Find an equation for the ellipse whose vertices are at (4,-3) and (4,7), and focus is at (4,4).

From geometry, we know that if two triangles are similar, then their corresponding sides are in proportion.

From the statement, we know that ΔABC is similar to ΔXYZ.

From the diagram, we see that:

• AB = 15 is the corresponding side to XY = 10,

• BC = 9 is the corresponding side to YZ = x.

So we must have the equality:

Solving for x, we get:

x = 6

Rational numbers are type of real numbers that can be represented as a simple fraction. Rational numbers can be formed by dividing 2 integers, Rational number can be represented in this form x/y. Where y is not equal to zero.

Example of rational numbers are as follows

By definition, let m be the slope a line, then m can be calculated by the following equation:

Given that (x1, y1) and (x2, y2) are known points of the line. By reflecting all the points of the line across the line y = x

Solve the inequality for v:

20 > v - 4

When the variable is at the right of the inequality, it's a good idea to flip the inequality, that is, swap the sides and (very important), swap the symbol:

v - 4 < 20

Now we add 4 to both sides:

v - 4 + 4 < 20 + 4

Operating:

v < 24

This is the answer

Given that we have to write the quadratic equation and then we have to solve it and represent it graphically.

Then,

let the equation be

To find the roots we will do the factorization then we have

So the roots are -12 and 2.

Since George earns $100 per week plus 10% of his weekly sales

Assume that his weekly sales are $x

Then he earns 100 + 10% of x

Since he makes $425 in a week, then

Subtract 100 from both sides

Divide both sides by 0.1

His sales for that week are $3250

The answer is D

Answer:

Explanation:

Given a circle, we want to identify its center

A way to do this is to draw two chords at any part of the circle

A chord is a line inside the circle that joins two points on the circumference

The next thing to do here is to draw a perpendicular bisector through each of these chords

Now, the point at which these perpendicular bisectors intersect is the center of the circle

This mean option B is the correct answer choice

For an daily balance of P in her charge account and an interest paid at a rate of r, her finance charge is given by the expression:

F = r*P

For r = 1.7% and P = $250.82, we have:

F = 0.017*250.82

F = $4.26

Answer: d

The z-score of a measure is given by the following formula

where x represents the measure, mu represents the mean of the distribution, and sigma represents the standard deviation.

If we have a z-score equal to zero, our measure will be

a z-score equal to zero represents the mean of the distribution.

For a z-score equal to 1, we have

Then, the interval between z = 0 and z = 1 is the interval between the mean and one positive standard deviation.

The graph that represents this interval is the first graph.

Remember the following property of invertible functions:

Then:

Then:

Therefore, the answer is: 7.

Answer:

8

Explanation:

The first ten natural numbers are:

To find the upper quartile, separate the numbers into two halves:

• Lower Half: 1,2,3,4,5

• Upper Half: 6,7,8,9,10

The upper quartile is the number in the middle of the upper half.

The number in the middle of the upper half = 8

Therefore, the upper quartile of the first ten natural numbers is 8.

Given the line

The line is expressed in slope-intercept form:

Where

m is the slope

b is the y-intercept

1) Any line that has the same slope as this line will be parallel to it.

The slope of the line is m=2

From the given options, the only one that has the same slope as the given line is the first one

2) For perpendicular lines, the slope of a line perpendicular to another is the inverse negative of the slope of the line.

So let

Represent the equation of the line perpendicular to the given one. The relationship between their slopes can be expressed as:

The slope of the line is m=2 so the slope of the perpendicular line is

A line with slope -1/2 will be perpedicular to the given one. Looking at the options, the line that can be perpendicular to this one is

The correct option is the third one.

Answer:

1800 degrees

Explanation:

The sum of the interior angles of a dodecagon can be calculated using the following equation:

Sum of the interior angles = ( n - 2 ) x 180

Where n is the number of sides of the polygon.

So, if we replace n by 12, we get:

Sum of the interior angles = ( 12 - 2 ) x 180

Sum of the interior angles = 10 x 180

Sum of the interior angles = 1800

Therefore, the sum of the interior angles of a dodecagon is 1800 degrees.

Arithmetic progression: -25, -37, -49

d = - 12

General formula

An = -25 + (n -1)*(-12)

A85 = - 25 + 84*(-12) = -1033

Given: Two positive consecutive odd integers.

Required: To find two positive consecutive odd integers whose product is 63.

Explanation: Let x be a positive odd integer. Then (x+2) is the consecutive positive odd integer. Now according to the question

Or

which can be factorized as follows

Which gives

Since x is a positive odd integer,

Hence the two required integers are

We can also verify our result as the product of 7 and 9 is 63.

Final Answer: Option D is correct.

Answer:

The sequence is not an arithmetic sequence.

Explanation:

Given the sequence:

Calculate the difference between the terms below:

Observe that the differences between the terms are not the same all through.

Thus, there is no common difference which implies that the sequence is not an arithmetic sequence.

Our objective for this case is find the final altitude for this problem

The first distance is x1=35 m after 2 min =120 sec

The second distance is :

Then flight up:

Then the final altitude would be:

And replacing we got:

And after we operate we got:

Step 1

Given; Find the slope of the line passing through the points (-3, 5) and (-6, 4).

Step 2

Slope is given as;

Answer;

Given:

BAC = 33 degrees

BDC = 35 degrees

Solution:

From the properties of an isosceles triangle:

The base angles of an isosceles triangle are equal. Hence from triangle BDC, we have:

We can obtain angle DBC using the theorem that the sum of angles in a triangle is 180 degrees:

To find angle ABD, we use the theorem of congruency. i.e

Hence,

Since the angles ABD, ABC and DBC lie at a point, we have:

Answer : angle ABD = 125 degrees

Hanna, this is the solution:

As you can see there are three equal sectors colored yellow, blue, red, therefore, the sample space for spinning the spinner two time is:

{yellow-yellow, blue-yellow, red-yellow, red-blue, red-red, blue-blue}

Spin the spinner one time:

• Red = 1/3 or 0.33

• Blue = 1/3 or 0.33

• Yellow = 1/3 or 0.33

Spin the spinner a second time:

• Red - Red = 1/3 * 1/3 = 1/9 or 0.11

• Red - Blue = 1/3 * 1/3 = 1/9 or 0.11

• Red - Yellow = 1/3 * 1/3 = 1/9 or 0.11

• Blue - Blue = 1/3 * 1/3 = 1/9 or 0.11

• Blue - Red = 1/3 * 1/3 = 1/9 or 0.11

• Blue - Yellow =1/3 * 1/3 = 1/9 or 0.11

• Yellow - Yellow = 1/3 * 1/3 = 1/9 or 0.11

• Yellow - Red = 1/3 * 1/3 = 1/9 or 0.11

• Yellow - Blue = 1/3 * 1/3 = 1/9 or 0.11

•

If they are similar then the ratio between RS and RQ has to be tha same to the ratio between WV and WX:

RS/RQ = WV/WX

8/5 = 24/15 = 3(8)/3(5) = 8/5

8/5 = 8/5

Answer:

Therefore both rectangles are similar because the ratio of their lenght to their widht is the same (8/5)

Given:

Last year's enrollment is 500.

Enrollment increased percentage is 3%

the ratio is,

so 2 x 10 ^-12 is 200 times smaller than 4 x 10 ^-10

Every polynomial can be written in the form:

The a_1, a_2.... are the roots of the polynomial, meaning that f(a_1) = f(a_2) = ... = 0. This happens wen the graph of the polynomial intersects or tangency the x-axis. Whe it only tangecy the x-axis, it means that you have two of the root.

In this case, we have the polynomial tangency the x-axis in x = -2 and intersect the x-axis in x = 3. This means that the polynomial has roots -2, -2 (again) and 3. So:

Since the order doesn't metter, we can right in this way:

Which corresponds to alternative D.

The mean of 8 3 9 8 6 8 is

The mean is 7

hello

the standard linear equation can be written as

in the question here, the options that corresponds to the answer here are

Solution

In the first paragraph,

It is given that a group of 26 people started a settlement and the population increased by an average of 2.6 people a year.

We can represent the population function as ;

g(x) = 26 + 2.6 x

Where x denotes the number of years and g(x) is the population after some certain years.

At a nearby community, it was discovered that the population can be written as;

f(x) = -5.3x + 256

Part A.

The population can be expressed as a function because the population at a particular time depends on the number of years x.

Specifically, it can be represented as a linear function because the rate at which the population increases per year is constant.

Part B.

Equating the functions

-5.3x + 256 = 26 + 2.6x

=> 5.3x + 2.6x = 256 - 26

=> 7.9x = 230

=> x = 29

Therefore, if the number of years is less than 29

The population of the first community will be less than the population of the second community

If the number of years is greater than 29

The population of the first community will be greater than the population of the second community

Given: The system of equation below

To Determine: The number of solutions

Solution

Combine the two equations and solve

Multiply equation by 3 and equation 2 by 2

Add equation 3 and 4

Substitute y in equation 1

Hence, x = -4, y = 3

We need to subtract 2 from our x-coordinate and add 1 to our y-coodrinate. Doing this gives us

And hence, we have correctly given the coordinates of our translated points.

A linear function is represented by a straight line, that means the right answers are those graph with straight lines.

• The first graph represents a linear function with a positive slope.

• The last graph represents a linear function with a negative slope.

First and last one.

uhh yeah its right i jus tried it