A person has 100 notes of Rs. 10 and Rs. 20 each. He went to a shop and bought items for Rs. 220. In how many ways can he pay this amount using the notes he has?

Combine the fractions and factorize.

[tex]\dfrac{3a^2b}{a-b} + \dfrac{3ab^2}{b-a} = \dfrac{3a^2b}{a - b} - \dfrac{3ab^2}{a - b} \\\\ ~~~~~~~~ = \dfrac{3a^2b - 3ab^2}{a - b} \\\\ ~~~~~~~~ = \dfrac{3ab (a - b)}{a - b} \\\\ ~~~~~~~~ = 3ab[/tex]

I'm guessing you mean

[tex]S_{k+1} = S_k + a_{k+1}[/tex]

and that [tex]S_k[/tex] is the sum

[tex]S_k = 6 + 12 + 18 + \ldots + 6k = 6 (1 + 2 + 3 + \ldots + k) = 3 k (k+1)[/tex]

using the well-known formula

[tex]\displaystyle \sum_{i=1}^n i = 1 + 2 + 3 + \cdots + n = \frac{n(n+1)}2[/tex]

Then by substitution,

[tex]S_{k+1} = 6 (1 + 2 + 3 + \cdots + k + (k+1)) = 3 (k+1) (k+2)[/tex]

and hence

[tex]a_{k+1} = S_{k+1} - S_k[/tex]

[tex]a_{k+1} = 3 (k+1) (k+2) - 3k (k+1)[/tex]

[tex]a_{k+1} = 3 (k+1) \bigg((k+2) - k\bigg)[/tex]

[tex]\implies \boxed{a_{k+1} = 6 (k + 1)}[/tex]

The area of the base of cube B is 25/9 times larger than the area of the base of cube A.

Because the cubes are similar, then we know that the dimensions of cube B are a dilation of scale factor K of the dimensions of cube A.

Then, the volume of cube B is K³ times the volume of cube A.

The area of any face of cube B is K² times the area of any face of cube A

From this we can write:

125 in³ = K³*27in³

(125/27) = K³

If we apply the cubic root in both sides, we get:

∛(125/27) = K = 5/3

Then the relation between the areas is equal to:

K² = (5/3)^2 = 25/9

The area of the base of cube B is 25/9 times larger than the area of the base of cube A.

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Answer:

25/9

Step-by-step explanation:

I Just Took the Test.

a)

Gain on disposal=$12,900

b)

Loss on disposal=$5,900

Prepare a tabular summary to show the cost of equipment disposed of, the accumulated depreciation, and gain or loss recorded on disposal?

Note that initially when the equipment was purchased, it would be debited to an asset account, whereas, it would be credited upon disposal since the company no longer owns it.

The accumulated depreciation was originally a credit entry in the balance sheet and needs to be debited now that the equipment has been sold.

Note that the excess of the sum of the accumulated depreciation and the cash received over the initial cost of the equipment is a gain and the reverse means a loss was recorded on disposal.

Account                                DR                  CR

Asset                     $49,600

Gain on disposal      $12,900

Accumulated depreciation                               $24,600  

Cash received                                              $37,900  

gain on disposal=$24,600+$37,900-$49,600

gain on disposal=$12,900

Account                                 DR                    CR

Asset                                                           $49,600

Accumulated depreciation   $24,600  

Cash received                         $19,100  

Loss on disposal                     $5,900  

Loss on disposal=$49,600-$24600-$19,100

Loss on disposal=$5,900

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Answer:

4x -51

Step-by-step explanation:

m(n(x)) = m(x - 10) = 4(x-10) - 11 = 4x -40 -11 = 4x -51

Answer:

m[n(x)] = 4x - 51

Given following:

Solving steps:

Answer:

2

Step-by-step explanation:

2.is best possible answer as it.says below 1000...

Answer:

the answer is

x^2 – 2y ≥ 7000

2x + 5y < 1000

so it would be the second option

Step-by-step explanation:

just took the test:)

Answer: 14.25

Step-by-step explanation:

Because 14 and 10 inches don't indicate that the ruler can measure to the nearest 0.25 inches. They indicate that the ruler can measure to the nearest inch.

14.2598 inches cannot be measured with this ruler.

That leaves 14.25.

Hope this helped.

The type of transformation that preserves the symmetry of an even function f(x) but does not preserve the symmetry of an odd function g(x) is vertical translation.

Vertical translation of a graph is done by moving the base graph up or down in the y-axis direction. Each point on a graph is moved k units vertically to translate the graph by that many units.

The vertical translation is the movement of the curve along the y-axis by a certain number of units without altering the function's shape or domain.

The function's form is preserved in the case of vertical translation.

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Answer:

Let the angle be x

∘

. Then it's complement = (4x)

∘

.

We know that if the sum of two angles is equal to 90

∘

then the angles are said to be complementary.

Step-by-step explanation:

4x+x=90°

5x=90°

x=90°/5

x=18

4×18=72°

This is the complete solution!

(ﾉ◕ヮ◕)ﾉ*.✧STAY CONNECTED ❣️

Differentiating both sides of

[tex]x^2 + 2xy - y^2 + x = 20[/tex]

with respect to [tex]x[/tex] yields

[tex]2x + 2y + 2x \dfrac{dy}{dx} - 2y \dfrac{dy}{dx} + 1 = 0 \\\\ \implies (2x-2y) \dfrac{dy}{dx} = -1 - 2x - 2y \\\\ \implies \dfrac{dy}{dx} = \dfrac{1 + 2x + 2y}{2(y-x)}[/tex]

At the point (3, 4) (so [tex]x=3[/tex] and [tex]y=4[/tex]), the tangent line has slope

[tex]\dfrac{dy}{dx} = \dfrac{1 + 2\times3 + 2\times4}{2(4-3)} = \dfrac{15}2[/tex]

Then the tangent line to (3, 4) has equation

[tex]y - 4 = \dfrac{15}2 (x - 3) \implies \boxed{y = \dfrac{15}2 x - \dfrac{37}2}[/tex]

Answer:

-9/11

Step-by-step explanation:

slope is change in y/change in x

change in y is 9 (12-3)

change in x is -11 (-17--8)

slope is -9/11

Answer:

Mikhail is 44 years old.

Step-by-step explanation:

Set both Gabrielle and Mikhail's age to a variable.

Gabrielle is x, Mikhail is also x.

Now create an equation using the variables with the sum.

Age1 + Age2 + 15 = 103

x + x + 15 = 103

Now we solve.

1. Combine like terms

2x + 15 = 103

2. Make all the numbers on one side of the equation, and the variables of the other, so subtract.

2x + 15 - 15 = 103 - 15

2x = 88

3. Simplify further by dividing.

x = 44

Mikhail is 44 years old.

Check your work:

44 + (x + 15) = 103

x + 15 = 59

x = 44

Answer:

Step-by-step explanation:

Let Gabrielle's age be x.

The age of the milk will be x - 15.

x + (x - 15) = 103.

2x - 15 = 103

2x = 118

x = 59

The milk's age = x - 15 = 59 - 15 = 44.

Answer:

slope = - 32 , y- intercept = 5

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = - 32x + 5 ← is in slope- intercept form

with slope m = - 32 and y- intercept c = 5

[tex]\frak{Hi!}[/tex]

[tex]\orange\hspace{300pt}\above2[/tex]

                          We have the equation [tex]\boldsymbol{\sf y=-32x+5}[/tex].

                          We need to know its slope and y-intercept.

                         If an equation has the y=mx+c form,  the slope is always

                         multiplied by x, the x co-ordinate. Such is the case here,

                          thereupon we note that the slope is [tex]\boldsymbol{\sf{-32}}[/tex].

                         As for the y-intercept, that's a constant. Do you remember

                         that constants have no variables attached to them?

                         Since the only number that has no variables attached to it is

                         5, we note that this is the desired value, the y-intercept.

done!!

[tex]\orange\hspace{300pt}\above3[/tex]

                        [tex]\large\boldsymbol{\sf{calligraphy}}[/tex]

Answer:

Not going to give answer, but let you solve

Step-by-step explanation:

You first have to start by drawing a number line and mark two integers between the fraction lines. Then you have to divide the section between the two integers in an equal number of parts which is equal to the denominator.

Hope I helped

The point P could be located in quadrant I, quadrant IV and the x-axis

The coordinate of point P is given as:

P = (a, b)

Where a is positive

When a is positive, then the likely locations of P are:

Hence, point P could be located in quadrant I, quadrant IV and the x-axis

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The relationship between temperature and the coffee sales is a negative exponential of temperature

relation is subject of order between to sets or how the connected to each other.

The temperature of liquid is essential in the  process of brewing because its affects the rate of evaporation or extraction. it refers to the test and matters that are dissolved from the coffee beans. The hot is the water, the quick it is to extract. At a high temperature, it’s tougher to control the rate of extraction. This can lead to over-evaporation of liquid, making your coffee taste too bitter since the heat strips away a lot of oxygen.

since the temperature varies over the year, which implies the taste of coffee also vary in a manner that in cold days people love coffees and in hotter days the people love to drink cold drinks instead of coffees
so in cold days the sales of coffees is grater in comparison with hot days

Thus the relationship between the sales of coffees and temperature is negative exponential of temperature.

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The difference based on the numbers given is -80.

The information given illustrates that the difference will be:

= (9 - 1) - (43) - (2 - 3) - 50

= 8 - 43 - (-1) - 50

= 8 - 43 + 1 - 50

= -80

Therefore, the difference or subtraction among the numbers given is -80.

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Answer:

[tex]\sf \dfrac{1}{4} \pi \quad or \quad \dfrac{7}{9}[/tex]

Step-by-step explanation:

The width of a square is its side length.

The width of a circle is its diameter.

Therefore, the largest possible circle that can be cut out from a square is a circle whose diameter is equal in length to the side length of the square.

Formulas

[tex]\sf \textsf{Area of a square}=s^2 \quad \textsf{(where s is the side length)}[/tex]

[tex]\sf \textsf{Area of a circle}=\pi r^2 \quad \textsf{(where r is the radius)}[/tex]

[tex]\sf \textsf{Radius of a circle}=\dfrac{1}{2}d \quad \textsf{(where d is the diameter)}[/tex]

If the diameter is equal to the side length of the square, then:
[tex]\implies \sf r=\dfrac{1}{2}s[/tex]

Therefore:

[tex]\begin{aligned}\implies \sf Area\:of\:circle & = \sf \pi \left(\dfrac{s}{2}\right)^2\\& = \sf \pi \left(\dfrac{s^2}{4}\right)\\& = \sf \dfrac{1}{4}\pi s^2 \end{aligned}[/tex]

So the ratio of the area of the circle to the original square is:

[tex]\begin{aligned}\textsf{area of circle} & :\textsf{area of square}\\\sf \dfrac{1}{4}\pi s^2 & : \sf s^2\\\sf \dfrac{1}{4}\pi & : 1\end{aligned}[/tex]

Given:

[tex]\implies \sf \textsf{Area of square}=6^2=36\:in^2[/tex]

[tex]\implies \sf \textsf{Area of circle}=\pi \cdot 3^2=28\:in^2\:\:(nearest\:whole\:number)[/tex]

Ratio of circle to square:

[tex]\implies \dfrac{28}{36}=\dfrac{7}{9}[/tex]

Answer:

-0.61

Step-by-step explanation:

0.55/2=0.275

Read 0.275 from normal distribution tables

Gives -0.61

Answer:

3 nikels and 2 cents

Step-by-step explanation:

1 niquel = 5 cents

5+5+5= 15

15+ 2= 17

Answer:

Each group will have 122

Step-by-step explanation:

It technically means divide 488 by 4

[tex](d) \: \: y = - x - 1[/tex]

[tex]a \times \frac{ - 2}{3} = - 1 \\ a = \frac{3}{2} [/tex]

[tex](d) \: \: \: \: y = \frac{3}{2} x - 4[/tex]

Answer:

1. y = -x - 1

2. y = (3/2)x - 4

Step-by-step explanation:

1. Let y = ax + b be the equation of the line

that passes Through (4,-5) and parallel to y = -x + 1

Where ‘a’ is the slope and b the y value of the y-intercept point.

The lines are parallel

then

they have the same slope

then

a = -1

we get :

y = -x + b and the point (4 , -5) lies on the line

then

-5 = -(4) + b

Then

b = -5 + 4 = -1

Conclusion:

y = -x - 1

………………………………………

2. Let y = mx + p be the equation of the line

that passes Through (2,-1) and perpendicular to y = -2/3x + 5

Where ‘m’ is the slope and p the y value of the y-intercept point.

The lines are perpendicular  

then

The product of their slopes = -1

Then

m × (-2/3) = -1

Then

m = 3/2

we get :

y = 3/2x + p and the point (2 , -1) lies on the line

then

-1 = (3/2)×(2) + p

Then

p = -1 - 3 = -4

Conclusion:

y = (3/2)x - 4

The maximum concentration is greatest at; t = 4.926 hours

We are given the equation that represents the concentration as;

C = (3t² + t)/(50 + t³)

The maximum value of C is obtained when the slope of C' is zero (can be a local maxima too). So we are going to find solutions of C'.

C' = (-3t⁴ - 2t³ + 300t + 50)/(50 + t³)

At C' = 0, we have;

-3t⁴ - 2t³ + 300t + 50 = 0

Using online polynomial root calculator, the only valid root of this is;

t = 4.926 hours

Thus, the maximum concentration is greatest at t = 4.926 hours

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Answer:

$1.26

Step-by-step explanation:

A 20% off means multiplying by 1-0.2=0.8

4.39*0.8=3.512

3.512-1=2.512

2.512-1.25=1.262

1.262 rounded to the nearest cent is $1.26

The value of x from the given diagram is 16.6

In order to determine the value of x from the given figure, we will use the secant-secant theorem shown by the equation.

(6 +12) * 6 = (5 + x) * 5

Expand

36+72 = 25 + 5x

108 = 25 + 5x

5x = 108 - 25

5x = 83

x = 83/5

x = 16.6

Hence the value of x from the given diagram is 16.6

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Hello and Good Morning/Afternoon:

Let's take this problem step-by-step:

What does the information want:

Let's gather some information:

             ⇒ Angle B is shared by both triangles

             ⇒ Angle A' and A are the same, as they are both on parallel

                   lines, A'C' and AC, and both angles are formed with the

                   same line AB

                 ⇒ by the Angle-Angle Theorem*, they are similar triangles

If they are similar triangles:

   ⇒ their side lengths are proportional to each other

          ⇒ let's set up a proportion

                 [tex]\frac{A'B}{AB} =\frac{A'C'}{AC} \\\frac{30}{x+30} =\frac{14}{22} \\14(x+30) = 30*22\\14x + 420 = 660\\14x = 240\\x = 17.143[/tex]

          ⇒ let's set up a proportion

                 [tex]\frac{BC'}{BC} =\frac{A'C'}{AC} \\\frac{y}{y+15} =\frac{14}{22} \\22y=14(y+15)\\22y=14y+210\\8y=210\\y=26.25[/tex]

Answer:

Hope that helps!

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Answer:

D.  -924 feet

Step-by-step explanation:

For this problem, we'll need the relationship [tex]d=vt[/tex] where "d" is the distance traveled, "v" is the velocity the object is traveling, and "t" is the amount of time that it traveled.

Velocity is a "vector" quantity, which has both a magnitude and a direction.  The magnitude is the speed (42 feet per second) and the direction is downward.  Collectively, the velocity is -42 feet per second.  This will address the change in altitude and signify that the change in altitude is downward.

All quantities should be using units that match.

In this case, the distances provided in the answers are all measured in feet, and the speeds are measured in feet per second, so the feet match.

Also, the times are measured in seconds, and the speeds are measured in feet per second, those also match.

[tex]d=vt[/tex]

[tex]d=(\frac{-42\text{ feet}}{\text{second}})(22\text{ seconds})[/tex]

[tex]d=-924 \text{ feet}[/tex]

The equation which can be used to represent the total tolls Stephanie will pay is y = 1.35x

let

y = 1.35x

If the number of 3½ miles on the route is 5

Then, the total toll paid is

y = 1.35x

= 1.35(5)

= $6.75

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