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The absolute value function y = |x - 3| + 5 generates the representation set on Cartesian plane.

In this question we need to determine the equation behind a representation set on a Cartesian plane. After a quick inspection, we find that the representation shows an absolute value function of the form:

y = |x - a| + b

Where:

Based on all the given facts, the primitive absolute value function (f'(x) = |x|) is translated horizontally 3 units in the +x direction and vertically 5 units in the +y direction. If we know that a = 3 and b = 5, then we find the absolute value function y = |x - 3| + 5, whose representation is shown below.

In a nutshell, the representation comes from the absolute value function y = |x - 3| + 5.

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The location of the points A and B on side PQ and PR, and the information that segment AB is parallel to QR indicates;

Part A: Triangle ΔPQR is similar to ΔPAB by AA similarity postulate

Part B: The line segment on triangle ΔPAB that corresponds to line segment QR is segment AB

Part C: The angle on triangle ΔPAB that corresponds to angle ∠Q is angle ∠A

Please find attached the drawing of triangles ΔPQR and ΔPAB created with MS Word

The in formation in the question are;

Line [tex]\overline{AB}{[/tex] is parallel to [tex]\overline{QR}[/tex], [tex]\left(\overline{AB} \parallel \overline{QR}\right)[/tex]

ΔPQR and ΔPAB overlap

Part A: Angle ∠PQR is congruent to angle ∠PAB (corresponding angles to parallel lines having a common transversal)

∠PRQ is congruent to ∠PBA (Corresponding angles formed by a common transversal to parallel lines)

ΔPQA is similar to ΔPAB (Angle-Angle, AA similarity postulate)

Part B: Corresponding sides of triangles are located on the same relative position within the triangle

Segment QR is the included segment to ∠PQR and ∠PRQ, which are each congruent to ∠PAB and ∠PBA, respectively in ΔPAB and segment AB is the included side to ∠PAB and ∠PBA, therefore, the line segment on triangle ΔPAB that corresponds to line segment QR is segment AB

Part C: Angle ∠Q on triangle ΔPQR is adjacent to segment QR on the right and angle ∠P on the left, while angle ∠A is adjacent segment AB on the right and ∠P on the right, segment AB in ΔPAB corresponds to segment QR on triangle ΔPQR, therefore, by the relative position of angle ∠A on triangle ΔPAB, it is the angle that corresponds to angle ∠Q

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The distance between points (-1, 4) and (5, 4) is 6 units.

From the question, we are to determine the distance between two points.

The given points are (-1, 4) and (5, 4)

Using the formula for calculating the distance between two points

d = √[(x₂ - x₁)² + (y₂ - y₁)²]

From the given information,

x₁ = -1

x₂ = 5

y₁ = 5

y₂ = 4

Put the parameters into the equation

d = √[(x₂ - x₁)² + (y₂ - y₁)²]

d = √[(5 - (-1))² + (4 - 4)²]

d = √[(5 + 1)² + 0²]

d = √(6²)

d = 6 units

Hence, the distance is 6 units.

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Answer:

Step-by-step explanation: The distance between two points can be calculated using the formula:

d = √ ((x2 – x1)² + (y2 – y1)²)

where (x1, y1) and (x2, y2) are the coordinates of the two points.

In this case, the two points are (-1, 4) and (5, 4). Therefore:

d = √ ((5 - (-1))² + (4 - 4)²)

d = √ (6² + 0²)

d = √36

d = 6

Therefore, the distance between (-1, 4) and (5, 4) is 6 units.

I hope that helps! Let me know if you have any other questions!

Answer: C

Step-by-step explanation:

g(5)=1

The length of XN is 6

Calculation

By angle bisector theorem

[tex]\frac{AX}{NX} =\frac{AY}{NY}[/tex]

[tex]\frac{18}{NX} =\frac{12}{4}[/tex]

[tex]NX=\frac{18*4}{12} =6[/tex]

Therefore, the length of side NX in the given triangle is 6.

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The length of side NX in the given triangle is 6.

By angle bisector theorem

According to the angle bisector theorem, PQ/PR = QS/RS or a/b = x/y. An angle bisector is a line or ray that divides an angle in a triangle into two equal measures

Therefore, the length of side NX in the given triangle is 6.

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There is a 0.091125 probability that all three randomly chosen houses have dogs.

In light of this, imagine that a recent survey of American homes regarding pet ownership revealed that 45% of households with pets were dog-owning, 34% were cat-owning, and 10% were bird-owning households.

• Three families are chosen at random, replaced, and with mutually exclusive ownership.

The calculation of probability is as follows based on the facts above:

=0.43^3

= 0.091125

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Answer:

3/5x 150

= 450/5

= 90

150+90

= 240 ans

Sam's average score based on the six quizzes is 78%.

The average is the mean, a central tendency value.

We compute the mean by summing the values of a data set and dividing by the number of items in the collection.

In this situation, the average of 5 quizzes multiplied by 5 gives the total score in the 5 quizzes, which resulted in the average score.

This total is added to the score in the sixth quiz to get the total score for the six examinations before dividing the sum by 6, giving the overall average.

The average score in 5 quizzes = 74%

Total score in the 5 quizzes = 370% (74 x 5)

The score on the sixth quiz = 99%

Total score in six quizzes = 469% (370 + 99)

The average score in the 6 quizzes = 78.167% (469/6)

= 78%

Thus, Sam scored an average of 78% on the six tests.

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Answer:

A. y = -4x

B. y = 20

Step-by-step explanation:

A. y = xk

Where k is constant

Substitute y for -8 and x for 2

-8 = 2k

Divide both sides by 2

-8/2 = 2k/2

-4 = k

k = -4

y = x(-4)

y = -4x

B. y when x = 5

y = 5(-4)

y = 20

Answer:

The object has fallen [tex] \boxed{\sf 289} [/tex] feet from ts intial position.

Step-by-step Explanation:

Given:

Formula:

[tex] \rm v = \sqrt{2gh} [/tex]

Where,

v = velocity (in feet per second)

h = Height fallen (in feet)

g = acceleration due gravity (in feet per second squared) = approximately 32 ft/s²

To find:

How far an object has fallen if its velocity (v) is 136 ft/s

Solution:

By substituting the value of g & v in the formula we get:

[tex]\rm \implies 136 = \sqrt{2 \times 32 \times h} \\ \\ \rm \implies 136 = \sqrt{64h} \\ \\ \rm \implies 64h = {136}^{2} \\ \\ \rm \implies h = \dfrac{ {136}^{2} }{64} \\ \\ \rm \implies h = \dfrac{18496}{64} \\ \\ \rm \implies h = 289 \: ft[/tex]

Answer:

  (9, 7)

Step-by-step explanation:

You want the coordinates of the image of point (9, -7) after it has been reflected across the x-axis.

The image point will be as far above the x-axis as the original point is below the x-axis. The y-coordinate of -7 tells you the point is 7 units below the x-axis. The reflected point will be 7 units above the x-axis, so will have a y-coordinate of +7.

The image coordinates are (9, 7).

__

Additional comment

Reflection across the x-axis changes the sign of the y-coordinate.

Reflection across the y-axis changes the sign of the x-coordinate.

The probability of each event will be

a. 0.122

b. 0.1

c. 0.64

d. 0.63

Probability of a $2 winner is 1 in 10

Probability of a $5 winner is 1 in 50

Probability of a $10 winner is 1 in 500

The formula to find probability is

1. no. of favorable outcomes / total no. of favorable outcomes

                                                  OR

2. P(A) = n(A)/n(S)

where

P(A) is the probability of an event “A”

n(A) is the number of favorable outcomes

n(S) is the total number of events in the sample space

Now we will use formula to find probability of different events happening

a. To find the probability of getting either a $2, or $5, or $10 winner we

will find probability of $2 , $5 and $10 and add them together.

1/10 + 1/50 + 1/500 = 0.122

b. The probability of getting a $2 winner will be

1/10 = 0.1

c. The probability of getting no $5 winner is (49/50)^50 = 0.36

So the probability of getting $5 winner will be 1 - 0.37 = 0.64

d. The probability of getting no $10 winner is (499/500)^500 = 0.37

And we can take probability of total no. of outcomes as 1.

So the probability of getting $10 winner will be 1 - 0.37 = 0.63

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Answer: 7/6

Step-by-step explanation:

Ok so first we must take these fractions and make them have a common denominator. The best way to do this is to take 2/3 and multiply the numerator and denominator by 8 giving us 16/24. Next take 4/8 and multiply the numerator and denominator by 3 giving us 12/24. Now we have both a common denominator. Now we add the numerators of both (16+12) to get 28/24 but now we have an improper fraction divide the numerator and denominator by 4 to get us 7/6.

Hope this Helps :)

Nadia was 1cm off the actual measurement of 5 cm. That is a percent error of 20%.

Sasha was 4 cm off the actual measurement of 100 cm. That’s a percent error of 4%.

From the information, the measurement was 4cm and the actual measurement was 5cm. Therefore, the difference will be:

= 5cm - 1cm

= 4cm

The percentage error will be:

= Difference in measurement / Actual measurement × 100

= 1/5 × 100

= 20%.

The percentage error for Sasha will be:

= 4/100 × 100

= 4%

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The equation of the line that passes through the point (-8,-3) and has a slope of -3/4 is y = -3/4x - 9

From the question, we have the following parameters that can be used in our computation:

Slope, m = -3/4

Points, (x₁, y₁) = (-8, -3)

A linear equation can be represented as

y = slope * x + y-intercept i.e. y = m(x - x₁) + y₁

Substitute the known values in the above equation

So, we have the following equation

y = -3/4(x + 8) - 3

Open the brackets

So, we have the following equation

y = -3/4x - 6 - 3

Evaluate the like terms in the above equation

So, we have the following representation

y = -3/4x - 9

The above equation cannot be further simplified

Hence. the linear equation is y = -3/4x - 9

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Answer:6 is the correct answer

Step-by-step explanation:

Because 16 + 20 equals 36 and the sq root of 36 is 6. So you chose the correct answer.

Answer:

6

Step-by-step explanation:

[tex]\sqrt{16+20}[/tex]

[tex]\sqrt{36}[/tex]

6

Answer:

48cm = 480mm

Step-by-step explanation:

1cm = 10mm

48cm = 48 X 10 mm

48cm = 480mm

Answer:

480mm

When converting from cm to mm, multiply by 10.

48 x 10 = 480

I hope this helps!

42x +55y =380

42 is value of ∠JNM because ∠JNM & ∠KNL are vertically opposite angles.

What is vertically opposite angles?

∠JNM = ∠KNL

4x + 6 = 7x - 21

7x - 4x = 21 + 6

   3x = 27

   x = 27/3

   x = 9

∠JNM = 4 * 9 + 6 = 36 + 6

∠JNM =  42

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Answer:

3

Step-by-step explanation:

45*64=2880

48*60=2880

Answer: The answer is 8

Step-by-step explanation: 16 tablespoon is 1 cup now find half of 16. Half of 16 is 8. So 8 tablespoon should be equal 1/2 cup

The expression equivalent to (-3.3x + (-3.2)) + (5.7x + (−1) is  -3.3x + 5.7x) + ((-3.2) + (-1))

The commutative property of addition states that any change in the order of the numbers being added does not affect the sum.

a + b = b + a

The given expression is  (-3.3x + (-3.2)) + (5.7x + (−1))

on simplifying we get, -3.3x - 3.2 + 5.7x - 1 = 2.4x - 4.2

Upon checking the options provided

-3.3x + (-3.2) + 5.7x + (-1)

= 2.4x - 4.2

(-3.3x (-1)) + ((-3.2)x - 5.7)

-9 - 6.7

-3.3x + (-3.2)) + (5.7x- (-1))

2.4x - 2.2

(-3.3x + 5.7x) + ((-3.2) + (-1))

2.4x - 4.2

Therefore, the expression equivalent to (-3.3x + (-3.2)) + (5.7x + (−1) is  -3.3x + 5.7x) + ((-3.2) + (-1))

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Answer:

1200

Step-by-step explanation:

1,500-300=1200

The rate in mm per hour at which the height of the water is changing when the height of the water is 2mm is 55.2

Given data,

A partially filled inverted cone contains water. The inverted cone has a 16 mm radius. The inverted cone is 18 mm in height. if the water's volume is growing at a pace of 548 cubic millimeters per hour.

The rate in mm per hour at which the height of the water is changing when the height of the water is 2 mm;

r/h = 16/18

    = 8/9

r = 8h/9

The volume of the cone is;

v = [tex]\frac{1}{3}\pi r^2h[/tex]

v = [tex]\frac{1}{3}\pi (8h/9)^2h[/tex]

v =  [tex]\frac{64}{243}\pi h^3[/tex]

Now, differentiating concerning x;

[tex]\frac{dv}{dt}[/tex]= [tex]\frac{d}{dt}[/tex]        [tex]\frac{64}{243}\pi h^3[/tex]

[tex]\frac{dv}{dt}[/tex]=  64π/243*[tex]\frac{d}{dt}[/tex] h³

[tex]\frac{dv}{dt}[/tex]= [tex]\frac{64}{81}\pi h^2\frac{dh}{dt}[/tex]

We have;

[tex]\frac{dv}{dt}[/tex]= 548 and h = 2mm

[tex]\frac{dh}{dt} = \frac{548*81}{256\pi }[/tex]

[tex]\frac{dh}{dt}[/tex] = 55.19

           [tex]\frac{dh}{dt}[/tex] = 55.2mm per hour.

Hence, the rate in mm per hour at which the height of the water is changing when the height of the water is 2mm is 55.2

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The linear equation that represent the amount vaccine that remain is g = 61 - 0.061n. The vaccine remains in the body 24 hours after it was administered 59.536 mg. There were only 5mg of the vaccine remaining in the body after 918.033 hours.

What is rate?

A rate is a unique ratio where the two words are expressed in several units.

Given that the amount of vaccine is 61 mg.

The vaccine leaves the body at a rate of 6.1% per hour.

After 1 hour the body will consume 6.1% = 6.1/100 = 0.061 mg.

After n hour the body will consume 6.1%× n =  0.061n mg.

The remaining amount of vaccine is (61 - 0.061n).

The required linear equation that represent the remaining amount of vaccine is g = 61 - 0.061n.

Putting n =24 in the equation:

g = 61 - 0.061×24

g = 59.536 mg

The vaccine remains in the body 24 hours after it was administered 59.536 mg.

The graph represents that there were only 5mg of the vaccine remaining in the body after 918.033 hours.

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The value of y is 24 when x is 7.

A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0.

Given,

There are direct variations

y= 24 when x=2

We need to find value of y when x =7

This can be found by forming an equation.

Let the value of unknown y be a

2/24=7/a

Apply cross multiplication

2a=24(7)

2a=168

We need to divide by 2 on both sides

a=24

Hence the value of y is 24 when x is 7.

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False, As the sample size is increased, the standard deviation of a sampling distribution of the sample's mean drops.

The term "standard error" also refers to the sample mean's standard deviation. The high dimensionality theorem establishes that as sample size increases, the sample mean's sampling distribution becomes more or less normal.

Using the formula below, the sample mean's standard deviation is determined.

σ ÷ √n

where n is the sample size and would be the population standard deviation.

As the denominator, or n, increases, the standard variance of the sample average would also decrease, as shown by the aforementioned calculation.

It follows that the standard deviation of a sample's average decreases as the sample size grows.

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