Find the 6th term of a geometric sequence t3=444 t7=7104

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.

Answer:

x-axis

Step-by-step explanation:

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.

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)

Final answer:

In an isosceles triangle with angles B and C congruent, and with m∠A equal to 40°, the equation to find x is 40° + 2(3x + 1)° = 180°. Solving this equation yields x = 23°, which corresponds to option b.

Explanation:

Since ΔABC is an isosceles triangle and angles B and C are congruent, m∠B = m∠C. Given that m∠A = 40°, we can set up an equation to find x since the sum of all angles in a triangle equals 180°.

Equation: 40° + (3x + 1)° + (3x + 1)° = 180°

Combining like terms:

40° + 2(3x + 1)° = 180°

40° + 6x + 2° = 180°

6x + 42° = 180°

6x = 180° - 42°

6x = 138°

x = 23°

Therefore, the value of x is 23°, which corresponds to option b.

Answer:

Answer is approx 12%

Step-by-step explanation:

Total land owned by Andre = [tex]\frac{1}{4}=0.25[/tex] acres

He wants to construct a 120 feet x 80 feet tennis court on the lot.

Means the area of the court will be = [tex]120\times80=9600[/tex] square feet.

9600 square feet = 0.22 acres (divide the area value by 43560  as 1 acre has 43560 sq feet)

Area left in acres = [tex]0.25-0.22=0.03[/tex] Acres

Hence, the approximate percentage left over will be = [tex]\frac{0.03}{0.25}\times100= 12[/tex]%

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

The graph shown in option C. is the correct representation of the equation [tex]y = \dfrac{3}{4}x -3[/tex].

A graph means a visual representation of a set of entities, known as vertices or nodes, interconnected by connections, called edges.

Follow the following steps to draw the graph of the given equation:

Thus, the line [tex]y = \dfrac{3}{4}x -3[/tex] is plotted.

Learn more about Graphs here:

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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: b

Step-by-step explanation: i got it right

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)

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 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.

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

Answer: The converse of the given statement is if  [tex]x^2=9[/tex] ,then x=3.→ which is not true.

We cannot form a biconditional statement for the  given statement because the converse is not true.

Step-by-step explanation:

Given statement: If x = 3, then [tex]x^2=9[/tex]

The converse statement of conditional statement that "if p then q" is "if q then p".

therefore, the converse of the given statement is if  [tex]x^2=9[/tex] ,then x=3.

But the converse is not true since if  [tex]x^2=9[/tex] then x can be 3 or -3 .

∵  [tex]3^2=9[/tex] and  [tex](-3)^2=9[/tex]

 A biconditional statement is true if and only if both the conditional statement and its converse are true.

Therefore, we cannot form a biconditional statement for the  given statement because the converse is not true.

The converse of the conditional statement 'If x=3, then x²=9' is 'If x²=9, then x=3'. As both these statements are true, they can be combined into a biconditional statement 'x=3 if and only if x²=9'.

In your question, you asked how to write the converse of a given conditional statement and then combine them if the converse is also true. The original conditional statement is 'If x = 3, then x² = 9.' The converse of this statement would be 'If x² = 9, then x=3.' In this case, the converse is also true because if x² equals 9 then x does indeed equal 3. Therefore, we can combine the conditional statement and its converse into a biconditional statement: 'x = 3 if and only if x² = 9.'

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