a line passes through the point (3,3) and is parallel to the line given by the equation y = –2∕3x – 2. what's the equation of the line?

Therefore, the limit of the sequence as n approaches infinity is 0.

To find the limit of the sequence {-sin(n)/(6n)}, we can analyze the behavior of the sequence as n approaches infinity. As n gets larger and larger, the numerator, -sin(n), oscillates between -1 and 1. However, the denominator, 6n, grows without bound.

Since the numerator remains bounded while the denominator grows, the value of the sequence {-sin(n)/(6n)} becomes increasingly small as n approaches infinity.

Therefore, the limit of the sequence as n approaches infinity is 0.

So, the correct choice is:

B. The limit of the sequence is 0.

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Answer:

2 6 12

Step-by-step explanation:

there are the only factor of 12 there

Answer:

She should walk approximately 1,463.34369 feet along the sidewalk going to the east, then walk the remaining straight line distance along the grass.

====================================================

Explanation:

Refer to the diagram below.

Alaina starts at point A. If she stays on the sidewalk the entire time, then she can go from A to C to D in that order.

If she takes the direct line route, then she would go from A to D across the grass entirely.

The two paths have pros and cons. The optimal solution is a mix of the two routes. This means she'll be on the sidewalk for some amount of time, and then cut along the grass once reaching a certain point.

Let's say point B is the point where she decides to cut along the grass. In the diagram below, I made \(\text{BC} = x\) so that I could find \(\text{BD} = \sqrt{x^2+600^2}\) through the pythagorean theorem fairly quickly.

If \(\text{BC} = x\), then the remaining bit of the east/west side walk is \(\text{AB} = 2000-x\) since the two portions must add to 2000 feet.

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

If she travels along the side walk at a rate of 6 ft/sec, and travels 2000-x feet (from A to B), then it will take her

time = distance/speed = \(\frac{2000-x}{6}\) seconds

Then if she cuts across the grass to follow path BD, then she'll take another

time = distance/speed = \(\frac{\sqrt{x^2+600^2}}{4}\) seconds since she's traveling 4 ft/sec here.

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

If Alaina goes from A to B to D in that order, then she takes a total of

\(\text{(time from A to B)}+\text{(time from B to D)}\\ = \frac{2000-x}{6}+\frac{\sqrt{x^2+600^2}}{4}\)

That represents the total time taken when following this path at those specified speeds mentioned.

The goal is to find the minimum of that function. So we'll need to compute the derivative.

\(f(x) = \frac{2000-x}{6}+\frac{\sqrt{x^2+600^2}}{4}\\\\ f \ '(x) = -\frac{1}{6}+2x*\frac{1}{2*4\sqrt{x^2+600^2}}\\\\ f \ '(x) = -\frac{1}{6}+\frac{x}{4\sqrt{x^2+600^2}}\\\\\)

Set the derivative equal to zero and solve for x

\(f \ '(x) = 0\\\\ -\frac{1}{6}+\frac{x}{4\sqrt{x^2+600^2}} = 0\\\\ \frac{x}{4\sqrt{x^2+600^2}} = \frac{1}{6}\\\\ 6x = 4\sqrt{x^2+600^2}\\\\ (6x)^2 = \left(4\sqrt{x^2+600^2}\right)^2\\\\ 36x^2 = 16(x^2+600^2)\\\\ 36x^2 = 16x^2+16*600^2\\\\\)

\(36x^2 = 16x^2+5,760,000\\\\ 36x^2-16x^2 = 5,760,000\\\\ 20x^2 = 5,760,000\\\\ x^2 = 5,760,000/20\\\\ x^2 = 288,000\\\\ x = \sqrt{288,000}\\\\x \approx 536.65631\)

If you were to perform the first derivative test, you should find that the local min occurs at roughly x = 536.65631

This means she must walk a approximately 2000-x = 2000-536.65631 = 1,463.34369 feet when going from A to B such that to minimize the walking time.

Side note: you can use the minimum feature on your calculator to confirm the answer

The measure of the inscribed angle is equal to 90 degrees

The inscribed angle theorem mentions that the angle inscribed inside a circle is always half the measure of the central angle or the intercepted arc that shares the endpoints of the inscribed angle's sides. In a circle, the angle formed by two chords with the common endpoints of a circle is called an inscribed angle and the common endpoint is considered as the vertex of the angle.

In this problem, the side length of the square is 5 which forms 90 degrees to all the other sides.

The measure of the circumscribed angle is 90 degree

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a. Segment AC is a radius of the circle = 7.5 cm

b. Segment CD is a diameter of the circle = 15 cm.

The radius of a circle is the line segment that is drawn from the center of the circle to any point on the circumference of the circle. The length of a radius is half the length of the diameter of a circle.

The diameter of a circle is the line segment that divides the circle at its center into two halves. The length of the diameter of any circle is twice the length of the radius of the circle.

a. In the image given below, a radius of the circle is segment AC.

AC = 1/2(15)

Length of segment AC = 7.5 cm.

b A diameter in the circle is CD.

The length of segment CD = 15 cm.

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Answer:

3rd one

Step-by-step explanation:

12

To solve the equation -2.5(e + 17.4) = -50, we can use algebraic techniques to isolate the variable e on one side of the equation.

First, we can simplify the left-hand side of the equation by distributing the -2.5 to the expression inside the parentheses:

-2.5e - 2.5(17.4) = -50

Next, we can simplify the expression on the left-hand side by multiplying:

-2.5e - 43.5 = -50

To isolate the variable e, we can add 43.5 to both sides of the equation:

-2.5e = -6.5

Finally, we can solve for e by dividing both sides of the equation by -2.5:

e = 2.6

Therefore, the solution to the equation -2.5(e + 17.4) = -50 is e = 2.6.

Answer:

X = 2

Step-by-step explanation:

Answer:

$0.57

Step-by-step explanation:

20% of $2.85 =

= 0.2 * $2.85

= $0.57

2.85 x 0.2 = 0.57

Yoon saves 57 cents

Answer:

I think the constraint of proportionality is 25 because each dot it increases buy 25.

I also believe that at 10 the total should be at 225.

Answer:

Im not too sure but it might be d?

It looks like the given equation is

sin(2x) - sin(2x) cos(2x) = sin(4x)

Recall the double angle identity for sine:

sin(2x) = 2 sin(x) cos(x)

which lets us rewrite the equation as

sin(2x) - sin(2x) cos(2x) = 2 sin(2x) cos(2x)

Move everything over to one side and factorize:

sin(2x) - sin(2x) cos(2x) - 2 sin(2x) cos(2x) = 0

sin(2x) - 3 sin(2x) cos(2x) = 0

sin(2x) (1 - 3 cos(2x)) = 0

Then we have two families of solutions,

sin(2x) = 0   or   1 - 3 cos(2x) = 0

sin(2x) = 0   or   cos(2x) = 1/3

[2x = arcsin(0) + 2nπ   or   2x = π - arcsin(0) + 2nπ]

… … …   or   [2x = arccos(1/3) + 2nπ   or   2x = -arccos(1/3) + 2nπ]

(where n is any integer)

[2x = 2nπ   or   2x = π + 2nπ]

… … …   or   [2x = arccos(1/3) + 2nπ   or   2x = -arccos(1/3) + 2nπ]

[x = nπ   or   x = π/2 + nπ]

… … …   or   [x = 1/2 arccos(1/3) + nπ   or   x = -1/2 arccos(1/3) + nπ]

Among the given sets of vectors, the sets that can be bases for ℝ³ are (a) (2, 0, 0), (4, 4, 0), (6, 6, 6) and (b) (3, 1, -3), (6, 3, 3), (9, 2, 4). The correct options are (a) and (b).

In order for a set of vectors to form a basis for ℝ³, they must satisfy two conditions: (1) The vectors must span ℝ³, meaning that any vector in ℝ³ can be expressed as a linear combination of the given vectors, and (2) the vectors must be linearly independent, meaning that no vector in the set can be expressed as a linear combination of the other vectors.

(a) (2, 0, 0), (4, 4, 0), (6, 6, 6): These vectors span ℝ³ since any vector in ℝ³ can be expressed as a combination of the form a(2, 0, 0) + b(4, 4, 0) + c(6, 6, 6). They are also linearly independent, as no vector in the set can be expressed as a linear combination of the others. Therefore, this set forms a basis for ℝ³.

(b) (3, 1, -3), (6, 3, 3), (9, 2, 4): These vectors also span ℝ³ and are linearly independent, satisfying the conditions for a basis in ℝ³.

(c) (4, -3, 5), (8, 4, 3), (0, -10, 7): These vectors do not span ℝ³ since they lie in a two-dimensional subspace. Therefore, they cannot form a basis for ℝ³.

(d) (4, 5, 6), (4, 15, -3), (0, 10, -9): These vectors do not span ℝ³ either since they also lie in a two-dimensional subspace. Hence, they cannot form a basis for ℝ³.

In conclusion, the correct options for sets of vectors that form bases for ℝ³ are (a) and (b)

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Answer:

r=60

Step-by-step explanation:

Answer:

60

Step-by-step explanation:

3-r/8=-9/2

r/8=3-(-9/2)

r/8=3+9/2

r/8=6/2+9/2

r/8=15/2

r=(15/2)*(8/1)

r=120/2

r=60

The graph of 3x-2y≤6 is the third graph, for 3x-2y<6 is the first graph, for 3x-2y>6 is the fourth graph and for 3x-2y≥6 is the second graph. The solution has been obtained using concept of linear inequality.

What is linear inequality?

A linear inequality is one that would produce a linear equation if the equals relation were used instead of the inequality. When multiplying or dividing both sides by a negative number in order to solve the inequality, the direction of the inequality is reversed. The entire set of solutions to an inequality is known as the solution set.

We are given for graphs, of which two graphs are dotted and two are simple straight line graphs.

The dotted graphs are drawn for the inequalities having < or >

Whereas the simple straight line graphs are drawn for the inequalities having ≤ or ≥.

Now, to notice the shaded pattern, we will see whether the equations are true for (0,0) or not

1. 3x-2y≤6

⇒ 0≤6

So, the equation is true for the point.

Hence, the third graph represents this equation.

2. 3x-2y<6

⇒ 0<6

So, the equation is true for the point.

Hence, the first graph represents this equation.

3. 3x-2y>6

⇒ 0>6

So, the equation is false for the point.

Hence, the fourth graph represents this equation.

4. 3x-2y≥6

⇒ 0≥6

So, the equation is false for the point.

Hence, the second graph represents this equation.

Hence, the graphs are matched with the inequalities.

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Since, there are multiple questions so, the question answered above is attached below.

Answer:

SA= 3603.84cm^2

Step-by-step explanation:

the Surface Area SA is the total area of the sides and the base.

The area of the base= 32*32= 1024cm^2

the area of one of the sides = slant height of pyramid * base edge/2

the slant height l of the pyramid

l= sqrt(16^2+37^2) = 40.31cm

area of the side =( 40.31*32)/2 =644.96cm^2

there are 4 sides so the area of the sides are

4* 644.96=

addig the area of the base we get the Surface Area SA of the pyramid

SA = 2579.84 + 1024 = 3603.84cm^2

Answer:

16a^3b^2c - 8a^4b^3c^2 - 4a^2b^2c

Step-by-step explanation:

(8a^bc × 2ab) - (4a^3b^2c^2 × 2ab) - (2abc × 2ab)

(16a^3b^2c) - (8a^4b^3c^2) - (4a^2b^2c)

0, becous A (-1x2) can't be negative.

Answer:

20

Step-by-step explanation:

Answer: trapezius

Step-by-step explanation:

The given muscle shown in the image is the trapezius muscle. Option A is correct.

Soft tissues include muscles. Your muscles are made up of numerous elastic fibers.

The flat, triangular muscle of the shoulder girdle is known as the trapezius muscle (trapezius muscles, hood muscle). It is divided into three divisions, each of which has a different purpose, and is situated in the neck and upper back region.

Thus, the given muscle shown in the image is the trapezius muscle. Option A is correct.

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The answer is 77520.

How many different (ordered) playlists are possible?

Number of possible playlists = 77520

Explanation:

Total number of songs = 20

Songs in the playlist = 7

So, we need to select 7 songs out of 20. This can be done using combinations.

n = 20 , r=7

C( n , r ) = ?

C( n , r ) = C (20 , 7)

              = 20! / ( 7! (20-7)!)

              =  20! / ( 7! × 13! )

              = 77520

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Answer:

y = 25

Step-by-step explanation:

Given y = kx and k = 5 then

y = 5x ← equation of variation

When x = 5 , then

y = 5 × 5 = 25

Answer:

I think is: odd

Step-by-step explanation:

This study was conducted to explore whether the perception of money by preschool-age children is influenced by their family wealth.

This was investigated by testing how the children would recall the size of a coin, with the assumption that the size recalled related to the value placed on the coin. To conduct the study, three local daycare facilities specializing in preschool-age children were randomly selected.

Consent forms were sent home to the parents of the kids, which also asked parents for their average yearly household income. Since everyone from the three selected facilities was used in the study, this is a census sampling.

The income data collected was quantitative data at the ratio level of measurement. From the parents who consented, the children were divided into two groups:

those whose family income was greater than $40,000, and those whose family income was less than $40,000. Each child was asked to draw a nickel.

The resulting circle's diameter was then measured. When the shape drawn was not a perfect circle, the largest and smallest diameters were averaged. The coin diameter data were continuous data at the interval level of measurement. The gender of each child was also collected.

This data was categorical data at the nominal level of measurement. Because this data was collected at one point in time, this is a cross-sectional study. Since we are not imposing treatment on the children, this is not an experiment.

It is hypothesized that children from lower-income families would draw larger coins than children from higher-income families.

This study used census sampling to investigate the relationship between family wealth and the perception of money in preschool-age children.

Data on average yearly household income, coin diameter, and gender were collected. The income data was quantitative at the ratio level of measurement, while the coin diameter data was continuous at the interval level of measurement, and the gender data was categorical at the nominal level of measurement.

This study is a cross-sectional study, and it hypothesized that children from lower-income families would draw larger coins than children from higher-income families.

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Answer:

Check out the image below the explanation.

Step-by-step explanation:

1. First, let's simplify the equation.

2. Since the equation is y = 3x + 13:

Now, here's the graph!

The regular polygon with a sum of interior angles equal to 900 degrees is a heptagon. So, the correct answer is a. heptagon.

The sum of the interior angles of a regular polygon can be found using the formula (n-2) * 180 degrees, where n represents the number of sides of the polygon.

For a regular polygon with a sum of interior angles equal to 900 degrees, we can set up the equation:

(n-2) * 180 = 900

Simplifying the equation:

n - 2 = 5

n = 7

As a result, a heptagon is a regular polygon with a sum of internal angles equal to 900 degrees.

Heptagon is the right answer, thus.

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So, 3.6 x 10^6 is 5 times larger than 7.2 x 10^5.

To determine how many times larger 3.6 x 10^6 is than 7.2 x 10^5, we can divide the first number by the second number:

(3.6 x 10^6) / (7.2 x 10^5)

To simplify this division, we can divide the numerical parts and subtract the exponents:

3.6 / 7.2 = 0.5

10^6 / 10^5 = 10^(6-5) = 10^1 = 10

Therefore, 3.6 x 10^6 is 0.5 times 10 times larger than 7.2 x 10^5. Simplifying further:

0.5 x 10 = 5

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By Pythagorean theorem, 35 Cm tall is the porch .

What is the Pythagorean theorem in plain English?

The Pythagorean Theorem states that the squares on the hypotenuse of a right triangle, which is the side that faces the right angle, are equal when added together.

             This is written as a2 + b2 = c2 in the usual algebraic notation.A right-angled triangle's sides can be found using Pythagoras' Theorem. The third side of a right triangle can be found if we are aware of the first two sides.

AC= √(AB² -BC²)

= √(91² - 84²)

=  √8281  - 7056

 = √1225

  = 35

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Answer:

the answer isn't there; the answer is 2.5

Step-by-step explanation: