What is the slope of the line?

The equation that represents a line with a slope of 1/2 and a y-intercept at (0,6) is option D, which is x + 2y = 6.

To determine the equation of a line, we can use the slope-intercept form, which is y = mx + b, where m represents the slope and b represents the y-intercept. In this case, the slope is 1/2 and the y-intercept is (0,6). Plugging these values into the slope-intercept form, we get y = (1/2)x + 6.

To convert this equation into the standard form, we need to eliminate the fraction. By multiplying both sides of the equation by 2, we obtain 2y = x + 12. Rearranging the terms, we get x + 2y = 12. However, the question states that the y-intercept is at (0,6), not (0,12). By subtracting 6 from both sides, we arrive at x + 2y = 6, which matches option D.

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Answer:

• 5x + 20 = 5(x + 4)

• 5(2x + 8) = 10x + 40

• 5(x + 8) = 5x + 5.8

If the function is vertically compressed, the resulting function will be g(x) = 3/4x^2

Quadratic functions are functions that has a leading degree of 2. Given the parent function f(x) = ax^2

where

2 is the exponent/degree

If the function is vertically compressed, the value of a must be less than 1, hence the possible expression when vertically compressed is g(x) = 3/4x^2

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Answer:

$497.28

Step-by-step explanation:

First, you need to find 16% of 592. To do this, turn 16% into a decimal by dividing by 100:

16/100 = 0.16

Then, multiply 0.16 by 592, to get 94.72.

Then, subtract this number from 592:

592 - 94.72 = 497.28

Answer:

Step-by-step explanation:

Answer:

the equation of yours is wrong. the equation would be y=1/3x.

Step-by-step explanation:

here's the graph. hope it helps.

all of them are the correct answer

Answer:

x - intercept = 5

y- intercept = 2

Step-by-step explanation:

2x + 5y = 10

Write the equation in   \(\frac{x}{a}+\frac{y}{b}=1\)  form

So, divide the equation by 10

\(\frac{2x}{10}+\frac{5y}{10}=\frac{10}{10}\\\\\frac{x}{5}+\frac{y}{2}=1\)

x - intercept = 5

y- intercept = 2

Answer:

(5,0) and (0,2)

Step-by-step explanation:

Basically, all we need to do is enter 0 for both variables. We can do this because the y-value of an x-intercept will always be 0, and the x-value of a y-intercept will always be 0.

So, to find the x-intercept we can set y equal to 0 and then solve for x.

\(2x+5(0)=10\\2x=10\\x=5\)

So the x-intercept will be (5,0).

We can do the same thing to find the y-intercept.

\(2(0)+5y=10\\5y=10\\y=2\)

The y-intercept is (0,2)

Hope this helps!

Answer:

Look at attached screenshot.

Step-by-step explanation:

Alright, I'll first explain how to graph this problem.

Graph with a y intercept (point it hits the y axis) of 2. Then, every 6 y units you count up, count 10 x units foward and draw a point to connect the lines.

The Binary Search Tree is as follows:

                                                   E

                                            /            \

                                         S                T

                                        /                    \

                                      I                       W

                                   /                            \

                                A                               M

                              /                                    \

                             C                                     G

                              \

                                D

The set of letters is {I, D, S, A, E, T, C, G, M, W} and len (I, D, S, A, a) = 5

Binary Search Tree:The binary search tree based on the alphabetical ordering of the letters is:

post-order sequence is: C, D, A, G, M, I, W, T, S, E.

To draw the binary search tree for the given post-order sequence, follow the steps below:

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To find the sum of the first 15 terms of the arithmetic sequence 13, 11, 9, ..., we can use the formula for the sum of an arithmetic series. We find that the sum of the first 15 terms is 135.

The formula is given by Sn = (n/2)(2a + (n-1)d), where Sn is the sum, n is the number of terms, a is the first term, and d is the common difference. Plugging in the values. The given arithmetic sequence is 13, 11, 9, ... with a common difference of -2. We want to find the sum of the first 15 terms of this sequence.

Using the formula for the sum of an arithmetic series, Sn = (n/2)(2a + (n-1)d), we can calculate the sum. In this case, n = 15 (number of terms), a = 13 (first term), and d = -2 (common difference). Plugging in these values, we have Sn = (15/2)(2(13) + (15-1)(-2)) = (15/2)(26 + 14(-2)) = (15/2)(26 - 28) = (15/2)(-2) = -15(2) = -30. Therefore, the sum of the first 15 terms of the arithmetic sequence 13, 11, 9, ... is -30.

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Answer:

inversely proportional

Step-by-step explanation:

0.3514 * 380 ≈ 133.7 To find out how many students had scores between 35 and 61, we need to first calculate the interquartile range (IQR) which is the difference between the third quartile (Q3) and the first quartile (Q1).
Q1 is the median of the lower half of the data, which in this case is (11+35)/2 = 23.
Q3 is the median of the upper half of the data, which in this case is (70+79)/2 = 74.5.
So, IQR = Q3 - Q1 = 74.5 - 23 = 51.5.

Scores between 35 and 61 fall within one IQR from Q1. So, we need to find out what proportion of the scores fall within this range.
To do this, we need to calculate the z-scores for 35 and 61, using the formula z = (x - μ)/σ, where x is the score, μ is the mean, and σ is the standard deviation.
We don't have the mean and standard deviation, but we can estimate them using the five-number summary. The median (Q2) is (61+35)/2 = 48, and the mean is likely to be close to this value since the data is roughly symmetric. The range (max-min) is 79-11 = 68, so the standard deviation is roughly σ = range/4 = 17.
Using these estimates, we can calculate the z-scores as follows:
z1 = (35 - 48)/17 = -0.76
z2 = (61 - 48)/17 = 0.76

We can look up the proportion of scores between these two z-scores in a standard normal distribution table, or use a calculator or software to calculate it. It turns out to be about 0.3514, or 35.14%.
To find out how many students had scores between 35 and 61, we can multiply this proportion by the total number of students:
0.3514 * 380 ≈ 133.7
So, the answer is not one of the choices given.

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The answer is not one of the choices given.0.3514 * 380 ≈ 133.7 To find out how many students had scores between 35 and 61, we need to first calculate the interquartile range (IQR) which is the difference between the third quartile (Q3) and the first quartile (Q1).

Q1 is the median of the lower half of the data, which in this case is (11+35)/2 = 23.

Q3 is the median of the upper half of the data, which in this case is (70+79)/2 = 74.5.

So, IQR = Q3 - Q1 = 74.5 - 23 = 51.5.

Scores between 35 and 61 fall within one IQR from Q1. So, we need to find out what proportion of the scores fall within this range.

To do this, we need to calculate the z-scores for 35 and 61, using the formula z = (x - μ)/σ, where x is the score, μ is the mean, and σ is the standard deviation.

We don't have the mean and standard deviation, but we can estimate them using the five-number summary. The median (Q2) is (61+35)/2 = 48, and the mean is likely to be close to this value since the data is roughly symmetric. The range (max-min) is 79-11 = 68, so the standard deviation is roughly σ = range/4 = 17.

Using these estimates, we can calculate the z-scores as follows:

z1 = (35 - 48)/17 = -0.76

z2 = (61 - 48)/17 = 0.76

We can look up the proportion of scores between these two z-scores in a standard normal distribution table, or use a calculator or software to calculate it. It turns out to be about 0.3514, or 35.14%.

To find out how many students had scores between 35 and 61, we can multiply this proportion by the total number of students:

0.3514 * 380 ≈ 133.7

So, the answer is not one of the choices given.

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To calculate the slope use the

gradient formula

¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯

∣

∣

∣

2

2

m

=

y

2

−

y

1

x

2

−

x

1

2

2

∣

∣

∣

−−−−−−−−−−−−−−−−−

where m represents the slope and

(

x

1

,

y

1

)

,

(

x

2

,

y

2

)

2 coordinate points

here the 2 points are (10 ,-8) and (7 ,-8)

let

(

x

1

,

y

1

)

=

(

10

,

−

8

)

and

(

x

2

,

y

2

)

=

(

7

,

−

8

)

⇒

m

=

−

8

−

(

−

8

)

7

−

10

=

0

−

3

=

0

A slope of zero indicates that the line is horizontal, parallel to the x-axis and passes through all points in the plane with the same y-coordinate.

For the 2 given points both y-coordinates are - 8 and so the equation of the line is

y=-8

.

If you note this fact then it can be stated that the slope is zero without using the gradient formula.

graph{y-0.001x+8=0 [-20, 20, -10, 10]}

Answer:

\(\frac{-7}{17}\)

Step-by-step explanation:

To find the slope simply use the rise over run.

The change in y value (rise) from (7,1) to (-10,8) is y=1-8

The change in x value (run) from (7,1) to (-10,8) is y=7-(-10)

As a fraction this can be modeled by \(\frac{1-8}{7-(-10)}\)

\(\frac{-7}{17}\) is the slope as it is rise over run and cannot be simplified further.

The $1314^\text{th}$ digit past the decimal point is 2.

To find the $1314^\text{th}$ digit past the decimal point in the decimal expansion of $\frac{5}{14}$, we can use long division to compute the decimal expansion of the fraction.

The long division of $\frac{5}{14}$ is as follows:

```

0.35    <-- Quotient

-----

14 | 5.00

   4.2    <-- Subtract: 5 - (14 * 0.3)

   -----

     80   <-- Bring down the 0

     70    <-- Subtract: 80 - (14 * 5)

     -----

     100   <-- Bring down the 0

      98    <-- Subtract: 100 - (14 * 7)

      -----

       20   <-- Bring down the 0

       14    <-- Subtract: 20 - (14 * 1)

       -----

        60   <-- Bring down the 0

        56    <-- Subtract: 60 - (14 * 4)

        -----

         40   <-- Bring down the 0

         28    <-- Subtract: 40 - (14 * 2)

         -----

         120   <-- Bring down the 0

         112    <-- Subtract: 120 - (14 * 8)

         -----

           80   <-- Bring down the 0

           70    <-- Subtract: 80 - (14 * 5)

           -----

           ...

```

We can see that the decimal expansion of $\frac{5}{14}$ is a repeating decimal pattern with a repeating block of digits 285714. Therefore, the $1314^\text{th}$ digit past the decimal point is the same as the $1314 \mod 6 = 0^\text{th}$ digit in the repeating block.

Since $1314 \mod 6 = 0$, the $1314^\text{th}$ digit past the decimal point in the decimal expansion of $\frac{5}{14}$ is the first digit of the repeating block, which is 2.

So, the $1314^\text{th}$ digit past the decimal point is 2.

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The measure of arc BC is 720 times the measure of angle BAC.

Given that AC is the diameter of the circle and AB is a chord with a length of 16 units, we need to find BC (the length of the other chord) and mBC (the measure of angle BAC).

To find BC, we can use the property of chords in a circle. If two chords intersect within a circle, the products of their segments are equal. In this case, since AB = BC = 16 units, the product of their segments will be:

AB * BC = AC * CE

16 * BC = 2 * r * CE (AC is the diameter, so its length is twice the radius)

Since the area of the circle is given as 289 square units, we can find the radius (r) using the formula for the area of a circle:

Area = π * r^2

289 = π * r^2

r^2 = 289 / π

r = √(289 / π)

Now, we can substitute the known values into the equation for the product of the segments:

16 * BC = 2 * √(289 / π) * CEBC = (√(289 / π) * CE) / 8

To find mBC, we can use the properties of angles in a circle. The angle subtended by an arc at the center of a circle is double the angle subtended by the same arc at any point on the circumference. Since AC is a diameter, angle BAC is a right angle. Therefore, mBC will be half the measure of the arc BC.

mBC = 0.5 * m(arc BC)

To find the measure of the arc BC, we need to find its length. The length of an arc is determined by the ratio of the arc angle to the total angle of the circle (360 degrees). Since mBC is half the arc angle, we can write:

arc BC = (mBC / 0.5) * 360

arc BC = 720 * mBC

Therefore, the length of the arc BC equals 720 times the length of the angle BAC.

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Side PW is congruent to side XG because corresponding parts of congruent triangles are congruent.

Generally speaking, the base angles of an isosceles trapezoid are congruent and equal. This ultimately implies that, an isosceles trapezoid has base angles that are always equal in magnitude.

By critically observing the image of this isosceles trapezoid, we can write a two column table proof to prove that PW ≅ XG as follows;

Statements                                                                         Reasons

1. TRGP is an isosceles trapezoid                                     Given

TW ≅ RX                      2. Altitudes of an isosceles trapezoid are congruent.

TW ⊥ PG and RX ⊥ PG                                                 Altitudes form a 90°

∠TWP and ∠RXG are right angles    Perpendicular lines form right angles.

3. ∠TWP ≅ ∠RXG                                        All right angles are congruent.

4. ∠TPW ≅ ∠RGX            5. Angles opposite to congruent sides are congruent.

6. ∠TWP ≅ ∠RXG                                       AAS Congruence Theorem.

PW ≅ XG                    Corresponding parts of congruent triangles are congruent.

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11 1/4

Step-by-step explanation:

the yards have to be converted to feet

1 yards = 3 feet

5 yards x 3 = 15 feet

Area of a rectangle = length x width

15 x 2 1/4

15 x 9/4 = 33 3/4

33 3/4 x 1/3 = 135 /12 = 11 1/4

Step-by-step explanation:

x2 + bx +5 = 0,

where a,b and c are rational numbers.

Also it is given that the quadratic has 2 distinct zeros and one of it's zero is irrational.

We know that if it has a one irrational zero, the conjugated couple of the one zero is also a null with the same polynomial balance for a polynomial equation with rational coefficients." Therefore, in this case it is a quadratic equation, one is null and irrational; thus, the other zero is irrational.

The needed sample size is 1419. Sample Size is defined as the number of observations in the study.

In the question we have ,

estimate value of all voters who believe global warming ( p) = 82% = 0.82

margin of error (M.E) = 2% = 0.02

confidence of interval is calculated by estimate point value and add or subtract margin of error .

here,we have the value of confidence of interval is 95% = 0.95

Margin of error formula is

M.E = Z × √(p(1-p)/n)

where, p --> is estimated value

n---> sample size , which we required

Z ----> is z-value for observation

for the confidence of interval level 95% , the Z-value is 1.96 exist.

put all value in above formula we get,

0.02 = 1.96 × sqrt( ( 0.82)(1-0.82)/n)

=> 0.02 = 1.96× √(0.82×0.18/n)

= 0.02/1.96 = √0.1476/n => 0.000104= 0.1476/n

=> n = 1419

So, sample size is large and it is 1419.

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For any given event, the probability of that event and the probability of the non-occurrence of the event must sum to one.

A probability is a number that reflects the chance or likelihood that a particular event will occur. Probabilities can be expressed as proportions that range from 0 to 1, and they can also be expressed as percentages ranging from 0% to 100%.

The probability of occurrence formula, also known to some as the “probability of occurrence formula PMP” is a tool for determining the chance that a given risk will occur. The formula requires two data points: number of favourable events possible and the total number of events possible.

Non occurrence patterns identifies the absence of events when detecting a pattern.

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Answer:

15-14=1  16-14=2

2 is the answer

Step-by-step explanation:

believe me i got it right (U,U).-

Answer

a nd b

Step-by-step explanation:

The given sequence;–3.2, 4.8, –7.2, 10.8, is a geometric progression common ratio of -1.5.

When all the terms of a geometric sequence are added, then that expression is called geometric series.

The given sequence ;

–3.2, 4.8, –7.2, 10.8, …

The common ratio

= -4.8/ 3.2

= - 1.5

The terms having a common ratio of -1.5 best describe the relationship between the successive terms in the sequence of the terms.

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Answer:

Opposite 12= -12

Absolute value of 12: Just -12.

Step-by-step explanation:

I don't know.

Answer:

it is a horizontal line resting at 15 on the y axis

Step-by-step explanation:

because there is no x on the left side of the equation, it must be flat. it is 15, so that is where it lies

The graph of the function y=15 is the horizontal line resting at 15 on the y-axis

A graph is the representation of the data on the vertical and horizontal coordinates so we can see the trend of the data.

The graph of the function y=15 is the horizontal line resting at 15 on the y-axis because there is no x on the left side of the equation, it must be flat. it is 15, so that is where it lies.

Therefore the graph of the function y=15 is the horizontal line resting at 15 on the y-axis. The graph is attached with the answer below.

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To perform a translation of moving the equation x² + y² = 121 up 3 units, we modify the equation by adding 3 to the y-coordinate. The resulting equation is x² + (y + 3)² = 121.

To perform a translation of moving the equation x² + y² = 121 up 3 units, we need to modify the equation to reflect the new position. Since the translation is upward, we add 3 to the y-coordinate in the equation.

By adding 3 to the y-coordinate, the equation becomes x² + (y + 3)² = 121. This new equation represents the original equation shifted upward by 3 units.

The equation x² + (y + 3)² = 121 describes a circle centered at the origin with a radius of 11 units. The translation shifts this circle upward by 3 units, preserving its shape and size but changing its position in the coordinate plane.

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