On the first of January, Jed had £48 in his bank account and Esther had £180 in her bank account. From then on, at the end of each month Jed put £40 into his account and Esther put £34 into her account. After how many months did they have the same amount of money in their accounts?​

Answer: The two lines intersect at (-4,3)

Step-by-step explanation:

So our first step would be to turn both of these into standard slope-intercept form.

1.)

4y + 3x = 0

4y = -3x

y = -3/4x

2.)

4y - x = 16

4y = x + 16

y = 1/4x + 4

Now that we have our 2 equations, y = -3/4x and y = 1/4x + 4 we can graph them to get an intersection at (-4,3)

The probability of being dealt an ace=4/52

The probability of being dealt another ace = 3/51

What is probability?

Simply put, probability measures how probable something is to occur. We can discuss the probabilities of various outcomes, or how likely they are, whenever we are unsure of how an event will turn out. Statistics is the study of events subject to probability.

The likelihood that a population parameter will be less than a given value when the null hypothesis is true is expressed as the p-value, also known as a probability value or a measure of significance, for a particular statistical model.

The probability of drawing one of the four aces from a typical 52-card deck is 4/52; but, the probability of drawing a second ace is merely 3/51 since, after the first ace was drawn, there were only three more aces remaining in the remaining 51 cards.

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The simplified form of the expression  √10•√8 is 4√5.

Expression:

Expression refers the mathematical statements that have two terms at least that contain variables, numbers, or both.

Given,

Here we have the expression √10•√8.

Now we have to find the simplified form of these expression.

Now, we have to multiply the values inside the square root then we get,

=> √10 x √8 = √(10  x 8)

After the multiplication we can get,

=> √80

Now, we have to expand this as the following,

=> √16 x 5

We know that √16 is equivalent for 4²,

So, it can be written as,

=> √4² x 5

Now, we have to simplify this as,

=> 4√5

Therefore, the simplified expression is 4√5

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Answer:

Coordinates of A are (-2.5, -1.5)

Coordinates of B are (4.5, -3.5)

Answer:

Step-by-step explanation:

{x,y}={0,-3}

The equation of line that is perpendicular to the line y = 1/2x + 2 is y = -2x - 7

A perpendicular line is a straight line through a point. It makes an angle of 90 degrees with a particular point through which the line passes. Coordinates and line equation is the prerequisite to finding out the perpendicular line.

The equation of perpendicular line is given as

(y - y₁) = m(x - x₁)

m = slope of the line.

But the slope of a perpendicular line is given as

m₁m₂ = -1

m₁ = 1/2, m₂ = ?

1/2m₂ = -1

m₂ = -2

The new slope is -2.

Substituting the values into the equation above,

(y - y₁) = m(x - x₁)

y - 1 = -2(x - (-4))

y - 1 = -2x - 8

y = -2x - 7

The new equation is y = -2x - 7

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Answer:

-180

Step-by-step explanation:

You would plug in x=3 and y=-6 into the equation

So, the first part would be 36x when x=3, 36(3)=108

The second part would ne -8y^2 when y=-6 (-6 squared is 36), -8(36)=-288

Putting these together, you get 108-288 which is -180

Answer: -180

hops this helps

have a good day

Step-by-step explanation:

The bicycle wheel performs 10 revolutions every minute

A revolution in math is a full rotation, or a complete, 360-degree turn. In a 360-degree rotation, the object starts and ends in the same position. A mathematical revolution can be visualized when a top spins.

The bicycle wheel makes 1 complete revolution which is equal to the circumference of the wheel = πD

but D =  diameter = 42 inches, converting inches to feet

12inches is 1 foot, then 42 inches = 42/12 = 7/2 inches

Also circumference = 22/7 x 7/2 = 11 feet/rev

Also if the rider travelled 110 feet per minute.

Then the wheel's revolution per minute = 110/11
                                                                   = 10 rev/minute

In conclusion the bicycle wheel revolves 10 times every minute

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Answer:

negative x over 4 + three-fourths = 12

Answer:

Step-by-step explanation:

(StartFraction negative x over 4 EndFraction + three-fourths = 12

The relation y = x² represents y as a function of x because every x-value returns a unique y-value.

Using the definition of a function, y=x² is a function because you will only get one unique y-value for each x-value in your domain.

The vertical line test is a quick check you can perform. The function y=x² is a parabola, and if you draw vertical lines anywhere on it, they will only cross the parabola once.

As a result, it is a function. A circle is not an example of a function because a vertical line drawn on a circle crosses at two different points.

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∠G+∠H+∠J=180 and ∠K+∠L+∠M=180 from the angle sum property of triangle, ∠H=∠L (3rd Angle Theorem) and ∆GHJ≅∆KLM from ASA congruency theorem.

In the given question we have to prove ∆GHJ congrurnce ∆KLM.

Given that: ∠G≅∠K, ∠J≅∠M, [tex]\over{HJ}[/tex] ≅ [tex]\over{LM}[/tex].

As given that;

∠G≅∠K

∠J≅∠M

[tex]\over{HJ}[/tex] ≅ [tex]\over{LM}[/tex]

So from the angle sum property of triangle

∠G+∠H+∠J=180................(1)

∠K+∠L+∠M=180.................(2)

Now equation equation 1 and 2

∠G+∠H+∠J=∠K+∠L+∠M

As we know that ∠G=∠K, ∠J=∠M

So now the expression is

∠G+∠H+∠J=∠G+∠L+∠J

After solving ∠H=∠L (3rd Angle Theorem)

Since, ∠H=∠L, HJ=LM and ∠G=∠K, so from the theorem Angle Side Angle(ASA) congruency,

∆GHJ≅∆KLM

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The percentage reduction of the jacket is 20 percent.

Percentage decrease or reduction means subtracting a given percentage of a value from the original value.

Therefore, the jacket cost 80 dollars and it is reduced to 64 dollars.

The percentage reduction of the jacket can be calculated as follows:

% reduction = (Decreased Value / Original Value) × 100

Decreased value = 80 - 64 = 16

Original Value = 80

% reduction = 16 / 80 × 100

% reduction = 1600 / 80

% reduction = 20%

Therefore, the percentage reduction is 20%.

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For a year, 1750 students were able to donate to the school.

A % in mathematics is a quantity or ratio that is stated as a fraction of 100 (from the Latin per centum, "by a hundred"). Although the abbreviations "pct.", "pct.", and occasionally "pc" are also used, the percent sign, "%," is frequently used to indicate it  by % lacks dimensions and has no associated unit of measurement.

The Latin word per centum, which means "hundred" or "by the hundred," is where the word "percent" originates. The % calculator computes a variety of percentage-based numbers, such as the percentage difference between two provided values.

Given,

The annual salary of a football player is 210000

1 student ----------$120

x  ------------$210000$

x=(210000/120)

x=1750 students

1750 students could send their donation to the school for 1 year.

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The value of x is 5 when the line is JL and the midpoint of the JL is K.

Given that,

The line is JL and the midpoint of the JL is K.

JL= 13x-9 and JK= 28.

We have to find the value of x.

The midpoint is the point on a line that connects two points that is exactly in the middle of the line.

We know that,

JL= JK+ JK

JL=2JK

13x-9 = 2×28

13x-9= 56

13x= 56+9

13x= 65

x=65/13

x=5

Therefore, The value of x is 5 when the line is JL and the midpoint of the JL is K.

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Answer:

1,265

Step-by-step explanation:

10^3=1000*2=2000

105*7=735

2000-735

During the progressive era many state and local governments adopted initiative referendum and recall together these procedures gave citizens a more direct voice in government.

At the progressive era the citizens was given by a more direct voice in government because of the three principles they are initiative ,referendum and recall.

Initiative:

Proposed law with backing can be put on the ballot at election,in that case the petitions must be approved with valid signatures.

Referendum:

plebiscite is a kind of referendum in which meaning decree of the people it depends on nature of advisory called as referendum.

Recall:

Recall defines that voters may remove a public official from office that must be before the expiration.

Therefore During the progressive era many state and local governments adopted initiative referendum and recall together these procedures gave citizens a more direct voice in government.

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Answer:20

Step-by-step explanation:

The function that could be used to represent the total cost of the shoes by applying the $15 coupon first and the 20% member discount second for original cost, using proportions, is of:

C(x) = 0.8(x - 15).

A proportion represents a fraction relative to a total amount, and this fraction is combined with the basic arithmetic operations, especially division and multiplication, to find the desired amounts in whichever context of the problem.

The value of shoe is given as follows:

x.

The discounts are given as follows:

Hence the function that gives the total cost paid is presented as follows:

C(x) = 0.8(x - 15).

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According to the imaginary number, the real solution between 30 and 80 is 60

Imaginary number

An imaginary number refers a real number multiplied by the imaginary unit i, which is defined by its property i² = −1.

Given,

Here we have to use the digits -9 to 9 (each only once) to create a real solution between 30 and 80 (a+bi)(c+di).

We know that the digits from -9 to 9 are listed as follows:

(-9,-8,-7,-6,-5,-4,-3,-2,-1,0,1,2,3,4,5,6,7,8,9)

Now, we have to choose the digits -9 to 9, as the value of a, b, c and d,

For that we have to choose the value of a = 3, b = -9, c = 2 and d = 6,

Now, we have to apply these value on the given imaginary equation, then we get,

(a + bi) (c + di) = (3 + -9i) (2 + 6i)

When we simplify this one then we get,

=> 6 + 18i + (-18i) – 54i²

We know that value of i² =  -1, then the equation is written as,

=> 6 - 54(-1)

=> 6 + 54

=> 60

Therefore, 60 is a real solution between 30 and 80.

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The number of ways to select the banners is given as follows:

a. Matching with the country: 362,880.

b. Not matching with the country: 60,949,324,800

To select the banners matching the country, only the nine countries are chosen, and then the specific banner regarding the country is chosen, thus the arrangements formula is used.

The number of possible arrangements of n elements is given by the factorial of n, that is:

[tex]A_n = n![/tex]

Hence for item a the total number of outcomes is the factorial of nine, which is the number of countries, is given as follows:

Total = 9! = 362,880.

Then just nine banners are taken at random from a set of 20. The order is important, hence the permutation formula is used.

The number of possible permutations of x elements from a set of n elements is given by:

[tex]P_{(n,x)} = \frac{n!}{(n-x)!}[/tex]

In this problem, 9 banners are selected from a set of 20, hence the number of ways is:

N = 20!/(20 - 9)! = 20!/11! = 60,949,324,800.

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The number of days it would take to collect 2600 cans is; 11 days

We are given the equation that represents the number of cans that Nicholas collected as; y = 235x + 15

where;

x represents the number of days.

y represents the number of cans collected.

Now, we want to make x the subject of the formula;

y = 235x + 15

Subtract 15 from both sides to get;

y - 15 = 235x

divide through by 235 to get;

(y - 15)/235 = x

When y = 2600;

x = (2600 - 15)/235

x = 11 days

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The distance between the points, (-8, -2) and (12, 10), is 23.3

From the question, we are to determine the distance between the two given points.

From the given information,

The points are (-8, -2) and (12, 10)

The distance between two points in given by the formula

d = √[(x₂ - x₁)² + (y₂ - y₁)²]

Where d is the d is the distance between the points

Thus,

d = √[(12 - (-8))² + (10 - (-2))²]

d = √[(12 + 8)² + (10 + 2)²]

d = √[(20)² + (12)²]

d = √[400 + 144]

d = √[544]

d = 23.3

Hence, the distance is 23.3

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Answer:

x-3

Step-by-step explanation:

2x²-6x=0

divide both sides by x

2x²/x -6x/x=0

2x-6=0

2x=6

x=6/2

x=3

or (x-3)

Answer:

All you simply do is divide 23,500 by 500....that is equal to 47. So 47 is the answer

Step-by-step explanation:To find out how many reams were used, all we have to do is divide 23,500 by 500.

This gives us: 47 reams

If she did some research and learned that the exchange rate is 6 Tala for $2. The number of tala she get if she exchanged $6 is 18 tala.

Given data:

Exchange rate = 6 Tala for $2

Let x represent the tala Ming will get if she exchange $6

$2/6 = $6/X

Cross multiply

2x = 6× $6

2x = 36

Divide both side by 2x

x = 36/2

x = 18 tala

Therefore she would get 18 tala.

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Answer: -15 degrees

Step-by-step explanation:

Answer:

∠W = 36.6°

Step-by-step explanation:

Hello!

If angles are complementary, it means that they add up to 90°.

Since the measure of Angle X is 53.4, we can find measure of Angle W by subtracting 53.4 from 90.

The value of W is 36.6°.

The correct expression will be;

⇒ 3n - 15 - n = 101

What is an expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The algebraic expression is;

''A number, n, is added to 15 less than 3 times itself. The result is 101.''

Now,

Since, The algebraic expression is;

''A number, n, is added to 15 less than 3 times itself. The result is 101.''

So, We can formulate;

⇒ 3n - (15 + n) = 101

⇒ 3n - 15 - n = 101

Thus, The correct expression will be;

⇒ 3n - 15 - n = 101

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Answer:

The Answer is C.

Step-by-step explanation:

It's important to know how the standard form of an equation works.

Remember that y = mx + b, where y is the output value, m is the slope of the equation, and b is the y-intercept (the initial value) of the equation. We know that the pool starts with 25 inches of water in it, so the initial value, or y-intercept is 25, because the pool starts with 25 inches of water after 0 hours. We know that the pool fills up 4 inches per hour, meaning as each hour progresses, the equation will increase by 4. This is the slope. y has been replaced with h in this equation. So, your answer would be h = 4t + 25.