If two boats sail at a 45° angle to the wind as shown, and the wind is constant, will their paths ever cross? Explain your reasoning. Which of the angle pair did you use and what does the theorem state? wind 45° 45°
please with the explanation​

The geometric rule for the nth term of the geometric sequence for which a1 =−6 and a5=−486 is -6 × 3^(n - 1)

First term, a1 = -6

Fifth term, a5 = -486

a5 = ar^(n - 1)

-486 = -6 × r^(5-1)

-486 = -6r⁴

r⁴ = -486 / 6

r⁴ = 81

r = 4√81

r = 3

Geometric rule:

nth term = ar^(n-1)

nth term = -6 × 3^(n - 1)

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Explanation:

Let's use an example to see why this is

A = {1,2,3,4,5,6,7}

B = {x,y,z}

A U B = {1,2,3,4,5,6,7, x,y,z}

We simply glue the two sets together to form one single big set. Because sets A and B have no overlap, this means we dont have to worry about tossing out duplicates (since there aren't any).

There are 7 items in set A, and 3 items in set B.

Therefore, we have 7+3 = 10 items in set A U B

The symbol U refers to the set union operator.

If you wanted to make a Venn Diagram, then you'd have two circles overlapping. In circle A will be the numbers 1 through 7. These values are not in the overlapped region. For circle B, the letters x,y,z are inside but not in the overlapped region. The overlapped region remains empty.

The set A U B talks about the collection of everything mentioned. It's the set of stuff in set A or in set B or in both sets.

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

If you want a formula to write down on a notecard or reference sheet, then it would be

n(A U B) = n(A)+n(B)

where A and B are mutually exclusive, aka disjoint. This means they have nothing in the overlapped region

hat is the answer to a math problem I had it on khan academy but the problem I

1 2/7 divided by (-2 1/4)

Answer:

-4/7

Step-by-step explanation:

1 2/7 divided by (-2 1/4)

1 2/7 = 9/7

-2 1/4 = -9/4

9/7 divided by -9/4 =

9/7 multiplied by -4/9 =

9's cancel out

1/7 multiplied by -4/1 =

-4/7

Answer: Your answer is going to be 32

Step-by-step explanation:

Answer:

32

Step-by-step explanation:

1/8 is nothing but 0.125

4/.125 = 32

.125 goes into four 32 times.

Step-by-step explanation:

[tex] \sin {}^{2} ( - 300) \cos {}^{2} (120) + \cos {}^{2} ( - 240) \sin {}^{2} (390) = \frac{1}{4} [/tex]

[tex] \sin {}^{2} (60) \cos {}^{2} ( {}^{} 120) + \cos {}^{2} (120) \sin {}^{2} (30) [/tex]

[tex] \frac{3}{4} \frac{1}{4} + \frac{1}{4} \frac{1}{4} [/tex]

[tex] \frac{3}{16} + \frac{1}{16} = \frac{4}{16} = \frac{1}{4} [/tex]

Answer:

Step-by-step explanation:

Answer:

The basic sine and cosine functions have a period of 2π. The function sin x is odd, so its graph is symmetric about the origin. The function cos x is even, so its graph is symmetric about the y-axis. The graph of a sinusoidal function has the same general shape as a sine or cosine function.

They are the three x-intercepts, the maximum point, and the minimum point. All of these are on your unit circle. The values of sin x correspond to the y-values, so those key points are (angle, y-value) or (0,0), (π/2, 1), (π, 0), (3π/2, -1), (2π, 0).

Work Shown:

[tex]V = (4/3)*\pi*r^3\\\\V \approx (4/3)*3.14*18^3\\\\V \approx 24416.64\\\\[/tex]

Of these cities, the place that has the lowest temperature than Toledo is Youngstown.

The town is known to have a temperature that is less than 20. This shows that the temperature has fallen below all other temperatures in the table.

Hence it can be concluded that the lowest table here is the temperature of Youngstown at -20 degrees.

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An equation that describes the graph is [tex]y=-x^{2} +1[/tex]

"It is a mathematical statement which consists of equal symbol between two algebraic expressions."

"It is a curve, such that a point on the curve is equidistant from a fixed point, and a fixed line. "

For given question,

The graph describes the parabola.

The parabola opens downward, so the equation of the parabola would be,

[tex]y=-x^{2}[/tex]

We know that, for a function f(x) is transformed to f(x) + c if c > 0 then the graph of the function moves up by c units.

if c < 0 then the graph of the function moves down by c units.

As the graph of the parabola moves down by 1 unit, the equation of the parabola would be,

[tex]y=-x^2+1[/tex]

Therefore, the equation that describes the graph is [tex]y=-x^{2} +1[/tex]

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Answer:

y= -1/2x+5

Step-by-step explanation:

Answer:

1.5:1

Step-by-step explanation:

the original answer is 12:8, so you have to simplify it down. you can get it down to 3:2 with whole numbers, but to get it down to a ratio with one, you'll have to divide each number by 2 because the bottom number is 2, so the final answer would be 1.5:1

Answer:

x^2-1^2

Step-by-step explanation:

formula:

(a-b)(a+b)=a^2-b^2

The number of boxes will weigh 18 ounces or less will be 138. Then the correct option is A.

The z-score is a statistical evaluation of a value's correlation to the mean of a collection of values, expressed in terms of standard deviation.

The z-score is given as

z = (x - μ) / σ

Where μ is the mean, σ is the standard deviation, and x is the sample.

The weights of boxes of rice produced at a factory are normally distributed with a mean of 20 ounces and a standard deviation of 1.5 ounces.

Consider a shipment of 1500 boxes of rice.

Then the number of the boxes will weigh 18 ounces or less will be

z = (18 - 20) / 1.5

z = -1.33

Then the probability will be

P(x ≤ 18) = P(z ≤ -1.33)

P(x ≤ 18) = 1 - P(z > -1.33)

P(x ≤ 18) = 1 - [1 - P(z < -1.33)]

P(x ≤ 18) = P(z < -1.33)

P(x ≤ 18) = 0.091211

Then the number of the boxes will weigh 18 ounces or less will be

⇒ 0.091211 x 1500

⇒ 136.8

approximately 138 boxes.

Then the correct option is A.

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Volume is a three-dimensional scalar quantity. The volume of the cube with side length of 4 inches is 64 inches³.

A volume is a scalar number that expresses the amount of three-dimensional space enclosed by a closed surface.

Given the volume of a cube is the cube of the length of a side. If a side is S, the volume is S^3. Therefore, the volume of cube with side 4 inches will be,

Volume of the cube = (4 in)³ = 64 in³

Hence, the volume of the cube with side length of 4 inches is 64 inches³.

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[tex]y= 6x -4~~~~~~...(i)\\\\y = 5x -3~~~~~~...(ii)\\\\\text{From (i) and (ii):}\\\\~~~~~6x -4 = 5x -3\\\\\implies 6x -5x = -3 + 4\\\\\implies x = 1\\\\\text{Substitute x = 1 in equation (i):}\\\\y = 6(1) -4 = 2\\\\\text{Hence,}~ (x,y) = (1,2)[/tex]

Answer:

1st answer supplementary angles

2nd answer complementary angles

3rd answer neither

4th ananswe complementary angles

5th answer complementary angles

6th answer supplementary angles

hope you find this helpful

Answer:

θ = 53.1°  (to the nearest tenth)

Step-by-step explanation:

FORMULA :

Let θ be the measure of the angle between U and V :

[tex]\cos \theta =\frac{\overrightarrow{U} .\overrightarrow{V} }{\left\Vert \overrightarrow{U} \right\Vert \times \left\Vert \overrightarrow{V} \right\Vert }[/tex]

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

[tex]\overrightarrow{U} \times \overrightarrow{V} =6\times 2+\left( -3\right) \times 1=9[/tex]

[tex]\left\Vert \overrightarrow{U} \right\Vert =\sqrt{6^{2}+\left( -3\right)^{2} } =\sqrt{45} =3\sqrt{5}[/tex]

[tex]\left\Vert \overrightarrow{U} \right\Vert =\sqrt{2^{2}+\left( 1\right)^{2} } =\sqrt{5}[/tex]

[tex]\left\Vert \overrightarrow{U} \right\Vert \times \left\Vert \overrightarrow{V} \right\Vert =3\sqrt{5} \times \sqrt{5} = 15[/tex]

…………………………………………………

Then

[tex]\cos \theta =\frac{9}{15} =\frac{3}{5}[/tex]

[tex]\theta =\cos^{-1} \left( \frac{3}{5} \right) =53.130102354156[/tex]

Answer:

The answer is 97

Step-by-step explanation:

According to PEMDAS, we will solve the multiplication first. 2 × 42 is 84. Next, we will add or subtract from left to right. 9 + 84 + 6 – 2 is 97, the answer to our problem.

9 + 2 × 42 + 6 - 2

Multiply 2 and 42 to get 84.

9 + 84 + 6 - 2

Add 9 and 84 to get 93.

93 + 6 - 2

Add 93 and 6 to get 99.

99 - 2

Subtract 2 from 99 to get 97.

97 ===> Answer

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Answer:

20% of sales : $1000

and salary+commission : $1000+ 600

So total salary : $1600

Answer:

Seconds:  2    ||  3     || 5     || 10     ||

---------------------||-------||--------||--------||

Gallons:   312  || 486 || 780 || 1560 ||

Answer:

equivalent. not equivalent. not equivalent

Step-by-step explanation:

Answer:

2 * 21

3 * 14

6 * 7

Step-by-step explanation:

7 * 2 = 14

56 - 14 = 42

Multiples of 42 = 2,3,6,7, 14, 21

The possible dimensions of the larger rectangle are:

21 centimeters by 2 centimeters

14 centimeters by 3 centimeters

7 centimeters by 6 centimeters

Let the dimensions of the larger rectangle be length L and width W.

We know that the total area of the two rectangles is 56 square centimeters.

Area of the smaller rectangle = 2 cm * 7 cm = 14 square centimeters

Area of the larger rectangle = Total area - Area of the smaller rectangle

Area of the larger rectangle = 56 square centimeters - 14 square centimeters

Area of the larger rectangle = 42 square centimeters

Now, we need to find the possible dimensions of the larger rectangle with an area of 42 square centimeters.

To find the possible dimensions, we can list all the pairs of whole numbers (L, W) whose product is 42.

7 * 2 = 14

56 - 14 = 42

Multiples of 42 = 2,3,6,7, 14, 21

Remember that the length (L) should be greater than or equal to the width (W) to avoid counting duplicates.

The possible dimensions are:

L = 42, W = 1 (42 cm * 1 cm = 42 square centimeters)

L = 21, W = 2 (21 cm * 2 cm = 42 square centimeters)

L = 14, W = 3 (14 cm * 3 cm = 42 square centimeters)

L = 7, W = 6 (7 cm * 6 cm = 42 square centimeters)

So, the possible dimensions of the larger rectangle are:

42 centimeters by 1 centimeter

21 centimeters by 2 centimeters

14 centimeters by 3 centimeters

7 centimeters by 6 centimeters

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Answer:

16 cm²/m²

Step-by-step explanation:

The formula to find the area of a triangle is:

 Area of the triangle = [tex]\frac{1}{2}[/tex] × base × height

Where base = 8 and height = 4

 So, the area of the triangle =  [tex]\frac{1}{2}[/tex] × 8  × 4 = 16 cm²/m²

Answer:

C

Step-by-step explanation:

Remark

You must do the changes in order. Add 1 then multiply by 2

Answer: 7 14 15 30

Answer:

7.070 to the nearest thousandth

Step-by-step explanation:

You could use a calculator or do it manually using long division:

61)431 .2500(7.0695 <---------Quotient

    427

        425

         367

           580

           549

              310

               305

Answer:

3.5

Step-by-step explanation:

Step-by-step explanation:

650065 = (a² + 1)(c² + 1)

and

650065 = (ac - 1)² + (a + c)² = the sum of 2 squared numbers (ac - 1)² and (a + c)².

we see that 5 and 13 and therefore 5×13=65 are all factor of 650065. and then 650065/65 = 10001.

and we know that 65 = (64 + 1) = (8² + 1)

and 10001 = (10000 + 1) = (100² + 1)

so, a = 8, c = 100

that means the 2 squared numbers summing up to 650065 are

(ac - 1)² = (8×100 - 1)² = 799² = 638,401

(a + c)² = (8 + 100)² = 108² = 11,664

650,065 = 638,401 + 11,664 = 799² + 108²