Use transformations on the basic function listed below to write a rule

Answer:

Step-by-step explanation:

The cost of each cell phone case is $7.15, and the cost of each screen protector is $2.25.

To solve this problem, we can create a system of equations.

Let x represent the cost of one cell phone case and y represent the cost of one screen protector.

Then, we can write the following equations:

1x + 2y = 18.95     (equation 1)

2x + 5y = 41.40    (equation 2)

We can solve for x and y by multiplying equation 1 by 2 and subtracting it from equation

2.2x + 5y = 41.40(2 x 1x + 2 x 2y = 2 x 18.95)2x + 5y = 41.4002x + 4y = 37.90

Subtracting equation 1 from equation 2 gives us:

2x + 5y = 41.400- (0.2x + 0.4y = 3.790)

1.8x + 4.6y = 37.61

Now we can solve for y.

1.8x + 4.6y = 37.61

=> 46y = 46.29

=> y = 1.05

Then we can solve for x using equation

1.1x + 2y = 18.95

=> 1x + 2(1.05) = 18.95

=> x = 7.15

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Question:

You order a cell phone case and 2 screen protectors online for a total of $18.95. Your friend orders 2 cell phone cases and 5 screen protectors at the same unit prices for a total of $41.40. What is the cost of each cell phone case? Each screen protector?

The restaurant can store approximately [tex]6.864 * 10^6[/tex] cubic centimeters of grease in the recycling tank in the shape of a cylinder.

The formula for the volume of a cylinder is V = π[tex]r^2[/tex]h, where V is the volume, r is the radius of the circular base, and h is the height of the cylinder.

To use this formula, we need to know the values of r and h for the grease recycling tank. The problem tells us that the diameter of the tank is 197.2 cm, which means the radius is half of the diameter:

r = d/2 = 197.2 cm / 2 = 98.6 cm.

The problem also tells us that the height of the tank is 223.7 cm.

Now we can plug in the values of r and h into the formula for the volume of a cylinder:

V = π[tex]r^2[/tex]h

V = π[tex](98.6 cm)^2(223.7 cm)[/tex]

V = [tex]3.14 * (98.6 cm)^2 * (223.7 cm)[/tex]

V ≈ [tex]6.864 * 10^6 cm^3[/tex]

Therefore, the volume of the grease recycling tank is approximately [tex]6.864 * 10^6[/tex] cubic centimeters, which means that the restaurant can store that amount of grease in the tank.

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The measure of the angle that turns through 2 parts of a circle divided into 5 equal parts is 144 degrees.

What is the circumference of a circle?

The circumference of a circle is the distance around its outer edge or boundary. It is the total length of the circular arc, which is the curved part of the circle.

The formula for the circumference of a circle is C = 2πr

If a circle is divided into 5 equal parts, each part corresponds to an angle of 360/5 = 72 degrees.

To find the measure of the angle that turns through 2 parts, we need to multiply 2 by 72 degrees:

2 parts x 72 degrees/part = 144 degrees

Hence, the measure of the angle that turns through 2 parts of a circle divided into 5 equal parts is 144 degrees.

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The answers of the following questions are mentioned below respectively.

Scale factor is the ratio of the lengths of corresponding sides of two similar figures. Two figures are considered similar if they have the same shape, but not necessarily the same size.

19.To find the scale factor of PQRS to JKLM, we can use the fact that the corresponding sides of similar figures are proportional. Thus, we have:

PQ/JK = QR/KL = RS/LM

Substituting the given values, we get:

w/25 = 12/15 = 10/x

Simplifying, we get:

w = 5/3 * 25 = 41.67 (approx)

x = 15/2 = 7.5

y = 25 * 7.5 / 15 = 12.5

Therefore, the scale factor of PQRS to JKLM is PQ/JK = w/25 = 41.67/25 = 1.6667 (approx).

20. To find the scale factor of JKLM to PQRS, we can take the reciprocal of the scale factor of PQRS to JKLM. Thus, we have:

JK/PQ = 1/(PQ/JK) = 1/1.6667 = 0.6 (approx)

Therefore, the scale factor of JKLM to PQRS is JK/PQ = 0.6 (approx).

21. To find the values of ti.. .r. and v, we need more information or equations.

22. To find the perimeter of each polygon, we can add up the lengths of the sides. Thus, we have:

Perimeter of JKLM = KJ + JM + ML + LK = 25 + y + x + 15 = y + x + 40 = 20 + 7.5 + 40 = 67.5

Perimeter of PQRS = PQ + QR + RS + SP = w + 12 + 10 + 16 = w + 38 = 41.67 + 38 = 79.67 (approx)

Therefore, the perimeter of JKLM is 67.5 and the perimeter of PQRS is 79.67 (approx).

23. To find the ratio of the perimeter of PQRS to the perimeter of JKLM, we can divide the perimeter of PQRS by the perimeter of JKLM. Thus, we have:

Ratio of perimeter of PQRS to perimeter of JKLM = Perimeter of PQRS / Perimeter of JKLM = 79.67 / 67.5 = 1.18 (approx)

Therefore, the ratio of the perimeter of PQRS to the perimeter of JKLM is 1.18 (approx).

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19. The scale ratio of PQRS to JKLM is PQ/JK = 1.6667. (approx).

20. JK/PQ is the scale factor of JKLM to PQRS is = 0.6 (approx).

22. The JKLM perimeter is 67.5 and the PQRS perimeter is 79.67 (approx).

23. The PQRS perimeter's ratio to the JKLM perimeter is 1.18. (approx).

The ratio of the lengths of the respective sides of two similar figures is known as the scale factor. When two figures share the same shape but not necessarily the same height, they are said to be similar.

19. We can use the knowledge that the corresponding sides of comparable figures are proportional to determine the scale factor of PQRS to JKLM.

So, here we are:

[tex]\frac{PQ}{JK}=\frac{QR}{KL}=\frac{RS}{LM}[/tex]

Replace the specified numbers in the aforementioned equation,

[tex]\frac{w}{25}=\frac{12}{25}=\frac{10}{x}[/tex]

Simplifying, we get:

w = 5/3 * 25

 = 41.67 (approx)

x = 15/2 = 7.5

y = 25 * 7.5 / 15

 = 12.5

As a result, PQ/JK = w/25 is the scale factor for PQRS to JKLM.

                                                    = 41.67/25

                                                    = 1.6667 (approx).

20. We can take the inverse of the scale factor of PQRS to JKLM to determine the scale factor of JKLM to PQRS. So, here we are:

JK/PQ = 1/(PQ/JK)

           = 1/1.6667

           = 0.6 (approx)

As a result, JK/PQ is equal to 0.6 when converting JKLM to PQRS. (approx).

21. To find the values of ti.. .r. and v, additional details or formulae are required.

22. We can sum up the side lengths of each polygon to determine its perimeter. So, here we are:

Perimeter of JKLM = KJ + JM + ML + LK

                 = 25 + y + x + 15

                 = y + x + 40

                 = 20 + 7.5 + 40

                 = 67.5

Perimeter of PQRS = PQ + QR + RS + SP

                                = w + 12 + 10 + 16

                                = w + 38

                                = 41.67 + 38

                                = 79.67 (approx)

As a result, the JKLM perimeter is 67.5 and the PQRS perimeter is 79.67 (approx).

23. By dividing the perimeters of the two systems, we can determine the percentage of the perimeters of PQRS and JKLM. So, here we are:

Ratio of the PQRS periphery to the JKLM perimeter = Perimeter of PQRS / Perimeter of JKLM = 79.67 / 67.5 = 1.18 (approx)

As a result, the PQRS perimeter's relationship to the JKLM perimeter is 1.18. (approx).

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Answer: identical to/same as

Step-by-step explanation:

Answer:

The ≡  sign means identical to, similar but not exactly the same as, equals

Step-by-step explanation:

Hope this helps! =D

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The blue line is the tangent line that passes through the point (0.75, 0.25). The point on the tangent line is (3, 4). The gradient of the curve is approximately 0.6.

Answer:

gradient = [tex]\frac{1}{4}[/tex]

Step-by-step explanation:

calculate the gradient m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (4, 2) and (x₂, y₂ ) = (8, 3) ← 2 points on the line

m = [tex]\frac{3-2}{8-4}[/tex] = [tex]\frac{1}{4}[/tex]

Answer:

Fold the paper in half lengthwise. Unfold it, then fold it in half again widthwise. Unfold it, then fold it in thirds lengthwise. Unfold it and then fold it in half again widthwise. You should now have a paper with 8 sections, with 1 on top of 2, 2 on top of 3, 3 on top of 4, etc. You can flip the numbers upside down or backwards as desired.

Step-by-step explanation:

Answer:

(2a + 3b)² = 121

Step-by-step explanation:

given 4a² + 9b² = 25 and ab = 8

(2a + 3b)² ← expand using FOIL

= 4a² + 6ab + 6ab + 9b²

= 4a² + 9b² + 12ab ← substitute given values from above

= 25 + 12(8)

= 25 + 96

= 121

Ms. Mazzei can have 44 animal pens in her 12 acres of land.

Algebra is a branch of mathematics that deals with the manipulation and properties of mathematical expressions, including variables and symbols representing numbers, as well as the rules governing their relationships and operations.

Algebraic equations typically involve variables, which are represented by letters or symbols, and are used to express relationships between different quantities or unknowns. These equations can be manipulated using algebraic operations such as addition, subtraction, multiplication, division, and exponentiation to solve for the value of the variables.

The study of algebra includes a wide range of topics, including linear algebra, abstract algebra, number theory, and algebraic geometry. It is a fundamental part of mathematics and plays a crucial role in many areas of modern science and technology.

To find the number of animal pens Ms. Mazzei can have in 12 acres of land, we need to divide the total area by the area of each pen:

Number of pens = Total area / Area of each pen

Total area = 12 acres

Area of each pen = 3/11 acres

Number of pens = 12 / (3/11)

Number of pens = 44

Therefore, Ms. Mazzei can have 44 animal pens in her 12 acres of land.

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The distance north of Helicopter A from helicopter B is 1. 03 km.

The shortest distance between the polar bear and the conservationists is 9.36 km.

To find the distance from Helicopter A to Helicopter B in the north direction, we can use trigonometry. We can create a right triangle with the north direction as one side, the distance between the helicopters as the hypotenuse, and the angle of 122° between them.

Let N be the north distance between A and B. We can use the sine function:

sin(angle) = opposite side / hypotenuse

sin(122°) = N / 1.2 km

Now, solve for N:

N = 1.2 km x sin (122°) = 1.03 km

The polar bear's position is given as 3 km eastward and on a bearing of 104°. To find the shortest distance between the polar bear and the conservationists, we need to consider the right triangle formed by the eastward direction, the north direction, and the distance between the polar bear and the conservationists as the hypotenuse.

Let D be the shortest distance between the polar bear and the conservationists. We can use the cosine function:

cos(angle) = adjacent side / hypotenuse

cos(104°) = 3 km / D

Now, solve for D:

D = 3 km / cos(104°) = 9.36 km

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Answer: The probability of a student taking the SATs is p = 0.61. Let's consider the first student we sample. The probability that this student does not take the SATs is q = 1 - p = 0.39.

If the first student does not take the SATs, we need to sample another student. The probability that the second student does not take the SATs, given that the first student did not take the SATs, is still q = 0.39.

Similarly, if the second student also does not take the SATs, we need to sample a third student. The probability that the third student does not take the SATs, given that the first two students did not take the SATs, is still q = 0.39.

We continue this process until we find the first student who takes the SATs. Let X be the number of students we sample until we find the first student who takes the SATs. Then X can take on the values 1, 2, 3, and so on.

The probability that we find the first student who takes the SATs on the first try is p = 0.61. The probability that we find the first student who takes the SATs on the second try is (q)(p) = (0.39)(0.61) = 0.238.

Similarly, the probability that we find the first student who takes the SATs on the third try is (q)(q)(p) = (0.39)(0.39)(0.61) = 0.147.

In general, the probability that we find the first student who takes the SATs on the kth try is (q)^(k-1)(p).

Therefore, the probability that we find the first student who takes the SATs in exactly k tries is:

P(X=k) = (q)^(k-1)(p)

We want to find the probability of sampling five successive students at random until we find the first student to take the SATs. So we want to find:

P(X=1) ∗ P(X=2) ∗ P(X=3) ∗ P(X=4) ∗ P(X=5)

= p ∗ (q)(p) ∗ (q)(q)(p) ∗ (q)(q)(q)(p) ∗ (q)(q)(q)(q)(p)

= (0.61) ∗ (0.39)(0.61) ∗ (0.39)(0.39)(0.61) ∗ (0.39)(0.39)(0.39)(0.61) ∗ (0.39)(0.39)(0.39)(0.39)(0.61)

= 0.61 ∗ 0.238 ∗ 0.147 ∗ 0.0905 ∗ 0.0554

≈ 0.00028

Therefore, the probability of sampling five successive students at random until you find the first student to take the SATs is approximately 0.00028 or 0.028%.

Step-by-step explanation:

Answer: The area of the mosaic is 175 cm². To calculate this, multiply the two sides of each triangle together (7 cm * 5 cm = 35 cm²) and then multiply that by the number of tiles (35 cm² * 20 = 175 cm²).

Step-by-step explanation:

Therefore, the only solution to the equation cot² x cos x = cot²x on the interval [0, 2m) is x = 0.

An equation is a mathematical statement that shows the equality between two expressions. The expressions on either side of the equals sign are called the left-hand side and the right-hand side of the equation. An equation can be written in many different forms, but the most common form is: Left-hand side = Right-hand side

In the given question,

We start by bringing all the terms to one side of the equation, which gives:cot² x (cos x - 1) = 0

Now, we need to solve for x such that this equation holds on the interval [0, 2m).

First, we consider the case where cot² x = 0. This occurs when cot x = 0, or x = π/2, 3π/2, 5π/2, etc. However, none of these solutions are in the given interval [0, 2m), so we can ignore this case.

Next, we consider the case where cos x - 1 = 0. This occurs when cos x = 1, or x = 2nπ, where n is an integer. The only solution that is in the given interval [0, 2m) is x = 0.

Therefore, the only solution to the equation cot² x cos x = cot² x on the interval [0, 2m) is x = 0.

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Answer:

perpendicular slope = 2

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = - [tex]\frac{1}{2}[/tex] x + 7 ← is in slope- intercept form

with slope m = - [tex]\frac{1}{2}[/tex]

given a line with slope m then the slope of a line perpendicular to it is

[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{-\frac{1}{2} }[/tex] = 2

Answer:

The area of the rectangle is given by the formula A = lw. Substituting the given values, we get:

A = (x+14)(3x+1)

Expanding the expression, we get:

A = 3x^2 + x + 42x + 14

A = 3x^2 + 43x + 14

Therefore, the area of the rectangle is given by the polynomial expression 3x^2 + 43x + 14.

The mean of the data is X = 85. The variance is 187.5. The standard deviation is σ = 13.7

Standard deviation is a measure of the amount of variability or dispersion of a set of data points from the mean value. It is calculated by finding the square root of the variance, which is the average of the squared differences between each data point and the mean. The standard deviation indicates how far the data points are from the mean on average, with larger values indicating greater variability and smaller values indicating less variability. The standard deviation is a commonly used measure of spread in statistics and is often used to describe the distribution of a dataset. It is denoted by the symbol σ (sigma) for a population and s for a sample.

To find the mean of the data, we add up all the values and divide by the total number of values:

X = (90 + 75 + 60 + 85 + 65 + 80 + 70 + 75) / 8

= 680 / 8

= 85

So the mean of the data is X = 85.

To find the variance, we need to first find the deviation of each value from the mean, square each deviation, and then take the average of the squared deviations:

deviation of 90 from mean = 90 - 85 = 5

deviation of 75 from mean = 75 - 85 = -10

deviation of 60 from mean = 60 - 85 = -25

deviation of 85 from mean = 85 - 85 = 0

deviation of 65 from mean = 65 - 85 = -20

deviation of 80 from mean = 80 - 85 = -5

deviation of 70 from mean = 70 - 85 = -15

deviation of 75 from mean = 75 - 85 = -10

Now, we square each deviation and find the average:

variance = [(5)² + (-10)² + (-25)² + (0)² + (-20)² + (-5)² + (-15)² + (-10)²] / 8

= (25 + 100 + 625 + 0 + 400 + 25 + 225 + 100) / 8

= 1500 / 8

= 187.5

So the variance is 187.5.

Finally, the standard deviation is the square root of the variance:

σ = √(187.5)

= 13.7 (rounded to the nearest tenth)

Therefore, the standard deviation is σ = 13.7 (rounded to the nearest tenth).

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The correct answer is: Bus 18, with an IQR of 9

To determine the most consistent bus, we need to calculate the measure of variability, which gives us an idea of the spread of the data.

In this case, we'll use the Interquartile Range (IQR) as the measure of variability.

The IQR is the range between the first quartile (Q1, the 25th percentile) and the third quartile (Q3, the 75th percentile) of the data.

A smaller IQR indicates more consistency in travel times.

Bus 47 Travel Times: 4, 6, 10, 10, 12, 12, 14, 16, 16, 16, 18, 18, 22, 22, 28

Q1 (25th percentile): 10

Q3 (75th percentile): 22

IQR: 22 - 10 = 12

Bus 18 Travel Times: 6, 6, 8, 9, 10, 10, 12, 12, 14, 14, 16, 16, 18, 20, 22

Q1 (25th percentile): 9

Q3 (75th percentile): 18

IQR: 18 - 9 = 9

Comparing the IQRs, we can see that Bus 18 has a smaller IQR (9) compared to Bus 47 (12).

This means that Bus 18 has more consistent travel times than Bus 47.

So, the correct answer is:

Bus 18, with an IQR of 9

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The image of (-5,-9) after dilation by a scale factor of 3 centered at the origin is (-15,-27).

To find the image of the point (-5,-9) after dilation by a scale factor of 3 centered at the origin.

We can use the following formula:

(x', y') = (kx, ky)

Where (x', y') are the coordinates of the dilated point, (x, y) are the coordinates of the original point, and k is the scale factor.

In this case, k = 3, and the coordinates of the original point are (-5,-9).

So we have:

x' = 3(-5) = -15

y' = 3(-9) = -27

Therefore, the image after dilation is (-15,-27).

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The shapes that are nets of a pentagonal-based pyramid are shapes A and D.

A net of a pentagonal-based pyramid is a 2-dimensional pattern that can be folded into a 3-dimensional pentagonal-based pyramid. The net of a pentagonal-based pyramid has the following properties:

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Thus, the most direct path between the bottle caps and Ann is found as:

d = 10.63 units.

The algebraic phrase known as the distance formula, which provides the distances between two places in terms of respective coordinates (in coordinate system).

The distance formulas with points in rectangular coordinates in two- through three-dimensional Euclidean space are based here on Pythagorean theorem.

The formula used to calculate the distance between both the points (x1, y1) and ((x2, y2)

d = √[(x2 - x1)² + (y2 - y1)²]

Coordinates of pile of bottle caps -:(x1, y1) =   (4, -10).

Coordinates of ANN - (x2, y2) =  (-4, 3).

Using the distance formula:

d = √[(x2 - x1)² + (y2 - y1)²]

d = √[(-4 - 4)² + (-3 + 10)²]

d = √[(64) + 49]

d = 10.63 units

Thus, the most direct path between the bottle caps and Ann is found as:

d = 10.63 units.

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complete question

A pile of bottle caps is located at (4, -10). find the length of the most direct path between Ann and the bottle caps?

The graph for the question is given.

Answer: 4 days

Step-by-step explanation:

If it takes 4 people 8 days to paint a wall. We can only assume that doubling the number of people would be 2 times as fast. So divide 8/2=4.

The polynomial function of least degree possible using the given information.

Real roots: −1 (with multiplicity 2), 1 and (2,

f(2)) = (2, 7) is f(x) = x³ - 3x² + 3x - 1.

Since the polynomial function has real roots at -1 (with multiplicity 2) and 1, we know that the factors of the polynomial are (x + 1)² and (x - 1).

Let the polynomial be of the form f(x) = ax³ + bx² + cx + d. We know that f(2) = 7, so:

a(2³) + b(2²) + c(2) + d = 7

8a + 4b + 2c + d = 7

Now we need to use the fact that the roots are -1 (with multiplicity 2) and 1. Since the polynomial has factors of (x + 1)² and (x - 1), we can write the polynomial as:

f(x) = a(x + 1)²(x - 1)

Expanding this expression, we get:

f(x) = a(x² - 2x + 1)(x - 1)

f(x) = ax³ - 3ax² + 3ax - a

Now we can equate the coefficients of this expression with the coefficients of our assumed polynomial f(x) = ax³ + bx² + cx + d:

a = a

-3a = b

3a = c

-a = d

Therefore, our polynomial function is:

f(x) = x³ - 3x² + 3x - 1

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Step-by-step explanation:

The points are 15 units apart

the FIRST expression shows this

No; the triangles are not congruent by any of the congruence criteria.

To determine if two triangles are congruent, we must use one of the five congruence criteria: Side-Angle-Side (SAS), Angle-Angle-Side (AAS), Angle-Side-Angle (ASA), Side-Side-Side (SSS), and Hypotenuse-Leg (HL). To be congruent, the triangles must have three pairs of congruent sides and three pairs of congruent angles.

In the case of △ABC and △DEF, we can compare their sides and angles to determine if they are congruent. We can see that the sides of the two triangles are not equal in length, nor do the angles have the same measure. Therefore, △ABC is not congruent to △DEF.

In order to prove that the two triangles are not congruent, we can use the formula for determining the measure of the angles in a triangle, known as the Law of Cosines. This formula states that c² = a² + b² - 2ab cos γ, where c is the length of the longest side of the triangle, a and b are the lengths of the other sides of the triangle, and γ is the measure of the angle opposite the side c.

Using this formula, we can calculate the measure of the angles in both triangles. For △ABC we have angle A = arccos ( (b² + c² - a²) / 2bc ) and for △DEF we have angle D = arccos ( (e² + f² - d²) / 2ef ). The measure of angle A is not equal to the measure of angle D, so we can conclude that △ABC ≠ △DEF

Therefore, based on the calculation of the angles and the lengths of the sides, it can be concluded that △ABC is not congruent to △DEF.

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