Solve the equation with the quadratic
formula. Enter the smallest solution
first and round to the nearest tenth.
2x² - 4x - 48 = 0
x = [?], [?]

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 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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Answer: Dr. Johnson is conducting an experimental study to test the effectiveness of a new therapy for individuals with arachnophobia, which is the fear of spiders. He is measuring the pulse rate of the participants before and after the therapy as an indicator of their fear response when confronted by an actual spider. The data collected will likely be used to determine if the therapy is effective in reducing the participants' fear of spiders as measured by their pulse rate.

It is important to note that while pulse rate is a good indicator of fear response, it is not the only indicator of fear and it is also not a definitive measure of the effectiveness of the therapy. Other factors such as self-reported fear, behavioral changes, and physiological changes should also be considered to get a comprehensive understanding of the therapy's effectiveness.

Step-by-step explanation:

Answer:

C.

Step-by-step explanation:

The area of a rectangle is typically written as:

[tex]A = l x w[/tex]

where: l represents the length and w represents the width.

Since, in the given problem, we already know the value of the length which is 14.4 inches, and the value of width is one-third of the length. Thus, the width would be:

[tex]= (14.4)(\frac{1}{3})\\= \frac{24}{5} \\= 4.8 inches[/tex]

We will simply substitute this value to the formula to get the area.

[tex]A = lxw\\A = (14.4)(4.8)\\A = 69.12 in^{2}[/tex]

Answer:

its c i did this test

Step-by-step explanation:

The sampling technique being used in this scenario is simple random sampling.

It can be determined that simple random sampling is being used because individuals are selected at random from an alphabetical list of all registered voters. In simple random sampling, a random sample of individuals is selected from a larger population using a random procedure such as using a random number generator or drawing names out of a hat. The selection of individuals is completely random and every individual in the population has an equal chance of being selected.

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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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Answer:32/5

Step-by-step explanation:

32/5

Answer:

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

Step-by-step explanation:

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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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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A: (a) The 98% confidence interval would be wider than the 95% interval. As the confidence level increases, the margin of error increases, thus making the interval wider.

(b) The width of the confidence interval would decrease as the sample size increases. This is because a larger sample size will result in a more accurate representation of the population, thus allowing for a narrower confidence interval.

(c) The manufacturer cannot adjust the confidence interval to take this nonresponse into account, as the nonresponse does not affect the accuracy of the sample. The confidence interval is based on the sample itself and not the population from which it was drawn.

Random sampling is a method of selecting a sample of individuals from a population such that each member of the population has an equal chance of being selected.

Random sampling is often used in research studies to ensure that the sample is representative of the population as a whole.

Random sampling is also used to minimize bias and ensure that the sample is not influenced by any particular group or individual.

Random sampling is important because it helps ensure that the results of the study are accurate and valid.

Random sampling helps to ensure that the sample is representative of the population and that the results are not influenced by any particular group or individual.

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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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An equation to represent the total cost (y) for any number of rides (x) is y = 4x + 10.

In order to write an equation that model this situation, we would assign variables to the number of rides at an amusement park and the total cost respectively, and then translate the word problem into algebraic equation as follows:

Next, we would translate the word problem into an algebraic equation based on the fact that it cost $4 per ride, plus a $10 fee to get in as follows;

y = 4x + 10.

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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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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:

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!!

A graph which shows this relationship is: B. graph of a line passing through the points negative 2 comma negative 1 and 0 comma 0.

In order to determine the ordered pairs and linear function that could represent a linear relationship in the given table, we would have to determine the slope of based on the data points.

In Mathematics, the slope of a linear function can be calculated by using this this mathematical expression;

Slope = (Change in y-axis, Δy)/(Change in x-axis, Δx)

Slope = (y₂ - y₁)/(x₂ - x₁)

Slope = (0 + 1)/(0 + 2)

Slope = 1/2

Slope = 0.5.

At data point (-2, -1), a linear function of this line can be calculated in point-slope form as follows:

y - y₁ = m(x - x₁)

Where:

y + 1 = 0.5(x + 2)

y = 0.5x + 1 - 1

y = 0.5x

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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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Answer:

53.3%

Step-by-step explanation:

14 + 16 = 30

16/30 x 100 = 53.3% are laptops

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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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

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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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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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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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.

Answer:

Step-by-step explanation:

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

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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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 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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