a dilation will always preserve both the orientation of a figure and the orientation of the vertices

Answer:

[tex]-16[/tex]

Step-by-step explanation:

[tex]f(5)=4(5)-1=19 \\ \\ g(5)=2^5+3=35 \\ \\ (f-g)(5)=f(5)-g(5)=19-35=-16[/tex]

Answer:

Step-by-step explanation:

6x [tex]\geq[/tex]15

x= $2.5

since it deals with money make it $2.50

_made my kharis:)

Carson expects to spend at least $15 on the popsicles, so the cost of each popsicle multiplied by the number of popsicles he is buying (6) must be greater than or equal to $15. Therefore, the inequality 15 ≤ 6x describes the problem.

Step 1: Let x represent the cost of each popsicle.

Step 2: Multiply 6 (the number of popsicles) by x (the cost of each popsicle): 6x

Step 3: Set the equation equal to 15 (the amount of money Carson expects to spend on the popsicles):

6x = 15

Step 4: Divide both sides of the equation by 6:

6x/6

= 15/6

Step 5: Simplify to get the answer:

x = $2.50

Carson wants to buy 6 popsicles from the ice cream truck and expects to spend at least $15. To figure out how much each popsicle should cost, I used an inequality. I let x represent the cost of each popsicle, multiplied it by 6 (the number of popsicles Carson is buying), and set the equation equal to 15 (the amount of money Carson expects to spend). After dividing both sides of the equation by 6 and simplifying, I got the answer that each popsicle should cost $2.50. Therefore, Carson should expect to spend at least $15 on the 6 popsicles.

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The quadrilaterals with vertices (a, b) (-b, a) (-a, -b) (b, -a) is square.

A square is a quadrilateral with four equal sides and four equal angles that is a regular quadrilateral. The square's angles are at a straight angle or 90 degrees. The square's diagonals are also equal and split at a 90-degree angle.

A rectangle with two opposite sides that have the same length can also be referred to as a square.

Given the  quadrilaterals with vertices:

(a, b) (-b, a) (-a, -b) (b, -a),

Let A(a, b), B(-b, a),  C(-a, -b),  and D(b, -a) are the vertices,

let a = 1 and b = 2

coordinate is  A(1, 2), B(-2, 1),  C(-1, -2),  and D(2, -1)

distance between two coordinates is given by,

d = √((x₂ – x₁)² + (y₂ – y₁)²)

finding distance between AB, BC, CD, DA

Distance between AB = √((-b – a)² + (a – b)²)

Distance between AB = √((-2 -  1)² + (1 – 2)²)

Distance between AB = √10 units

Distance between BC = √((-1 + 2)² + (-2 + 1)²)

Distance between BC = √10 units

Distance between CD = √((2 + 1)² + (-1 + 2)²)

Distance between CD = √10 units

Distance between DA = √((2 - 1)² + (-1 - 2)²)

Distance between DA = √10 units

since distance between AB = BC = CD = DA

so the quadrilateral is square.

Hence the quadrilateral is square.

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The slope is −0.1. Starting at 3.9, the GPA will be decreased by 0.1 for every text sent in class. The answer is the first option.

The equation of a line has the following form:

y = mx+ b

Where m is the slope of the line and b is the intercept with the axis of y.

In this case, the equation is:

y = 3.9 − 0.1x

y = -0.1x + 3.9

Observe that

m = - 0.1

b = 3.9

So if x represents the number of texts sent during classes, this means that x ≥ 0.

When x increases by one unit then y decreases by -0.1. For example when x = 1 then y = 3.9 - 0.1 = 3.8

Then the greatest value it can take the GPA is 3.9. Therefore we can say that the function starts at y = 3.9.

So, the answer is the first option.

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The complete question is-

A student believes there is a correlation between the number of texts sent during class and GPA. the student collected data and found that the line of fit can be modeled by the equation ŷ = 3.9 − 0.1x.

Identify and interpret the slope in this scenario.

The slope is −0.1. Starting at 3.9, the GPA will decrease by 0.1 for every text sent in class.

The slope is 0.1. Starting at 3.9, the GPA will increase by 0.1 for every text sent in class.

The slope is −3.9. Starting at 0.1, the GPA will decrease by 3.9 for every text sent in class.

The slope is 3.9. Starting at 0.1, the GPA will increase by 3.9 for every text sent in class.

The balanced half- cell reaction for the process that occurs at the anode in acidic solution: V⁺² + H₂O → VO₂⁺ + 2H⁺ + e⁻.

Cell notation is a condensed notation for the two half-cell reaction in an electrochemical or galvanic cell. These two half-cell reactions are divided by a salt bridge, with the cathode cell on the right and the anode cell on the left.

At the anode, oxidation happens, whereas at the cathode, reduction happens.  Cell notation is used to represent the reaction that is being given. The reaction occurring on the anode is written first in cell notation.

Oxidation occurs at the anode while reduction occurs at the cathode. Anode is a positive electrode in this case, and cathode is a negative electrode. Oxidation occurs at the anode while reduction occurs at the cathode.

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Answer:The rational root theorem states that if the leading coefficient is taken to be an and the constant coefficient is taken to be a0 the possible roots of the equation can be expressed as : Now, from the given options, the possible choices can be : A, B, C and E D can be there because after taking any pair the rational root can't be 3

Step-by-step explanation:

The two variables in a scatter plot are called the x-variable or independent variable and the y-variable or also called dependent variable.

The x-variable is typically plotted along the horizontal axis, and the y-variable is typically plotted along the vertical axis. The x-variable is the variable that is being used to explain or predict changes in the y-variable. In other words, it is the variable that is being manipulated or changed to observe changes in the y-variable.

For example, if the x-variable is a person’s age and the y-variable is their income, then the x-variable is the variable that is being changed (age) to observe changes in the y-variable (income). Scatter plots are useful for visualizing the relationship between two variables and can be used to identify correlations, outliers, and trends.

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The breakeven point is the point at which a company's revenue is equal to its costs. In this case, the combined fixed and variable expenses for the production and sale of 500,000 items are $10,000,000, so the breakeven point for this item would be $10,000,000 / 500,000 items = $100000000/500000=$20 per item.

To determine the price at the breakeven point, we need to know the total revenue that the company is aiming to achieve. If the company's goal is to sell the items at a price above the breakeven point in order to make a profit, then the price at the breakeven point would be $20 per item.

However, if the company is simply trying to recover its costs, then the price at the breakeven point would be the same as the breakeven point, or $20 per item.

The length of segment EG in this problem is given as follows:

EG = 164.

The segment lengths given in this problem are listed as follows:

These segment lengths represent the diagonals of the rectangle.

The quadrilateral in this problem is a rectangle, meaning that the diagonal lengths are equal.

Considering that the diagonal lengths are equal, the value of s is obtained as follows:

6s - 82 = 4s

2s = 82

s = 82/2

s = 41.

Considering the value of s = 41, the length of segment EG is given as follows:

EG = 6(41) - 82

EG = 164 units.

(replacing the lone instance of s by it's numeric value of 41 on the expression for the length of EG).

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A minimum of 6" - 300.14 of the free conductor must typically be left when wires are drawn to a junction box that measures 12" x 12" x 4" in order to make splices or attach devices like luminaires or other devices.

An electrical conductor is a substance or material that allows electricity to flow through it. When voltage is applied, electrical charge carriers, frequently electrons or ions, move readily from atom to atom in a conductor.

Conductivity, in general, is the property of a material to carry heat or electricity. Electricity can go through a conductor because there is little to no resistance while electrons are moving across it. Copper is among the majority of metals that are thought to be good conductors, whereas insulators and nonmetals are thought to be poor conductors.

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The area of the trapezium is 21cm²

You should know that a trapezium is a quadrilateral with two parallel opposite sides while thw other two are not parallel.

The area of the trapezium is denoted by the formular

Area= 1/2(a+b)*h

Where

We are told that the trapezium occupies centimeter grid

a= = 5, b=9 and h=3

This implies that Area = 1/2*(5+9)*3

Area= 1/2*14*3

=7*3 =21 cm²

In conclusion the trapezium has an area of  21cm²

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The value of variable x that makes -4x-(-10 - 8x) = -(12x-14) true is 1/4. thus, option c is correct.

In algebra, a symbol known as a variable (typically a letter) is used to represent an equation's undetermined numerical value. Frequently used variables include t, r, and s, as well as X and Y, which are real-number unknowns, as well as z, which is a complex-number unknown (arc length).

Given

-4x-(-10 - 8x) = -(12x-14)

-4x + 10 + 8x = -12x + 14

4x + 10 = 14 - 12x

4x + 12x = 14 - 10

16x = 4

x = 4/16

x = 1/4

Thus, Option C is correct, x = 1/4

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Step-by-step explanation:

(-10 + 1)/(k + 3)= 9

-9/(k + 3)= 9

9k + 27 = -9

9k = -36

k = -4

Answer:

(4m^3-2t)^2 = 16m^6 - 16m^3t + 4t^2

(2b^2-g)(2b^2+g) = 4b^4 - g^2

(4q+5t)(4q-5t) = 16q^2 - 25t^2

(7v-2)^2 = 49v^2 - 28v + 4

(Z+13)(Z-13) = Z^2 - 169

(X-10)^2 = X^2 - 20X + 100

(q+8)^2 = q^2 + 16q + 64

(n+9)^2 = n^2 + 18n + 81

Step-by-step explanation:

Answer:

B. One

Step-by-step explanation:

The system has one solution because when graphed, the lines intersect.

On solving the provided question, we can say that - the probability that A occurs given that B occurs is [tex]5/8 X 8/5 X 5/9 = 5/9[/tex]

A branch of mathematics known as probability measures the possibility of an event happening or a proposition being true. The probability of an occurrence is a number between 0 and 1, where roughly 0 denotes the event's improbability and 1 denotes certainty. A probability is a numerical representation of the possibility or probability that a specific event will take place. Probabilities can alternatively be stated as percentages ranging from 0% to 100%, or as percentages from 0 to 1. the proportion between the number of events in a comprehensive collection of equally likely outcomes that lead to a certain occurrence and the entire number of outcomes.

probability that the event A - [tex]5/8[/tex]

probability that event B - [tex]5/8,[/tex]

probability that A occurs given that B  - [tex]5/8 X 8/5 X 5/9 = 5/9[/tex]

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The domain and the range of the function is (d) D: {x ∊ ℝ | x ≠ -4}; R: {y ∊ ℝ | y ≠ 3}

The domain of a function is the set of values that we are allowed to plug into our function. This set is the x values in a function such as f(x). The range of a function is the set of values that the function assumes. This set is the values that the function shoots out after we plug an x value in.

The domain of the function

We have the function to be

f(x) = \frac{x^2 + 5x + 4}{x + 4}

Set the denominator to 0

x + 4= 0

Solve for x

x = -4

This means that the domain of the function is the set of all real numbers except -4

Hence, the domain of the function is {x ∊ ℝ | x ≠ -4}

The range of the function

We have the function to be

f(x) = \frac{x^2 + 5x + 4}{x + 4}

Factorize the numerator

f(x) = \frac{(x + 1)(x + 4)}{x + 1}

Simplify

f(x) = x + 4

The function is undefined at x= -1.

So, we have:

f(-1) = -1 + 4

f(-1) = 3

This means that the range of the function is the set of all real numbers except 6

Hence, the range of the function is {y ∊ ℝ | y ≠ 3}

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The domain of the function, f(x) = (x² + 5x + 4)/ (x + 4) is set of all real numbers except -4 and range of the function is set of all real numbers except -3.

Therefore the answer is d: {x ∊ ℝ | x ≠ −4}; r: {y ∊ ℝ | y ≠ -3}.

The domain of the function f is the set of all values of x for which the function is defined. In this case, the function is not defined when the denominator, x + 4, is equal to 0, which occurs when x = -4.

Therefore, the domain of the function is {x ∊ ℝ | x ≠ −4}.

The range of the function is the set of all possible values of y that the function can take on.

y = (x² + 5x + 4)/ (x + 4), that is

[tex]y = \frac{x^{2}+5x+4 }{x+4}[/tex]

[tex]y = \frac{x^{2} +x + 4x+4 }{x+4}[/tex]

y = (x + 4)(x+1)/(x + 4), that is

[tex]y = \frac{(x + 4)(x + 1) }{x+4}[/tex]

y = x + 1

x = y - 1

At x = -4

-4 = y -1

y = -3

But x ≠ -4, so y ≠ -3

In this case, the function can take on any value, except -3.

Therefore, the range of the function is {y ∊ ℝ | y ≠ -3}.

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The mean of the given dataset is 42 and mode is 46. SO the option b is correct.

In the given question we have to find the mean and mode of the following data set.

The given data set is

59   16   57   46   58   21   36   41   23   64   20   66   40   51   28   46

We firstly find the mean.

As we know that the mean is the ratio of sum of all number and total number. So

Mean = Sum of All Numbers/Total Number

Sum of all Numbers = 59 + 16 + 57 + 46 + 58 + 21 + 36 + 41 + 23 + 64 + 20 + 66 + 40 + 51 + 28 + 46

Sum of all Numbers = 672

Total Number = 16

Mean = 672/16

Mean = 42

As we know that,

The value that happens most frequently is the mode. The only average that is capable of having zero, one, or multiple values is the mode. Ordering the numbers first aids in determining the mode.

As we can see in the data that 46 is occur 2 times. So the mode is 46.

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The mean and mode of the given data set is 43.5 and 46 respectively.

The mean and mode of the given data set is to be calculated.

To calculate the mean, add together all of the values and divide by the number of values.

Mean = (59 + 16 + 57 + 46 + 58 + 21 + 36 + 41 + 23 + 64 + 20 + 66 + 40 + 51 + 28 + 46) / 16

Mean = 43.5

To calculate the mode, identify the value that appears in the data set the most.

Mode = 46

Therefore, the mean and mode of the given data set is 43.5 and 46 respectively.

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The system of equations 4x + 3y = - 2 and 8x + 6y = - 4 coincide and have an infinite number of solutions.

We know two simultaneous equations have a unique solution when they intersect at a point,

when they are parallel they have no solution and when they are coinciding they have an infinite no. of solutions.

Given, A system of equations,

4x + 3y = - 2 and 6y = - 4 - 8x.

Rearranging the equations,

4x + 3y = - 2 and 8x + 6y = - 4.

Now, The second equation is a multiple of the first as,

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

Therefore, The system of equations 4x + 3y = - 2 and 8x + 6y = - 4 these two lines coincide and they have an infinite number of solutions as each point of one line lies to another.

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A graph of the image of the triangle with vertices (3, 1), (3, 4), and (1, 4) when reflected across the y-axis is shown in the image attached below.

In Mathematics, a reflection can be defined as a type of transformation which moves every point of the geometric figure by producing a flipped, but mirror image of the geometric figure.

In Geometry, a reflection over the y-axis (y = x) is given by this transformation rule (x, y) → (-x, y). This ultimately implies that, a reflection over the y-axis would maintain the same y-coordinate while the sign of the x-coordinate changes from positive to negative or negative to positive.

By applying a reflection over the y-axis to the coordinates of this triangle the image coordinates include the following:

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

Coordinate A = (3, 1)   →  Coordinate A' = (-(3), 1) = (-3, 1).

Coordinate B = (3, 4)   →  Coordinate B' = (-(3), 4) = (-3, 4).

Coordinate C = (1, 4)   →  Coordinate C' = (-(1), 4) = (-1, 4).

Next, we would use an online graphing calculator to plot the coordinates of the image as shown in the image attached below.

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The number of contacts that Kamal has more than Emma, given the relationship between their phone contacts, is 396 contacts

First, find the number of contacts Emma has :

= 8 + ( 1 / 3 x Marcus's contacts )

= 8 + ( 1 / 3 x 243 )

= 8 + 81

= 90 contacts

The number of contacts for Kamal is:

= 2 x Marcus

= 2 x 243

= 486 contacts

The number of contacts that Kamal has more than Emma is:

= 486 - 90

= 396 contacts

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The radius and the diameter for each circle is given as follows:

16. r = 17 cm, d = 34 cm.

17. r = 35 cm, d = 70 cm.

18. r = 29 ft, d = 58 ft.

19. The circumference of the circle is given as follows:

38 feet.

The area of a circle of radius r is given by π multiplied by the radius squared, as follows:

A = πr²

Hence the formula for the radius, depending on the area, is given as follows:

r = square root(A/π)

The diameter is twice the radius.

Hence the radius for each circle is given as follows:

The circumference of a circle of diameter d is given as follows:

C = πd.

Hence the circumference for item 19 is given as follows:

C = 12π

C = 38 feet.

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Radius of circle is 3.95 meter

What is Radius?

The line segment formed when we connect a point on a circle's circumference to its precise center is referred to as the ring's radius. The radius of a circle is the distance between the center and any point on its circumference.  The diameter is twice the radius. Typically, the radius is denoted by r or R.

As we well aware, the formula for the circle's area is

Area=π[tex]r^{2}[/tex]

From the question, we know that area is 49 ㎡ substituting π=3.14 rearranging the above formula in terms of radius we get

[tex]r=\sqrt{\frac{Area}{3.14} } \\\\r=\sqrt{\frac{49}{3.14} } \\\\r=3.95 m[/tex]

Hence Radius of the circle is 3.95 meter.

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Answer:

64

Step-by-step explanation:

using the rule of exponents

[tex](a^{m}) ^{n}[/tex] = [tex]a^{mn}[/tex] , then

[tex](2^{3}) ^{2}[/tex]

= [tex]2^{3(2)}[/tex]

= [tex]2^{6}[/tex]

= 64

18. An infant weighs 11 pounds which is equivalent to 4.98 kg. Using the 100/50/20 Rule, the required amount of fluid per day for an infant between 11-20 kg is 50 ml/kg/day. So, the required amount of fluid per day in ml is 4.98 kg x 50 ml/kg/day = 249 ml/day.

19. A child weighs 31lbs and 8 ozs which is equivalent to 14.21 kg. Using the 100/50/24 Rule, the required amount of fluid per day for a child over 20 kg is 20 ml/kg/day. So, the required amount of fluid per day in ml is 14.21 kg x 20 ml/kg/day = 284.2 ml/day.

If no oral fluids are consumed, the hourly IV flow rate to maintain proper hydration would be: 284.2 ml/day / 24 hours/day = 11.8 ml/hour.

The question is about fluid requirements for infants and children, and it is using the 100/50/20 Rule for Daily Fluid Requirements (DFR) to calculate the required amount of fluid per day for different weight ranges. The 100/50/20 Rule is a guideline used to determine the appropriate amount of fluid that infants and children should receive on a daily basis based on their weight. The rule states that for infants and children up to 10 kg, the recommended fluid intake is 100 ml/kg/day, for those between 11-20 kg it is 50 ml/kg/day, and for those over 20 kg it is 20 ml/kg/day.

The question also asking about the hourly IV flow rate to maintain proper hydration if no oral fluids are consumed.

This subject is part of pediatrics, more specifically in the field of fluid and electrolyte balance and management.

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the total number of hats and scarves he can make cannot exceed 13.

x ≤ 5

y ≤ 8

x + y ≤ 13

x ≤ 5 represents the most hats Ronald can make, which is 5. y ≤ 8 represents the most scarves Ronald can make, which is 8.

x + y ≤ 13 represents the total number of hats and scarves Ronald can make, which is 13.

The inequalities among the constraints for this situation are x ≤ 5, y ≤ 8, and x + y ≤ 13.

The given situation is that Ronald has enough yarn to make 5 hats and 8 scarves, and it takes him 12 hours to knit a hat and 6 hours to knit a scarf; he has 20 hours to knit. The inequalities among the constraints for this situation are x ≤ 5, y ≤ 8, and x + y ≤ 13. This means that Ronald can make a maximum of 5 hats, 8 scarves, or a combination of the two that is no more than 13 in total. x stands for the number of hats made, and y stands for the number of scarves made. In order for Ronald to meet the constraints, he must make at least one hat and one scarf, and the maximum number of hats he can make is 5 and the maximum number of scarves he can make is 8. Additionally, the total number of hats and scarves he can make cannot exceed 13.

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Inequality representing the constraints for the given situation of making hats and scarves is given by :

x ≤ 5

y ≤ 8

12x + 6y ≤ 20

As given in the question,

Let 'x' represents the number of hats made by Ronald.

And 'y' represents the number of scarves made by Ronald.

As per given condition for hat and scarves , the inequality of constraints to represents the given situation is written as :

Enough yarn represents the quantity:

x ≤ 5

y ≤ 8

Knitting represent the inequality of time,

Time to knit hats is 12 hours

Time to knit scarves is 6 hours

Total time to knit is 20 hours

12x + 6y ≤ 20

Therefore, the inequality to represents the constraints of the given situation is given by :

x ≤ 5

y ≤ 8

12x + 6y ≤ 20

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