How long is the minor axis for the ellipse shown below?

(x+3)^2/64 + (y-7)^2/4=1

A. 16
B. 4
C. 8
D. 64

Imagine is shown above.

How Long Is The Minor Axis For The Ellipse Shown Below?(x+3)^2/64 + (y-7)^2/4=1A. 16B. 4C. 8D. 64Imagine

Answers

Answer 1

The length of the minor axis is 4

Step-by-step explanation:

Step 1 :

The given equation  is  [tex]\frac{(x-3)^{2}}{64} + \frac{(y-7)^{2}}{4} = 1[/tex]

Here we see the denominator below the variable x is greater than below y. Hence the ellipse's major axis and the minor axis are parallel to x-axis  and  y-axis respectively

Step 2 :

The square of the semi minor axis will be the denominator of the y variable. So in the given ellipse ,

the square of the semi minor axis = 4

Hence the length of the semi minor axis  = [tex]\sqrt{4}[/tex]  = 2

Step 3 :

The length of the minor axis = 2 times the length of the semi minor axis

                                               = 2 × 2 = 4

Answer :

The length of the minor axis is 4

Answer 2

Final answer:

The length of the minor axis of the given ellipse is 4 units, as the semi-minor axis length is derived from the square root of the denominator of the y-term in the ellipse equation. The correct option is B.

Explanation:

The minor axis of an ellipse is the shortest diameter of the ellipse, and it runs perpendicular to the major axis. In the given equation of the ellipse, (x+3)²/64 + (y-7)²/4=1, the denominators of the fractions correspond to the squares of the semi-axes lengths. Therefore, the length of the semi-minor axis 'b' is the square root of 4, which is 2. Since the minor axis is twice the length of the semi-minor axis, we must multiply 2 by 2 to get the length of the minor axis, which is 4.

So the correct answer for the length of the minor axis for the given ellipse is 4 units, which corresponds to option B.


Related Questions

A mother gives birth to a 9 pound baby. Every 4 months, the baby gains 2 pounds.
If x is the age of the baby in months, then y is the weight of the baby in pounds.
Find an equation of a line in the form y = mx + b that describes the baby's weight.

Answers

Answer:

y=2/4x+9

Step-by-step explanation:

If 3 hamburgers cost $4.20, then how much does 1 hamburger cost?

Answers

Answer:

$1.40

Step-by-step explanation:

Divide 4.20 by 3.

Answer:

$1.4

Step-by-step explanation:

The price of one hamburger will be equal to the total price of the hamburgers divided by the number of hamburgers .

Therefore $4.20/3

$1.4

So each hamburger cost $1.4

Which of the following is the solution to the compound inequality below? 5+ x >3 or 6x +1 <-29

Answers

Final answer:

The solution to the compound inequality is x > -2 and x < -5, or (-∞, -5) ∪ (-2, ∞).

Explanation:

To find the solution to the compound inequality, we need to solve the individual inequalities separately and then find the intersection of their solution sets.

First, solve the inequality 5 + x > 3:
5 + x > 3
x > 3 - 5
x > -2Next, solve the inequality 6x + 1 < -29:
6x + 1 < -29
6x < -29 - 1
6x < -30
x < -5

The solution to the compound inequality is the intersection of the solution sets of the individual inequalities, so the solution is x > -2 and x < -5. To express this in interval notation, we write (-∞, -5) ∪ (-2, ∞).

Learn more about Compound inequality here:

https://brainly.com/question/20296065

#SPJ12

The linear equation y=2x represents the cost y for x pounds of apples.Which ordered pair lies on the graph of the equation?

Answers

Answer:(1,2), (2,4), (3,6), and alot more here is the graph so you can see!

Step-by-step explanation: hope this helps have a great day!

Let f(x)= x2 - 14 and g(x) = 6-X.
Find (fq)(7).

Answers

Answer:

[tex](fg)(7) = - 35[/tex]

Step-by-step explanation:

The given functions are:

[tex]f(x) = {x}^{2} - 14[/tex]

and

[tex]g(x) = 6 - x[/tex]

We want to to find

[tex](fg)(7)[/tex]

Note that:

[tex](fg)(x) = f(x) \times g(x)[/tex]

We substitute the functions to obtain:

[tex](fg)(x) = ( {x}^{2} -1 4 ) \times (6 - x)[/tex]

We now substitute x=7, to get:

[tex](fg)(7) = ( {7}^{2} -1 4 ) \times (6 - 7)[/tex]

This implies that

[tex](fg)(7) =( 49-1 4 ) \times (6 - 7)[/tex]

[tex](fg)(7) = 35 \times - 1 = - 35[/tex]

fraction between - 3/4 and - 1/3

Answers

We simplify the fractions to a common denominator=-9/12 and -4/12

-6.5/12 which turns into -13/24.

So, -13/24 is the fraction between -3/4 and -1/3.

I hope this helps!

Your graphing the speed your car goes on the interstate from the time you enter the ramp until you arrive at the next exit ramp 6 miles away. The speed of the highway is 70 mph. The X axis represents time and Y represents speed. The graph has five tick marks on the X axis and 10 tick marks on the Y axis. What would be a good scale for each axis?

Answers

Answer:

1 minute on the x-axis; 10 mph on the y-axis

Step-by-step explanation:

The distance between exit ramps is less than 6 miles and since you are traveling at 70 mph on the highway you should get there in less than 5 mins, so the scale on the x-axis should be 1 minute. Since you have 10 tick marks on the y-axis and will be going at a speed of 70 mph at some point, the scale on the y-axis should be 10 mph (100 mph total). A good scale would be 1 minute on the x-axis; 10 mph on the y-axis.

Answer:

1 minute on the x-axis; 10 mph on the y-axis

Step-by-step explanation:

Is 5(2x-3y) and 10x-3y equivalent?

Answers

Answer:

No

Step-by-step explanation:

Apply the distributive property to 5(2x - 3y):

Multiply 5 by each term inside the parentheses.

5(2x - 3y) = 10x - 15y

The other expression is 10x - 10y.

The terms 10x in both expressions are equal.

Since the term -15y is not equal to the term -10y, the expressions are not equivalent.

Two cylinders are similar. The volume of the larger cylinder is 343ft3 and the volume of the smaller cylinder is 125ft3. The height of the smaller cylinder is 5ft. What is the height of the larger cylinder? Enter your answer in the box.

Answers

Answer:

The answer would be 7ft.

Step-by-step explanation:

Let the radius of the cylinder be rft. and its height be hft. Again the radius of the larger cylinder is R ft and its height is H ft. Given h = 5 ft.

As the cylinders are similar we can say   [tex]R/r[/tex] = [tex]H/h[/tex]

Now the volume of the smaller cylinder is  πr²h = 125

and that of larger one is   πR²H = 343

SO  πR²H/πr²h = 343/125

⇒ H²/h² × H/h = 343/125

⇒ H³/h³ = 7³/5³

⇒ H/h = 7/5

⇒ H =  7/5 × h = 7/5 × 5 = 7ft

Hope this Helped:)

a hammer that normally sells for $24 is on sell for $12. what percentage is the discount?

Answers

Answer:

50%

Step-by-step explanation:

You can figure out the percentage that it is off by diving the price it is not at (12) by the full amount (24) and then multiplying it by 100 because it is a percent.

(12/24)= 0.5

(0.5)*(100)= 50%

Use the distributive property to write an expression that is equivalent to each given expression.
-3(2x - 4)

Answers

Answer:-6x+12

Step-by-step explanation:-3 • 2x = -6x

-3 • -4 = 12. Distribute the -3 to both numbers in the parentheses

The answer or expression is: -6 • (x - 2)

Jacob copies 30% of a document. He copies 8 pages. Write the number of pages in the
document.​

Answers

Answer:

27

Step-by-step explanation:

Number of documents

jacob copies 30% of a document which is 8 pages

we can solve this using cross multiplication

30 %       :        8

100%      :         x

30%x = 100%*8

30% x = 8

x = 8/ 30%

x = 26.667

to 2sf

number of pages in the documents 27

There are 27 pages in the doc

Tom rented a truck for one day. There was a base fee of 19.95 , and there was an additional charge of 85 cents for each mile driven. Tom had to pay 216.30 when he returned the truck. For how many miles did he drive the truck?

Answers

Answer:

231 miles.

Step-by-step explanation:

Tom rented a truck with a base fee of 19.95. You will subtract this from the total since you just want to get the mileage.

Tom is getting charged .85 cents per mile driven.

Tom payed 216.30 subtotal minus the 19.95 base fee since we are trying to only see how many miles he drove.

(216.30-19.95=196.35) This will be total for each mile. All we need to do is divide to get the total of miles

(196.35÷.85= 231)

231 is the number of miles Tom drove.

Vanessa's cell phone company charges $45 for a monthly fee and $0.03 for each text sent If Vanessa's bill is $76.23, how many texts did Vanessa send?

A.)94
B.)141
C.)1,041
D.)3,974​

Answers

The answer is C. 1041

Answer:

C

Step-by-step explanation:

I chose C and got it right.

Let event A = the place is a city let B = the place is in North America what is P(A and B)

A. 5/7
B. 3/7
C.4/7
D.2/7

Answers

Answer:

  D. 2/7

Step-by-step explanation:

We assume that the intention is that one of the places is chosen at random from the list of 7 places.

2 of those are cities in North America, so the probability that a place randomly chosen from this list is a city in North America is ...

  P(A & B) = 2/7

Answer: 4/7

Step-by-step explanation:

write an expression that represents the edge length of jewelry box

Answers

Answer:

The cubed-root of v (/v)

Step-by-step explanation:

Like your work on the second question illustrated, the cubed root of v (which is 216) is your expression for the edge length of the box in inches.

Hope this helps!

Step-by-step explanation:

Part A

Since volume of jewelry box is v cubic inches

Therefore,

Answer: Length of edge = v inches

Part B

Answer: 6 inches

the root of quadratic equation are (3-√3) and (3+√3). find its equation​

Answers

Answer: [tex]x^{2} - 6x +6 = 0[/tex]

Step-by-step explanation:

The formula for finding quadratic equation is given as :

[tex]x^{2}[/tex] - sum of roots[tex](x)[/tex] + product of roots = 0

sum of roots implies :

(3-√3)+(3+√3) =6

product of roots implies :

(3-√3) x (3+√3) = 9 +[tex]3\sqrt{3}[/tex] - [tex]3\sqrt{3}[/tex] - 3

(3-√3) x (3+√3) = 6

substituting into the equation we have:

[tex]x^{2} - 6x +6 = 0[/tex]

You have 20 quarters. You find 40% more quarters in your room. Then you go shopping and spend 50% of the total number of quarters. Write a expression that represents the total number of quarters you take with you when you go shopping. How much money do you have left

Answers

Answer:

a) 28 quarters

b) 14 quarters  

Step-by-step explanation:

We are given the following in the question:

Number of quarters = 20 quarters

Number of quarters in room = 40%

Total number of quarter in room =

[tex]=40\%\times (20)\\\\=\dfrac{40}{100}\times 20\\\\=8[/tex]

Thus, the total quarters taken to shopping =

[tex]=20 +40\%\times (20)\\\\=20+8\\=28[/tex]

Thus, 28 quarters were taken to shopping.

Quarter spent on shopping = 50%

Total number of quarter spent in shopping =

[tex]=50\%\times (28)\\\\=\dfrac{50}{100}\times 28\\\\=14[/tex]

Money left =

Money taken for shopping - Money spent

[tex]= 28-14\\=14[/tex]

Thus, we are left with 14 quarters after shopping.

4x+6=2x+10 find value of x makes equation true

Answers

Answer:

x = 2

Step-by-step explanation:

[tex]4x + 6 = 2x + 10 \\ \\ 4x - 2x = 10 - 6 \\ \\ 2x = 4 \\ \\ x = \frac{4}{2} \\ \\ x = 2[/tex]

Which statements are true?

Select each correct answer.



a. 30x4−12x3=6x3(5x−2)
b. 4x2+10x=2x(2x+5)
c. 100x3+5=5x3(20x+1)
d. 8x3−6x=2x3(4−3x3)

Answers

Answer:

30x^4−12x^3=6x^3(5x−2) = True

4x^2+10x=2x(2x+5) = True

100x^3+5=5x^3(20x+1) = False

8x^3−6x=2x^3(4−3x3) = False

Step-by-step explanation:

The statements which are true are 30x4−12x3=6x3(5x−2) ,  4x2+10x=2x(2x+5)  and  100x3+5=5x3(20x+1)

To determine which of the statements are true, we can simplify each equation and compare.

Option a :

30x4−12x3=6x3(5x−2): Factoring out the common term we can see this equation is true.
Option b:

4x2+10x=2x(2x+5): After simplifying both sides we find that 2x(2x + 5) = 4x2 + 10x, so statement (b) is true.

Option c:

100x3+5=5x3(20x+1): Attempt to simplify this equation as 5x3(20x + 1). Since this simplification holds, statement (c) is also true.

Option d:

8x3−6x=2x3(4−3x3): Simplifying the right side does not give us the left side; thus, statement (d) is false. The correct form would be 2x(4x2 - 3), assuming a typo in exponent notation.

Find the sum or difference. Write your answer in the simplest form. 5 1/3 + 6 1/6

Answers

Answer:

The answer for addition one is 11 1/2. The answer for subtraction would be -5/6.

Hope this helps. Can I please get brainliest if possible?

The answer you are looking for is 11 and 1/2.

To find this answer, you must first add the fractions together. Before you do so, you must make sure they have a common denominator. So, multiply 1/3 by 2/2 to get 2/6. Now, add 2/6 and 1/6 to get 3/6. 3/6 simplified (divided by 3/3) is 1/2.

Next, add the whole numbers. 5 + 6 is 11. Thus making your final answer 11 and 1/2.

I hope this helps!

£2300 is invested for 4 years at 5% per year simple interest. Work out the total interest

Answers

Answer: £460

Step-by-step explanation:

Use this formula to find the total interest [tex]I=\frac{P*R*T}{100}[/tex]

I stands for interest, P is principal, R is rate, and T is time.

Principle = £2300

Rate = 5%

Time = 4 years

[tex]\frac{2,300*5*4}{100} =\frac{46,000}{100} =460[/tex]

Hope this helps, now you know the answer and how to do it. HAVE A BLESSED AND WONDERFUL DAY! :-)  

- Cutiepatutie ☺❀❤

Answer:

£460

Step-by-step explanation:

Simple interest =PRT/100

Where P = principal

R= rate

T = Time

Given

P= £2300

T= 4yrs

R = 5%

Interest = 2300 x 5 x 4/100

Multiply through

Interest = 46000/100

Interest = £460

Solve y = 1/-25 x 8 + 175

Answers

Answer:

174.68

Step-by-step explanation:

Use PEMDAS. First, multiply 1/-25 by 8. (-8/25 or-.32)

Then, add 175 and y should= 174.68.

I need help fast (26 POINTS!!)

Answers

First you multiply 4 by 5
4x5=20

Then you subtract 3 since he ate 3
20-3=17

And that’s your answer

A person buys 3 shirts for 42.00 how much would 8 shirts costs at that same price

Answers

Answer:

$112

Step-by-step explanation:

a bag is filled with 191 silver coins and 33 gold coins for what is the theoretical probability of pulling out a silver coin​

Answers

Answer:

191/224

Step-by-step explanation:

1991+33= 224

191/224

Answer:

191/240\

Step-by-step explanation:

which shape does NOT have perpendicular
perpendicular lines? Mark your answer.​

Answers

Answer:

Perpendicular lines are lines that cross one another at a 90° angle. They have slopes that are opposite reciprocals of one another. Unlike parallel lines that never touch, perpendicular lines must intersect.

Therefore, the shape with 2 lines that don't intersect/touch each other, is the shape that does not have perpendicular lines.

riangles have perpendicular sides, rectangles have both perpendicular and parallel sides, but other quadrilaterals might not.

Jill drove the 200 miles to Cincinnati at an average speed of 10 miles per hour faster than her usual average speed. If she completed the trip in 1 hour less than usual, what is her usual driving speed, in miles per hour

Answers

Let [tex]v[/tex] be the usual speed, and [tex]t[/tex] be the usual time.

Following the equation [tex]s=vt[/tex], where s is the space, v is the velocity and t is time, we know that usually we have

[tex]200=vt[/tex]

But this time we were 10mph faster and it took one hour less, so we have

[tex]200=(v+10)(t-1)[/tex]

Since both right hand sides equal 200, they must equal each other:

[tex]vt=(v+10)(t-1)=vt+10t-v-10 \iff 10t-v-10=0 \iff v=10t-10[/tex]

Plug this value in the first equation and we have

[tex]200=vt=(10t-10)t \iff 10t^2-10t-200=0[/tex]

This equation has solutions [tex]t=-4,\quad t=5[/tex]. We can only accept positive solutions, so we have t=5. We finally deduce, again from the first equation,

[tex]200=5v \iff v=\dfrac{200}{5}=40[/tex]

What is the slope intercept form of 11x+3y=-32

Answers

Answer:

y=−113x−323

Step-by-step explanation:

there u go

It is y=-11/3x-32/3 because it needs to be written in this format

What’s the answer to this?

Answers

Answer:

  P'(-3, 5)

Step-by-step explanation:

The transformation for a 90° rotation CCW is ...

  (x, y) ⇒ (-y, x)

  (5, 3) ⇒ (-3, 5)

The coordinates of the rotated point are (-3, 5).

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