Convert the rectangular coordinates (0, 6√3) into polar form. Express the angle using radians in terms of over the interval 0 ≤ 0 < 27, with a positive value of r.​

Answer:Angle x is congruent with the interior angle opposite side 8 (alternate interior angles)

Use tangent:

tan x = 8/15

x = arctan (8/15)

x = 28.1° (rounded)

Step-by-step explanation:

Answer:

weak positive

Step-by-step explanation:

weak because the line of best fit (the line passes through all points and used to express the relationship between them) doesn't pass through all ponts here.

positive because the values of data points are rising throughout the graph.

Equation: \( 4x\degree + 2x\degree = 180°\)

Answer:

120°, 60°

Step-by-step explanation:

Since, sum of any two Supplementary angles is always 180°.

\( \therefore 4x\degree + 2x\degree = 180°\\

\therefore 6x\degree = 180°\\

\therefore 6x = 180\\\\

\therefore x = \frac{180}{6}\\\\

\therefore x = 30\\

\implies \\

4x° = (4\times 30)° = 120°\\

\&\\

2x° = (2\times 30)° = 60°\\

\)

(x/5)-10 where x is "number"

Answer:

Kia makes 19.25 dollars an hour.

Step-by-step explanation:

6x4+8=32 (hours: 6 hours for 4 days, and 8 hours for 1 day)

616 divided by 32 = 19.25

Based on this data, for every inch in height, the arm span increases by 1.1 inches.

Here, we have,

I put the height of people on the x-axis because this is what I am trying to correlate the arm span to. I put the arm span on the y-axis because it is dependent on height.

I used point (60,61) and (70,72) to draw the line of best fit and to get the equation. First, to get the slope I would use the slope formula of m = 72-61/70-60 or 11/10 to get a slope of approximately 1.1. Then I used (60,61) to get the rest of the equation by plugging it in: y-61 = 1.1(x -60). This becomes y-61 = 1.1x - 66. Add 61 to both sides and the final equation is y = 1.1x – 5.

The slope represents the rate of change arm span based on height. The y intercept is the arm span.

Using points (66,68) and points (70,72) I plug each into the equation y=1.1x-5 to figure each out based on the difference from the actual points and get .4 for (66,68) and 0 for point (70,72) so I would say, based on .4 and 0 for these two points that this is a good line of best fit.

Based on this data, for every inch in height, the arm span increases by 1.1 inches.

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complete question:

There are many measurements of the human body that are positively correlated. For example, the length of one's forearm (measured from elbow to wrist) is approximately the same length as the foot (measured from heel to toe). They are positively correlated because, as one measurement increases, so does the other measurement.

The equation of the line is y = x/4 + 13/2 .

A line's slope, sometimes referred to as its gradient in mathematics, is a numerical representation of the line's steepness and direction.

If a line passes through two points (x₁ ,y₁) and (x₂, y₂) ,

then the equation of line is

y - y₁ = (y₂- y₁) / (x₂ - x₁) x (x - x₁)

To find the slope;

m =  (y₂- y₁) / (x₂ - x₁)

And here we have the slope,

m = 1/4

And (x₁ ,y₁)  =  (-2,6)

then the equation of line is

y - y₁ = m (x - x₁)

y - 6 = (1/4) (x +2)

y = x/4 + 13/2

Therefore, the equation is y = x/4 + 13/2.

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Note that the the five-number summary and interquartile range for each data set are:

Let's say the distances recorded for each airplane are:

Andre's: 18, 20, 22, 25, 28, 29, 30, 31, 32, 35

Lin's: 15, 16, 18, 20, 21, 22, 23, 25, 30, 33

Noah's: 10, 12, 13, 15, 18, 20, 21, 22, 23, 25

To find the five-number summary for each data set, we need to find the minimum, maximum, median, and quartiles. We can start by ordering the data sets from smallest to largest:

Andre's: 18, 20, 22, 25, 28, 29, 30, 31, 32, 35

Lin's: 15, 16, 18, 20, 21, 22, 23, 25, 30, 33

Noah's: 10, 12, 13, 15, 18, 20, 21, 22, 23, 25

Minimum:

Andre's: 18

Lin's: 15

Noah's: 10

Maximum:

Andre's: 35

Lin's: 33

Noah's: 25

Median:

Andre's: (28 + 29) / 2 = 28.5

Lin's: (21 + 22) / 2 = 21.5

Noah's: (18 + 20) / 2 = 19

First Quartile (Q1):

Andre's: (22 + 25) / 2 = 23.5

Lin's: (18 + 20) / 2 = 19

Noah's: (12 + 13) / 2 = 12.5

Third Quartile (Q3):

Andre's: (31 + 32) / 2 = 31.5

Lin's: (23 + 25) / 2 = 24

Noah's: (22 + 23) / 2 = 22.5

Interquartile Range (IQR):

IQR = Q3 - Q1

Andre's: 31.5 - 23.5 = 8

Lin's: 24 - 19 = 5

Noah's: 22.5 - 12.5 = 10

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Answer:

790 oz

Step-by-step explanation:

Ratio:

3oz syrup : 4oz water : 3oz apple juice: 1 serving: 10oz total mixture

We know there is 10oz total mixture because 3oz of syrup + 4oz of water + 3oz of apple juice = 10oz total mixture

We want to find

237oz apple juice: ?oz total mixture

To do this, we can multiply the ratio

3oz apple juice: 10oz total mixture by 237/3, because 237/3 * 3 = 237, getting us to 237oz apple juice on one side and maintaining the ratio so that we can find the total mixture amount, so we have

237oz apple juice: 10*237/3 oz total mixture = 10*79 = 790 oz

Answer:

1

Step-by-step explanation:

X-8=(2x-8)

x-7=2x-8

collect like terms

x-2x=-8+7

-x=-1

but we are looking for X not -x

so answer is 1

Hope this helped!

To determine the number of offspring with skin darker than their parents, we need more information about the specific genetic inheritance patterns and traits involved.

The answer depends on factors such as the dominance or recessiveness of genes controlling skin color, the genotype of the parents, and the specific combination of alleles passed on to the offspring.

Without additional information, it is not possible to provide an accurate count of the number of offspring with darker skin. Genetic inheritance is a complex process that involves multiple genes and interactions, making it necessary to consider specific genetic traits and their inheritance patterns to determine the outcome.

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The caloric content in candy A is 269 and that of candy B is 255.

The caloric content is the quantity of energy required to increase the temperature of one liter of water by one degree. A calorimeter was initially used to determine a food's calorie count.

Let us consider:

Caloric content of Candy A = x

Caloric content of Candy B = y

We can thereby make two equations:

Eqn 1: 1x + 2y = 779

Eqn 2: 2x + 1y = 793

By elimination method, we have

2x + 4y = 1558

Solving for x by subtracting with Eqn 2, we have,

3y = 765

y = 765 ÷ 3

y = 255.

Now substituting the value of y in Eqn 2, we have:

2x + 1y = 793

2x + 1 × 255 = 793

2x + 255 = 793

2x = 793 - 255

2x = 538

x = 538 ÷ 2

x = 269.

Hence caloric content in candy A is 269 and that of candy B is 255.

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Answer:

(-3, 2)

Step-by-step explanation:

To find the coordinates of a point being reflected across the x-axis you need to use the rule (x, -y) on the point. Example: If the point was (4, 7) you would make the y value negative since it is positive, which would give you (4, -7) which is the point after being reflected across the x-axis. I know this one is for reflecting on the x-axis but for future problems if you want to reflect across the y-axis you do the same thing but with the x value, so (-x, y)

Step-by-step explanation:

Simplifying

8x + -2(3x + -4 + 2y) + -12x = 0

Reorder the terms:

8x + -2(-4 + 3x + 2y) + -12x = 0

8x + (-4 * -2 + 3x * -2 + 2y * -2) + -12x = 0

8x + (8 + -6x + -4y) + -12x = 0

Reorder the terms:

8 + 8x + -6x + -12x + -4y = 0

Combine like terms: 8x + -6x = 2x

8 + 2x + -12x + -4y = 0

Combine like terms: 2x + -12x = -10x

8 + -10x + -4y = 0

Solving

8 + -10x + -4y = 0

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-8' to each side of the equation.

8 + -10x + -8 + -4y = 0 + -8

Reorder the terms:

8 + -8 + -10x + -4y = 0 + -8

Combine like terms: 8 + -8 = 0

0 + -10x + -4y = 0 + -8

-10x + -4y = 0 + -8

Combine like terms: 0 + -8 = -8

-10x + -4y = -8

Add '4y' to each side of the equation.

-10x + -4y + 4y = -8 + 4y

Combine like terms: -4y + 4y = 0

-10x + 0 = -8 + 4y

-10x = -8 + 4y

Divide each side by '-10'.

x = 0.8 + -0.4y

Simplifying

x = 0.8 + -0.4y

Answer:

As the value of x increases, the value of y decreases

We will find the sum of 3+ 1 1/2 with help of a

Answer:

Step-by-step explanation:

I got 22 my friend hope i helped.

Answer:

$18

Step-by-step explanation:

50% of 40 is 20, so 40-20=20

10% of 20 is 2, so 20-2=18

total price=$18

Considering the diagram, the correct option is

B. the bisector of angle PRQ

An angle bisector is a line or a ray that divides an angle into two congruent angles

It is the line or ray that splits an angle into two equal angles with the vertex of the angle being the common endpoint of the two angles

Since the bisector of the angle splits it into two equal parts then we refer to it as the locus of the point

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Explanation

We can find the differences in the table below.

The first differences are the values gotten from subtracting the values in the f(x) column. While the second differences are the values gotten from subtracting the values in the first differences column.

The table can be seen below

Answer A

1) False

2) True

3) False

Answer B: Quadratic function

Reason: A quadratic sequence is a sequence of numbers in which the second difference between any two consecutive terms is constant. Since the second difference being a constant implies a quadratic difference, modeling the values will ultimately give a quadratic function

The slope of the rapids is -0.067

Kannanaski Rapids drops  62 ft vertically

The horizontal distance of 920 ft.

tan θ is a commonly used trigonometric function along with other 5 functions. tan θ is also called as law of tangent. The tangent formula for a right-angled triangle can be defined as the ratio of the opposite side of a triangle to the adjacent side. It can also be represented as a ratio of the sine of the angle to the cosine of the angle.

Slope of Rapids= tanθ= \(\frac{y}{x}=\frac{-62}{920} \\\)

=-0.067

Therefore, the slope of rapids is -0.067.

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The equation to relate the flow of water from the 8-inch pipe (1600) to the flow of water from the 4-inch pipe (2400) is 2400.

To relate the flow of water from the 8-inch pipe to the flow of water from the 4-inch pipe, we can use the equation of continuity, which states that the product of the cross-sectional area of a pipe and the velocity of the fluid is constant.

Let's assume that the velocity of water flowing through the 8-inch pipe is V1 and the velocity of water flowing through the 4-inch pipe is V2. The cross-sectional area of the 8-inch pipe is A1 = π\((8/2)^2\) = 64π square inches, and the cross-sectional area of the 4-inch pipe is A2 = π\((4/2)^2\) = 4π square inches.

According to the equation of continuity, A1 * V1 = A2 * V2.

Substituting the given values, we have:

64π * V1 = 4π * V2

Simplifying, we get:

16V1 = V2

So, the equation to relate the flow of water from the 8-inch pipe (1600) to the flow of water from the 4-inch pipe (2400) is:

1600 * 16 = 2400

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A triangle prima has six vertices. A triangular prism has five faces, three rectangular and two triangular, nine vertices, and six edges.

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Answer:

x = -8

y = -3

Step-by-step explanation:

So first you're going to want to get x or y by itself using elimination or substitution. I used elimination to get x by itself.

You can multiply the second equation (2x + 2y = -22) by -2 so you can eliminate the y's. When you multiply it, you get -4x - 4y = 44

Then, you can add -3x + 4y = 12 and -4x - 4y = 44. The y's cancel out to leave -7x = 56. Divide both sides by -7 to get x = -8.

Now, you can plug in -8 for x in either one of the equations. I plugged it into the second equation to make it 2(-8) + 2y = -22.

2 · -8 = -16.

-16 + 2y = -22. Add 16 to both sides to get 2y = -6. Divide both sides by to get y = -3.

Hope this helps! :)

Answer:

4

Step-by-step explanation:

Answer:

9

Step-by-step explanation:

.9 is bigger than 5 so we can round 8 up to 9

Answer:

49% are pine trees

Step-by-step explanation:

im smart

The slope of the polar curve at the point where o = π/4 is -1.

In polar coordinates, a curve is defined by a radial function and an angular function. The given polar curve is represented by the equation r = 6(1 + cos(θ)), where r represents the radial distance from the origin, and θ represents the angle measured from the positive x-axis.

To find the slope of the polar curve at a specific point, we need to differentiate the radial function with respect to the angular variable. In this case, we want to determine the slope at the point where θ = π/4.

Differentiating the equation with respect to θ, we get dr/dθ = -6sin(θ).

Substituting θ = π/4 into the equation, we have dr/dθ = -6sin(π/4) = -6(1/√2) = -6/√2 = -3√2.

Therefore, the slope of the polar curve at the point where θ = π/4 is -3√2.

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Answer:

there are 5

Step-by-step explanation:

Answer:

i). 600 Boys

ii). 1080 Students

iii). 7 Trees each students On Second day

Step-by-step explanation:

According to the Question,

i).  If the number of trees planted by the students on the first day was 5400.

NOw, This 9x Planted 9x × 5 ⇒ 45x Trees on First Day.

45x = 5400 ⇔ x=120

So, The Number Of Boys Are 5x = 5 * 120 ⇒ 600Boys

And, The Number of Girls Are 4x = 4 * 120 ⇒ 480Girls

ii).  the total number of students who participated in this program is 600 boys + 480 Girls = 1080 Students.

iii). If the total number of trees planted on the second day was 7560. We Know Every Student Plant Equal Number Of trees on each day.

So, 1080 Students Planted 7560 Plants

Therefor, each Student Planted 7560/1080 = 7 Trees Each On Second day.

The solution of linear equations is (x, y) = (-0.8905, 0.708).

To solve this system of linear equations by elimination, first multiply both equations by the same number so that when you add the equations together, one of the variables is eliminated. In this case, we'll multiply the first equation by 3 and the second equation by 8.

8(8x+3y=-5)

3(3y=x+4)

24x + 9y = -15

24y = 8x + 32

Now add the two equations together:

24x + 24y = -15 + 32

24x + 24y = 17

Simplifying this equation, we get:

24y = 17

y = 17/24

y = 0.708

Now, plug in the value of y into one of the original equations to solve for x. We'll use the first equation:

8x + 3(0.708) = -5

8x + 2.124 = -5

8x = -7.124

x = -7.124/8

x = -0.8905

Therefore, the solution to the system of linear equations is (x, y) = (-0.8905, 0.708).

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