Solve for x. And determine the angle measure of angle FED. Assume line whichappears tangent is tangent.7x - 10EF120°X =

Answer:

$315

Step-by-step explanation:

The standard form of the equation of the ellipse \(x^2 / 16 + y^2 / 3 = 1\).

What is standard form of the equation of the ellipse?

For example, d2ydx2+4y=0 if your differential equation is homogeneous (it equals zero and not any function). y(x=0)=0 and y(x=2)=0 were given as the boundary conditions, and you were requested to answer the equation. Then the aforementioned boundary conditions are homogenous boundary conditions.

An ellipse is a type of conic section that is defined as the set of all points such that the sum of the distances from the point to two fixed points (called the foci) is constant. The standard form of the equation of an ellipse with center (h, k) is:

          \((x - h)^2 / a^2 + (y - k)^2 / b^2 = 1\)

where a and b are the lengths of the major and minor axes, respectively, and (h, k) is the coordinates of the center of the ellipse.

In this case, the center of the ellipse is (0, 0) and the focus is (3, 0), so we can use the distance formula to find the distance between the center and focus:

\(\sqrt{((3 - 0)^2 + (0 - 0)^2)} = 3\)

The distance between the center and focus is equal to the length of the major axis, so a = 3.

In addition, the vertex of the ellipse is (4, 0), which is 4 units away from the center. Since the distance between the center and vertex is equal to the length of the major axis, we can set a = 4 to find the length of the minor axis:

\((x - 0)^2 / 4^2 + (y - 0)^2 / b^2 = 1\)

Solving for b, we find that b = \(\sqrt{(3)}.\)

Therefore, the standard form of the equation of the ellipse with the given characteristics is:

\((x - 0)^2 / 4^2 + (y - 0)^2 / \sqrt{(3)^2} = 1\)

This can be simplified to:

\(x^2 / 16 + y^2 / 3 = 1\)

The standard form of the equation of the ellipse \(x^2 / 16 + y^2 / 3 = 1\).

To know more about standard form of the equation of the ellipse visit,

https://brainly.com/question/9429160

#SPJ4

Answer:

0.037

Step-by-step explanation:

Since the marbles are returned the total possibilites are always the same and the events are independent

Total marbles = 16

6/16 x 10/16 x 4/16 x 10/16 = 0.037

Answer:30

Step-by-step explanation:47-17 = 30

x = 301/56

Algebra is the branch of mathematics that deals with numbers and values which are represented with letters and symbols.

Sometimes, we do not want to mention a particular number, we can represent the number by a letter or a suitable symbol. This approach is algebraic.

For example, d + d = 2d

This is an example of an algebraic expression

Given the algebraic expression,

\(3\frac{1}{8} \div (x - 4 \frac{7}{28} ) = \frac{17}{18} + 1 \frac{5}{6} \)

Step 1:

Simplify the expression by converting the mixed numbers into improper fractions:

25/8 ÷ ( x - 119/28) = 17/18 + 11/6

Step 2: Simplify the right side of the equation

25/8 ÷( x - 119/28) = 17/18 + 33/18

25/8 ÷( x - 119/28) = 50/18

Step 3: Multiply both sides of the equation by (x - 119/28)

25/8 = 50/18 × (x - 119/28)

Step 4: Multiply both sides of the equation by (18/50)

25/8 × (18/50) = (x - 119/28)

Step 5: Simplify the left side of the equation

9/8 = (x - 119/28)

Step 6: Add 119/28 to both sides of the equation

9/8 + 119/28 = x

Step 7: Calculate the value of x:

x = 9/8 + 119/28

= 63/56 + 238/56

= 301/56

Learn more about algebraic expressions from:https://brainly.com/question/395066

#SPJ1

Answer:

a. Amplitude: 19.65446

b. Vertical Shift: 58.00713

c. Period: 2/0.22797 = 27.56146

d. 19.65446 * sin(0.22797x + 1.79552) + 58.00713

e. Model's Temperature at 10 A.M.: f(-7) = 61.91

   This value is 9.91 degrees higher than the actual value.

Step-by-step explanation:

With 1 am being timed as t = 1, we fitted the temperature data collected at different points during the day in Portland, Oregon using sine regression. After receiving the sine function, we respond to the many questions connected to the sine function's properties.

A smooth, repeating oscillation characterizes a sinusoidal function. Sine is an oscillation that is smooth and repeated, thus the name "sinusoidal." A pendulum swinging, a spring bouncing, or a guitar string vibrating are a few examples of commonplace objects that may be described by sinusoidal functions.

Given, The hourly temperature at Portland, Oregon, on a particular day is recorded.

Using sine regression on the given data with t = 1 being the hour 1 am etc, we get the following sine regression formula using the TI-83 Graphing Calculator where T is the temperature:

T = a sin(bt + c) + d

Where a = 19.65, b = 0.28, c = -2.93, d = 58.01

From the sine regression function above:

a. The amplitude of the sinusoidal function is a = 19.65.

b. The vertical shift is d = 58.01.

c. The period is 2*pi /b = 2*pi/ 0.28 = 22.44

d. At 5 PM, the time value is t = 17. Hence the temperature distribution with 5 PM being t = 0 will be

t = asin[b(t - 17) + c] +d.

e. From the table, at 10 AM, the actual value of the temperature is 52 degrees.

Using the model in part a., at 10 AM, with t = 10, the temperature will be

T = a sin(10b + c) + d

T = 55.46 degrees

Learn more about sinusoidal functions here:c. The period is

https://brainly.com/question/12060967

#SPJ2

Complete question:

Answer:

Step-by-step exi  i dont know but thanks for the points sorry

a) The amount left after paying the tax is $53300.

(b) The interest after 2 years is $540.

(c) The percentage interest is 4%.

We have,

a)

The amount of tax the man pays.

= $65000 x 0.18

= $11700

Therefore, he has left.

= $65000 - $11700

= $53300

(b)

The interest earned after 2 years.

= $4500 x 0.06 x 2

= $540

(c)

The total amount of interest paid on the loan.

= $25740 - $24750

= $990

The percentage interest.

= ($990 / $24750) x 100%

= 4%

Thus,

(a) The amount left after paying the tax is $53300.

(b) The interest after 2 years is $540.

(c) The percentage interest is 4%.

Learn more about percentages here:

https://brainly.com/question/11403063

#SPJ1

Supplementary angles are two angles that add up 180 degrees, since our two angles are supplementary:

(4x+20)+(x-10)=180

4x+20+x-10=180

5x+10=180

5x=180-10

5x=170

x=170/5

x=34

A physical quantity with both magnitude and direction is called a vector quantity.

A vector quantity is a physical quantity that has both magnitude and direction. One example of a vector quantity is velocity, which is defined as the rate of change of an object's position with respect to time. Velocity is a vector quantity because it has both a magnitude (speed) and a direction (the object's motion). For instance, if an object is moving with a speed of 20 meters per second to the north, its velocity would be 20 meters per second north. If the object's direction changes to east, its velocity would become 20 meters per second east. Therefore, velocity is a vector quantity because its value depends not only on the speed of the object but also on the direction in which it is moving.

To learn more about vector quantity click here

brainly.com/question/21797532

#SPJ4

Complete Question

Write down a vector quantity and explain your response.

Let's represent the number with the variable "x". According to the given property, we can write the following equation:

3(x + 4) < 7x

Now, let's solve this inequality to find the range of numbers that satisfy the property.

3x + 12 < 7x

Subtract 3x from both sides:

12 < 4x

Divide both sides by 4 (since the coefficient of x is 4):

3 < x

So, the range of numbers that satisfy the given property is x > 3.

Therefore, any number greater than 3 will satisfy the condition. For example, 4, 5, 6, 7, 8, etc.Step-by-step explanation:

Answer:

\(\text{$y$-intercept$\;=\log_2 \left(\dfrac{27}{64}\right) \approx -1.245$}\)

Step-by-step explanation:

The y-intercept is the value of y when x = 0.

Therefore, to find the y-intercept of y = 3 log₂(x + 3) - 6, substitute x = 0 into the equation and solve for y.

\(\implies y=3 \log_2(0+3)-6\)

\(\implies y=3 \log_2(3)-6\)

Using the log law logₐ(a) = 1, rewrite 6 with log base 2:

\(\implies y=3 \log_2(3)-6\log_2(2)\)

\(\textsf{Apply the log power law:} \quad n\log_ax=\log_ax^n\)

\(\implies y=\log_2(3)^3-\log_2(2)^6\)

\(\implies y=\log_2(27)-\log_2(64)\)

\(\textsf{Apply the log quotient law:} \quad \log_ax - \log_ay=\log_a \left(\dfrac{x}{y}\right)\)

\(\implies y=\log_2 \left(\dfrac{27}{64}\right)\)

Therefore, the exact value of the y-intercept of the given equation is log₂(27/64) which is approximately -1.245 to the nearest thousandth.

Answer:

Step-by-step explanation:

From the similarity of smaller triangles we get:

Use Pythagorean to find the length of m:

is simply changing from percentage form to a decimal form usually, but the fractional form works the same.  Check the picture below.

Answer:

No the number of egg whites used is not proportional to the cups of jelly used.

Step-by-step explanation:

if your jelly is 1/3 cup then just one egg white is not also 1/3 a cup

Alva nunez total pay for the week in which she presses 310 moldings is

The cost per unit of an item is represented by the unit price.

To determine the unit price of an item, we divide the price of a specific number of units by the number of units.

If she earns $0.95 for every holding she presses this means that the unit price is 0.95

for 310 moldings Alva nunez will earn

= 0.95 * 310

= 294.5

Learn about unit price at:

https://brainly.com/question/14286952

#SPJ1

Answer:

4^2+ 3^2=c^2

16+9=25

5

Step-by-step explanation:

The expression which is equivalent to the expression 14x+3−13x+(−2) is:

x +1

An expression is a sentence with at least two numbers or variables having mathematical operation. Math operations can be addition, subtraction, multiplication, division.

For example, 2x+3

Given that,

The expression,

14x+3−13x+(−2)

Now it can be simplify in the following way:

⇒ 14x - 13x + 3 - 2

the variable and constant terms can be clubbed together,

⇒ x + 1

Hence, the equivalent expression is x + 1

To know more about Expressions check:

brainly.com/question/16804733

#SPJ9

Answer:

Step-by-step explanation:

How Far Can A Snail Travel In One Hour

If a snail can travel over half an inch per minute, that means in one hour a snail can travel up to 40 inches. If you want to think about how far this is in feet, it means that snails move up to 3.5 feet per hour.

Consider the fact that the average human being can walk about a mile, or 5280 feet, in one hour.

This means that snails can take up to 1,500 days, or over 4 years, to travel just one mile.

Answer:

true

Step-by-step explanation:

the factors are simply what is being multiplied together. We can see there are 3 because we have 5,3,and 2. 30 is not a factor because that is the answer. I hope this helps!

Answer:

x = 2 and x = 4

Step-by-step explanation:

The solution of the given equation is shown on the graph

There are two intercepts with coordinates of

The x-coordinates are

Correct option is 3 or C.

Answer:

C

Step-by-step explanation:

On the graph, you can see that we are given two points; (2, 2) and (4, -22)

Since we are looking for the value of "x", we need the x value of the given points.

The x values in both points are 2 and 4. Thus are the solutions.

Best of Luck!

Answer:

2p-8

Step-by-step explanation:

Know you're amazing and smart!

Answer:

Step-by-step explanation:

4p+8-2p-16 combine like terms

2p-8

1) Since we were told to find the x-value in this system we can use the Elimination Method:

But first, let's rearrange the 2nd equation

2) Now let's multiply the first equation by 2, and divide the second by -1, and then we can add both equations simultaneously:

Answer:

Step-by-step explanation:

i am working on the assumption that nobody does all three of them

i got 4 because including the people that do swimming and park, the total number of people that do swimming is 22.

the same logic goes for cycling: including the people that do swimming and visit the national park, the total is 23.

so that means that find how many people do swimming and cycling, we have to add the people doing only swimming, with the people doing both swimming and park and then subtract that answer from 22 which gives you 4

SOLUTION

So we have detective story book represented as D

Mystery story book represented as M

And Comic book represented as C.

So, she can arrange it as follows

D C M

C D M

M C D

C M D

M D C and

D M C

So, the sample space is 6 ways

Or you can say

Therefore, the answer is 6 ways

a. Monthly payment for the bank's car loan is $407.67

b. Monthly payment for the savings and loan association's car loan is $315.99

c. Total amount paid would be $2,035 less for the bank's car loan than for the savings and loan association's car loan.

The cost of borrowing money, usually expressed as a percentage of the amount borrowed, is what a lender charges a borrower to use their money. This cost is known as an interest rate.

(a) To find the monthly payment for the bank's car loan, we can use the formula for the present value of an annuity:

\(PV = PMT * \frac{1 - (1 + \frac{r}{n})^{(-n*t)}}{\frac{r}{n} }\)

putting the given values,

⇒ \(21000 = PMT * \frac{1 - (1 + \frac{0.065}{12})^{(-12*5)}}{\frac{0.065}{12} }\)

Solving for PMT, we get:

PMT = $407.67

Therefore, the monthly payment for the bank's car loan is $407.67

(b) To find the monthly payment for the savings and loan association's car loan, we can use the same above formula:

where PV is still $21,000, PMT is the monthly payment, r is still 0.065, n is still 12, but t is now 7 years x 12 months/year = 84 payments.

putting the given values,

\(21000 = PMT * \frac{1 - (1 + \frac{0.065}{12})^{(-12*7)}}{\frac{0.065}{12} }\)

Solving for PMT, we get:

PMT = $315.99

Therefore, the monthly payment for the savings and loan association's car loan is $315.99.

(c) Bank's car loan: $407.67 x 60 = $24,460.20

Savings and loan association's car loan: $315.99 x 84 = $26,495.16

Therefore, the bank's car loan would have the lowest total amount to pay off, by: $26,495.16 - $24,460.20 = $2,034.96

Therefore, the total amount paid would be $2,035 less for the bank's car loan than for the savings and loan association's car loan.

To know more about loan, visit:

https://brainly.com/question/20688650

#SPJ1

There are 37 students in drama club and 27 students in yearbook club.

And the system of equations will be 1.x + 1.y = 64.

An equation is a combination of different variables, in which two mathematical expressions are equal to each other.

Given that,

Total number of students in drama club and yearbook club = 64,

Also, there is a yearbook club. Students in drama club has 10 more than yearbook club,

If x represents the number of students in the drama club and y represents the number of students in yearbook club.

According to given condition,

x+ y = 64        (1)

and x = y + 10

Substitute the value of x in equation (1),

y + 10 + y = 64

2y = 54

y = 27

And x = 27 + 10 = 37

The required system of equations,

1.x + 1.y = 64

To know more about Equation on:

https://brainly.com/question/187506

#SPJ1

Answer:

I think it's "C"

Step-by-step explanation:

Because a function is the independent variable to the dependent variable... Since, the cost relies on the weight, the cost is dependent. While, the weight is independent. I don't know if I'm right, I kinda suck at math

Answer:

Area of the base = (8×6)/2 = 24 yd²

Height of the prism = 8 yd

Perimeter of the base = 8+6+10 = 24 yd

Surface area = 2B + Ph = (2×24)+(24×8) = 48+192 = 240 yd²