What is the tangent ratio for angle f

1+tan^2(x) = sec^2(x)

sec^2(x) = 1/cos^2(x)

csc(-x) / 1/cos^2(x) =

cos^2(x) csc(-x)

yes thats the corrects answer -6 and 6 on the number line.

Answer:

x-axis

Step-by-step explanation:

Final answer:

There are 180 ways to place 5 basketball players on the court, selecting 2 guards, 2 forwards, and 1 center.

Explanation:

To determine the number of ways to place 5 basketball players on the court, we need to find the number of combinations of guards, forwards, and centers that can be selected from the available players. There are 4 guards, 5 forwards, and 3 centers in the team.

The number of ways to select 2 guards from 4 is C(4,2) = 6.

The number of ways to select 2 forwards from 5 is C(5,2) = 10.

The number of ways to select 1 center from 3 is C(3,1) = 3.

By the multiplication principle, the total number of ways to place the players on the court is 6 × 10 × 3 = 180.

Final answer:

The point where two or more rays meet in optics is known as the focal point, which is crucial in geometric optics. For a converging lens or mirror, it's where light rays converge, while for a diverging lens or mirror, it's where light rays appear to originate.

Explanation:

The point where two or more rays or 'arms' of an angle meet in the context of geometrical optics is known as the focal point. In terms of a converging lens or mirror, the focal point is where converging light rays intersect after passing through the lens or reflecting off the mirror surface. This is a fundamental concept in the study of geometrical optics, which deals with the ray aspect of light. A ray is a straight line that originates at a point and is used in geometric optics to represent the path along which light travels.

For a converging lens, which is also known as a convex lens, parallel light rays entering the lens will refract and converge at a single point on the opposite side of the lens. This single point is the focal point. Similarly, in concave mirrors, ray diagrams show the focal point as the point where reflected rays converge or appear to converge. The distance from the focal point to the mirror along the central axis is referred to as the focal length. Conversely, for a diverging lens or mirror, the focal point is the point from which diverging light rays appear to originate.

Answer:

Option B - [tex]\log_6 60-\log_6 30=\log_6 (2)[/tex]                

Step-by-step explanation:

Given : Expression [tex]\log_6 60-\log_6 30[/tex]

To find : Solve the given expression?

Solution :

Step 1 - Write the expression

[tex]\log_6 60-\log_6 30[/tex]

Step 2 - Applying logarithmic property, [tex]\log a-\log b=\log(\frac{a}{b})[/tex]

[tex]\log_6 60-\log_6 30=\log_6 (\frac{60}{30})[/tex]

Bases are same.

Step 3 - Solve

[tex]\log_6 60-\log_6 30=\log_6 (2)[/tex]

Therefore, The solution of expression is

[tex]\log_6 60-\log_6 30=\log_6 (2)[/tex]

So, Option B is correct.

The options (A) and (B) are correct.

"Trigonometric Ratios are defined as the values of all the trigonometric functions based on the value of the ratio of sides in a right-angled triangle. It is with respect to any of its acute angles are known as the trigonometric ratios of that particular angle".

For the given situation,

Cos θ = 15/17

By using Pythagoras theorem,

We know Cos θ = [tex]\frac{base}{hypotenuse}[/tex]

Sine θ = [tex]\frac{perpendicular}{hypotenuse}[/tex]

tan θ = [tex]\frac{perpendicular}{base}[/tex]

By Pythagoras theorem, [tex]Hypotenuse^{2}= base^{2}+perpendicular^{2}[/tex]

⇒[tex]17^{2}=15^{2}+perpendicular^{2}[/tex]

⇒[tex]perpendicular^{2}= 289-225[/tex]

⇒[tex]perpendicular=\sqrt{64}[/tex]

⇒[tex]perpendicular=8[/tex]

Thus, Sec θ = 17/15

Tan θ = 8/15

Sine θ = 8/17

Cosec θ = 17/8.

Hence we can conclude that the options (A) and (B) are correct.

Learn more about trigonometric ratios here

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Answer:

tan and sec

Step-by-step explanation:

A amd B

Answer:

c

Step-by-step explanation:

−5 ±square root 6

The solutions represent the additional length and width that need to be added to the original dimensions to achieve the desired area of 88 sq ft.

The equation is: (6+x)(9+x) = 88. Ginger is using the zero product property to solve for x. The solutions she finds represent the value of x that, when added to both the length and width of the original patio, will result in a patio with an area of 88 sq ft.

By solving the equation, Ginger will find the possible values of x that will make the area of the new patio equal to 88 sq ft. These values represent the additional length and width that need to be added to the original dimensions to achieve the desired area.

For example, if Ginger finds that x = 2, then the new patio dimensions would be 9+2 = 11 ft by 6+2 = 8 ft, resulting in an area of 11 * 8 = 88 sq ft.

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Answer:

Option 2 is correct.

Step-by-step explanation:

Given the diagram and also the condition  m∠14 + m∠2 = 180°

we have to tell which lines are parallel.

By the theorem of exterior angles

Same-side exterior angles which are formed outside of the parallel lines and on same side of transversal line.

The theorem states that when parallel lines are cut by a transversal line, the sum of the same-side exterior angles is 180° i.e these are supplementary.

∴ Lines a and b are are parallel by converse of same side exterior angle theorem.

To solve this problem let us say that,

h = height of the can

r = radius of the can

We try to minimize the amount of metal used which is the surface area (SA), and the equation for a cylinder is:

SA = 2πrh + πr^2

To get the minima, we take the derivative of this function and set it equal to 0. But first, the function is in two variables so we must eliminate one of them. We use the extra information given in the problem which is volume:

V = 8π = πr^2 h

Therefore,

h = 8/r^2

Plug this into the SA function to have it in terms of one variable only:

SA = 2πrh + πr^2

SA = 2πr(8/r^2) + πr^2

SA = 16π/r + πr^2

Taking the 1st derivative of the function:

0 = −16π r^−2 + 2πr

0 = −16π/r^2 + 2πr

16π/r^2 = 2πr

r^3 = 8

r = 2 in

By obtaining r, we calculate for h:

h = 8/r^2

h = 8/(2)^2

h = 8 / 4

h = 2 in               (ANSWER)

Option b is the correct answer. Exponents should be multiplied in the expression (1/3)^4*(1/3)^7, resulting in (1/3)^11.

The expression where the exponents should be multiplied is Option b. (1/3)^4*(1/3)^7. This is because when you multiply two expressions that have the same base, you add their exponents. In this case, you have the base (1/3) raised to the 4th power and then to the 7th power, so you add the exponents 4 + 7, which equals 11. Therefore, (1/3)^4*(1/3)^7 simplifies to (1/3)^11.

Another case where you multiply exponents would be when raising a power to another power, like in (5^3)^4. Here the exponents 3 and 4 are multiplied, resulting in (5^12).

Answer: b

Step-by-step explanation: i got it right

total = 19.99 + 0.10(x-300) + 0.25y

x = 375

y=54

total = 19.99 +0.10(375-300) +0.25(54)

total = 19.99 + 0.10(75) + 0.25(54)

total = 19.99 + 7.50 + 13.50

total = $40.99

The total monthly bill is $40.99 for 375 local minutes and 54 long distance minutes, given the cell phone company's rates.

The total monthly bill can be expressed as the sum of the basic rate, the extra charge for local minutes beyond the included 300, and the charge for all long distance minutes. The expression can be written as:

Total Monthly Bill = Basic Rate + (Local Extra Charge x Extra Local Minutes) + (Long Distance Rate x Long Distance Minutes)

Where:

For x = 375 local minutes and y = 54 long distance minutes, the total monthly bill is calculated as follows:

Total Monthly Bill = $19.99 + ($0.10 x (375 - 300)) + ($0.25 x 54)

Total Monthly Bill = $19.99 + $7.50 + $13.50

Total Monthly Bill = $40.99