How would you write this equation in terms of sin and cos as well as simplify it from there?
(1+cotx)(1-cotx)-csc^2 x

Answer with explanation:

→→Information given about Parabola

Vertex of the Parabola = (0,0)

Focus is located on the positive x- axis.

Definition of Parabola: A parabola is locus of all the points such that distance from a fixed point known as focus to distance from a fixed line called, Directrix  is always constant.

Let focus of the parabola be (k,0), where , k>0.

Distance between vertex (0,0) and focus(k,0) = Distance between vertex (0,0) and point on negative x-axis (-k,0).

Directrix will pass through point (-k,0).

So, equation of Directrix will be, x= -k

Directrix will pass through

Option B: The Negative part of the x -axis.

The number of stamps each could have purchased is 84

How to determine the number of stamps each purchased

From the question, we have the following parameters that can be used in our computation:

Andy = packs of 4

Erin = packs of 6

Jarred = packs of 7

Expand 4, 6 and 7

So, we have

4 = 2 * 2

6 = 2 * 3

7 = 7

The LCM of 4, 6 and 7 is then calculated as

LCM = 2 * 2 * 3 * 7

Evaluate

LCM = 84

Hence, the number of stamps each could have purchased is 84

A geometric series is the sum of an unlimited number of terms with a fixed ratio between them. The correct option is B.

A geometric series is the sum of an unlimited number of terms with a fixed ratio between them.

The given statement "If all terms of a series are​ positive, then the series sums to a positive number" is true because the series will converge to a positive number because the series contains no negative terms.

Hence, the correct option is B.

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Let the number of stickers in each pack be 'x'

Finn bought 2 packs of stickers.

Number of stickers in 2 packs = [tex] 2 \times x [/tex] = 2x

According to the question, a friend gave him 4 more stickers and now he has 24 stickers in all.

Therefore, [tex] 2x+4=24 [/tex]

[tex] 2x=24-4 [/tex]

[tex] 2x=20 [/tex]

x = 10

Therefore, number of stickers in each pack are 10.

Answer: The damaged area is equal to 8831.25ft^2

Step-by-step explanation:

We know that we have a circular area, where half of the grass has died. We know that the circular picnic is "150 feet across" I guess this means that if you walk in a straight line from the edge of the circular area, through the middle, and to the next edge, the distance is 150ft.

This would mean that the diameter is equal to 150ft.

With this we can calculate the total area of the circle; this is:

A = pi*r^2

where r is the radius, that is half the diameter, so we have r = 150ft/2 = 75ft

and pi = 3.14

so we have:

A = 3.14*(75ft^)^2 = 17662.5ft^2

And we know that half of that area has the grass damaged, so the amount of square feet of grass needed is equal to A/2 = (17662.5ft^2)/2 = 8831.25ft^2

a) π · (12 · tan 70°)2. To find the area of the ground covered by the conical tent, use the formula for the surface area of a cone, A = πr(r+√(r^2+h^2)).

To find the area of the ground covered by the conical tent, we can use the formula for the surface area of a cone. The formula is A = πr(r+√(r^2+h^2)), where r is the radius and h is the height of the cone.

In this case, the height of the cone is 12 feet and the angle it makes with the ground is 70°. To find the radius, we can use trigonometry. The radius is given by r = h tanθ, where θ is the angle with the ground. Plugging in the values, we get r = 12 tan(70°).

Now, substituting the value of r into the formula for the surface area of the cone, we get A = π(12 tan(70°))(12 tan(70°)+√((12 tan(70°))^2 + 12^2)). This simplifies to option a) π · (12 · tan 70°)2.

Answer with Step-by-step explanation:

Let

A:selecting a heart

Total cards=52

number of hearts=13

P(A)=13/52

B:selecting a 8

number of 8=4

P(B)=4/52

A∩B:selecting a heart with 8 on it

number of hearts with 8 on it=1

P(A∩B)=1/52

A∪B:selecting a heart or a 8

We have to find P(A∪B)

P(A∪B)=P(A)+P(B)-P(A∩B)

          = [tex]\dfrac{13}{52}+\dfrac{4}{52}-\dfrac{1}{52}[/tex]

          =[tex]\dfrac{13+4-1}{52}[/tex]

          = 16/52

          = 4/13

Hence, the probability of selecting a heart or a 8 is:

4/13

Fraction is a way to describe a part of a whole. The fraction is represented by the shaded part of the model is [tex]\dfrac{2}{1}[/tex].

A fraction is a way to describe a part of a whole. such as the fraction 1/4 can be described as 0.25

If we look at each of the shapes, we can observe that the whole of the shape is shaded therefore, the shaded part of the shape is equal to the shape which is represented by 1.

Now, in the image, there are two shapes given each of which is completely shaded, and the whole shape is represented by 1. therefore, these two shapes will be represented by 2.

The shaded shape can be written as,

[tex]2 = \dfrac{2}{1}[/tex]

Hence, the fraction is represented by the shaded part of the model is [tex]\dfrac{2}{1}[/tex].

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Final answer:

No, not every even number can be written as a sum of two primes. This is known as the Goldbach Conjecture, which states that every even number greater than 2 can be expressed as the sum of two prime numbers.

Explanation:

No, not every even number can be written as a sum of two primes. This is known as the Goldbach Conjecture, which states that every even number greater than 2 can be expressed as the sum of two prime numbers. So far, this conjecture has been tested for even numbers up to at least 4, and no counterexamples have been found. However, it has not been proven to be true for all even numbers.

For example, the number 4 can be expressed as the sum of two primes (2 + 2), but the number 6 cannot be expressed as the sum of two primes. On the other hand, the number 8 can be expressed as the sum of two primes (3 + 5). This pattern continues, with some even numbers being expressible as the sum of two primes and others not.

Answer:

I think its 5

Step-by-step explanation:

I may be wrong

If x = 3 inches, y = 10 inches, w = 5 inches, and z = 5 inches. Then the area of the given figure is 40 inches.

"The area is the amount of space within the perimeter of a 2D shape. It is measured in square units, such as cm², m², etc."

The area of the square is side times side i.e., a^2.

The area of the rectangle is length times width i.e., l*b.

Here,

x = 3 inches, y = 10 inches, w = 5 inches, z = 5,

In the given figure:

Area of the square BCDE is a^2 = 5^2 = 25

Area of the rectangle ABFG is l*b = 5*3 = 15

Total area of the figure is = area of the square + area of the rectangle = 25+15 = 40.

Hence, the answer is option B.

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Answer: The answer in order are false, false, true, true, false and (3,1)

Step-by-step explanation:

We know that image of a point (x,y) under the y-axis

is (-x,y) i.e. the sign of x coordinate changes

Similarly in case of x-axis sign of y coordinate changes

i.e (x,y) is reflected to (x,-y)

Also the reflection of (x,y) under the line y=x is (y,x)

and the reflection of (x,y) under the line y=-x is(-y,-x)

So  

a) Given image of (-3,-5) under x-axis is (3,-5).

Hence statement is false

b) Given image of (1,9) under y-axis is (1,-9)

Hence the statement is false

c) Given image of (8,7) under y=-x is (-7,-8)

i.e. the statement is true

d) Given image of (-6,-6) under y=x is (-6,-6)

i.e the statement is true

e) Given image of (2,4) under y axis followed by x-axis is (-2,-2)

Hence the statement is false

f) (3,-1) is reflected in x-axis to (3,1)

Hence the point k is (3,1)

Answer:

a

b

e

g

Step-by-step explanation:

I just did the assignment lol-