substitute 6x-5y=-1 and 6x+4y=-10

The coordinates of the image of the parallelogram are:

C = (-4, 8)

D = (-2, 4)

E = (6, 3)

F = (4, 7)

There are two ways of reflection.

Along x-axis:

(x, y) – (x, -y)

Along y-axis:

(x, y) - (-x, y)

We have,

Parallelogram CDEF with vertices:

C = (-4, -4)

D = (-2, 0)

E = (6, 1)

F = (4, -3)

The parallelogram is reflected over the line y = 2.

This means,

The y-coordinates will change and the x-coordinate will remain the same.

Now,

C = (-4, -4)

There are 6 units between y = 2 and y = -4 so,

C' = (-4, 2 + 6) = (-4, 8)

D = (-2, 0)

There are 2 units between y = 2 and y = 0 so,

D' = (-2, 2 + 2) = (-2, 4)

E = (6, 1)

There are 1 units between y = 2 and y = 1 so,

E' = (6, 2 + 1) = (6, 3)

F = (4, -3)

There are 5 units between y = 2 and y = -3 so,

F' = (4, 2 + 5) = (4, 7)

Thus,

The coordinates of the image are:

C = (-4, 8)

D = (-2, 4)

E = (6, 3)

F = (4, 7)

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The only number that is irrational is π

An irrational number is a number that can't be written as the quotient between two integers.

Also, square roots of non-square numbers are irrational.

In this case, the options are:

-15/4

-7/9

√4

π

The first 3 of these are rational, and the only irrational one is π, which is the quotient betwen the cicumference and the diameter of a circle.

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$97.056 is the total interest accrued after the first month.

A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics. If we need to compute a percentage of a number, we should divide it by its whole and then multiply it by 100. The proportion, therefore, refers to a component per hundred. Per 100 is what the term percent signifies. The letter "%" stands for it.

Given, You (or your parents) purchase a new car for $19,725.00 plus 4.75% sales tax. The down payment is $2,175.00 and you (or your parents) have an average credit rating.

The cost of car = 19,725*(1.0475) = 20,661.9375

Down payment = 2,175

So balance amount, P= 20661.9375-2175 = 18,486.9375

So interest for the average rating of a new car = 6.30%

So the interest accrued in first month = 18,486.9375*0.063/12 = $ 97.056

therefore, interest accrued after the first month is $97.056.

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The statements

(a) If x and y are integers such that 3xy then 3x.

(b) For any integers x, y, and z, if x y and xz, then x(y - z).

(c) If x and y are integers such that x > 1 and if x divides y, then the solution is x(y - 1)

are proved.

The term integers in math is defined as are the collection of whole numbers and negative numbers.

Here we know that x and y are the integers,

Then it takes both positive and negative numbers.

Then we take y=1, then we apply it on the expression then we get,

=> 3x(1) = 3x.

Similarly here we have take that xy|z means xy is a factor of z,

Here we can say xym = z for some integer m.

=> x × ym = z, and ym is an integer by closure hence x is a factor of z such that x|z.

Similarly here we can also y * xm = z, and consider xm is an integer, hence y is a factor of z, i.e. y|z.

Where in the third one, we can take x|y means there exists a constant is written as y = kx

Where as y|x means there exists a constant written as x = cy

When we compare these, then we get,

=> y = kx = kcy

Here we have to true if kc = 1 and since k and c are integers, then we have k = c = 1

Therefore y = kx becomes y = 1*x or y = x

Similarly x = cy becomes x = 1*y or x = y

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Answer:

C. 5/4

Step-by-step explanation:

Let s = the scale factor

4s = 5  divide both sides by 4

s = 5/4

Answer:

Yes, the answers are equivalent.

Step-by-step explanation:

The answers are equivalent because when adding a positive to something it does not change the value of the number. So by adding the + in front of the -1 the value of -1 does not change in the equation.

Hope this helps!!

The mean decreases by 2.9°. Therefore, option D is the correct answer.

In maths, the average value in a set of numbers is the middle value, calculated by dividing the total of all the values by the number of values. When we need to find the average of a set of data, we add up all the values and then divide this total by the number of values.

Given that, the average high temperatures in degrees for a city are 58, 61, 71, 77, 91, 100, 105, 102, 95, 82, 66, 57.

Here, average = Sum of all the observations/Number of observations

= (58+61+71+77+91+100+105+102+95+82+66+57)/12

= 965/12

= 80.41°

New average = 965+42.5/12+1

= 1007.5/13

= 77.5°

Difference in average =80.41-77.5

= 2.91°

Therefore, option D is the correct answer.

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Step-by-step explanation:

To solve this problem, we can use the law of cosines. The law of cosines states that for any triangle with sides a, b, and c, and an angle C opposite side c,

c² = a² + b² - 2abcos(C)

In this problem, we can consider the man's starting point as the origin, and the distance he travels in the first leg as the first side of the triangle (a = 4km). The distance he travels in the second leg is the second side of the triangle (b). The angle between the two legs is the angle opposite side c, which is 90 degrees since the man changes direction from due west to southwest.

Therefore, we can use the law of cosines to find the distance he traveled in the second leg:

c² = a² + b² - 2abcos(90)

c² = 4² + b²

c = √(4² + b²)

c = √(16 + b²)

We know that the bearing of the second leg is 197 degrees, which is equivalent to a bearing of -163 degrees, since bearing measurements are taken clockwise from due north.

So we can use the law of cosines to find the distance he traveled in the second leg:

b = √(c² + a² - 2ac cos (-163))

We can now plug in the values we know:

b = √(c² + 4² - 24c*cos(-163))

We can now solve for c:

c = √(b² + 16 - 8bc)

The man is then southwest of his starting point, so the distance from his starting point to the final point is c.

y= -2.6717 + 0.0043(660) + 0.0045(630) = 3.00 is the GPA Score for Bobby Eagle.

A statistical method known as multiple linear regression (MLR), usually referred to as multiple regression, employs a number of explanatory variables to forecast the result of a response variable. One explanatory variable is used just once in multiple regression, an extension of linear (OLS) regression. Financial and econometric inference both make heavy use of MLR.

Score on critical reading = 660

Score on mathematics  = 630

Intercept = -2.6717

Reading(x1) = 0.0043

Mathematics(x2) = 0.0045

Hence, y = -2.6717 + 0.0043(660) + 0.0045(630) is the GPA score for Bobby.

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Answer:

33/108290 = 0.000305

Step-by-step explanation:

There are 52 cards in a deck.

There are 3 face cards of each of 4 suits in a deck, so there are 12 face cards in a deck.

Taking all cards at once is the same as taking one card at a time with no replacement.

First card: p(face card) = 12/52 = 3/13

Now there are 11 face cards and a total of 51 cards left.

Second card: p(face card) = 11/51

Now there are 10 face cards and a total of 50 cards left.

Third card: p(face card) = 10/50 = 1/5

Now there are 9 face cards and a total of 49 cards left.

Fourth card: p(face card) = 9/49

Now there are 8 face cards and a total of 48 cards left.

Fifth card: p(face card) = 8/48 = 1/6

Since each drawing of a card is an independent event, the overall probability of drawing 5 face cards is the product of the individual probabilities.

p(5 face cards) = 3/13 × 11/51 × 1/5 × 9/49 × 1/6

p(5 face cards) = 33/108290 = 0.000305

The slope of the line represented by 4x-7y=62 is 4/7. A line's steepness is measured by its slope. The mathematical expression for slope is "rise over run."

Option A is correct.

In mathematics, a line's slope is the ratio of the change in the y coordinate to the change in the x coordinate. The net change in the y-coordinate and the net change in the x-coordinate, respectively, are denoted by the symbols delta y and delta x.

          We are given equation as 4x-7y=62

First, let's write it in the slope-intercept form .In general, slope-intercept form is                                    y=mx + b

where m is the slope

So, writing the equation in the form, we get

                                    ⇒-7y = 62-4x

                                        ⇒7y = 4x-62

                                          ⇒y = 4x/7-62/7

Now, matching the equation with the general form,

                                          m = 4/7

Hence, the slope of the line represented by 4x-7y=62 is 4/7.

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Two numbers are in the ratio 8cm:1m, he greater number is 3,125.

A ratio in mathematics demonstrates how many times one number is present in another. A ratio can have any number of quantities, such as counts of people or things or measurements of length, weight, time, etc. Both numbers must be positive in most situations. An ordered pair of integers, a fraction with the first number in the numerator and the second in the denominator, or the value represented by this fraction are all examples of ratios.

Given that, Two numbers are in the ratio 8cm:1m and smaller number is 250.

let the greater number is x.

ratio = 8cm/1m

= 8cm/100cm

= 1/12.5 or 1:12.5

1/12.5 = 250/x

⇒ x = 250 * 12.5

⇒ x = 3,125

So, the greater number is 3,125.

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The Raichu card was made 8 years ago.

To calculate this, we need to take into account the age of the Mewtwo card, the Snorlax card, and the Raichu card.

The Mewtwo card is twice as old as the Snorlax card, so the Mewtwo card is two years old. The Raichu card is five times as old as the Snorlax card, so it must be ten years old.

Since the Raichu card is two years older than the Mewtwo card, it must be eight years old. Therefore, the Raichu card was made eight years ago.

To summarise, the Mewtwo card is two years old, the Snorlax card is one year old, and the Raichu card is ten years old. Therefore, the Raichu card was made eight years ago.

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Answer:

Step-by-step explanation:

That"ll be 37% hope this helps:))

If the denominator is having a poor integer, then we can multiply the numerator and denominator each through -1, to carry the minus signal at the top.

What is supposed through integer ?

The variety 0 (0), a tremendous natural variety (1, 2, three, and so on.), or a terrible integer denoted by way of a minus sign (1, 2, 3, and many others.) are all examples of integers.

The inverse components of the equal superb numbers are the bad numbers.

the lowest organization and ring of the natural numbers are fashioned by using the integers.

to distinguish them from the more common algebraic integers, the integers in algebraic quantity theory are every so often particular as rational integers.

In truth, (rational) integers are rational numbers which are also algebraic integers.

inside the beyond, the word was used to refer to a a couple of of 1 or the whole aspect of a blended quantity.

we will multiply and divide -five with the aid of (-1), to get;

(-five)*(-1) = five

as a result, five is a effective rational range.

1 can be expressed inside the form of ratio, such that,

1 = 1*1

wherein each numerator and denominator, i.e. 1 and 1 are high-quality integers.

therefore, 1 is a high quality rational wide variety.

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By using the property of measure of an arc from the central angle

m(arc MQN) = 225°

m(arc MPN) = 135°

If m(arc KJH) = 312°

m∠1 = 48°

What is the measure of an arc from the central angle?

The measure of an arc from the central angle is the portion of the circumference of a circle that the arc spans. The measure of an arc is typically given in degrees.

In the given figure

by using the property of measure of an arc from the central angle

m(arc MQN) = 225°

m(arc MPN) = 360° - 225° = 135°

In the second figure,
If m(arc KJH) = 312°

m∠1 = 360° - 312° = 48°

Hence, by using the property of measure of an arc from the central angle

m(arc MQN) = 225°

m(arc MPN) = 135°

If m(arc KJH) = 312°

m∠1 = 48°

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The expression for the given conditions is Y=10+c

where Y=no. of books Brett has and c=no. of books Erica has.

what are expressions?

Expressions in math are mathematical statements that have a minimum of two terms containing numbers or variables, or both, connected by an operator in between. The mathematical operators can be of addition, subtraction, multiplication, or division. For example, x + y is an expression, where x and y are terms having an addition operator in between. In math, there are two types of expressions, numerical expressions - that contain only numbers; and algebraic expressions- that contain both numbers and variables.

e.g. A number is 6 more than half the other number, and the other number is x. This statement is written as x/2 + 6 in a mathematical expression. Mathematical expressions are used to solve complicated puzzles.

Now

Given No. of books Erica has = 19

and Brett has c more comic books than Erica has

let Y=no. of books Brett has

Hence, the expression will be

          Y=19+c

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The number of nickels, x, and the number of dimes y that Harper has are;

8 nickels and 3 dimes

From conversion of coins we know that;

1 nickel = $0.05

1 dime = $0.10

Thus, if she has 5 more nickels than dimes, then;

Let x = the number of dimes Harper has

Let x + 5 = the number of nickels Harper has

Thus;

$0.05(x + 5) + $0.10(x) = $0.70

0.05x + 0.25 + 0.10x = 0.70

0.15x = 0.70 - 0.25

0.15x = 0.45

x = 0.45/0.15

x = 3 dimes

Nickels = 8 nickels

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Zara extends the width of her garden by 11 feet. This can be calculated with the help of perimeter formula:

Equation used to solve the problem: P = 2L + 2W

2(12) + 2W = 46

24 + 2W = 46

2W = 22

W = 11

Zara extends the width of her garden by 11 feet.

The complete length of a shape's boundary is referred to as the perimeter in geometry. A shape's perimeter is calculated by adding the lengths of all of its sides and edges.

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Answer:32/5

Step-by-step explanation:

32/5

Answer:

Solution: 6.4% as a fraction is 32/5.

Step-by-step explanation:

Answer:

53.3%

Step-by-step explanation:

14 + 16 = 30

16/30 x 100 = 53.3% are laptops

No hay solución para la ecuación algebraica 3 · x + 15 = 3 · x + 10.

En este problema tenemos el caso de una ecuación algebraica con una variable única y es nuestra labor determinar su solución, en caso de existir, por métodos algebraicos. Primero, escriba la ecuación algebraica correspondiente:

3 · (x + 5) = 3 · x + 10

Segundo, halle la solución por propiedades algebraicas:

3 · x + 15 = 3 · x + 10

15 = 10 (CRASH!)

La ecuación algebraica 3 · x + 15 = 3 · x + 10 no tiene solución.

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well, it comes down to, if f(x) is indeed an inverse of g(x) and the other way around, then f(  g(x)  ) = x, and likewise g(  f(x)  ) = x, so let's check if f(  g(x)  =x

[tex]f(x)=3x+11\hspace{5em}g(x)=-\cfrac{1}{3}x-\cfrac{11}{3} \\\\[-0.35em] ~\dotfill\\\\ f(~~g(x)~~)=3\left( -\cfrac{1}{3}x-\cfrac{11}{3} \right)+11 \\\\\\ f(~~g(x)~~)=-x-11+11\implies f(~~g(x)~~)=-x ~~ \bigotimes[/tex]

now, we could do a test by doing g(  f(x)  ), however we don't need to, since f(  g(x)  ) ≠ x, they're not inverse of each other.

The quadratic equation to find the width of the rectangle by formulating the area and length value is 2w² - w - 91 = 0.

What is area?

An object's area is how much space it takes up in two dimensions. It is the measurement of the quantity of unit squares that completely cover the surface of a closed figure.

The value for the area of the rectangle is given as = 91 in²

Let the width for the rectangle be = w

Then the length of the rectangle is 1 less than twice its width, l = (2w - 1)

The formula for the area of the rectangle is -

Area = length × width

Substitute the values to get the equation for width -

91 = (2w - 1) × w

Use the arithmetic operation of multiplication -

91 = w(2w - 1)

91 = 2w² - w

Rearrange in quadratic form -

2w² - w - 91 = 0

Therefore, the equation is obtained as 2w² - w - 91 = 0.

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Answer:

y = x + 7  

Step-by-step explanation:

     [tex]\boxed{(y-y_1)=m(x -x_1)}[/tex]

m = 1

(1 , 8)  ; x₁ = 1  & y₁= 8;

    y - 8 = 1*(x - 1)

    y - 8 = x - 1

          y = x - 1 + 8

          y = x + 7

9 is the  common factor of 9x + 36.

A number system is defined as a system of writing to express numbers.

The given expression is 9x+36

Factor is a number or algebraic expression that divides another number or expression evenly i.e., with no remainder.

The factors of 9 are 1,3,9

The factors of 36 are 1,2,3,4,6,9,12 and 18

The highest common factor is 9.

Take 9 as common from the expression.

9(x+4)

Hence, 9 is the  common factor of 9x + 36.

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To meet the goal, the company should adjust the mean and/or standard deviation so that the probability of cans having a volume less than 355ml is less than 2.5%.

A probability is a numerical representation of the likelihood or chance that a specific event will take place.

We can use the z-score formula to find the probability of cans having a volume less than 355 ml.

z-score = (355 - 358.2) / 1.8 = -1.78

Probability of cans having a volume less than 355ml = P(z < -1.78) = 0.0372

The company is not meeting its goal since the probability of cans having a volume less than 355ml is 0.0372 which is greater than 2.5%.

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Inequality of 4x-6= 22 is  x=7

In mathematics, inequalities describe the connection between two values that are not equal. Equal implies to be equal, not. The "not equal symbol is typically used to indicate that two values are not equal. But different inequalities are used to compare the values to determine if they are less than or higher than.

Both equations and inequalities are mathematical phrases created by connecting two expressions. The equal sign (=) in an equation denotes that the two expressions are regarded as equal. In contrast, an inequality indicates that the two phrases are not always equal by using the symbols >,,, or.

To the other side, move -6.

Changes from a -6 to a +6 sign.

4x-6+6= 22+6

4x= 22+6

4x= 28

Divide each side by 4

4x/4= 28/4

x= 7

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The mother must drive at a speed of 6 mph to reach Anna in ten minutes.

To find the speed required for the mother to reach Anna in ten minutes, you need to calculate the distance between them and the time it takes to close the gap.

Let x be the speed of the mother's car in mph.

In one hour, Anna will have covered 6 miles.

In ten minutes, the mother will have covered x * 10/60 miles.

The total distance between them is 6 + x * 10/60 miles.

The mother must cover this distance in ten minutes, so:

x * 10/60 = 6 / (10/60)

x = 6 * (10/60) / (10/60)

x = 6 mph

Therefore, the mother must drive at a speed of 6 mph to reach Anna in ten minutes.

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