Loki wrote 1/6 of a page in 1/12 of a minute. How much time does it take him to write a full page?

Answer:

a) The location of the center of the ellipse is [tex](4,-6)[/tex]. It is determine by knowing the location of foci and Midpoint formula.

b) The standard equation of the ellipse is [tex]\frac{(x-4)^{2}}{31}+\frac{(y+6)^{2}}{81} = 1[/tex].

c) Major semiaxis ([tex]a[/tex]): [tex]a = 9[/tex], Minor semiaxis ([tex]b[/tex]): [tex]b = \sqrt{31}[/tex]

Step-by-step explanation:

a) Foci are located in the major axis of the ellipse, given the locations of ends of the major axis and locations of the foci. We can determine the location of the center of the ellipse by Midpoint formula:

[tex](h,k) = \frac{1}{2}\cdot F_{1}(x,y) + \frac{1}{2}\cdot F_{2} (x,y)[/tex] (1)

Where [tex]F_{1} (x,y)[/tex] and [tex]F_{2} (x,y)[/tex] are the locations of the foci.

If we know that [tex]F_{1}(x,y) = (4, -6-5\sqrt{2})[/tex] and [tex]F_{2} (x,y) = (4,-6+5\sqrt{2})[/tex], then the location of the center of the ellipse is:

[tex](h,k) = (4, -6)[/tex]

The location of the center of the ellipse is [tex](4,-6)[/tex]. It is determine by knowing the location of foci and Midpoint formula.

b) Now we need to determine the length of each semiaxis:

Major semiaxis ([tex]a[/tex])

[tex]a = \sqrt{[V_{2}(x,y)-(h,k)]\,\bullet\,[V_{2}(x,y)-(h,k)]}[/tex] (2)

[tex]V_{2}(x,y)-(h,k) = (4,3)-(4,-6)[/tex]

[tex]V_{2}(x,y) - (h,k) = (0, 9)[/tex]

[tex]a = 9[/tex]

Please notice that [tex]V_{2}(x,y)[/tex] is one of the vertices of the ellipse in the major axis.

Distance between focus and center ([tex]c[/tex])

[tex]c = \sqrt{[F_{2}(x,y)-(h,k)]\,\bullet\,[F_{2}(x,y)-(h,k)]}[/tex]

[tex]F_{2}(x,y) -(h,k) = (4-4,-6+5\sqrt{2}+6)[/tex]

[tex]F_{2}(x,y) - (h,k) = (0, 5\sqrt{2})[/tex]

[tex]c = 5\sqrt{2}[/tex]

Minor semiaxis ([tex]b[/tex])

[tex]c^{2} = a^{2}-b^{2}[/tex] (3)

[tex]b = \sqrt{a^{2}-c^{2}}[/tex]

If we know that [tex]a = 9[/tex] and [tex]c = 5\sqrt{2}[/tex], then the length of the minor semiaxis is:

[tex]b = \sqrt{31}[/tex]

In this case, the standard equation of the ellipse is defined by this formula:

[tex]\frac{(x-h)^{2}}{b^{2}}+\frac{(y-k)^{2}}{a^{2}} = 1[/tex]

If we know that [tex]a = 9[/tex], [tex]b = \sqrt{31}[/tex] and [tex](h,k) = (4, -6)[/tex], then the standard equation of the ellipse is:

[tex]\frac{(x-4)^{2}}{31}+\frac{(y+6)^{2}}{81} = 1[/tex]

The standard equation of the ellipse is [tex]\frac{(x-4)^{2}}{31}+\frac{(y+6)^{2}}{81} = 1[/tex].

c) The lengths of the axes are, respectively:

Major semiaxis ([tex]a[/tex]): [tex]a = 9[/tex]

Minor semiaxis ([tex]b[/tex]): [tex]b = \sqrt{31}[/tex]

Answer:

a) The location of the center of the ellipse is . It is determine by knowing the location of foci and Midpoint formula.

b) The standard equation of the ellipse is .

c) Major semiaxis (): , Minor semiaxis ():

Step-by-step explanation:

Answer:

yee its 34ft..........

Height of the school building is equals to 34ft.

" Height is defined as one of the dimension which represents the distance between base and the top."

Formula used

Pythagoras theorem

(Hypotenuse)² = (Opposite side)² + (adjacent side)²

According to the question,

'h+ 10 ' represents the height of the building

As shown in the figure,

In the right triangle

' Hypotenuse' represented by length of the cable = 25ft

Adjacent side = 7ft

'h' is the height of the triangle

Substitute the value in the Pythagoras theorem we get,

  [tex](25)^{2} = 7^{2} + h^{2}[/tex]

⇒ [tex]h^{2} = 625 - 49[/tex]

⇒ [tex]h = \sqrt{576}[/tex]

⇒ [tex]h = 24[/tex] ft.

Therefore,

Height of the school building [tex]' h + 10 '= 24 + 10[/tex]

                                                              [tex]= 34[/tex] ft.

Hence, height of the school building is equals to 34ft.

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Answer:

71 feet below the water.

Step-by-step explanation:

x=the divers position relative to the surface

when x=0, the diver is at the surface.

when x=-24, the diver is 24 feet below the surface, therefore -24-47=-71.

Answer:

Part A is no because after subtracting it is 6/10 and 6/10 is not equal to 1/2

Step-by-step explanation:

First you make the fraction's denominator equal

2/5 = 4/10

Camen's water bottle is 1 8/10

Jorge's water bottle is 2 4/10

1/2 = 5/10

Make the fractions into a improper fraction

Camen's is 18/10

Jorge's is 24/10

subtract it

24 - 18 = 6

So Part A is no because after subtracting it is 6/10 and 6/10 is not equal to 1/2

Answer:

AB = [tex]\frac{108}{7}[/tex]

Step-by-step explanation:

Δ ALM and Δ ACB are similar, then the ratios of corresponding sides are equal, that is

[tex]\frac{AM}{AB}[/tex] = [tex]\frac{AL}{AC}[/tex] , substitute values

[tex]\frac{12}{AB}[/tex] = [tex]\frac{14}{18}[/tex] = [tex]\frac{7}{9}[/tex] ( cross- multiply )

7AB = 108 ( divide both sides by 7 )

AB = [tex]\frac{108}{7}[/tex] ( = 15 [tex]\frac{3}{7}[/tex] )

Answer:

Ans = 76

Step-by-step explanation:

10y + [tex]x^{2}[/tex]

=> 10 * 4 + [tex]6^{2}[/tex]

=> 40 + 36

=> 76

Hope it helps :)

Answer: first one

Step-by-step explanation:

Answer:

254.34 in^2

Step-by-step explanation:

Answer:

g = 10

Step-by-step explanation:

-1.3g + 1.9 = -11.1

-1.3g = -11.1 - 1.9

-1.3g = -13

g = 10

answer:

11x

step-by-step explanation:

x + 4x + 6x

= 11x

Answer:

11x

Step-by-step explanation:

just add them all together

x + 4x = 5x

5x + 6x = 11x

hope this helps :)

Answer:

The answer would be C. Inference

Answer:

Step-by-step explanation:

Use Pythagorean

Answer:

in right angled triangle BCD

by using Pythagoras law

P²+B²=H²

A²+B²=C²

36²+18²=x²

x=√1620=18√5m

x=18√5 m is your answer

Where exactly are the alleged statements?

Answer:

280 Cubic inches

Step-by-step explanation:

When finding the volume, the equation is V=l*w*h

Therefore, the equation should be:

10.1*3.9*6.8

This is equal to exactly 267.852

However, the answer is 280 cubic in. because it's a larger number and it's about 13 from the actual answer. On the other hand, 250 cubic in. is about 17 from the actual number.

Answer: The answer should be 39 yard line

Step-by-step explanation: If you start at the 50 and remove 11 yards you will have 39 yards left

Answer:

Pizzas: $8, Breadsticks: $3

Step-by-step explanation:

1. Write an equation.

Let the variables p = price of pizzas, and b = price of breadsticks

The equation: 3p + 2b = $30 for the first customer. The equation: 4p + 3b = $41 for the other customer.

2. Use the Elimination Method.

 (4p+3b=41) x3 =  12p+9b=123

- (3p+2b=30) x4 = 12p+8b = 120

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

                                     8b = 3

Pizzas: $8

Breadsticks: $3

Answer:

17.25

Step-by-step explanation:

Ratio of clean clothes to dirty clothes = 3 : 5

Clean clothes = 3

Dirty clothes = 5

Total ratio = 3 + 5 = 8

Total clothing article = 46

how many were clean

Number of clean clothes = ratio of clean clothes / total ratio × total clothing article

= 3/8 × 46

= 0.375 × 46

= 17.25

Answer:

Event A = 1/3

Event B = 1/6

Step-by-step explanation:

The probability of drawing a number between 1 and 10 (Event A) is approximately 0.3333 or 33.33%.

To calculate the probability of Event A, we need to determine the total number of favorable outcomes (numbers between 1 and 10) and divide it by the total number of possible outcomes (all numbers from 1 to 30).

Counting the favorable outcomes:

Event A consists of numbers between 1 and 10. So, there are 10 favorable outcomes: {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}.

Counting the total possible outcomes:

The hat contains numbers from 1 to 30. So, there are 30 possible outcomes: {1, 2, 3, ..., 30}.

Calculating the probability of Event A (P(A)):

The probability of an event is given by the formula:

P(A) = (Number of Favorable Outcomes) / (Total Number of Possible Outcomes).

In this case,

P(A) = 10 (favorable outcomes) / 30 (total possible outcomes)

P (A) = 1/3 ≈ 0.3333 or 33.33%.

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Answer: neither Game A nor Game B is fair

Step-by-step explanation:

Answer:

Game A is not fair, and game B is fair.

Step-by-step explanation:

i took the iready tesyt

Answer:

√8x^7y^8

= 2x^3y^4 √2x

answer is C. third choice

Step-by-step explanation:

The expression is equivalent to given expression is [tex]2^{\frac{3}{2} }x^{\frac{7}{2} }.y^4[/tex].

Equivalent expressions are expressions that work the same even though they look different. If two algebraic expressions are equivalent, then the two expressions have the same value when we plug in the same value for the variable.

The given expression is √(8x⁷y⁸).

Here, √(8x⁷y⁸)

= [tex](8x^7y^8)^{\frac{1}{2} }[/tex]

= [tex]2^{\frac{3}{2} }x^{\frac{7}{2} }.y^{\frac{8}{2} }[/tex]

= [tex]2^{\frac{3}{2} }x^{\frac{7}{2} }.y^4[/tex]

Therefore, the equivalent expression is [tex]2^{\frac{3}{2} }x^{\frac{7}{2} }.y^4[/tex].

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Answer:

rational

Step-by-step explanation:

if it does not terminate nor become periotic it is irrational other wise it is rational

Answer:

the length of room is 24 feet

Step-by-step explanation:

Let the breadth be x .

Then, Length, l = x + 9

According to the question,

Area of rectangle = length × breadth

Putting the values of length and breadth, we get:

360 = ( x + 9 ) x

360 = x² + 9x

x² + 9x - 360 = 0

x² + 24x - 15x - 360 = 0

x( x + 24) - 15(x + 24) = 0

( x + 24 ) = 0 or ( x - 15 ) = 0

x = - 24 or x = 15 [ Negative number is ignored ]  

Now,  

Length, l = x + 9 = 15 + 9 = 24 feet

Thus, the length of room is 24 feet .

Answer:

yes, school is hard

thanks for points

have a good day ....❤

Answer:

The mistake is in step 1 when you do -2(x+4) you do the distributive property first -2 times x is -2x that's correct but -2 times 4 is not 8 it is -8

when you multiply by negatives the answer will always be a negative unless your multiply 2 negative number together then itll be positive ex. 4 × -4 = -16 (negative) but -4 × -4 = 16 (positive)

Answer:

(-2, 6)

Step-by-step explanation:

Plug in one of the equations into the y-variable (doesn't matter which):

2x + 10 = -4x - 2

Combine like terms by adding the 4x to both sides. This makes it cancel out on the right side, and 2x + 4x on the right side is 6x:

6x + 10 = -2

Combine like terms by subtracting 10 from both sides, making it cancel out on the left side, and on the right: -2 - 10:

6x = -12

Then isolate the x-variable by dividing both sides by 6:

x = -2

Taking the -2, plug it into an x-variable in either of the equations:

y = 2x +10

y = 2(-2) + 10

y = -4 + 10

y = 6

Answer:

y = 0 feet

Step-by-step explanation:

Given equation:

y = 25x

Where,

y = height (feet)

x = time (seconds)

25 = constant

Find the height of the elevator when the time is 0 seconds

y = 25x

y = 25(0)

y = 0 feet

The other no. is:

32

As you can see that in the ratio given, 3 is the smaller no. and 12 too.

So when we divide 12 by 3, we get 4

Then to find the other no. we need to multiply 4 with 8 (which is the other no.          in the ratio given)

Therefore, we get the other no. as 32

And also when you divide 12 by 32,

You get the answer as 3 by 8 (which is the given ratio)

Hope you found this helpful!

THANK YOU!!

∝ Sidhdi

Answer:

your answer is right its 90°