Input an ordered pair that satisfies the system of inequalities:
-
y < − x − 3
y> 2x - 4

I agree with both Priya's and Han's equations.

To determine if either Priya or Han equation is correct, we can substitute the coordinates of the given point (1,2) into each equation and check if the equation holds true.

For Priya's equation, y - 2 = (1/3)(x - 1), substituting x = 1 and y = 2:

2 - 2 = (1/3)(1 - 1)

0 = 0

The equation holds true, so Priya's equation is correct.

For Han's equation, 3y - x = 5, substituting x = 1 and y = 2:

3(2) - 1 = 5

6 - 1 = 5

5 = 5

The equation also holds true, so Han's equation is correct.

Both Priya's and Han's equations are valid equations of the line with a slope of 1/3 passing through the point (1,2). The equations have different forms, but they are algebraically equivalent and represent the same line. Therefore, I agree with both Priya's and Han's equations.

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Answer:

Step-by-step explanation:

Certainly! I'm here to assist you.

The given function is f(x) = -2(x - 3).

To simplify this expression, we can distribute the -2 to the terms inside the parentheses:

f(x) = -2 * x - (-2) * 3

Simplifying further:

f(x) = -2x + 6

Therefore, the simplified form of the function f(x) = -2(x - 3) is f(x) = -2x + 6.

The cost of a single unit is given as follows:

$1.05.

El costo de un plátano es el seguiente:

$1.05.

The cost of a single unit is obtained applying the proportions in the context of the problem.

The cost of 22 units is of $23.10, hence the cost of a single unit is obtained dividing the total cost by the number of units, as follows:

23.1/22 = $1.05.

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Answer:

Step-by-step explanation:

The proposal is as follows

Part III  -  The distance between buoys A and B is 12.8 kilometers.

Part IV  -  The length of the other two triangle legs are 10.2 kilometers and 8.4 kilometers.

Part V  - The total length of the race course is 31.4 kilometers.

Part VIII  - The winner's speed during last year's race was 10.8 knots.

See the proposal attached.

Dear Sponsor,

I'm seeking sponsorship for the San Francisco sailboat race.

With a proven track record and the determination to win, your investment of $5,500 covers travel costs and potential hazards.

By associating your brand with a winning sailor, you'll gain significant exposure to thousands of spectators. Join me in this thrilling race for success.

Sincerely,

[Your Name]

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(a) The average cost in 2010 is $2088.82.

(b) A graph of the function g for the period 2006 to 2015 is: D. graph D.

(c) Assuming that the graph remains accurate, its shape suggest that: B. the average cost increases at a slower rate as time goes on.

Based on the information provided, we can logically deduce that the average annual cost (in dollars) for health insurance in this country can be approximately represented by the following function:

g(x) = -1736.7 + 1661.4Inx

where:

x = 6 corresponds to the year 2006.

For the year 2011, the average cost (in dollars) is given by;

x = (2010 - 2006) + 6

x = 4 + 6

x = 10 years.

Next, we would substitute 10 for x in the function:

g(10) = -1736.7 + 1661.4In(10)

g(10) = $2088.82

Part b.

In order to plot the graph of this function, we would make use of an online graphing tool. Additionally, the years would be plotted on the x-axis while the average annual cost would be plotted on the x-axis of the cartesian coordinate as shown below.

Part c.

Assuming the graph remains accurate, the shape of the graph suggest that the average cost of health insurance increases at a slower rate as time goes on.

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The two options that would prove that ΔABC ~ ΔXYZ include the following:

A. BA/YX = BC/YZ = AC/XZ

C. AC/XZ = BA/YX, ∠A≅∠X

In Mathematics and Geometry, two triangles are said to be similar when the ratio of their corresponding side lengths are equal and their corresponding angles are congruent.

Based on the side, side, side (SSS) similarity theorem, we can logically deduce the following congruent angles and similar triangles:

BA/YX = BC/YZ = AC/XZ (ΔABC ≅ ΔXYZ)

Based on the side, angle, side (SAS) similarity theorem, we can logically deduce the following congruent angles and similar sides:

AC/XZ = BA/YX, ∠A≅∠X

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Answer:

l

Step-by-step explanation:

Answer:

The 3rd answer is correct.

Step-by-step explanation:

The question involves a mathematical understanding of graphs and data interpretation, specifically ratios. To answer a question like this, typically, you would need to analyze both the graph and table for consistent ratio values. Though the question specifics are unclear, the broader concept involves understanding how ratios can be graphically represented.

Given that the question involves ratios and cards, it appears to fall under a mathematical scope, specifically the interpretation of graphs and data. However, the information provided doesn't give specific details about Chad's data, the ratios of his sports game cards, or the graph he created that shows the possible ratios for Pitchers cards to Infield cards.

Typically, to validate any findings, you would need to look at the graph and the table. Comparing the values of the ratios in the table to the characteristics of the graph would help substantiate any claims. For instance, if Chad's graph shows that there's a 1:2 ratio of pitcher cards to Infield cards, this should be reflected in the table of his sports game cards.

Despite the ambiguous details in the question, you can still grasp the concept of ratios and how they can be represented graphically. For example, if you have a 3:5 ratio of oranges to apples, this can be depicted on a graph where one unit on the Y-axis represents 3 oranges and the corresponding unit on the X-axis signifies 5 apples.

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Answer:

3

Step-by-step explanation:

midline is the distance or the midway between the highest point and the lowest one or between maximum and minimum,

for the given graph,

maximum point = 5

minimum point = 1

midline = 5 +1 / 2 = 6 / 2 = 3

The formula to find the value of a combination is

[tex]C(n, r) = n! / (r!(n-r)!),[/tex]

where n represents the total number of items and r represents the number of items being chosen at a time. 10C0 is 1

In the  combination,

n = 10 and r = 0,

so the formula becomes:

C(10,0) = 10! / (0! (10-0)!) = 10! / (1 x 10!) = 1 / 1 = 1

This means that out of the 10 items, when choosing 0 at a time, there is only 1 way to do so. In other words, choosing 0 items from a set of 10 items will always result in a single set. This is because the empty set (which has 0 items) is the only possible set when no items are chosen from a set of items. Therefore, the value of the combination 10C0 is 1.

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Answer:

f(-1/2) = -1/6

Step-by-step explanation:

To find the value of f(x) when x = -1/2, we substitute -1/2 for x in the expression for f(x) and simplify:

f(x) = (-1/3)x - 1/3

f(-1/2) = (-1/3)(-1/2) - 1/3

= 1/6 - 1/3

= -1/6

So, f(-1/2) = -1/6.

The measure of the interior angle at vertex F is 72 degrees.

A hexagon is a polygon with six sides. The sum of the interior angles of a hexagon is equal to 720 degrees.

The angle of the hexagon is given in terms of x,

The sum of the angle is equal to 720 degrees

[tex]4\text{x}+4\text{x}+4\text{x}+4\text{x}+2\text{x}+2\text{x} = 720[/tex]

[tex]20\text{x} = 720[/tex]

[tex]\text{x} = 36[/tex]

[tex]\bold{2x = 72^\circ}[/tex]

Therefore, the measure of interior angle at vertex F is equal to 72 degrees.

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The opposite of -5 can be represented by situations such as a temperature increase of 5 degrees and a financial gain of $5. Additionally, it can also represent a distance traveled of 5 miles and a weight gain of 5 pounds.

The opposite of -5 is 5. The opposite of a number represents the number with the opposite sign. Here are three situations that can be represented by the opposite of -5:

Situation 1: Temperature Change

If the temperature is currently -5 degrees Celsius and it undergoes a change in the opposite direction, it means it increases by 5 degrees. Therefore, the opposite of -5 represents a temperature increase of 5 degrees.

Situation 2: Financial Gain

Suppose you owe someone $5, and you receive the opposite of that amount. The opposite of owing $5 would be gaining $5. So, the opposite of -5 represents a financial gain of $5.

Additional situations that can be represented by the opposite of -5:

Situation 3: Distance Traveled

If a car has traveled -5 miles, indicating it has moved in the opposite direction, the opposite of that distance would be 5 miles. So, the opposite of -5 represents a distance traveled of 5 miles.

Situation 4: Weight Gain

Imagine someone loses 5 pounds (which can be represented as -5). The opposite of losing 5 pounds would be gaining 5 pounds. Thus, the opposite of -5 represents a weight gain of 5 pounds.

In each of these situations, the opposite of -5 denotes a change in the opposite direction or the reverse of the initial value.

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The ratio of the amount charged in Mathematics to Consumer Studies is 4:5.

To find the ratio of the amount charged in Mathematics to Consumer Studies, we need to divide the amount charged in Mathematics by the amount charged in Consumer Studies.

The amount charged in Mathematics is R280 per month, while the amount charged in Consumer Studies is R350 per month.

Therefore, the ratio of the amount charged in Mathematics to Consumer Studies can be calculated as:

280 / 350

To simplify this ratio, we can divide both the numerator and denominator by their greatest common divisor, which in this case is 70.

Dividing 280 by 70 gives us 4, and dividing 350 by 70 gives us 5.

So, the simplified ratio of the amount charged in Mathematics to Consumer Studies is:

4/5.

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Answer:

If you are in Acellus trust me the answer is 394

Step-by-step explanation:

SA = 2 ( 2 x 12 ) + 2 ( 2 x 10 ) + ( 8 x 6 ) + 2 ( 3 x 8 ) + ( 3 x 6 ) + ( 12 x 16 )

SA = 48 + 40 + 48 + 48 + 18 + 192

SA = 394 square cm.

The required answers of the given questions are answered below.

a), b), c),  d)

A quadrilateral is geometric structure enclosed in 4 sides.

A) Because,

 1) the angle A = Angle D

 2) its has a common side

 3) the angle D = Angle B

 ∵ ΔEAB ≅ EDC

Thus, Both the triangle is congruent by ASA.

B.)

Jane conclusion is also write for AAA

because by angle E is congruent to angle B, implies angle F is congruent to angle C.

So that is why Jane conclude AAA.

C.) George conclusion is also perfect

George thinks the following conditions-

1) the angle A = Angle D

 2) its has a common side

 3) the angle D = Angle B

 ∵ ΔEAB ≅ EDC

Thus, Both the triangle is congruent.

Hence, Both the triangles are congruent by SSS.

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Answer: (5, -1)

Step-by-step explanation:

To rotate a point counterclockwise by 90° about the origin, we swap the x and y coordinates and negate the new x-coordinate. For the point (-1, 5), we swap the x and y coordinates to get (5, -1). The x-coordinate becomes positive, and the y-coordinate becomes negative. Therefore, the coordinates of the image of the point (-1, 5) after a counterclockwise rotation of 90° about the origin are (5, -1).

I think you put down the same answer choice twice and instead meant to say (5, -1) instead of (-5, -1) twice.

The product of the given fractions is 224/61.

To calculate the product of the given fractions, let's simplify and cancel out any common factors.

We have:

(4/5) x (5/7) x (7/9) x (9/11) x (11/13) x (13/15) x (15/17) x (17/19) x (19/21) x (21/23) x (23/25) x (25/27) x (27/28) x (29/37) x (31/35) x (33/33) x (35/31) x (37/29)

Starting from the numerator and denominator of the first fraction, we observe the following cancellations:

5 in the numerator and denominator cancel out.

7 in the numerator and denominator cancel out.

9 in the numerator and denominator cancel out.

11 in the numerator and denominator cancel out.

13 in the numerator and denominator cancel out.

15 in the numerator and denominator cancel out.

17 in the numerator and denominator cancel out.

19 in the numerator and denominator cancel out.

21 in the numerator and denominator cancel out.

23 in the numerator and denominator cancel out.

25 in the numerator and denominator cancel out.

27 in the numerator and denominator cancel out.

Now, let's multiply the remaining fractions:

(4/1) x (1/28) x (29/37) x (31/1) x (1/35) x (37/29)

This simplifies to:

(4 x 1 x 29 x 31 x 37) / (1 x 28 x 37 x 29 x 35)

Simplifying further:

(4 x 29 x 31) / (28 x 35)

We can calculate this to get the final result:

(4 x 29 x 31) / (28 x 35) = 3584 / 980 = 224 / 61.

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The equation 2y + 8x - 2 = 0 will satisfy the condition of having an infinite number of solutions when graphed with the given equation.

To form a system of equations that has an infinite number of solutions when graphed with the given equation, we need to find an equation that represents the same line or is a multiple of the given equation.

The given equation is: y + 4x - 1 = 0

To find an equation with an infinite number of solutions, we can multiply the given equation by a non-zero constant.

Let's multiply the given equation by 2:

2(y + 4x - 1) = 2(0)

2y + 8x - 2 = 0

The equation 2y + 8x - 2 = 0, when graphed with the given equation y + 4x - 1 = 0, will form a system that has an infinite number of solutions. The two equations represent the same line, just with different coefficients.

Therefore, the equation 2y + 8x - 2 = 0 will satisfy the condition of having an infinite number of solutions when graphed with the given equation.

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Answer:

59

Step-by-step explanation:

6 plus 4 equals 8 plus 9

Answer:

first one, the one you have selected

Answer:

Step-by-step explanation:

To find the number of antiviral proteins injected into the person, we can set up a proportion:

2 mL contains 2.3 × 10^3 antiviral proteins

x mL contains how many antiviral proteins?

The proportion can be written as:

2 mL / 2.3 × 10^3 = x mL / (unknown number of antiviral proteins)

We can solve this proportion by cross-multiplication:

2 mL * (unknown number of antiviral proteins) = 2.3 × 10^3 antiviral proteins * x mL

x = (2.3 × 10^3 antiviral proteins * x mL) / 2 mL

Simplifying, we get:

x = 1.15 × 10^3 * x mL

Therefore, the number of antiviral proteins injected into the person is 1.15 × 10^3.

The total number of cells in the person's body is approximately 1 × 10^14. If 8% of the person's cells are infected with the virus, we can calculate the percentage of cells that can be affected by the medication:

Percentage of cells affected = (Number of infected cells / Total number of cells) * 100

Number of infected cells = 8% of 1 × 10^14 cells

Number of infected cells = (8/100) * 1 × 10^14

Number of infected cells = 8 × 10^12

Percentage of cells affected = (8 × 10^12 / 1 × 10^14) * 100

Percentage of cells affected = 8 × 10^-2 * 100

Percentage of cells affected = 8%

Therefore, the administered medication can affect 8% of the person's cells.

To find the amount of medication needed to have 1 antiviral protein for every infected cell, we can set up a proportion:

2.3 × 10^3 antiviral proteins in 2 mL

1 antiviral protein in x mL

The proportion can be written as:

2.3 × 10^3 antiviral proteins / 2 mL = 1 antiviral protein / x mL

We can solve this proportion by cross-multiplication:

(2.3 × 10^3 antiviral proteins) * x mL = 2 mL * 1 antiviral protein

x = (2 mL * 1 antiviral protein) / (2.3 × 10^3 antiviral proteins)

Simplifying, we get:

x = 0.8696 mL

Therefore, to have 1 antiviral protein for every infected cell, approximately 0.8696 mL of medication needs to be administered. This is equivalent to 0.0008696 liters.

In a sample of 5000 students, the mean GPA is 2.80 and their standard deviation is 0.35 and 1428 students score below 2.60.

To find the number of students scoring below 2.60, we need to calculate the area under the normal distribution curve to the left of this value.

First, we need to standardize the value of 2.60 using the z-score formula: z = (x - μ) / σ, where x is the value (2.60), μ is the mean (2.80), and σ is the standard deviation (0.35). Plugging in the values, we get z = (2.60 - 2.80) / 0.35 = -0.57.

Now, we can use a standard normal distribution table or a statistical calculator to find the area to the left of -0.57. Consulting a standard normal distribution table, we find that the area to the left of -0.57 is approximately 0.2857.

To calculate the number of students scoring below 2.60, we multiply this area by the total number of students in the sample: 0.2857 * 5000 ≈ 1428.5.

Since the number of students must be a whole number, we round down to 1428 students.

Therefore, approximately 1428 students score below 2.60 in the sample of 5000 students, assuming a normal distribution with a mean of 2.80 and a standard deviation of 0.35.

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Answer:

Comparing the centers of the data sets:

- The median for Data Set A is greater than the median for Data Set B.

- The mean for Data Set A is greater than the mean for Data Set B.

Comparing the variability of the data sets:

- The range of Data Set A is 22, while the range of Data Set B is 27. Therefore, the range of Data Set B is greater.

- The standard deviation of Data Set A is greater than the standard deviation of Data Set B, indicating higher variability in Data Set A.

Step-by-step explanation:

Let Peter's present age be "p" and his father's age be "x"

So, p = x-24 ;

5 years from now,

Peter's age will be (x-24) + 5 = x-19

His father's age will be x+5.

It is given that 3(x-19)= x+5.

3x - 57 = x + 5 => 2x = 62.

On solving, his father's present age (x) is 31.

So Peter's present age is (p) is x - 24 = 31 - 24 = 7.

Now going in the reverse oder to check the answer.

Peter's present is 7.

5 years from now, it will be 12.

His father's age is 31.

5 years from now, his age will be 36 (which is 3x12).

Hence , the answer to the given problem is 7

Answer:

17.5

Step-by-step explanation:

The triangle is an equilateral triangle since all sides are equal

Area of a equilateral triangle is:

[tex]ar(triangle) = \frac{a^2\sqrt{3} x}{4}[/tex]

[tex]=\frac{5^2\sqrt{3} }{4} \\\\=\frac{25\sqrt{3} }{4} \\[/tex]

the sde of the square = diameterof the circle(d)

d = 6

r = d/2 = 3

ar(circle) = πr²

= π * 3²

= 9π

= 9*22/7

= 198/7

ar(shaded region) = ar(circle)-ar(triangle)

[tex]= \frac{198}{7} - \frac{25\sqrt{3} }{4}[/tex]

= 17.5

The data set has two outliers, namely the points (2, 225) and (8, 75).

Based on the given information about the scatterplot, we can observe that most of the points are grouped closely together and show a slight increase.

There are two points that lie outside of this cluster, specifically (2, 225) and (8, 75).

To determine if these points are outliers, we need to consider their deviation from the general pattern exhibited by the majority of the data points.

If these points deviate significantly from the overall trend, they can be considered outliers.

In this case, since (2, 225) and (8, 75) lie outside of the cluster of closely grouped points and do not follow the general pattern, they can be considered outliers.

These points are noticeably different from the majority of the data points and may have influenced the overall trend of the scatterplot.

The data set has two outliers, namely the points (2, 225) and (8, 75).

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