The radii of earth and Pluto are 6,371 kilometers and 1,161 kilometers, respectively. Approximately how many spheres the size of Pluto does it take to have the same volume as earth?

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.

Answer:

It´s x2/16-y2/1=1

Step-by-step explanation:

The equation of the hyperbola is x²/16 - y²/1 =1

A symmetrical open curve formed by the intersection of a circular cone with a plane at a smaller angle with its axis than the side of the cone. A plane curve generated by a point so moving that the difference of the distances from two fixed points is a constant : a curve formed by the intersection of a double right circular cone with a plane that cuts both halves of the cone.

Given here: hyperbola with center at (0, 0), with x-intercepts at (4, 0) and (-4, 0), with b = 1 . Now we know The standard equation of the hyperbola is [(x²/a²) – (y²/b²)] = 1, where the X-axis is the transverse axis and the Y-axis is the conjugate axis.

Therefore the hyperbola opening horizontally has the equation with  x-intercepts at (4, 0) and (-4, 0), with b = 1 is x²/16 - y²/1 =1

Hence, The equation of the hyperbola is x²/16 - y²/1 =1

Learn more about the hyperbola here:

https://brainly.com/question/28989785

#SPJ2

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.

https://brainly.com/question/24875240

#SPJ12

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 domain of a graph represents the set of all the possible x-values for a function. In the context of this question, the domain could represent all the possible time values it took for water to be pumped out of the pond. However, the exact domain can't be identified without specific graph or additional information.

To determine the domain of the graph related to the water being pumped out of a backyard pond, you would need to consider the horizontal range of the graph. The domain of a graph in mathematics represents the set of all the possible x-values that the function can have. In the context of this problem, the domain could represent the time over which the water was being pumped out. The dependence of the quantity of water on the time creates a function whose domain (all possible time values during the pumping) we are looking for. However, without the specific graph or additional information, we cannot directly identify the domain.

https://brainly.com/question/36431937

#SPJ11

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.

see attached picture

answer is 66 with remainder of 5

Answer: The remainder is 5

Step-by-step explanation:

599 /9

59 / 9 = 6

6 ×9 = 54

that means remainder 5

Join the 5 beside the last 9, making it 59 again

repeat the first process again, i.e 59/9 = 6

6×9 = 54

Remaining 5

Therefore 9 can go into 599, 66times with a remainder of 5

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]%

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: 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.'

https://brainly.com/question/19222807

#SPJ3

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:

https://brainly.com/question/17267403

#SPJ6

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)

Answer:

x-axis

Step-by-step explanation:

26 letters each place, 10 numbers each place

26 x 26 x 26 x 10 x 10 x 10 x 10 = 175,760,000 different plates can be made