Find the center of the ellipse.
x^2+36y^2-16x-72y+64=0

Answer:

∠2 = 35 degrees because it is the vertical angle of ∠3

∠6 = 35 degrees because it corresponds with ∠2

∠4 = 145 degrees because when added to ∠2 145 + 35 = 180

A straight line equals 180 degrees. ∠4 and ∠2 are on the same line which means they have to add up to 180 degrees.

Step-by-step explanation:

Answer:

The symbol should be equal to.

They are the same when the first expression is multiplied.

Answer:

=

Step-by-step explanation:

6.738 × 10^-11 = 0.00000000006.738

0.00000000006738 = 0.00000000006738

A counterexample that disproves her conjecture is that Easter date fell outside the first 22 days in April in the year 2024, 2027, 2032 and 2038.

Easter Sunday might come between March 22 and April 25. Easter is always celebrated on the Sunday immediately following the Paschal Full Moon date of the year. The Paschal Full Moon is the first Ecclesiastical Full Moon date after March 20. So, in Western Christianity, Easter is always celebrated on the Sunday immediately following the Paschal Full Moon.

Her conjecture over 2018 to 2021 is not a full reflection of the changes that occurs in these dates. To draw a more concrete assumptions, a wider range of year would need to be considered. Hence, the date variations between 2018 and 2021 is not enough for such conjectures.

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The bone is approximately 16384 years old, as solved by basic algebra and logarithm.

The values of y and t can be: t = 16384, y = 16380(a). (as calculated by basic algebra and logarithm).

Let 'a' be the original amount of the object.

Then, according to question, for y = amount of carbon in the object, y = 0.14(a) (as the bone contains 14% of its original carbon-14).

We are also given that: y = a [tex]e^{-0.00012t}[/tex]

On substituting the value of y, we get: 0.14a = a [tex]e^{-0.00012t}[/tex]

By basic algebra, we can solve it as:

=> 0.14 = [tex]e^{-0.00012t}[/tex]

=> ln (0.14) = ln ([tex]e^{-0.00012t}[/tex]) (taking natural logarithm on both sides)

=> ln (0.14) = - 0.00012t (as [tex]log_b(a)^m=m(log_b(a))[/tex]; further:  [tex]log_e(e) = 1[/tex])

=> [tex]\frac{ln(0.14)}{-0.00012}[/tex] = t

=> t = 16384 years (approx.)

The values of y and t can be as follows: t = 16384, y = a (0.9998(16384)) = 16380(a).

Hence, the bone is approximately 16384 years old, as solved by basic algebra and logarithm; The values of y and t can be: t = 16384, y = 16380(a). (as calculated by basic algebra and logarithm).

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Answer: 2

Step-by-step explanation:

4x-2y=6

Divide both parts of the equation by 2:

2x-y=3

2x-y+y=3+y

2x=3+y

2x-3=3+y-3

2x-3=y

y=2x-3

A recipe uses 2 cups of milk to make 6 servings. If the same amount of milk is used for each serving, Two gallons of milk will make 192 servings

Given data

2 cups of milk to make 6 servings.

Assuming

1 gallon 4 quarts

1 quart 2 pints

1 pint 2 cups

1 cup = 8 fluid ounces

if 1 quart 2 pints, then 4 quarts will be

= 4 * 2 = 8 pints

if 1 pint 2 cups, then 8 pints will be

= 8 * 2 = 16 cups

if 1 gallon is 16 cups, the 2 gallons will be

= 16 * 2 = 32 cups

If 1 cup is 6 servings, then 32 cups will be

= 32 * 6 = 192 servings

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Answer:

option D is the correct option

Answer:

I'm not completely sure, but it does look similar to a Florida Mockingbird to me, I'll do more research and comment on any new finds. Hope this helps.

Step-by-step explanation:

Answer:

yeah it might be a florida mocking bird i got a lot around where i live

Step-by-step explanation:

We get the product -9 9/20 after multiplying the given two mixed numbers  -1 3/4 and 5 2/5.

Mixed numbers: A mixed number is a whole number, and a proper fraction represented together.

Multiplication: In simple algebra, multiplication is the process of calculating the result when a number is taken times. The result of a multiplication is called the product.

Given are two mixed numbers  -1 3/4 and 5 2/5.

Explanation:

= -1 3/4 * 5 2/5

converting both the mixed numbers into improper fractions, we get

= -7/4 * 27/5

multiplying numerator by numerator and denominator by denominator, we get

= -189/20

= -9 9/20

Therefore, we get the product -9 9/20 after multiplying the given two mixed numbers  -1 3/4 and 5 2/5.

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The - sign outside the parentheses is 1-9t-4.3s

It follows from the task content that the expression which is equivalent to; −-4.3s-(9t+1) by distributing the "-" sign outside the parentheses is required.

Hence, it follows that each term in the parentheses is multiplied by the negative sign outside the parentheses as follows;

-4.3s-(9t+1)

=-4.3s--9t-1

=1-9t-4.3s

Ultimately, the expression which is equivalent to that given in the task content by distributing the "-" sign outside the parentheses is; 1-9t-4.3s.

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Answer:

I believe the answer is yes.

Step-by-step explanation:

Good Luck!!

The number of students in the group = 13

for this question,

Let n be the number of students.

Each student received a bacon cheeseburger and milkshake, and the total bill was $104.00

We need to find the total number of students in the group.

A Bacon Cheeseburger costs $4.75 and Milkshake costs $3.25.

Total cost of a bacon cheeseburger and milkshake is:

$4.75 + $3.25 = $8

The total bill was $104.00

So, we get an equation,

⇒ 8 × n = 104

By unitary method,

⇒ n = 104/8

⇒ n = 13

Therefore, the number of students in the group = 13

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Solution of logarithmic eq. log (3 - 2x) = -1 is , [tex]x = \frac{29}{20}[/tex]

In, mathematics a logarithmic equation is inverse of exponential equation. That means, we can easily convert the logarithmic equation into exponential equation and vice versa. The basic form of the logarithm function can be written as [tex]log_{a}x[/tex] .

where, a is the base of function or equation

           x is expression equation

Mathematically, if [tex]a^x = N[/tex] is an exponential function then, this can be converted to logarithmic function as  [tex]log_aN = x[/tex].

There are many formulas that are given to us for solving several simple and complex problems based on logarithmic functions and logarithmic equations.

Some important formulas of logarithms :

According to given statement,

log (3 - 2 x)= -1

now convert this equation to exponential form

=> 3 - 2x = 10^-1

=> 3 - 2x = 1/ 10

=> x = 29 / 10

Thus solution for this equation is x =29/20.

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The cyclist will pedal at given speed for minimum 1.25 and maximum 2.25 hours.

The relation between speed, distance and time is as follows -

Speed = distance ÷ time. The maximum and minimum number of hours will depend on the distance. The maximum number of hours will be spent when maximum distance is covered, and minimum number of hours will be spent when minimum distance is covered.

Maximum distance = 35 + 10

Maximum distance = 45 miles

Minimum distance = 35 - 10

Minimum distance = 25 miles

Maximum number of hours = 45 ÷ 20

Maximum number of hours = 2.25 hours

Minimum number of hours = 25 ÷ 20

Minimum number of hours = 1.25 hours

Thus, cyclist will pedal at given speed for minimum 1.25 and maximum 2.25 hours.

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The equation of the line is  y= 3 - 2x.

An equation is a mathematical expression that contains an equals symbol. Equations often contain algebra.

Given:

Coordinates (0, 3) and (2, -1)

So,

slope = -4/2=-2

and equation of line is

(y- y1) = m (x- x1)

y-3 = (-2)(x-0)

y-3 = -2x

y= 3 - 2x

Hence, the equation of line is y= 3 - 2x.

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The school that Ming goes to sell their tickets as follows: price of a senior citizen ticket is $6 and the price of a student ticket is $9

Given data

first day 8 senior citizen tickets and 4 student tickets for a total of $84

second dat 8 senior citizen tickets and 2 student tickets for a total of $66

let the price of a senior citizen ticket be x and the price of a student ticket be y. The equation is written as:

8x + 4y = $84    equation 1

8x + 2y = $66    equation 2

subtracting equation 2 from equation 1

( 8x - 8x ) + 4y - 2y = 84 - 66

0 + 2y = 18

2y = 18

y = 9

substituting y = 9 into equation 1

8x + 4y = 84

8x + 4 * 9 = 84

8x + 36 = 84

8x = 84 - 36

8x = 48

x = 6

Hence the price of a senior citizen ticket is $6 and the price of a student ticket is $9

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Answer:

A) 3.5

Step-by-step explanation:

                4.3t + 6.8 = 8.4t - 7.55

         Subtract 8.4t from both sides,

              4.3t - 8.4t +6.8 = -7.55

        Combine like terms,

                      -4.1t  + 6.8 = -7.55

                  To isolate 't' first subtract 6.8 from both sides.

                   -4.1t  = -7.55 - 6.8

                   -4.1t  = -14.35

                Divide both sides by (-4.1)

                      t = -14.35 ÷ (-4.1)

                      t =  3.5

Answer:

5

Step-by-step explanation:

because 8+8+8+8+8=40 or 8*5

and theres 8 five times

Answer:

cant answer without a function graphed

Step-by-step explanation:so yeah

If we solve the expression 4 log m-log n,then it will look like log([tex]m^{4}/n[/tex]) as single logarithm.

Given that the expression is 4 log m-log n.

We are told to write the expression as a single logarithm.

logarithm is basically the exponent or power to which a base must be raised to yield a given number. It is opposite to exponential function.

The expression is 4 log m-log n.

We know that log [tex]a^{b}[/tex]=b log a and log (m/v)=log m-log n.So,

4 log m-log n=log [tex]m^{4}[/tex]- log n

=log ([tex]m^{4}/n[/tex])

Hence if we solve the expression 4 log m-log n,then it will look like

log([tex]m^{4}/n[/tex]) as a single logarithm.

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When the result of subtracting 13 from the sum of two consecutive numbers is 18. The numbers are 15 and 16. The correct option is d.

From the information, the result of subtracting 13 from the sum of two consecutive numbers is 18.

Let the numbers be x and x+1.

Therefore, (x + x + 1) - 13 = 18

2x + 1 - 13 = 18

2x - 12 = 18

2x = 18 + 12

2x = 30

Divide

x = 30/2

x = 15

Therefore, when the result of subtracting 13 from the sum of two consecutive numbers is 18. The numbers are 15 and 16. The correct option is d.

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Answer:

that the greatest common factor of 24 and 32

Answer:

24 and 32

Step-by-step explanation:

Using sine formula, the seat on a Ferris wheel is 50√3 feet closer to the ground after rotating 60°.

One of the 6 trigonometric functions is the sine function. Sine function can be described as the ratio of the length of the opposite side of the triangle to its hypotenuse.

sin x = (opposite side) / (hypotenuse)

where "opposite side" is the length of the side opposite to angle x

If the wheel rotates 60°, causing the height of the seat to decrease, using sin formula, solve for the vertical distance between the positions before and after the rotation.

sin x° = (opposite side) / (hypotenuse)

where x = 60

opposite side = vertical distance between the positions before and after the rotation

hypotenuse = radius = 200 feet/2 = 100 feet

sin 60° = opposite side / 100 feet

opposite side = 50√3 feet

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The width of the box whose height is given as 7 inches and length is three inches more than the width given a volume of 910 is; 10 inches.

It follows from the task content that the height of the box is; 7 inches.

Let, x = width of the box and;

x+ 3 = length of the box.

Therefore, since the volume of a box is given by the formula;

V = l × b × h

Therefore, we have;

910 = 7 (x) (x+3)

Divide both sides by; 7

130 = x² + 3x

x² + 3x -130 = 0.

(x+13) (x-10) = 0

Therefore, x = -13 or x = 10.

Ultimately, the possible values of the width are; -13 or 10.

Since the width cannot be a negative number, it follows that the width of the box in discuss is; 10 inches.

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Using the description, area of triangle ACE is solved to be 150 square units

from the given data we fine AE using Pythagoras rule, as AE is the hypotenuse of the triangle AEM. So we solve as:

AE^2 = ME^2 + AM^2

AE^2 = 10^2 + 22^2

AE = √(100 + 484)

AE = √584

note AM is half of AB which is 44, it was given that M is the mid point of line AB, this makes AM = AB / 2 = 22

Area of triangle ACE

area of triangle when two sides and one angle is given is solved by the formula

= a b sin ∅ / 2

angle at A/2 = arc tan (10/22) = 24.44

= AC * AE * sin A/2 / 2

= 30 * √584 * sin 24.44 / 2

= 299.95 / 2

= 149.98 ≅ 150

Hence area of triangle ACE is solved to be 150 square units

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The graph is a dashed line, shaded area below the boundary line since y is less than (3/4)x + 1).

Given the inequality in the question;

-3x + 4y < 4

First, rearrange the inequality in slope-intercept form ( y = mx + b )by solving for y.

-3x + 4y < 4

4y < 3x + 4

Divide each term by 4

4y/4 < 3x/4 + 4/4

y < (3/4)x + 1

Now, compare to the slope-intercept form ( y = mx + b )

y < (3/4)x + 1

Slope m = 3/4

b = 1 which gives the y-intercept: ( 0,1 ).

Now, graph a dashed line, then shade the area below the boundary line since y is less than (3/4)x + 1 ( y < (3/4)x + 1 ).

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Answer:

y = - 5x + 3

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

given

10x + 2y = - 2 ( subtract 10x from both sides )

2y = - 10x - 2 ( divide through by 2 )

y = - 5x - 1 ← in slope- intercept form

• Parallel lines have equal slopes , then

y = - 5x + c ← is the partial equation

to find c substitute (1, - 2 ) into the partial equation

- 2 = - 5 + c ⇒ c = - 2 + 5 = 3

y = - 5x + 3 ← equation of parallel line

Answer: y = - 5x + 3

Step-by-step explanation: i took the test

The equation that can be use to represent the relationship between the actual length(a) in feet, and the length of the model (m), in inches is a = 2.4m or m = a / 2.4

The actual length of the car is 12 feet and is represented by 5 inches in the model.

The equation that can be use to represent the relationship between the actual length(a) in feet, and the length of the model (m), in inches is as follows:

12 feet = 5 inches

Hence,

m = 5 / 12 a

a = 2.4m

where

or

m = a / 2.4

Therefore, the  equation that can be use to represent the relationship between the actual length(a) in feet, and the length of the model (m), in inches is a = 2.4m or m = a / 2.4

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