describe an infinite list of decimals. all of which are greater than 3.514, but get closer and closer to 3.514

Answer:

  y = -x +3

Step-by-step explanation:

You want the slope-intercept equation of the line with the same intercept as -3y = -9 +3x, and the same slope as -2x -2y = -8.

The slope-intercept form of the equation of a line is ...

  y = mx +b . . . . . where m is the slope, and b is the y-intercept

For the given equations, we can put them in this form to find the desired parameters.

  -3y = -9 +3x

  y = -x +3 . . . . . . . . . . divide both sides by -3

We observe that the y-intercept is +3, which we will need for our answer.

The slope-intercept form of the second equation is ...

  -2x -2y = -8

  x + y = 4 . . . . . . . . . . divide by -2

  y = -x +4 . . . . . . . . . . subtract x

We observe that the slope (coefficient of x) is -1, which we will need for our answer.

We want the equation of the line with slope -1 and y-intercept 3. It is ...

  y = -x +3 . . . . . . . . . . same as the equation of the first line

__

Additional comment

The slope-intercept equation (green) is plotted using dots, so that you can see it is coincident with the line described by the first equation (red). Parallel lines have the same slope, so our desired line must be parallel to the blue line. (It is.)

The correct answer is option D: A line passes through the point (0, 0) and continues through the point (12, 3)

For the first question:

The table shows a proportional relationship between x and y. To describe what the graph of this proportional relationship would look like, we can examine the given data points.

The data points are (12, 3), (8, 26), and (24, ?). We can observe that as x increases, y also increases. This indicates a positive correlation between the variables. Additionally, we can see that the ratio of y to x remains constant for each data point.

Now, let's analyze the answer options:

A. A line passes through the point (0, 0) and continues through the point (3, 12).

This answer option does not align with the given data because there is no data point with an x-value of 3 and a corresponding y-value of 12.

B. A line passes through the point (0, 0) and continues through the point (2, 8).

This answer option aligns with the given data because (2, 8) is a valid data point from the table, and the line passes through the origin (0, 0).

C. A line passes through the point (0, 0) and continues through the point (6, 24).

This answer option does not align with the given data because there is no data point with an x-value of 6 and a corresponding y-value of 24.

D. A line passes through the point (0, 0) and continues through the point (12, 3).

This answer option aligns with the given data because (12, 3) is a valid data point from the table, and the line passes through the origin (0, 0).

Based on the analysis, the correct answer is option D: A line passes through the point (0, 0) and continues through the point (12, 3). This accurately represents the graph of the proportional relationship given in the table.

For the second question, I'm sorry, but you didn't provide the multiple-choice options or the complete question. Could you please provide the question and options so that I can assist you further?

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Answer:

Step-by-step explanation:

208

If a park has 2 cafés. Cafe 2 had more customers than Cafe 1 over the four weekends.

We can start by finding the total number of customers in each cafe over the 4 weekends.

For Cafe 1:

255 + 370 + 323 + 152 = 1,100 customers

For Cafe 2:

436 + 321 + 188 + 315 = 1,260 customers

So over the 4 weekends, Cafe 2 had more customers than Cafe 1, with a difference of 160 customers (1,260 - 1,100).

To describe the differences in more detail, we can calculate the difference in customers for each weekend.

Weekend 1: Cafe 2 had 436 - 255 = 181 more customers than Cafe 1

Weekend 2: Cafe 1 had 370 - 321 = 49 more customers than Cafe 2

Weekend 3: Cafe 1 had 323 - 188 = 135 more customers than Cafe 2

Weekend 4: Cafe 2 had 315 - 152 = 163 more customers than Cafe 1

We can see that the difference in customers between the two cafes varied from weekend to weekend. In two of the weekends (1 and 4), Cafe 2 had more customers than Cafe 1, while in the other two weekends (2 and 3), Cafe 1 had more customers than Cafe 2.

Overall, however, Cafe 2 had more customers than Cafe 1 over the four weekends.

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Answer: 2.333333...

Step-by-step explanation:

If we apply rise over run, we see that it rises 3.5 spaces, and runs 1.5, which means that   \(m = \frac{rise}{run} = \frac{3.5}{1.5} = 2.33333...\)

Answer:

It's C! y = 7

Step-by-step explanation:

After the double rotation, the vertices of the quadrilateral MNPQ are transformed to M'', N'', P'', and Q''. The shape of the quadrilateral may have changed, but the order of the vertices remains the same.

When a quadrilateral MNPQ is rotated counterclockwise at 90 degrees about the origin, each vertex undergoes a transformation.

The new positions of the vertices after this rotation can be denoted as M', N', P', and Q'. The order of the vertices remains the same.

Next, when the rotated quadrilateral M'N'P'Q' is further rotated counterclockwise at 270 degrees about the origin, each vertex undergoes another transformation.

The new positions of the vertices after this rotation can be denoted as M'', N'', P'', and Q''. Again, the order of the vertices remains the same.

It's important to note that a 270-degree counterclockwise rotation is equivalent to a 90-degree clockwise rotation.

The result of the double rotation is equivalent to a single clockwise rotation of 90 degrees.

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Answer:

Therefore, the correct statements are A, B, and E.

Explanation:

Based on my knowledge, a vector is a quantity that has both magnitude and direction. A scalar is a quantity that has only magnitude. When a vector is multiplied by a scalar, the magnitude of the vector is multiplied by the absolute value of the scalar, and the direction of the vector is either preserved or reversed depending on the sign of the scalar.

To answer your question, we need to find the component form, magnitude, and direction of the scalar product –4⇀

.

- The component form of −4⇀

is obtained by multiplying each component of ⇀

by –4. Therefore, −4⇀

= ⟨–8, –12⟩. This means that statement A is true.

- The magnitude of −4⇀

is obtained by multiplying the magnitude of ⇀

by 4. The magnitude of ⇀

is √(2^2 + 3^2) = √13. Therefore, the magnitude of −4⇀

is 4√13. This means that statement B is true.

- The direction of −4⇀

is opposite to the direction of ⇀

because the scalar –4 is negative. This means that statement C is false.

- The vector −4⇀

is in the third quadrant because its components are both negative. This means that statement D is false.

- The direction of −4⇀

is 180° greater than the inverse tangent of its components because it is opposite to ⇀

. The inverse tangent of its components is tan^(-1)(–12/–8) = tan^(-1)(3/2). Therefore, the direction of −4⇀

is 180° + tan^(-1)(3/2). This means that statement E is true.

Therefore, the correct statements are A, B, and E.

Answer:

y = 3x - 11

Step-by-step explanation:

(3, -2) and (5, 4)

m = 4+2/5-3

m = 6/2

m = 3

y = 3x + b

4 = 3(5) + b

4 = 15 + b

b = -11

y = 3x - 11

Thus, the given set of triangles ABC and DEF are not found to be similar triangles.

If the matching sides and angles of two polygons are proportional, then the polygons are comparable. If any two polygons meet the following two criteria, they are said to be similar.

For the given triangles ABC and DEF to be similar, the ratios of their sides muse be equal.

AB/DE = BC/EF = AC/DF

6/8 = 4/6 = 6/8

3/4 = 2/3 = 3/4

But,

3/4 ≠ 2/3  ≠ 3/4

Thus, the given set of triangles ABC and DEF are not found to be  similar triangles.

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Answer:

(13, 11)

Step-by-step explanation:

The number inside the absolute value is x, but with the opposite sign

The other number is y

Answer: 5/2

Step-by-step explanation:

slope equation: (y2-y1)/(x2-x1)

13-3/5-1 = 10/4 or 5/2

Answer:

2.5

Step-by-step explanation:

Gradient (slope) =

\(m = \frac{y2 - y1}{x2 - x1} = \frac{13 - 3}{5 - 1} = \frac{10}{4} = 2 \frac{1}{2} \)

Answer:

y=8x+5

Step-by-step explanation:

The volume of the composite solid is  452. 160 ft³

First, it is important to note that the formula for calculating the volume of a cone is expressed as;

V = πr²h/3

Such that the parameters of the formula are;

From the information given,

substitute the values

Volume = 3.14 × 6² × 12/3

Divide the values

Volume = 31.4 × 36 × 4

Multiply the values

Volume = 452. 160 ft³

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Answer:

33cm squared

Step-by-step explanation:

Answer:

33cm

Step-by-step explanation:

The missing fourth vertex needed to create a rectangle is (25, 3) option D.

Vertices (singular: vertex) are the corners or points where two or more lines, edges, or curves intersect and form an angle.

Here, the width of one side of the rectangle;

⇒ +3 - (-6) = 9 unit                (left side y-coordinates)

Similarly the length of the rectangle;

⇒ 25 - (-15) = 40 unit             (up-side x-coordinates)

Since a rectangular shape has two sets of equal sides of equivalent width (y-coordinates) and length (x-coordinates), we realize that the missing fourth vertex should be 9 units and 40 units over the point (25, -6). and (-15, 3)

So, we add 9 to the y-coordinate of (25, -6) and add 40 to the x-coordinate of (-15, 3) to get the missing vertex:

⇒ (25, -6+9) = (25, 3)

⇒ (-15+40, 3) = (25, 3)

Therefore, the missing fourth vertex is (25, 3)

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9514 1404 393

Answer:

  1.9 degrees per second

Step-by-step explanation:

The angle α the line makes with the water can be described by ...

  Sin = Opposite/Hypotenuse

  sin(α) = 10/(25 -1.9t)

Taking derivatives gives ...

  α'·cos(α) = -10(-1.9)/(25 -1.9t)²

Then the rate of change of the angle at t=0 is ...

  α' = 19/(25²·cos(α))

Of course, cos(α) = √(1 -sin(α)²) = √(1 -(10/25)²) = √(21/25), so we have ...

  α' = 19/(125√21) . . . radians/second

  α' ≈ 0.033269 radians/s ≈ 1.90 degrees/s

Answer:

For the fractions question:

1/4<1/2

3/4<2/3

5/7<3/5

8/9>8/10

7/10<6/8

Hope this helps! (:

The slope of the line passing through given points is 5/7

We know that the slope is the ratio of the change in y-values to the change in x-values.

We use slope formula,

m = (y2 - y1)/(x2 - x1)

For pair of points (1, 3) and (8, 8),

m1 = (8 - 3)/(8 - 1)

m1 = 5/7

For pair of points (8, 8)  and (15, 13),

m2 = (13 - 8)/(15 - 8)

m2 = 5/7

For pair of points (22,18)  and (29, 23),

m3 = (23 - 18)/(29 - 22)

m3 = 5/7

For pair of points (15, 13)  and (22, 18),

m4 = (18 - 13)/(22 - 15)

m4 = 5/7

Since the rate of change of output values to the input values is constant i.e., 5/7, the slope of the line is 5/7

Therefore, the slope of the line passing through given points is 5/7

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Answer:

60

Step-by-step explanation:

100 - 40 =  60

Common Math

Answer:

2·2·2·2 = 16

Step-by-step explanation:

everytime a number is raised by another, that means you are going to multiply the base number  times itself as many times as the exponents tells you. this is a little but tricky to explain, so let me give you some examples:

2² → in this case the base number is 2 and the exponent is 2 as well, so you will multiply 2 times itself, 2 times:

2² = 2 · 2 = 4

2³ → in this case the base number is 2 and the exponent is 3, so you will multiply 2 times itself, 3 times:

2³ = 2 · 2 · 2 = 8

In the question asked, 2 is being raised by 4, so you will multiply 2 times itself, 4 times:

2^4 = 2·2·2·2 = 16

the same format will be used regardless of the base number and the exponent

i hope this helps! :)

A polynomial function for each set of zeros is f(x) = (x - 5)(x+3)(x -12), f(x) = (x - 4)(x -6)(x +1),f(x) = (x +2/5)(x -2).

What is  polynomial function?

In an equation such as the quadratic equation, cubic equation, etc., a polynomial function is a function that only uses non-negative integer powers or only positive integer exponents of a variable. For instance, the polynomial 2x+5 has an exponent of 1.

Suppose you are given that a polynomial f(x) has zeroes { a, b, c }

Then the polynomial, if it is known that it is cubic, is,

f(x) = (x - a)(x - b)(x - c)

For : 5,-3, 12

f(x) = (x - 5)(x+3)(x -12)

For : 4, 6, -1,0

f(x) = (x - 4)(x -6)(x +1)

For : - 2/5,2

f(x) = (x +2/5)(x -2)

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A polynomial function for each set of zeros is f(x) = (x - 5)(x+3)(x -12), f(x) = (x - 4)(x -6)(x +1),f(x) = (x +2/5)(x -2).

What is  polynomial function?

In an equation such as the quadratic equation, cubic equation, etc., a polynomial function is a function that only uses non-negative integer powers or only positive integer exponents of a variable. For instance, the polynomial 2x+5 has an exponent of 1.

Suppose you are given that a polynomial f(x) has zeroes { a, b, c }

Then the polynomial, if it is known that it is cubic, is,

f(x) = (x - a)(x - b)(x - c)

For : 5,-3, 12

f(x) = (x - 5)(x+3)(x -12)

For : 4, 6, -1,0

f(x) = (x - 4)(x -6)(x +1)

For : - 2/5,2

f(x) = (x +2/5)(x -2)

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b equal for the top of the bookcase to have the correct area= 5 cm2

A solid object's surface area is a measurement of the total area that the surface of the object takes up.

The definition of arc length for one-dimensional curves and the definition of surface area for polyhedra (i.e., objects with flat polygonal faces), where the surface area is the sum of the areas of its faces, are both much simpler mathematical concepts than the definition of surface area when there are curved surfaces.

A smooth surface's surface area is determined using its representation as a parametric surface, such as a sphere.

This definition of surface area uses partial derivatives and double integration and is based on techniques used in infinitesimal calculus.

Henri Lebesgue and Hermann Minkowski at the turn of the century sought a general definition of surface area.

L × b = 300

b = 300 / L

b = 300 / 60 = 5

Hence, b equal for the top of the bookcase to have the correct area= 5 cm2.

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An Annual is not an example of an agreement.

The average score for the class on the exam was 78 points with a standard deviation of 6.4 points. The student who took the make-up exam scored 79.25points.

1. Calculate the mean of the first 23 exams:

Mean = 78 points

2. Calculate the standard deviation of the first 23 exams:

Standard Deviation = 6.4 points

3. Calculate the mean of the entire class:

Mean = (78 x 23) + 62 = 1840 + 62 = 1902

Total = 24

Mean = 1902 / 24 = 79.25 points

The average exam score for the class of 24 students was 78 points with a standard deviation of 6.4 points. This means that most students in the class scored between 71.6 and 84.4 points on the exam. The student who took the make-up exam the following day scored 79.25points. This score is significantly lower than the average score of the class, suggesting that the student may have not done as well on the exam compared to the other students. It is also possible that the student faced additional challenges that the other students did not have to face, such as taking the exam on a different day. Regardless, the student's score was significantly lower than the average score of the class.

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