Sam and Bethan share £54 in the ratio 5:4 how much does each person get

The solution of the equation for x is x = 4y - 12

Inverse functions are the opposite of an original equation. This means that for a function f(x), the inverse of the function f(x) is f-(x); it also represents the opposite function

The function y is given as

y = 1/4x + 3

As a general rule, we start by writing y as a variable (say y = f(x)).

So, the equation of the function becomes

y = 1/4x + 3

The next step is to switch/swap the positions of x and y in the above equation y = 1/4x + 3 (in this case, it is not necessary)

So, the equation remains the same

y = 1/4x + 3

The next step is to make x the subject of the formula in the above equation y = 1/4x + 3

The equation becomes

1/4x = y - 3

This is done by subtracting 3 from both sides of the equation.

So, we have:

1/4x = y - 3

Multiply through the sides of the equation by 4

So, we have

x = 4y - 12

Express as an inverse function

f-1(x) = 4x - 12 --- this is not  compulsory

So, the solution of the equation for x is x = 4y - 12

Hence, the rewuired solution of the equation for x is x = 4y - 12

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The three questions mentioned above which translated to one variable linear equation.

Problem first,
The rank of a student is 5 more than the other, Sum of their rank is 7
The solution, rank of student be x
            rank of another student = x + 5
          According to the question,
          x + x + 5 = 7
              2x = 2
                 x = 1

Problem second.
A student has 2 pens less than their friend, the sum of their pens is 6
Solution-
               let the student has x pens
               His friends have = x + 2 pens
               Now. total = x + x + 2
                             6 = 2x + 2
                             x = 2

Problem third,
Ashwin is 2 times older than his friend and his friend's age is 24 what is the age of Ashwin,
Solution,
             Let the age of Ashwin be x
                according to question
                    x = 24 + 2
                     x = 26

Thus, the three questions mentioned above which translated to one variable linear equation.

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The complete paragraph is shown:

The complex number - 2 + i 8 has modulus of 2√17. When - 2 + i 8 is multiplied by 5, the modulus of the product of 10√17.

Multiplying a complex number by a real number is a scalar of a complex number. The quadrant location of the complex number and its product with the real number are the same.

In this problem we have a paragraph, in which we must fill the blanks with the results of operations with complex numbers. The modulus of a complex number is found by using the Pythagorean theorem:

r = √[(- 2)² + 8²]

r = √(4 + 64)

r = √68

r = 2√17

And the product between the real number and the complex number is done by distributive property:

5 · (- 2 + i 8)

5 · (- 2) + i (5 · 8)

- 10 + i 40, whose modulus is 10√17.

Graphically speaking, the scalar of a complex number remains in the same quadrant of the complex plane.

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The required change in altitude is 900ft

From the question, we are given the following parameters

Initial height =5400ft

Final height = 6300ft

Determine the change in altitude

Change in altitude = Final - Initial

Change in altitude  = 6300ft - 5400ft

Change in altitude = 900ft

Hence the required change in altitude is 900ft

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The solution of the given linear equation is (103.16 + 4x).

The given equation is;

= 9(3.2)² + 4x - 11

For finding (3.2)² = 3.2×3.2

(3.2)² = 10.24

Put the value in equation;

= 9×10.24  + 4x - 11

Multiply 9×10.24 = 92.16

Put the value;

= 92.16 + 4x + 11

Now, add the constant value

= (92.16 + 11) + 4x

= 103.16 + 4x

As, 4x is a variable part, it will not get added to the constant 103.16.

Thus, the solution of the equation is  103.16 + 4x.

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The numbers that represents c and d and aligns with the information will be 24 - 10 = 14.

It should be noted that from the proportion, a = 60 and b = 25.

It was also stated that c - d = 14.

It should be noted that 60 and 25 have a common factor of 5. Therefore, the number that's equivalent to them will be:

(60 ÷ 2.5) = 24

25 ÷ 2.5 = 10

Therefore 24 - 10 = 14

The values are 24 and 10.

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Answer:

sin = 12/15  cos = 9/15  tan = 12/9

Step-by-step explanation:

Easy way to remember this is

SOH CAH TOA

O is opposite ( 12 in this problem )

H is hypotenuse i.e. opposite of the right angle ( 15 in this problem )

A is adjacent ( 9 in this problem )

The probability of randomly selecting someone who does not believe that statistics teachers know the true meaning of life is 31.9%

The given parameters are

P = 68.1%

The above probability represents the probability that Americans say they believe that statistics teachers know the true meaning of life

The complement probability is

Q = 1 - P

This gives

Q = 1 - 68.1%

Evaluate

Q = 31.9%

Hence, the probability of randomly selecting someone who does not believe that statistics teachers know the true meaning of life is 31.9%

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The expression to show the total number of sport cards that Adele bought will be Bb +5d.

From the information, it was stated that Adele bought B packs of baseball cards and five packs of book bar cards right in expression that shows how many packs of sport cards Adele bought in all.

Let the number of baseball = b

Let the back cards =d

Therefore, the expression to show the number of sport cards will be:

= (B × b) + (5 × d)

= Bb +5d

Therefore, the expression to show the total number of sport cards that Adele bought will be Bb +5d.

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Adele bought B packs of baseball cards and five packs of book bar cards right in expression that shows how many packs of sport cards Adele bought in all. Write an expression for this

Answer:

y = -1/6x - 7/3

Step-by-step explanation:

slope = rise/run

(y2 - y1) / (x2 - x1)

ordered pairs: (-2,-2) and (4,-3)

-3 - (-2) = -1

4 - (-2) = 6

-1/6 = -1/6

m = -1/6

find b

take one ordered pair

y = mx + b

-3 = (-1/6)(4) + b

-3 = -4/6 + b

-3 + 4/6 = -2 2/6  

-2 2/6 = -14/6

-14/6 = -7/3

b = -7/3

Step-by-step explanation:

Answer:

The number of students increased by 40%

Answer:

it's 88

Step-by-step explanation:

a century = 100

so 100-12 =88

The measure of the largest angle is 84°

It should be noted that the total angles on a triangle is 180°.

Let the smallest angle = x

Second angle = x + 40

Third angle = 3x

Therefore 3x + x + x + 40 = 180

5x = 180 - 40

5x = 140

x = 140/5

x = 28

Therefore, the largest angle will be:

= 3x

= 3 × 28°

= 84°

Therefore, the measure of the largest angle is 84°

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Answer:

George C. x=2 is the equation of the line through (2,3) with undefined slope.

Step-by-step explanation:

Answer:

x = 2

Step-by-step explanation:

A line with an undefined slope is a vertical line parallel to the y- axis with equation

x = c ( c is the value of the x- coordinates the line passes through )

the line passes through (2, 3 ) with x- coordinate 2 , then

x = 2 ← is the equation of the line

Answer:

-174

Step-by-step explanation:

58x2=116<----First two 58's

116+58=174<----last 58

We need to add the negative symbol since it should be negative, so the final answer is -174.

Answer:13

Step-by-step explanation:

Answer:

13

Step-by-step explanation:

i hope it's helpful for you

Answer: 11

Step-by-step explanation:

f(t)=2(t)-3

f(t)=2t-3

f(7)=2(7)-3

f(7)=14-3

f(7)=11

Solve the quadratic equation

  c² +16c+64 = 0

Step-by-step explanation:

Given that

             c² +16c+64 = 0

To find

So, according to the question

we have,

We can solve this quadratic equation by factorising method.

So, we have to convert it on factors,

        c² +16c+64 = 0

For getting it's factors, we have to divide 16c part in two parts,

So, we can write 16c = 8c + 8c,

        c² +16c+64 = 0

        c² +8c+ 8c+ 64 = 0

Now,

        c(c +8) + 8(c+ 8) = 0

                  (c+8)(c+8) = 0

                        (c+8)² = 0

 or,

                       (c + 8) = √0   (∵  √0  = 0)

                         c + 8 = 0

Now, we can say that

                              c = -8 or 0

Answer:

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Answer:

  -8.8x +5

Step-by-step explanation:

You want to simplify the expression -0.8x+40-8x-35.

The expression is simplified by combining like terms. Like terms have the same (set of) variables.

  -0.8x +40 -8x -35

  = -0.8x -8x +40 -35 . . . . . . group like terms

  = (-0.8 -8)x +(40 -35)

  = -8.8x +5

Answer:

85

Step-by-step explanation:

use the largest digit in the tens place, that is 8

use the next largest digit in the units place, that is 5

the largest 2- digit number is 85

(ii)

514 is the closest to 500 ( 14 units away )

485 is also close ( but 15 units away )

so 514 is the closest to 500

Answer: i) 85 & ii) 514

Step-by-step explanation:

Here, 8>5>4>1

So,

i) 85

ii) 514

Answer: The answer for this would y=-2x+b in slope form and y=-2x+3 in standard form.

Step-by-step explanation:

First we have to figure out what the slope is and you should this formula y2-y1/x2-x1 you plug in the coordinates and your equations should look like this -3-5/3-(-1)= -8/4 which simplified into -2. In standard form you put in the same equation but plug in the coordinates with the slope so it would look like this. -3=-2(3)+b and you would get 3 as b and then you substitute it in the equation again y=mx+b and it should like this in standard form y=-2x+3.

Answer:

(4xy)(5x^2yz) = 20x^3y^2z

Step-by-step explanation:

                                        [tex]\begin{aligned}\\\small (4xy)(5x^2yz) &\equiv \small (4\times5)\times (x \times x^2) \times (y\times y) \times (z)\\\\&\equiv 20 \times x^3 \times y^2 \times z\\\\&\equiv 20x^3 y^2 z\end{aligned}[/tex]

Answer:

75

Step-by-step explanation:

35+4x where x is 10

35+4*10

35+40

75

Answer:

75

Step-by-step explanation:

4 packs of balloons which each have 10 balloons is 40 total balloons she bought. Add 40 to 35 which is 75.

For the given graph:

And yes, it is a function.

For a given function y = f(x), the domain is the set of the inputs (possible values of x) and the range is the set of outputs (possible values of y).

To identify the domain we need to look at the x-axis (the horizontal one)

We can see in the left side that the first value is -2, whith a closed circle, meaning that the value belongs to the domain.

The right side is x = 0, with a open circle, which means that it does not belong to the domain.

Then the domain is D: [-2, 0)

Similarly, by looking at the y-axis (vertical axis) we can find the range which is:

R: [0, 2)

Finally, how to know if this is a function?

There is something called the "vertical line test". This test says that if you can't draw a vertical line that intersects the graph in two points or more, then it is a function.

And the graph clearly meets that test, so it is a function.

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The required angle of obtuse angles are <BMD  ,<AMC  and <AME.

In Plane Geometry, a figure which is formed by two rays or lines that shares a common endpoint is called an angle and corner whether constituting a projecting part or a partially enclosed space.

Given:

The given figure is shown

<BMC=EMC=90°

According to given question we have

Angles between 90 and 180 degrees (90°< θ <180°) are known as obtuse angles.

Angles that are 90 degrees (θ = 90°) are right angles.

Angles that are 180 degrees (θ = 180°) are known as straight angles.

Angles between 180 and 360 degrees (180°< θ < 360°) are called reflex angles.

<BMC=EMC=90° (right angles)

<BME =<AMD= 180°( straight angles)

<BMD=<AMC=<AME =90°< θ <180°  (obtuse angles )

Therefore, the required angle of obtuse angles are <BMD  ,<AMC  and <AME.

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Answer:

1200 ml

Explanation:

Let x be the quantity ( in ml ) of b solution,

∵  solution a is 100 milliliters less of than solution  b.

So, the quantity of solution a = 100 - x,

Now, solution a has 13% alcohol,

∴ Alcohol in solution a = 13% of (100-x) =  = 0.13(x-100),

While solution b has 17% alcohol,

∴ Alcohol in solution b = 17% of x = 0.17x,

So, the quantity of alcohol in the mixture of a and b = 0.13(x-100) + 0.17x

= 0.13x - 13 + 0.17x

= 0.30x  - 13

According to the question,

Total quantity of alcohol in the mixture = 347 ml,

⇒ 0.30x  - 13 = 347

⇒ 0.30x = 347 + 13

⇒ 0.30x = 360

⇒ x =  = 1200

Hence, the quantity of solution b is 1200 ml.

The number of tracks on 4 CDs are 132.

Here, we are given that a CD holds 2t + 3 tracks.

Thus, the number tracks on 4 CDs will be given as-

4(2t + 3)

Simplifying the expression further, we get

(4 × 2 × t) + (3 x 4)

= 8t + 12

Therefore, the expression for the number of tracks on 4 CDs is 8t + 12

Now, if t = 15

Then, the number of tracks on 4 CDs can be found by substituting the value t = 15 in the expression (8t + 12)

= 8(15) + 12

= 120 + 12

= 132

Thus, there are 132 number of tracks on 4 CDs.

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Using the normal distribution, the height of a woman with a z-score of -1.5 is of 66.75 inches.

The problems asks for the height of a woman with a z-score of -1.5.

The z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

For this problem, the parameters are given as follows:

[tex]\mu = 69, \sigma = 1.5, z = -1.5[/tex]

The height is found solving for x, hence:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

-1.5 = (X - 69)/1.5

X - 69 = -1.5 x 1.5

X = 66.75.

The height of a woman with a z-score of -1.5 is of 66.75 inches.

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