The radius of a sphere is 6 inches. Find the length of a chord connecting two perpendicular radii.

Answer:

- The center of hyperbola is (-2 , 3)

- The left vertex, if the hyperbola opens horizontally, or the

  bottom vertex, if it opens vertically, is (-6 , 3)

- The other vertex is (2 , 3)

Step-by-step explanation:

* Lets study the equation of the hyperbola

- The standard form of the equation of a hyperbola with  

  center (h , k) and transverse axis parallel to the x-axis is

  (x - h)²/a² - (y - k)²/b² = 1, Where

- The length of the transverse axis is 2a

- The coordinates of the vertices are (h ± a , k)

- The length of the conjugate axis is 2b

- The coordinates of the co-vertices are (h , k ± b)

- The coordinates of the foci are (h ± c , k), where c² = a² + b²

* Now lets solve the problem

∵ (x + 2)²/4² - (y - 3)²/5² = 1

∵  (x - h)²/a² - (y - k)²/b² = 1

∴ a = 4 , b = 5

∴ h = -2 , k = 3

∵ The center of the hyperbola is (h , k)

∴ The center of hyperbola is (-2 , 3)

∵ The coordinates of the vertices are (h + a , k)  , (h - a , k)

∴ The coordinates of the vertices are (-2 + 4 , 3)  , (-2 - 4 , 3)

∴ The coordinates of the vertices are (2 , 3)  , (-6 , 3)

∴ The left vertex, if the hyperbola opens horizontally, or the

  bottom vertex, if it opens vertically, is (-6 , 3)

∴ The other vertex is (2 , 3)

The center of a hyperbola is determined by the coordinates (h, k) in its equation. The vertices are the points where the hyperbola intersects its major axis, and their positions depend on whether the hyperbola opens horizontally or vertically. If it opens horizontally, the left vertex is at (h - A, k), and if it opens vertically, the bottom vertex is at (h, k - B).

In the equation of a hyperbola, the center of the hyperbola can be found by identifying the coordinates (h, k). These are the constants in the denominators of the fractions on the left-hand side of the equation. For instance, in the equation ((x-h)²/A²) - ((y-k)²/B²) = 1, the center would be at the point (h, k).

The vertices of the hyperbola are the points where the hyperbola intersects its major axis. If the hyperbola opens horizontally, the left vertex will be located at the coordinate (h - A, k), and the other vertex will be at (h + A, k). If the hyperbola opens vertically, the bottom vertex will be at the coordinate (h, k - B), with the other vertex at (h, k + B).

Remember, A represents the distance from the center to a vertex along the major axis, and B represents the distance from the center to a vertex along the minor axis.

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Answer:

I can tell you that B is NOT correct as I got it wrong.  I bet the right answer is C as it is holding steady at 1:95.

Step-by-step explanation:

These are the choices for Plato

A. The exchange rate between the U.S. dollar and the yen changes from 1:95 to 1:102.

B. The exchange rate between the U.S. dollar and the euro changes from 1:95 to 1:92. - Wrong answer

C. The exchange rate between the U.S. dollar and the euro remains 1:95

Answer:

Step-by-step explanation:

From what I understand about parabolic motion in the English system, the equation for flight is

[tex]s(t)=-16t^2+v_{0}t+h_{0}[/tex]

where [tex]v_{0}t[/tex] is the initial upwards velocity and

[tex]h_{0}[/tex] is the initial height from which the object was launched.  Filling in that equation with those values gives you

[tex]s(t)=-16t^2+64t+3[/tex].  That's a.

In order to determine how long it will take the ball (or rocket...the problem is mixing up the 2) to reach its max height you need to put the equation into vertex form, since the vertex of a parabola is the absolute max (or min depending upon the parabola) of the function.  The absolute max is the heighest that the ball will go.  Completing the square is the way to solve this.  Begin by setting the equation equal to 0, the moving the 3 over by subtraction:

[tex]-16t^2+64t=-3[/tex]

Now factor out the -16 since the leading coefficient HAS to be a positive 1:

[tex]-16(t^2-4t)=-3[/tex]

Now take half the linear term (half of 4t which is 2), square it (4) and add it into the parenthesis:

[tex]-16(t^2-4t+4)=-3[/tex]

BUT since you added in a 4*-16 on the left you have to add it in on the right:

[tex]-16t^2(t^2-4t+4)=-3-64[/tex]

which simplifies to

[tex]-16(t-2)^2=-67[/tex]

Now bring the 67 over by addition and you have your vertex:

[tex]s(t)=-16(t-2)^2+67[/tex].

The vertex is (2, 67).  The 2 stands for time, so 2 seconds, and the 67 stands for feet, so at 2 seconds the max height is 67 feet.

How long it will be in the air is found by factoring to find the zeros.  These can be found by plugging the quadratic into the quadratic formula and getting that the zeros are -0.046 and 4.046

So the quadratic starts a tiny tiny bit to the left of the origin, but for all intents and purposes we can say it starts at the origin (x = 0) and ends at

x = 4.05 seconds.  Which makes sense if you know anything about parabolic motion and physics.  The vertex indicates not only the time and the max height at that time, it also is indicative of the halfway mark.  Meaning that if it takes 2 seconds to reach its max height, it will hit the ground at 4 seconds.  And 4.05 is close enought to 4 (but since you were told to round to the nearest hundredth, that .05 matters).  Sorry it's so long, but it's not a question that can be answered with just a few sentences.

Step-by-step explanation:

The triangles are congruent isosceles, therefore LM ≅ MN ≅ NO ≅ OL.

All four sides are equal, so be definition, quadrilateral LMNO is a rhombus.

Answer:

LMNO is a rhombus

Step-by-step explanation:

btw i love ur pfp! BLM

Answer:

  c(3) is the largest

Step-by-step explanation:

For positive values of x, j(x) > a(x), so the comparison is between c(x) and j(x).

Without evaluating the functions, you can subtract 5x from them to get ...

  c'(x) = c(x) -5x = 3x² +22

  j'(x) = j(x) -5x = 7x

Now the question is whether c'(3) is larger than j'(3). The latter is ...

  j'(3) = 7·3 = 21

Since c'(3) has an added constant of 22 and x² will be positive, we know that ...

  c(3) > j(3) > a(3)

The function with the largest value at x=3 is c(x).

_____

You can, of course, simply evaluate the functions:

  c(3) > j(3) > a(3) . . . . . . . c(3) is the largest

Answer:

It’s D

Step-by-step explanation:

a(x)

Answer:

Step-by-step explanation:

Apply the Pythagorean Theorem:   hyp² = 7² + (-4)² = 49 + 16 = 65.

The magnitude of this vector <7, -4> is 8.1, to the nearest tenth.

Answer:

True

Step-by-step explanation:

A negative exponent turns into positive when it is put into fraction form.

5^-2 = 1/5^2

5^-2 = 1/25

Answer:

Step-by-step explanation:

It's true. A minus power means that you put the denominator in the numerator and the numerator in the denominator. For example

(5/3)^(-2) = (3/5)^2 = 9/25

Answer:

20/28 which is about 71%

Step-by-step explanation:

so first you add up how many balls there are. 8+20=28. So 28 is the denominator for the fraction. there are 20 black balls, so that is the numerator. so 20/28 is the fraction. then you divide 20 by 28 to get the rounded percent.

Answer:

Step-by-step explanation:

m = megs age

v = vectors age

meg is 2 years older than vector   + 2

therefore

m = v +2

Answer:

6

Step-by-step explanation:

Arc length = radius * central angle

s = rθ

A circle is 2π radians, so 1/3 of that is 2/3 π.

Given that s = 12 and θ = 2/3 π:

12 = r (2/3 π)

r = 18/π

r ≈ 6

The number is 3.

3x3 is 9, which is 3 less than 12.

Answer:

The number is 5.

Step-by-step explanation:

12 plus 3 is 15.

5 x 3 = 15

15 - 3 = 12

3 less than 3 times a number is 12.

It sounds like 3 less from a number IS 12. So adding 3 to 12 will get 15, and 15 divided by 3 equals 5.

I hope this is correct and that it helps! :)

Answer:

D) No, corresponding angles are not congruent and corresponding sides are not proportional.

;]

Step-by-step explanation:

Answer:

the answer is D i just answered it with D and its correct

good luck on your assignment :)

Step-by-step explanation:

Answer:

2

Step-by-step explanation:

Kelly ran at an average speed of 8 miles per hour. If she finished the race in one and a half hours that means she ran 12 miles.

8=x

?=3/2x

12=x

We now know the road is 12 miles long. Ava has an average speed of 6 miles so she will finish it in 12/6 hours.

12/6=2

It takes Ava to finish the race in 2 hours.

Kelly ran at an average speed of 8 miles per hour.

If she finished the race in one and a half hours that means she ran 12 miles.

The average speed is the distance traveled divided by the time taken.

8=x

12=x

We now know the road is 12 miles long.

Ava has an average speed of 6 miles so she will finish it in 12/6 hours.

12/6=2hours

Therefore, It takes Ava to finish the race in 2 hours.

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Answer:

Associative property of multiplication

Explanation:

The associative property states that you can add or multiply regardless of how the numbers are grouped. By 'grouped' we mean 'how you use parenthesis'. In other words, if you are adding or multiplying it does not matter where you put the parenthesis.

Answer:

C

Step-by-step explanation:

Using the coefficients of each term and evaluating for h = - 4

- 4 | 1   - 7   - 7   20

      ↓   - 4   44   - 148

     ---------------------------

      1   - 11   37   - 128 ← remainder

Quotient = x² - 11x + 37 , R - 128

Answer:

[tex](x+3)^2 + y^2 =25[/tex]

Step-by-step explanation:

The general equation of a circle has the form:

[tex](x-h)^2 + (y-k)^2 =r^2[/tex]

Where the point (h, k) is the center of the circle and r is the radius

In this case the center is (-3, 0) and the radius is [tex]r=5[/tex]

So [tex]h=-3\\k=0[/tex]

Finally the equation of the circle is:

[tex](x-(-3))^2 + (y-0)^2 =5^2[/tex]

[tex](x+3)^2 + y^2 =25[/tex]

(X+3)^2 +y^2 =25

This is the correct answer

Check on Desmos

To solve for Sydney's age, we used an equation based on the relationship that Devaughn is 11 years younger than Sydney and the sum of their ages is 83. Solving the equation 2S - 11 = 83, we found that Sydney is 47 years old.

To find Sydney's age, we need to set up and solve an equation based on the information given: Devaughn is 11 years younger than Sydney, and the sum of their ages is 83.

Let's let Sydney's age be represented by S and Devaughn's age be represented by D. Given that Devaughn is 11 years younger than Sydney, we can express Devaughn's age as D = S - 11.

The sum of their ages is given as 83, so we can write the following equation: S + D = 83.

Substituting Devaughn's age in terms of Sydney's age, we get: S + (S - 11) = 83. This simplifies to 2S - 11 = 83. Solving for S, we add 11 to both sides, resulting in 2S = 94, and then we divide by 2 to find S = 47.

Therefore, Sydney's age is 47 years old.

Answer:

80 mph

Step-by-step explanation:

Since Natasha is driving at a rate of 4 miles every 3 minutes, we are asked to find her speed in mph. Since there are 60 minutes in an hour, we can make a proportion: 4/3 = x/60. Solving for x, we get x to be 80. So Natasha is driving at 80 miles an hour.

Answer:

80 miles per hour

Step-by-step explanation:

60 / 3 = 20

4 x 20 = 80

So if we have the number after the 36% increase in population, we would want to subtract that 36% from 51000.

36% of 51000 can be found by multiplying 51000 by 0.36 (0.36 is the decimal equivalent of 36%)

51000 x .36 = 18360

So you simply subtract 18360 from 51000, which is 32,640.

d. $0.53 because..

3/5.25 = 1/1.75

5/9.75 = 1.95

7/12.60 = 1.80

10/14.20 = 1.42

12/18.24 = 1.52

then do ;

most expensive deal - least expensive deal = how much he’ll save

1.95 - 1.42 = .53

Answer: The answer would be D.

like she said down there !

!

Step-by-step explanation:

Answer:

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

Step-by-step explanation:

It is called an inverse or reciprocal function of [tex]f[/tex] to another function [tex]f^{-1}[/tex] that fulfills that:

If [tex]f(a)=b[/tex], then [tex]f^{-1} (b)=a[/tex]

To calculate the inverse of the function [tex]y=2x+1[/tex]

[tex]f(x)=y[/tex]

So, rewritting the function

[tex]f(x)=2x+1[/tex]

Changing the x for y

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

Let's clear y

[tex]y=\frac{x-1}{2}[/tex]

Ordering the function above

[tex]y=\frac{x}{2}-\frac{1}{2}[/tex]

So, the inverse of the function [tex]f(x)=2x+1[/tex] is:

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

.

Find the area of the square, which has a side length of 2.

Area of square = 2 x 2 = 4  

Now multiply the area by the length b

Volume = 4 x 5 = 20 square units total.

Answer:18.66

Step-by-step explanation:

Answer:

A.

Step-by-step explanation:

The question is on laws of logarithms

For example to find the log₁₀ 100

⇒log₁₀ 100 = 2................how?

we take In 100 / 1n l0 = 2

where  10²=100

⇒Thus   logₓ y = In y / In x

Answer:

The length of MN is [tex]\sqrt{5}[/tex] units.

Step-by-step explanation:

The given Quadrilateral KLMN has vertices at K(-4,-1), L(-1,-1) M(-2,-5) and N(-4,-4).

We use the distance formula to find the length of MN.

[tex]|MN|=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

We plug in the values to get

[tex]|MN|=\sqrt{(-4--2)^2+(-4--5)^2}[/tex]

[tex]|MN|=\sqrt{(-2)^2+(1)^2}[/tex]

[tex]|MN|=\sqrt{4+1}[/tex]

[tex]|MN|=\sqrt{5}[/tex]

The length of MN is [tex]\sqrt{5}[/tex] units.

Answer:

B

Step-by-step explanation:

Answer:

it is d

Step-by-step explanation:

formula of sphere=4/3* pi*r cubed

Answer:

D

Step-by-step explanation:

A is nothing.

B is the surface area

C is nothing

D is the volume of a sphere.

Check the picture below.

Answer:

B. 7.5 square units.

Step-by-step explanation:

We have been given an image of a right triangle. We are asked to find area of our given triangle.

We can see that base of our given triangle is 5 units as difference between point S and point T is 5 units.

[tex]2--3=2+3=5[/tex]

The height of our given triangle (RT) is 3 units.

[tex]1--2=1+2=3[/tex]

[tex]\text{Area of triangle}=\frac{1}{2}\times \text{Base}\times \text{Height}[/tex]

[tex]\text{Area of triangle}=\frac{1}{2}\times \text{5 units}\times \text{3 units}[/tex]

[tex]\text{Area of triangle}=\frac{1}{2}\times 15\text{ units}^2[/tex]

[tex]\text{Area of triangle}=7.5\text{ units}^2[/tex]

Therefore, area of our given triangle is 7.5 square units and option B is the correct choice.

Answer:

The solution is (-3, 10.8)

Step-by-step explanation:

While it's rather obvious that you want to solve this system of linear equations, you should share that instruction when you post the problem.

To solve this system using elimination by addition and subtraction, combine the two equations as shown below (to eliminate y):

-0.18x + y = -6.54

-2.8x - y = -2.4

--------------------------

-2.98x = -8.94

Dividing both sides by -2.98, to isolate x, yields:  x = -8.94 / (-2.98) = -3.

Then x = 3.  Find y from -2.8x - y = -2.4:  -2.8x + 2.4 = y, and here,

y = -2.8(-3) + 2.4 = 8.4 + 2.4 = 10.8

Then the solution is (-3, 10.8)

Cosidering the ray BC.

It is clear that:

1) A ray starts from one point and extends infinitely in ONE direction.

2) The ray BC cannot be measured. But the line-segment BC can be Measured.

3) B and C are the only two points on the given ray.

Hence the statement: "There are only two points on the entire ray" is the correct one.

Hope it helps...

Regards;

Leukonov/Olegion.

The ray given in the figure is passing in one direction and does not have a finite length as far as the ray segment is considered so options (A), and (D) are true.

A line section that can connect two places is referred to as a segment.

In other words, a line segment is just part of a big line that is straight and going unlimited in both directions.

The line is here! It extends endlessly in both directions and has no beginning or conclusion.

Given,

A ray is passing through points B and C.

(A) The ray extends infinitely in one direction which is True.

(D) There are only two points on the entire ray which is also true.

Hence, The ray given in the figure is passing in one direction and does not have a finite length as far as the ray segment is considered.

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