cosx} = 1+1=2[/tex]

Given the following data:

In Trigonometry, you should take note of the following mathematical expression:

[tex]sin^2x + cos^2x = 1[/tex]

Therefore, we can obtain the following:

[tex]sin^2x = 1 - cos^2x[/tex]   ...equation 1.

[tex]cos^2x = 1 - sin^2x[/tex]    ...equation 2.

Substituting the equations respectively, we have:

[tex]\frac{\sqrt{1 \;-cos^2x} }{sinx} + \frac{\sqrt{1 \;-sin^2x} }{cosx} = \frac{\sqrt{sin^2x} }{sinx} + \frac{\sqrt{cos^2x} }{cosx}\\\\[/tex]

Taking the square roots, we have:

[tex]\frac{sinx}{sinx} + \frac{cosx}{cosx} = 1 +1\\\\1+1=2[/tex]

Therefore, for x such that 0 < x < [tex]\frac{\pi}{2}[/tex], the expression is:

[tex]\frac{\sqrt{1 \;-cos^2x} }{sinx} + \frac{\sqrt{1 \;-sin^2x} }{cosx} = 1+1=2[/tex]

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Answer:

-16.1y + 14

Step-by-step explanation:

–7(2.3y − 2)

=> -16.1y + 14

Therefore, -16.1y + 14 is the simplified form.

Hoped this helped

[tex]GeniusUser[/tex]

Answer:

53

Step-by-step explanation:

sorry if im incorrect

Answer:

10:24

Step-by-step explanation:

if school starts at 7:15 and you stay in the first 4 periods for 47 minutes each, that totals 3 hours, 8 minutes

7:16 + 3 hrs, 8 min = 10:24

It is the 3rd one from the top

Answer:

I believe the answer would be C.

Step-by-step explanation:

First of all, the solution to the answer really is 1/20. If you figure out the decimal form of 4/5, it is 0.80, which is closer to 1 than to 1/2 and 0. The decimal form of 3/4 is 0.75, which is equally close to 1 and 1/2, being 0.25 from both. But it is closer to 1 than 0. I hope I’m right, and I hope this helps. :)