What is the period for the cotangent function?

Answer:

# Answer B is true ⇒ KL = 2(JL)

# Answer C is true ⇒ JK = √3(JL)

# Answer F is true ⇒ JK = √3/2(KL)

Step-by-step explanation:

* Lets explain the ratio between the sides of the triangle

- In Δ JKL

∵ The measure of angle J is 90°

∴ KL is the hypotenuse

∵ The measure of angle K is 30°

∴ JL is the opposite side to angle 30°

∵ The measure of angle L is 60°

∴ JK is the opposite side to the angle 60°

- There is a fact in the triangle which has angles 30° , 60° , 90°

# The length of the side opposite to the angle of measure 30° is

  half the length of the hypotenuse

∵ KL is the hypotenuse

∵ JL is the opposite side to the angle of measure 30°

∴ JL = 1/2 KL  OR KL = 2 JL

# The length of the side opposite to the angle of measure 60° is

  √3 the length of the opposite side to the angle 30°

∵ JK is the opposite side to the angle of measure 60°

∵ JL is the opposite side to the angle of measure 30°

∴ JK = √3 JL

# The length of the side opposite to the angle of measure 60° is also

  half √3 the length of the hypotenuse

∵ JK is the opposite side to the angle of measure 60°

∵ KL is the hypotenuse

∴ JK = √3/2 KL

- From the relation above

# Answer B is true ⇒ KL = 2(JL)

# Answer C is true ⇒ JK = √3(JL)

# Answer F is true ⇒ JK = √3/2(KL)

Answer:

It is a and B in C & D

Step-by-step explanation:

These are the closest answers

Mike's slower rate of driving across country was 65 mph.

Let the slower rate be represented as r mph. The faster rate will be r+10 mph. The total distance covered (495 miles) is the product of the time and the rate:

Adding up the distances, we get:

Simplifying the equation:

Combining like terms:

Subtracting 40 from both sides:

Dividing by 7:

Therefore, the slower rate is 65 mph.

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The correct answer for the slower rate at which Mike drove is 65 mph.

To find the slower rate at which Mike drove, let's denote the slower rate as r mph. Mike drove at this rate for 3 hours. He then drove for 4 hours at a rate that is 10 mph faster than the slower rate, which would be r + 10 mph.

The total distance covered by Mike is the sum of the distances covered at each rate. We can set up an equation to represent this:

[tex]\[ 3r + 4(r + 10) = 495 \][/tex]

Expanding the equation, we get:

[tex]\[ 3r + 4r + 40 = 495 \][/tex]

Combining like terms, we have:

[tex]\[ 7r + 40 = 495 \][/tex]

Now, we need to solve for r We can do this by subtracting 40 from both sides of the equation:

[tex]\[ 7r = 495 - 40 \] \[ 7r = 455 \][/tex]

Dividing both sides by 7 to solve for r, we get:

[tex]\[ r = \frac{455}{7} \] \[ r = 65 \][/tex]

Therefore, the slower rate at which Mike drove is 65 mph.

Answer: Because there are no values

Step-by-step explanation: Since there are no numbers in the problem, there is no sum. making it 0. You can't add two letters to make another letter, So it becomes a 0. anything with a variable subtracted, divided, added, ect by another variable, is 0

ANSWER

The dot product is 10.

EXPLANATION

The given vectors are (2,4) and (1,2).

If we have the vectors

u=(a,b) and v=(c,d)

Then the dot product of the two vectors is given by

[tex]u \bullet \: v = ac + bd[/tex]

This implies that,

[tex](2,4) \bullet(1,2) = 2 \times 1 + 4 \times 2[/tex]

This simplifies to;

[tex](2,4) \bullet(1,2) = 2 + 8 = 10[/tex]

Answer:

-6

Step-by-step explanation:

took test

Answer:

[tex]f^{-1}(8)=1.5[/tex]

Step-by-step explanation:

If y=f(x)=2x+5, to find the inverse function express x n terms of y:

[tex]y=2x+5\\ \\2x=y-5\\ \\x=\dfrac{y-5}{2}[/tex]

Now, change y into x and x into y:

[tex]y=\dfrac{x-5}{2}\\ \\f^{-1}(x)=\dfrac{x-5}{2}[/tex]

Substitute x=8 into [tex]f^{-1}(x)[/tex] expression:

[tex]f^{-1}(8)=\dfrac{8-5}{2}\\ \\f^{-1}(8)=\dfrac{3}{2}=1.5[/tex]

Answer:

3/2

Step-by-step explanation:

f(x) = 2x+5

f⁻¹(2x+5) = x

2x+5 = 8 => 2x+5 = 8 => 2x = 3 =>

=> x = 3/2

=> f⁻¹(8) = 3/2

Answer:

No, because they do not have the same area.

Step-by-step explanation:

For the piece of paper to cover once without overlap or gaps, it must have the same area as the the total surface area of the prism.

The total surface area of the rectangular prism is: [tex]2(3.5\times2+3.5\times1.5+2\times1.5)=30\frac{1}{2}in^2[/tex]

The area of the rectangular sheet is:[tex]5\times 8=40in^2[/tex]

Since the area of the piece of paper is more than the surface area of the rectangular prism there will be an overlap.

Answer: the first one is True and the second one is false

Step-by-step explanation:

3 + 5x = 23

so replace x with 4 you get 3 + 5 * 4 = 3 + 20 = 23

this is equal to 23 so it is true

2x - 6 = 9

do the same you get

2 * 8 - 6 = 9

16 - 6 = 10

the answer is 10 not nine therefore it is false

Answer:

V -E +F = 2

Vertices = 2 + Edges -Faces

Vertices = 2 + 90 -32

Vertices = 60

Step-by-step explanation:

Answer:

has two rays that share a common end point.

Answer:

Angle has two rays that share a common endpoint.

Step-by-step explanation:

Given : Angle.

To find : Which is a property of an angle.

Solution : We have given properties of an angle .

Angle : the space between two intersecting lines or surfaces at or close to the point where they meet.

Vertex is also called the angle.

Therefore, Angle has two rays that share a common endpoint.

Answer:

0.18 cents

Step-by-step explanation:

2.34 divided by 13= 0.18

To check my answer, 0.18 x 13 = 2.34

Answer:

$0.18/ounce

Step-by-step explanation:

Divide the price by the weight.

($2.34)/(13 ounces) = $0.18/ounce

Answer:

Step-by-step explanation:

Answer:

Length 34 cm

Width 8 cm

Step-by-step explanation:

Let

x-----> the length of the rectangle

y----> the width of the rectangle

we know that

The perimeter of rectangle is equal to

P=2(x+y)

P=84 cm

so

84=2(x+y)

42=x+y ----> equation A

x=4y+2 -----> equation B

substitute equation B in equation A and solve for y

42=(4y+2)+y

5y=42-2

y=40/5=8 cm

Find the value of x

x=4y+2 ----> x=4(8)+2=34 cm

The dimensions are

Length 34 cm

Width 8 cm

The width of the rectangle is 8 cm and the length is 34 cm.

To determine the dimensions of the rectangle, we need to set up equations based on the given information.

Let's denote the width of the rectangle by W (in cm). According to the problem, the length L is 2 cm more than four times the width. Therefore, we can express the length as:

L = 4W + 2

The perimeter of a rectangle is calculated using the formula:

Perimeter = 2L + 2W

Given that the perimeter is 84 cm, we can substitute the expressions for L and W into the perimeter formula:

84 = 2(4W + 2) + 2W

Simplify the equation:

Now that we have the width, we can find the length:

L = 4(8) + 2 = 32 + 2 = 34

Thus, the dimensions of the rectangle are:

Answer:

The probability of not drawing a black marble is : 8/10, 4/5, 80%

The probability of drawing a red marble is: 3/10, or 30%

Step-by-step explanation:

Blue marbles: 5

Black marbles: 2

Red marbles: 3

Total marbles: 10

The probability of not drawing a black marble is :

NOT drawing a black marble means you'll draw either a blue or a red one.  Combined, red and blue marbles account for 8 marbles out of 10.

So the probability of NOT drawing a black marble is 8/10, 4/5 or 80%

The probability of drawing a red marble is:

There are 3 red marbles, out of 10 marbles.... so the probability of drawing a red marble is 3/10, or 30%

Answer:

it would take you 41 weeks

(rounded to 42 if that is a choice answer because when you divide 7500 by 180 it gives you 41.66666)

Step-by-step explanation:

Answer:

(f + g)(x) = 7x - 1

Step-by-step explanation:

Given :  f(x) = 5x – 2 and g(x) = 2x + 1

We have to find  (f + g)(x)

Consider  (f + g)(x) = f(x) + g(x)

Also, given  f(x) = 5x – 2 and g(x) = 2x + 1

Substitute, we have,

f(x) + g(x) = 5x - 2 + 2x + 1

Like Terms are terms having same variable with same degree.

Simplify by adding like terms,  we have,

f(x) + g(x) = 5x + 2x - 2  + 1

f(x) + g(x) = 7x  - 1

Thus, (f + g)(x) = 7x - 1

Answer:

Thus, (f + g)(x) = 7x - 1

Step-by-step explanation:

(f + g)(x) = 7x - 1

Step-by-step explanation:

Given :  f(x) = 5x – 2 and g(x) = 2x + 1

We have to find  (f + g)(x)

Consider  (f + g)(x) = f(x) + g(x)

Also, given  f(x) = 5x – 2 and g(x) = 2x + 1

Substitute, we have,

f(x) + g(x) = 5x - 2 + 2x + 1

LIKE TERMS are terms having same variable with same degree.

Simplify by adding like terms,  we have,

f(x) + g(x) = 5x + 2x - 2  + 1

f(x) + g(x) = 7x  - 1

Thus, (f + g)(x) = 7x - 1

Answer:

k = 2cw

Step-by-step explanation:

1. 11cw + 2k = 15cw

2. Subtract 11cw from both sides:

2k = 4cw

3. Divide by 2 on both sides:

k = 2cw

Answer: 9cm

Step-by-step explanation:

[tex]7x10=70cmx^{2}[/tex]

4(x)=4x

1.) 70+4x=106 (subtract 70 on both sides)

2.)4x=36 (divide 4 on both sides)

3.)x=9

answer=9

7x10=70cmxsquare

4(x)=4x

70+4x=106

4x=36

x=36/4

x=9

Answer:

160cm^3

Step-by-step explanation:

V=Lwh

so, (5x8x4)

v=160cm^3

Hope my answer has helped you!

The answer is:

The correct option is:

A) The function g(x) has a higher y-intercept.

To solve the problem, we need to find the y-intercept of the g(x) function, and then, compare to the y-intercept of the f(x) function which is equal to -1 (we can see it on the picture).

Also, we need to remember the slope-interception form of the line:

[tex]y=mx+b[/tex]

So,

Finding the y-intercept of the g(x) function, we have:

Calculating the slope of the function, using the first two points (4,9) and (6,13), we have:

[tex]m=\frac{y_2-y_1}{x_2-x_1}\\\\m=\frac{13-9}{6-4}=\frac{4}{2}=2[/tex]

Now,

Calculating the value of "b", we have:

Using the first point (4,9), the slope of the function, and the slope-intercept form of the function, we have:

[tex]y=mx+b[/tex]

[tex]y=2x+b[/tex]

[tex]9=2*(4)+b[/tex]

[tex]9=8+b[/tex]

[tex]9-8=b[/tex]

[tex]b=1[/tex]

So, the equation of the line will be:

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

We know that "b" represents the y-intercept, so, the function g(x) has its y-intercept at y equal to 1.

Comparing, we have that the function f(x) has a y-intercept located at y equal to "-1" and the g(x) function has a y-intercept located at y equal to "1".

Hence, the correct option is:

A) The function g(x) has a higher y-intercept.

Have a nice day!

Answer:

A.

The value of Ann’s bonds has increased by $45.28 more than the value of her stocks.

Step-by-step explanation:

The value of Ann’s bonds has increased by $45.28 more than the value of her stocks. Option A is correct.

We have given that,

Much of Ann’s investments are in Cilla Shipping.

By this, we mean that share prices change because of supply and demand. If more people want to buy a stock (demand) than sell it (supply), then the price moves up.

Ten years ago, Ann bought seven bonds issued by Cilla Shipping, each with a par value of $500. The bonds had a market rate of 95.626.

Ann also bought 125 shares of Cilla Shipping stock, which at the time sold for $28.00 per share.

Today, Cilla Shipping bonds have a market rate of 106.384, and Cilla Shipping stock sells for $30.65 per share.

The value of Ann’s bonds has increased by $45.28 more than the value of her stocks. Option A is correct.

To learn more about the stock increase visit:

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To determine which equations have a lower unit rate than the rate in the table, calculate the unit rate or slope from the table and compare it to the slopes of the other equations. Equations with a smaller slope have a lower unit rate.

To answer this question, we need to calculate the unit rate of the original equation. The unit rate is the ratio of the increase in the dependent variable (usually represented by y) to the increase in the independent variable (usually represented by x).

For example, if the table shows x increasing by 2 and y increasing by 4, then the unit rate is 4/2 = 2 which is the slope.

The equations with a lower unit rate than this would have a smaller ratio of the increase in y to the increase in x. For instance, if the slope of another equation is 1, that means for each unit increase in x, y increases by only 1, which is less than the original rate of 2.

Therefore, to decide which equations have a lower unit rate, compare the slopes of the equations to the unit rate calculated from the original table. Any equation with a smaller slope has a lower unit rate.

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The area of a kite is half the product of the diagonals.  

Area = ½(d1 x d2)  

Plug in the values of the diagonals.

Area = ½(7.8 * 6)  

Multiply, and you should get -

Area = 23.4 ft²

Answer: Option 'A' is correct.

Step-by-step explanation:

Since we have given that

Diagonals of kite are as follows:

7.8 ft and 6 ft

As we know the formula for "Area of kite":

Area of kite is given by

[tex]\dfrac{1}{2}\times d_1\times d_2\\\\=\dfrac{1}{2}\times 7.8\times 6\\\\=3\times 7.8\\\\=23.\ ft^2[/tex]

Hence, Option 'A' is correct.

Answer:

x^5 - 5 x^4 + 9 x^3 - 9 x^2 + 12 x - 12

Step-by-step explanation:

(x ^4 - 3x^3 + 3x^2 - 3x + 6) (x - 2)

Distribute the x to all the terms in the first parentheses

(x^ 4  *x - 3x^ 3  *x + 3x^ 2   *x - 3x   *x + 6*x)

Then simplify

(x^5 - 3x^4 + 3x^ 3 - 3x2 + 6x)

Distribute the -2 to all the terms in the first parentheses

(x^ 4  *(-2) - 3x^ 3  *(-2) + 3x^ 2   *(-2) - 3x   *(-2) + 6*(-2))

Then simplify

(-2x^4 +6x^3 -6x^ 2 +6x -12)

Add the terms together

(x^5 - 3x^4 + 3x^ 3 - 3x2 + 6x) +(-2x^4 +6x^3 -6x^ 2 +6x -12)

x^5 - 5 x^4 + 9 x^3 - 9 x^2 + 12 x - 12

Answer:

x^3 -x^2 + x -1 + 4/x-2

Step-by-step explanation:

;)

The total cost Dani will pay for the movie including discount and sales tax is $13.23

To find the total cost Dani will pay for the movie:

Calculate the discount: $18 x 0.30 = $5.40

Subtract the discount from the original price: $18 - $5.40 = $12.60

Calculate the 5% sales tax: $12.60 x 0.05 = $0.63

Total cost: $12.60 + $0.63 = $13.23

Answer:

width = 8 feet and length = 29 feet

Step-by-step explanation:

perimeter of a rectangle P = 2(L + W)

width W = x

length L = 3x + 5

P = 74 feet

74 = 2(3x + 5 + x)

37 = 3x + 5 + x

37 = 4x + 5

4x = 37 -5

4x = 32

x = 8

W = 8 feet

Answer:

29

Step-by-step explanation:

Answer: 29

Step-by-step explanation:

It is important to know the definition.

The average of a set of number is defined as the sum of all these numbers divided by the total numbers that are in this set.

So, knowing this, we know that if we have a set of three numbers:"a", "b" and "c" , we can calculate  the average of them with this procedure:

[tex]average=\frac{a+b+c}{3}[/tex]

Therefore, we can calculate the average of the numbers 23, 33 and 31. This is:

[tex]average=\frac{23+33+31}{3}=\frac{87}{3}=29[/tex]

Answer:

35 different watches

Step-by-step explanation:

I don't know if this is correct so sorry if it's not.

5 faces x 7 bands.

So, 5 x 7

=

35

i hope that helps... it might not, sorry

Answer:

35 different watches/combos.

Step-by-step explanation:

5 watches, 7 different wrist bands

5 x 7 = 35

1 watch consist of 1 watch and 1 band so he can have 35 different watch combinations.

Answer:

64% as a fraction and decimal: 16/25 and .64

1/8 as a percent and decimal: 12.5% and .125

1.4 as a percent and fraction: 140% and 1 2/5

2 3/4 as a percent and decimal: 275% and 2.75

8 percent as a decimal and fraction: .08 and 2/25

Step-by-step explanation:

the answer should be,

A. shows that 9^1 - 4^1=5

hope this helps! :)

Answer:

800 meters

Step-by-step explanation:

y is inversely proportional to x is the same as y is inversely proportional to [tex]\frac{1}{x},[/tex] that means

[tex]y=\dfrac{k}{x}.[/tex]

If a wave with a frequency of x=720 kilohertz has a length of y=500 meters, then

[tex]500=\dfrac{k}{720}\\ \\k=500\cdot 720=360000.[/tex]

Hence, the length of a wave y with a frequency of x=450 kilohertz is

[tex]y=\dfrac{360000}{450}=800[/tex]

The relationship between the frequency and wavelength of a wave is given by the formula:
\[ c = f \times \lambda \]
where:
- \( c \) is the speed of light (or the speed of the wave in another medium, but for radio waves in the air or vacuum, it's approximately the speed of light),
- \( f \) is the frequency of the wave,
- \( \lambda \) is the wavelength of the wave.
Given that the relationship is inverse, when the frequency goes up, the wavelength goes down, and vice versa.
We are given that a wave with frequency 720 kilohertz has a length of 500 meters. We can represent this with the equation:
\[ c = 720 \times 500 \]
We are asked to find the wavelength when the frequency is 450 kilohertz. Since the speed of light doesn't change, we set up the proportion using the formula, keeping \( c \) constant:
\[ 720 \times 500 = 450 \times \lambda_{\text{new}} \]
Now we solve for \( \lambda_{\text{new}} \):
\[ \lambda_{\text{new}} = \frac{720 \times 500}{450} \]
To simplify this, we can divide both the numerator and the denominator by a common factor. In this case, let's divide by 90:
\[ 720 \div 90 = 8 \]
\[ 450 \div 90 = 5 \]
\[ 500 \text{ remains unchanged} \]
Now we can substitute these simplified numbers back into our equation:
\[ \lambda_{\text{new}} = \frac{8 \times 500}{5} \]
\[ \lambda_{\text{new}} = \frac{4000}{5} \]
\[ \lambda_{\text{new}} = 800 \]
So the length of a wave with a frequency of 450 kilohertz is 800 meters.