The following graph represents the solution to which system?

1. y= - 7x+3
y = 3x-2

2. y= 3x-7
y= -2x+3

3. y= 2x+3
y= 3x-7

4. y= 2x +3
y= - 3x-7​

a) 2y = 3x + 8 This equation represents the line passing through the midpoints of BC and AD.

b) the length of the line segment joining the midpoints is indeed half the sum of the lengths of the parallel sides.

a) To show that the line segment joining the midpoints of BC and AD is parallel to both AB and DC, we need to demonstrate that the slopes of the lines are equal.

Let's first find the coordinates of the midpoints of BC and AD:

Midpoint of BC: ( (−2+−4)/2 , (1−2)/2 ) = (−3,-1/2)

Midpoint of AD: ( (1+2)/2 , (2+0)/2 ) = (3/2, 1)

Now, let's calculate the slopes:

Slope of AB: (1-2)/(-2-1) = -1/3

Slope of DC: (-2-0)/(-4-2) = -1/3

Since both slopes are equal, AB is parallel to DC.

Next, let's find the equation of the line passing through the midpoints of BC and AD. We'll use the point-slope form.

Slope of the line passing through the midpoints:

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

Using the midpoint (−3,-1/2), we can write the equation of the line as:

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

y + 1/2 = (3/2)(x + 3)

2y + 1 = 3x + 9

2y = 3x + 8

This equation represents the line passing through the midpoints of BC and AD.

b) To show that the length of this line segment is half the sum of the lengths of the parallel sides, we need to calculate the lengths of AB, DC, and the line segment joining the midpoints.

Length of AB:

√((-2-1)^2 + (1-2)^2) = √(9 + 1) = √10

Length of DC:

√((-4-2)^2 + (-2-0)^2) = √(36 + 4) = √40 = 2√10

Length of the line segment joining the midpoints:

√((3/2-(-3))^2 + (1-(-1/2))^2) = √((9/2)^2 + (3/2)^2) = √((81/4) + (9/4)) = √(90/4) = √(9/4 * 10) = (3/2)√10

The sum of the lengths of AB and DC is:

√10 + 2√10 = 3√10

The length of the line segment joining the midpoints is:

(3/2)√10

We can see that the length of the line segment is indeed half the sum of the lengths of AB and DC:

(3/2)√10 = (1/2) * 3√10 = (1/2) * (√10 + 2√10) = 3/2√10 = 3/2√10

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The 7 types of hazards in the home are Psychosocial  Risks,Physical

Dangers , Chemical Dangers, Biological risks, Constrained Areas,

Changing Equipment and Biohazards

Psychosocial  Risks

Physical dangers include a subgroup called psychosocial hazards. For some workers, these risks might be more severe or restrictive than for others. Poor management or a lack of feedback may be the cause of these risks.

Physical Dangers

Environmental and occupational hazards are two different categories of physical risks. These include unguarded machines, heat, cold, vibration, noise, and temperature extremes. Engineering controls can lessen some physical dangers.

Chemical Dangers

Toxic, flammable, explosive, self-reactive, oxidizing, or corrosive compounds are considered chemical dangers. Chemical risks can have negative health impacts and need special handling techniques and equipment.

Biological risks

Many workplaces have biological risks, which can be harmful to people. They include waste debris, food, fungi, food, hair, skin, and saliva.

Constrained Areas

Flammable gases can accumulate in small places. These gases tend to gravitate toward lower elevations, yet they can rise to the surface if a lid is closed or if they are hanging in the air.

Changing Equipment

For workers, the moving machinery hazard provides a distinct set of mechanical risks. Injuries caused by it include crushing, shearing, tangling, air being ejected, striking, abrading, and trapping.

Biohazards

There are many danger thresholds for biohazards. Agents of biohazard level I pose little risk to people. On the other hand, biohazard class II agents may be extremely contagious and may result in serious sickness if consumed or dispersed through the air.

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\(\huge{\mathbb{\tt{QUESTION↓}}}\)

1. in how many ways can you arrange five mathematics books,four science books,and three english books, on a shelf such as that books of the same subject are kept together.

\(\huge{\mathbb{\tt{SOLUTION↓}}}\)

\(\textsf{ Given that: M=5 , S=4 , E=3}\)

\(\begin{gathered}\\\end{gathered} \)

\(\textsf{ Using the Linear Permutation:} \)

\(\sf{P=n!}P=n!\)

\(\sf{P=5!}P=5!\)

\(\sf{P=5×4×3×2×1}\)

\(\sf{P=120}\)

\(\begin{gathered}\\\end{gathered}\)

P=n!}

P=4!

P=4×3×2×1

P=24

P=n!

P=3!

P=3×2×1

P=6

Multiply all the permutations:

P=120×24×6

P=17,280

\(\huge{\mathbb{\tt{ANSWER↓}}}\)

There are 17,280 ways we can arrange in a shelf.

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Answer:

I can see the pdf

Step-by-step explanation:

Answer:

Yes, they do because both of the morning graphs had a better range in grades than the afternoon students.

Step-by-step explanation:

Mrs. Ross should expect to have about 26,417 books with no damage in the entire collection. Rounded to the nearest whole number, the answer is 26,417.

Mrs. Ross found that 902 out of the sample of (902 + 80 + 43) = 1025 books had no damage. This means that the proportion of books with no damage in the sample is 902/1025. We can use this proportion to estimate the number of books with no damage in the entire collection.

Let X be the number of books with no damage in the collection of 30,000 books. Then we can write:

902/1025 = X/30000

To solve for X, we can cross-multiply and simplify:

902 × 30000 = 1025 × X

X = 902 × 30000 / 1025

X ≈ 26,417.07

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If you are trying to accommodate a party of 8 and you have square tables that seat 4 people each, you would need to bring in 2 tables and push them together to fit the party of 8.

The reason for this is that 4 people can be seated at each table, and 2 tables together would provide enough seating for 8 people. Pushing the tables together will create a larger table that can accommodate the party of 8. It's important to ensure that the tables are pushed together securely so that they don't move or separate during the meal.

It's also important to consider the layout of the tables and how they will fit in the space where they will be used. It's a good idea to measure the space and the tables to ensure that they will fit comfortably and provide enough room for people to sit and move around. If the tables need to be rearranged or moved, it's important to do so carefully to avoid damaging the tables or injuring yourself or others.

When setting the tables, it's also important to consider the comfort of the diners. Make sure that there is enough room for people to sit comfortably and move their arms and legs, and that the tables are positioned so that everyone has a clear view of their surroundings and is not blocked by other diners or objects.

In conclusion, to accommodate a party of 8, you would need to bring in 2 square tables that seat 4 people each and push them together. It's important to consider the layout and comfort of the diners, as well as the safety of the tables and those who are setting them up.

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Answer:

Step-by-step explanation:

b

The solution of the inequality is k > 8.82

The expression is in words so we have to convert it to an inequality to be able to solve for k.

An inequality is an expression that has the following symbols: <, >, ≤ and ≥.

Therefore, the inequality can be solved as follows:

k / - 1.8 < - 4.9

Therefore, let's solve for the variable k.

k / - 1.8 < - 4.9

multiply both sides of the inequality by - 1.8

Hence,

k / - 1.8 (-1.8) < - 4.9 (-1.8)

k / 1 > 8.82

Note the sign had to change after we multiply both side of the inequality with a negative number.

Therefore,

k > 8.82

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The point estimate for µ is 25.2 years, with a margin of error to be determined. The 99% confidence interval for µ is (24.06, 26.34) years.

a. The point estimate for µ, the population mean, is obtained from the sample mean, which is 25.2 years. The margin of error represents the range within which the true population mean is likely to fall. To determine the margin of error, we need to consider the sample variance, which is 16.4, and the sample size, which is 100. Using the formula for the margin of error in a t-distribution, we can calculate the value.

b. To calculate the 99% confidence interval for µ, we need to consider the point estimate (25.2 years) along with the margin of error. Using the t-distribution and the sample size of 100, we can determine the critical value corresponding to a 99% confidence level. Multiplying the critical value by the margin of error and adding/subtracting it from the point estimate, we can establish the lower and upper bounds of the confidence interval.

The resulting 99% confidence interval for µ is (24.06, 26.34) years. This means that we can be 99% confident that the true population mean falls within this range based on the sample data.

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Answer:

x is 3.

Step-by-step explanation:

Vertically opp angle are equal.

The correct answer for detecting nonrandomness in errors is E. control charts. Control charts are a statistical tool used to monitor processes and detect deviations from randomness or expected behavior. They are commonly used in quality control and process improvement to identify any systematic or nonrandom patterns in the data.

Control charts help visualize data over time and compare it to predetermined control limits. If the data falls within these limits and shows a random pattern, it suggests that the process is stable and operating within acceptable limits of variation. However, if the data exhibits nonrandom patterns, such as trends, cycles, or unusual points, it indicates the presence of special causes or systematic errors in the process. By analyzing the control chart, individuals can identify the sources of nonrandomness, investigate the underlying causes, and take corrective actions to improve the process and reduce errors. Therefore, control charts provide an effective method to detect nonrandomness and ensure the quality and consistency of processes.

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The main answer is that the infinite number of types of matter arises from the unique combinations of elements and their arrangements in terms of composition and geometry.

While the number of elements is limited, their combinations and arrangements allow for an infinite number of types of matter. Elements can combine in different ratios and configurations, forming various compounds and structures with distinct properties.

Additionally, the arrangement of atoms within a molecule or the spatial arrangement of molecules within a material can create different types of matter. These factors, along with the possibility of isotopes and different states of matter, contribute to the vast diversity and infinite types of matter despite the limited number of elements.

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Answer:

They rise upward to the right and they start at the origin

Answer:

4n + 1

Step-by-step explanation: The numbers are rising by 4, so this gives us 4n. Term number 1: 4n = 4, but the first number in the sequence is 5 so we have to add 1.

Term number 2: 4n = 8, but the second number in the sequence is 9 so, again, we have to add 1.

Answer:

Write out all the pairs of numbers which can be multiplied to produce c.

Add each pair of numbers to find a pair that produce b when added.

If b > 0, then the factored form of the trinomial is (x + d )(x + e).

Check: The binomials, when multiplied, should equal the original trinomial.

The distance between the points (-3, 4) and (6, 1) will be 9.49 units.

It is the measure of distance between the two points and is known as length. The length is measured in meters generally.

Let one point be (x, y) and another point be (h, k).

Then the distance between the points will be

D² = (x - h)² + (y - k)²

The points are given below.

(-3, 4) and (6, 1)

The distance between the points (-3, 4) and (6, 1) will be given as,

D² = (- 3 - 6)² + (4 - 1)²

D² = (-9)² + (3)²

D² = 81 + 9

D² = 90

Take square root on both sides. Then we have

D = √90

D = 9.49 units

The distance between the points (-3, 4) and (6, 1) will be 9.49 units.

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Answer:

(3,4)

Step-by-step explanation:

To find the x coordinate of the midpoint, add the x coordinates of the endpoints and divide by 2

(2+4)/2 = 6/2 =3

To find the y coordinate of the midpoint, add the y coordinates of the endpoints and divide by 2

(5+3/2 = 8/2 =4

The midpoint is (3,4)

Answer:

Hey there!

Using the midpoint formula we find the midpoint to be: (3, 4)

Let me know if this helps :)

Answer:

whats the question

Step-by-step explanation:

Answer:

Step-by-step explanation:

400: 100 you find 1% you multiply it by 20 and you have 20%

400 : 100 * 20 =

4 * 20 =                                    

Answer:

The magnitude is sqrt((-4)^2 + (-9)^2) = 9.85. The angle is atan(-9/-4) = 180 deg + 66 deg = 246 deg = -114 deg.

Step-by-step explanation:

hope it help

Answer:

9.85

Step-by-step explanation:

|v|= √9²+(-4)²

=√81+16

=√97

|v|= 9.85

To simplify the expression 3(x + 5) - 2x, let's break it down step by step:

First, apply the distributive property by multiplying 3 with each term inside the parentheses:

3(x + 5) - 2x = 3x + 15 - 2x

Next, combine like terms by grouping the x terms together:

3x - 2x + 15 = (3x - 2x) + 15

Simplifying the x terms, we get:

(3x - 2x) + 15 = x + 15

Therefore, the simplified expression is x + 15.

This means that the original expression, 3(x + 5) - 2x, is equivalent to x + 15.

To further explain, the expression 3(x + 5) - 2x represents three times the quantity of x plus 5, subtracted by two times x. By distributing the 3, we get 3x + 15, and then combining the x terms yields x + 15.

So, the expression x + 15 is equivalent to 3(x + 5) - 2x. It represents the same mathematical relationship and simplifies the original expression by grouping like terms.

It's important to note that this simplification assumes x is a variable and not a specific value. If x has a specific value, then the simplified expression x + 15 will represent a numerical result based on that value.

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Answer:

103.125

Step-by-step explanation:

110.00 times 15% = 16.5

16.5 times 6.25% = 103.125

Answer - 103.125

Answer:

With the coupon and sales tax, the bicycle costs $100.38.

Step-by-step explanation:

First, we need to find 6.25% of $110.

110 x 0.0625 = 6.88

Now, let's add this to the total, or $110.

110 + 6.88 = $116.88

After that, we need to find 15% of this total.

116.88 x 0.15 = 17.53

Now, we need to subtract this from the total, which is now $116.88.

116.88 - 16.5 = $100.38

Now, with the coupon and sales tax, the bicycle costs $100.38.

Hope this helps! :D

The requried simplified value of the given expression is -4x³ + 3x² + 8x.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

here,
Given expression,
= (2x³+7x²-x)+(-6x³-4x²+7x)

Adding like terms
= -4x³ + 3x² + 8x

Thus, the requried simplified value of the given expression is -4x³ + 3x² + 8x.

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Answer: The point (-2, 4) is on the circle (x - 5)^2 + (y + 3)^2 = 25.

Step-by-step explanation: The point (-2, 4) is on the circle (x - 5)^2 + (y + 3)^2 = 25. To check if a point is on the circle, we can substitute the point's x and y coordinates into the equation of the circle. If the equation is true, then the point is on the circle. In this case, substituting (-2, 4) into the equation of the circle.

Step-by-step explanation:

so, I read here

2/3 x + 3x/x = 4x/2 × (3x + 6)

that is

2/3 x + 3 = 4x/2 × (3x + 6)

2x/3 + 3 = 2x × (3x + 6)

2x + 9 = 6x × (3x + 6)

2x + 9 = 18x² + 36x

18x² + 34x - 9 = 0

the general solution to a quadratic equation is

x = (-b ± sqrt(b² - 4ac))/(2a)

in our case

a = 18

b = 34

c = -9

x = (-34 ± sqrt(34² - 4×18×-9))/(2×18) =

= (-34 ± sqrt(1156 + 648))/36 =

= (-34 ± sqrt(1804))/36 =

= (-34 ± sqrt(4×11×41))/36 =

= (-34 ± 2×sqrt(451))/36

x1 = (-34 + 2×sqrt(451))/36 =

= 0.235375588...

x2 = (-34 - 2×sqrt(451))/36 =

= -2.124264477...

Answer:

\(x=\dfrac{-17+ \sqrt{451} }{18}, \quad x=\dfrac{-17- \sqrt{451} }{18}\)

Step-by-step explanation:

\(\textsf{Given equation}:\)

\(\dfrac{2}{3}x+\dfrac{3x}{x}=\dfrac{4x}{2}(3x+6)\)

\(\textsf{Cancel the common factor } x \textsf{ in }\dfrac{3x}{x}:\)

\(\implies \dfrac{2}{3}x+3=\dfrac{4x}{2}(3x+6)\)

\(\textsf{Simplify }\dfrac{4x}{2}\textsf{ by dividing the numbers}:\)

\(\implies \dfrac{2}{3}x+3=2x(3x+6)\)

\(\textsf{Apply the distributive law}\quad \:a\left(b+c\right)=ab+ac:\)

\(\implies \dfrac{2}{3}x+3=6x^2+12x\)

\(\textsf{Multiply both sides by 3 to cancel the denominator of }\dfrac{2}{3}:\)

\(\implies \dfrac{2}{3}x\cdot 3+3\cdot 3=6x^2\cdot 3+12x \cdot 3\)

\(\implies 2x+9=18x^2+36x\)

\(\textsf{Switch sides}:\)

\(\implies 18x^2+36x=2x+9\)

\(\textsf{Subtract }2x \textsf{ from both sides}:\)

\(\implies 18x^2+36x-2x=2x+9-2x\)

\(\implies 18x^2+34x=9\)

\(\textsf{Subtract 9 from both sides}:\)

\(\implies 18x^2+34x-9=9-9\)

\(\implies 18x^2+34x-9=0\)

Solve using the Quadratic Formula:

\(x=\dfrac{-b \pm \sqrt{b^2-4ac} }{2a}\quad\textsf{when }\:ax^2+bx+c=0\)

Define the variables:

\(\implies a=18, \quad b=34, \quad c=-9\)

Substitute the defined variables into the quadratic formula and solve for x:

\(\implies x=\dfrac{-34 \pm \sqrt{34^2-4(18)(-9)} }{2(18)}\)

\(\implies x=\dfrac{-34 \pm \sqrt{1156+648} }{36}\)

\(\implies x=\dfrac{-34 \pm \sqrt{1804} }{36}\)

\(\implies x=\dfrac{-34 \pm \sqrt{4 \cdot 451} }{36}\)

\(\implies x=\dfrac{-34 \pm \sqrt{4}\sqrt{451} }{36}\)

\(\implies x=\dfrac{-34 \pm 2\sqrt{451} }{36}\)

\(\implies x=\dfrac{-17 \pm \sqrt{451} }{18}\)

Therefore, the solutions to the given equation are:

\(x=\dfrac{-17+ \sqrt{451} }{18}, \quad x=\dfrac{-17- \sqrt{451} }{18}\)

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The correct option is D) seriousness and permanence.

In Passage 1, Burke indicates that a contract between a person and society differs from other contracts mainly in its seriousness and permanence.

Sociologists define a society as a group of people who share similar geography, interaction, and culture. Social groups are made up of two or more individuals who interact & identify with each other.

Some key features regarding society are-

As a result, Burke suggests that a contract here between person and society differs from those other contracts primarily in its gravity and permanence.

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Answer:

11 hours as a cashier

and 2 hours as a teacher

11 x 8 = 88

6 x 2 = 12

88 + 12 = 100

Step-by-step explanation:

The correct answers are: (a) True (b) True (c) True (d) False

(a) If f'(c) = 0, then f has a relative maximum or minimum at x = c.
- This statement is true. When the derivative of a function, f'(x), is equal to zero at a point x = c, it indicates a potential turning point in the graph of the function.

At this point, f(x) can have a relative maximum or minimum. However, it's important to note that the derivative being zero does not guarantee the presence of a relative maximum or minimum; it only suggests the possibility.

(b) If f'(x) changes from positive to negative at x = a, then f has a relative maximum at x = a.
- This statement is true. If the derivative of a function, f'(x), changes from positive to negative at a point x = a, it indicates a change from increasing to decreasing. This change implies the presence of a relative maximum at x = a, where the function reaches its highest point locally.

(c) If f'(x) > 0 on (a, b), then f is increasing on the interval (a, b).
- This statement is true. If the derivative of a function, f'(x), is greater than zero on the interval (a, b), it indicates that the function is increasing throughout that interval. The positive derivative implies that the function's slope is positive, leading to an upward trend in its graph.

(d) If f'(c) does not exist, then f(x) has a critical point at x = c.
- This statement is false. A critical point occurs when the derivative of a function does not exist or is equal to zero.

However, the converse is not always true. If f'(c) does not exist, it does not necessarily mean that f(x) has a critical point at x = c. The function could have a corner or a vertical tangent at that point instead.

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