What are the new coordinates of point A when
it is rotated about the origin by
a) 90° clockwise?
-4
b) 180°?
c) 270° clockwise?
-3 -2 -1
Y
4-
3-
ΤΑ
2.⁰⁰
1
0
-1-
-2-
--3-
-4-
1
N.
2
3 4
X

Step-by-step explanation:

Part A: The first step where Margie made an error is Step 1:

−2.67b + 11 + (−5.38b) + 15

The error lies in the addition of the two terms: (−5.38b) + 15. Margie incorrectly added the two terms together instead of subtracting them.

Part B: To correctly write the expression in the fewest terms, we need to correct the error from Part A. The correct step-by-step process is as follows:

Given: (−2.67b + 11) − (5.38b − 15)

Step 1: Distribute the negative sign to the terms inside the second parentheses:

−2.67b + 11 − 5.38b + 15

Step 2: Combine like terms:

(−2.67b − 5.38b) + (11 + 15)

Step 3: Simplify:

−7.05b + 26

Therefore, the correct expression, written in the fewest terms, is −7.05b + 26.

Answer:

Step-by-step explanation:

The indicated operation is the composition of functions. To perform this operation, we substitute the expression for g(x) into f(x). The composition of f(g(x)) is given by f(g(x)) = (4x - 1)^2 + 2.

To compute f(g(x)), we first evaluate g(x) by substituting x into the expression for g(x): g(x) = 4x - 1. Next, we substitute this result into f(x): f(g(x)) = f(4x - 1).

Now, let's expand and simplify f(g(x)):

f(g(x)) = (4x - 1)^2 + 2

        = (4x - 1)(4x - 1) + 2

        = 16x^2 - 8x + 1 + 2

        = 16x^2 - 8x + 3.

The domain of f(g(x)) is the same as the domain of g(x) since the composition involves g(x). In this case, g(x) is defined for all real numbers. Therefore, the domain of f(g(x)) is also all real numbers.

In summary, the composition of f(g(x)) is given by f(g(x)) = 16x^2 - 8x + 3, and the domain of f(g(x)) is all real numbers.

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The length of the shortest path ABCD is 7 units.

To find the length of the shortest path ABCD, we need to determine the coordinates of points B and C and then calculate the distances between these points.

Given that B has a y-coordinate of 2, it lies on a horizontal line. Therefore, the y-coordinate of B is 2, and the x-coordinate is the same as the x-coordinate of point A, which is 7. So, B is the point (7, 2).

Similarly, C lies on a vertical line, and its x-coordinate is the same as the x-coordinate of point D, which is -5. So, C is the point (-5, 0).

Now, we can calculate the distances between the points. The distance between A and B can be found using the distance formula:

AB = √[tex]((x2 - x1)^2 + (y2 - y1)^2[/tex])

Substituting the coordinates of A and B, we have:

AB = √[tex]((7 - 7)^2 + (2 - 4)^2) = √(0^2 + (-2)^2[/tex]) = √4 = 2

The distance between B and C is simply the difference in their y-coordinates:

BC = |y2 - y1| = |2 - 0| = 2

Finally, the distance between C and D can be calculated using the distance formula:

CD = √[tex]((-5 - (-5))^2 + (0 - (-3))^2)[/tex] = √[tex](0^2 + 3^2)[/tex] = √9 = 3

Therefore, the length of the shortest path ABCD is the sum of the distances AB, BC, and CD:

Shortest path ABCD = AB + BC + CD = 2 + 2 + 3 = 7

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The correct statement is OB. The average rate of change of f is more than the average rate of change of g.

To determine the average rate of change (slope) of the functions f and g, we can use the formula:

Average Rate of Change = (f(x2) - f(x1)) / (x2 - x1)

For function f, using the given table, we can calculate the average rate of change between the points (0, 0) and (2, -2):

Average Rate of Change (f) = (-2 - 0) / (2 - 0) = -2 / 2 = -1

For function g, using the given points (-3, 5) and (0, 14), we can calculate the average rate of change:

Average Rate of Change (g) = (14 - 5) / (0 - (-3)) = 9 / 3 = 3

Comparing the average rates of change, we find that the average rate of change of f is -1, while the average rate of change of g is 3.

Therefore, the correct statement is:

OB. The average rate of change of f is more than the average rate of change of g.

The average rate of change of f is greater than the average rate of change of g, indicating that the function f is increasing at a faster rate than function g over the given interval.

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Answer:

[tex]x = \frac{3\pi}{64} +\frac{9}{16}[/tex]

Step-by-step explanation:

We have

∠D = 45° = 45* π/180 radians = π/4 radians - eq(1)

big arc + small arc = 2π

small arc = 16x - 9

⇒ big arc = 2π - small arc

big arc = 2π - 16x + 9

[tex]\angle D = \frac{big \;arc - small \;arc}{2}[/tex]

[tex]\angle D = \frac{2\pi - 16x + 9 - 16x +9}{2}\\\\= \angle D = \frac{2\pi - 32x + 19 }{2}\\\\\angle D = \pi - 16x + 9[/tex]

Equating with eq(1)

π - 16x + 9 = π/4

⇒ 16 x = π - (π/4) +9

⇒ 16 x = (3π/4) +9

⇒ [tex]x = \frac{1}{16} (\frac{3\pi}{4} +9)[/tex]

[tex]x = \frac{3\pi}{64} +\frac{9}{16}[/tex]

The regression equation that correctly models the data is: y = 5.71x + 27.6.

The correct answer to the given question is option D.

Regression equations are mathematical models that relate two or more variables to find the relationship between them. One variable, denoted as y, is considered the dependent variable. The other variable, denoted as x, is considered the independent variable.

In this case, the independent variable is the size of the outdoor deck, while the dependent variable is the estimated cost to construct it.

There are different types of regression equations. The one that fits this scenario is the linear regression equation, which has the form y = mx + b, where m is the slope of the line and b is the y-intercept.

The slope represents the change in y for each unit change in x, while the y-intercept represents the value of y when x is zero. To find the regression equation that correctly models the data, we need to calculate the slope and the y-intercept using the given values.

We can use the following formulas:

Slope:  m = [(n∑xy) - (∑x)(∑y)] / [(n∑x2) - (∑x)2]

Y-intercept: b = (∑y - m∑x) / n Where n is the number of data points, which is 6 in this case.

Using the given values, we get: Slope: m = [(6)(2,010,500) - (1,193)(6,950)] / [(6)(346,337) - (1,193)2] = 5.71

Y-intercept: b = (6,950 - (5.71)(1,193)) / 6 = 27.6

Therefore, the regression equation that correctly models the data is: y = 5.71x + 27.6

The answer is option D.

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A

no, because they are both right triangles and

the one on the left is 88° at the right anglr

Answer:

Step-by-step explanation:

To find the equation of a line that is perpendicular to a given line and passes through a specific point, we need to follow a few steps:

Find the slope of the provided line.

The point-slope form of a line is given by: y - y1 = m(x - x1), where (x1, y1) represents the given point.

Substituting the values, the equation of the perpendicular line becomes:

y - 5 = (-1/m)(x - 2)

Simplifying the equation further, we can rewrite it in point-slope form:

y - 5 = (-1/m)x + (2/m)

Answer:

6b + 5n = 101

Step-by-step explanation:

The correct system of equations that can be used to find b, the number of bracelets Ily sold, and n, the number of necklaces she sold is:

b + n = 18

6b + 5n = 101

In this system, the first equation represents the total number of items sold, which is 18. Since b represents the number of bracelets and n represents the number of necklaces, the equation b + n = 18 reflects that the total number of bracelets and necklaces sold should add up to 18.

The second equation represents the total amount of money Ily earned from selling bracelets and necklaces. Since bracelets were sold for $6 each and necklaces for $5 each, the equation 6b + 5n = 101 represents the total amount of money earned, which is $101.

Therefore, the correct system of equations is:

b + n = 18

6b + 5n = 101

Answer:

violence figer in the past two years

The correct graph of the linear inequality 1/2x - 2y > -6 is the one where a solid straight line has a positive slope and goes through (negative 4, 2) and (4, 4), and everything below and to the right of the line is shaded.

The density of lead is 11.3 kg/m³.

The density of lead can be calculated by using the formula D = M/V, where D represents density, M represents mass and V represents volume. The density of lead is the ratio of the mass of lead to the volume occupied by it.

Density of Lead:

Given that the lead has a mass of 3.390 kg and occupies a volume of 0.3 m³.

Density of Lead (D) = Mass of Lead (M) / Volume of Lead (V)D = 3.390 kg / 0.3 m³D = 11.3 kg/m³

Therefore, the density of lead is 11.3 kg/m³.

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Answer: the answer is 110.8

Step-by-step explanation: add um all up

The vessel in distress is located at (-x, y), with the exact coordinates depending on the specific distances and positions of ships A and B.

To determine the location of the vessel in distress, we can analyze the information given about the distress signals received by ships A and B.

Ship A received a distress signal from the northeast, while Ship B received a distress signal from the west.

Let's consider the compass directions:

Northeast (NE) is a direction that lies between north and east.

West (W) is a direction perpendicular to both north and south.

From this information, we can deduce that the vessel in distress must be located at the intersection of the northeast and west directions.

To find this intersection point, we can draw a diagram or use a coordinate system. Let's assume the origin (0,0) represents the starting point of both ships A and B.

Based on the given information, we know that ship A received a distress signal from the northeast. This means that the vessel in distress must be located in the direction of the positive x-axis (east) and the positive y-axis (north) from the origin.

On the other hand, ship B received a distress signal from the west. This indicates that the vessel in distress must be located in the direction of the negative x-axis (west) from the origin.

Combining these two pieces of information, we can conclude that the vessel in distress is located at the point where the positive y-axis (north) intersects with the negative x-axis (west). In coordinate notation, this point can be represented as (-x, y), where x and y are positive values.

Therefore, the vessel in distress is located at (-x, y), with the exact coordinates depending on the specific distances and positions of ships A and B.

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Answer:

[tex]x = 5\sqrt3[/tex]

Step-by-step explanation:

We can solve for the side length x in this 30-60-90 triangle by using the ratio of side lengths for that specific type of right triangle:

In this triangle, we can identify the smallest side (corresponding to 1 in the ratio) as 5. This means we can solve for x by multiplying 5 by [tex]\sqrt3[/tex]. Thus:

[tex]\boxed{x = 5\sqrt3}[/tex]

The calculated equation of the line is y = -2x + 3

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

The graph

Where, we have

(1, 1) and (0, 3)

The equation of the line is calculated as

y = mx + c

Where

c = y when x = 0

So, we have

y = mx + 3

Using the points, we have

m + 3 = 1

So, we have

m = -2

This means that

y = -2x + 3

Hence, the equation of the line is y = -2x + 3

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Answer:

math = 227.98

programming = 42.55

Step-by-step explanation:

We have
3m + 4p = 854.14 -eq(1)

8m + 1p = 1866.39 -eq(2)

rq(2) x 4: 32m + 4p = 7465.56 -eq(3)

eq(3)-eq(1):

32m + 4p = 7465.56

- ( 3m + 4p = 854.14)

--------------------------------

29m = 6611.42

--------------------------------

⇒ m = 6611.42/29

m = 227.98

sub in eq(1)

3(227.98) + 4p = 854.14

4p = 854.14 - 683.94

4p = 170.2

p = 170.2/4

p = 42.55

Answer:

Angle C must measure 40 degrees.

Step-by-step explanation:

All angles in a triangle add up to 180 degrees

(90-50)=40 degrees

We can check our answer by adding all the angles up

90+50+40=180

Angle C must be 40 degrees

The average rate of change for the number of pounds of metal per person per day between 1980 and 1988 is -0.00125 pounds per year.

To calculate the average rate of change for the number of pounds of metal per person per day between 1980 and 1988, we need to find the difference in the values and divide it by the number of years.

In 1980, the pounds of metal per person per day was 0.35, and in 1988, it was 0.34. The difference between these values is -0.01.

The number of years between 1980 and 1988 is 1988 - 1980 = 8 years.

Now, we can calculate the average rate of change:

Average rate of change = (Change in pounds of metal) / (Number of years)

= (-0.01) / 8

= -0.00125

The average rate of change for the number of pounds of metal per person per day between 1980 and 1988 is -0.00125 pounds per year.

Interpretation:

The negative value of the average rate of change (-0.00125) indicates that there was a decrease in the number of pounds of metal per person per day from 1980 to 1988.

Specifically, on average, there was a decrease of approximately 0.00125 pounds per year.

This suggests that there was a declining trend in the use or disposal of metal waste during this period.

It could indicate improvements in recycling or waste management practices, or a shift in consumer behavior towards reducing metal waste.

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The side length that prove a right angle triangle is √2, √3 and √5.

A right angle triangle is a triangle that has one of its angles as 90 degrees. The sum of angles in a triangle is 180 degrees.

Therefore, a right angle triangle can be proved by using the Pythagoras's theorem as follows:

Hence,

c² = a² + b²

where

Therefore,

(√2)² + (√3)² = (√5)²

Hence, the right angle triangle is the triangle with sides √2, √3 and √5.

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The list of ordered pairs that is a function is Option D.

A math function is a relationship that assigns a unique output value to each input value. It describes how one quantity depends on another.

Functions are commonly represented using mathematical notation, such as f(x), and they play a fundamental role in various areas of mathematics and its applications.

A  function is a relation in which one input (x-value) is assigned to exactly one output (y-value).

Since option D's x-values do not repeat, then it is a function.

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Answer:

The one at the bottom right above the next button

Step-by-step explanation:

The function rule that describes the given translation is T-9, 1(x, y).

The first value in the function rule represents the horizontal translation, while the second value represents the vertical translation. In this case, the square is translated 1 unit to the right, indicating a positive horizontal translation.

Additionally, the square is translated 9 units down, indicating a negative vertical translation. Therefore, the correct function rule is T-9, 1(x, y).

In the coordinate plane, the x-coordinate represents the horizontal position, and the y-coordinate represents the vertical position. When we apply the function rule T-9, 1 to the coordinates of the square, we subtract 9 from the y-coordinate and add 1 to the x-coordinate.

This results in the square being moved 9 units down and 1 unit to the right from its original position.

The negative sign in front of the 9 indicates a downward movement, and the positive sign in front of the 1 indicates a rightward movement. Hence, the translation is accurately described by the function rule T-9, 1(x, y).

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Answer:

C

Step-by-step explanation:

The calculated value of x in the triangle is 40°

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

The figure (see attachment)

Using the theorem of linear pair, we have

∠DBA + ∠ABC = 180°

Using the given values, we have

∠100° + ∠ABC = 180°

Collect the like terms

∠ABC = 180° - 100°

Evaluate

∠ABC = 80°

The sum of angles of a triangle is 180° .

So, in triangle ABC

∠A + ∠B + ∠C = 180°

Using the given values, we have

x + 80 + 60 = 180°

Evaluate the sum

x + 140 = 180°

Collect the like terms

x = 180° - 140°

Evaluate

x = 40°

Hence, the value of x is 40°

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The result of the row operation on the matrix is given as follows:

[tex]\left[\begin{array}{cccc}1&0&0&8\\0&8&0&3\\0&0&5&6\end{array}\right][/tex]

The matrix in this problem is defined as follows:

[tex]\left[\begin{array}{cccc}2&0&0&16\\0&8&0&3\\0&0&5&6\end{array}\right][/tex]

The row operation is given as follows:

[tex]R_1 \rightarrow \frac{1}{2}R_1[/tex]

The first row of the matrix is given as follows:

[2 0 0 16]

The meaning of the operation is that every element of the first row of the matrix is divided by two.

Hence the resulting matrix is given as follows:

[tex]\left[\begin{array}{cccc}1&0&0&8\\0&8&0&3\\0&0&5&6\end{array}\right][/tex]

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1. The indefinite integral of (v + 1) / (2v - 20)^5 dv is -1 / (8(2v - 20)^4) + C.

2. The indefinite integral of x^2 / (x - 5) dx is (1/2) x^2 + 5x + 25 ln|x - 5| + C.

3. The indefinite integral of x cos(8x^2) dx is (1/16) sin(8x^2) + C.

4. The indefinite integral of 176 / e^(-x) + 1 dx is 176 ln|1 + e^x| + C.

1. To find the indefinite integral of (v + 1) / (2v - 20)^5 dv:

Let u = 2v - 20. Then du = 2 dv.

The integral becomes:

(1/2) ∫ (1/u^5) du

Now we can integrate using the power rule:

(1/2) ∫ u^(-5) du

Applying the power rule, we get:

(1/2) * (u^(-4) / -4) + C

= -1 / (8u^4) + C

Substituting back u = 2v - 20:

= -1 / (8(2v - 20)^4) + C

Therefore, the indefinite integral of (v + 1) / (2v - 20)^5 dv is -1 / (8(2v - 20)^4) + C.

2. To find the indefinite integral of x^2 / (x - 5) dx:

We can use polynomial long division to simplify the integrand:

x^2 / (x - 5) = x + 5 + 25 / (x - 5)

Now we can integrate each term separately:

∫ x dx + ∫ (5 dx) + ∫ (25 / (x - 5) dx)

Using the power rule, we get:

(1/2) x^2 + 5x + 25 ln|x - 5| + C

Therefore, the indefinite integral of x^2 / (x - 5) dx is (1/2) x^2 + 5x + 25 ln|x - 5| + C.

3. To find the indefinite integral of x cos(8x^2) dx:

We can use the substitution method. Let u = 8x^2, then du = 16x dx.

The integral becomes:

(1/16) ∫ cos(u) du

Integrating cos(u), we get:

(1/16) sin(u) + C

Substituting back u = 8x^2:

(1/16) sin(8x^2) + C

Therefore, the indefinite integral of x cos(8x^2) dx is (1/16) sin(8x^2) + C.

4. To find the indefinite integral of 176 / e^(-x) + 1 dx:

We can simplify the integrand by multiplying the numerator and denominator by e^x:

176 / e^(-x) + 1 = 176e^x / 1 + e^x

Now we can integrate:

∫ (176e^x / 1 + e^x) dx

Using u-substitution, let u = 1 + e^x, then du = e^x dx:

∫ (176 du / u)

Integrating 176/u, we get:

176 ln|u| + C

Substituting back u = 1 + e^x:

176 ln|1 + e^x| + C

Therefore, the indefinite integral of 176 / e^(-x) + 1 dx is 176 ln|1 + e^x| + C.

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Answer: A,

Step-by-step explanation:

8 people, times whatever each person payed will equal to 55$ in total