3. Trapezoid JKLM with vertices J(-4, 3), K(-2, 7),L(2,7), and M(3, 3) in the line y = 1.what would the reflection coordinates be

Answer:

P = 0.04

Explanation:

The probability is equal to the number of options where the first spinner is landing on the color pink and the second spinner is landing on the number 5 divided by the total number of options.

Since there is only one option that satisfies the condition P5 and there are 25 possible outcomes, the probability is:

So, the answer is P = 0.04

Volume of a cube with edge lengths of 1/4m:

Volume of the rectangular prism:

Divide the volume of the prism into the volume of the cubes:

2x² + x - 6

The coefficient of x² is 2 and the constant term is -6. The product of 2 and -6 is -12. The factors of -12 which sum 1 are -3 and 4 so:

2(2x - 3) + x(2x - 3)

Factor 2x - 3 from 2(2x - 3) + x(2x - 3):

(2x - 3)(x + 2)

Solution

Step 1:

Step 2

Step 3

Domain definition

Final answer

Given:

Tangent segment, of a circle

Apply formulas

20^2 - 15^ 2 = AB^2

Also

15^2 = 20•( 20 - AB)

225 = 400 - 20AB

Then

20AB = 400-225= 175

AB = √ 175= 13 + 6/25 =13.24

1) Let's visualize the points

2) To find the equation for the line of best fit we'll need to follow some steps.

2.1 Let's find the mean of the x values and the mean of the Y values

2.2 Now It's time to find the slope, with the summation of the difference between each value and the mean of x times each value minus the mean over the square of the difference of the mean of x and x.

To make it simpler, let's use this table:

The slope then is the summation of the 5th column over the 6th column, we're using the least square method

The Linear coefficient

3) Finally the equation of the line that best fit is

The given line is

The line passes through (5, -1),

Perpendicular lines have opposite slopes, so we use the following equation to find the new slope knowing that the slope of the given line is -2.

Now, we use the slope, the point, and the point-slope formula to find the equation.

So, she's not correct, she didn't substitute the correct x and y values.

The reduced ratio form of 13 nickels to 43 dimes is 13/86.

What is a ratio?

a ratio let us know that how many times one number contains another number.

We are given 13 nickels and 43 dimes.

We know that 1 dime equal to 2 nickels.

Hence 43 dimes equals 86 nickels.

Now we find the ratio of the 2.

Which will be [tex]\frac{13}{86}[/tex]

Hence the reduced ratio form is 13/86.

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SOLUTION:

Case: Circle theorems

Method:

From the given circle

Theorem: The angle at the center of the circle is twice the angle at the circumference formed by the same segment.

The implication to the circle in the question is:

Final answer

The association between the variables art class and playing a sport is classified as follows:

There is a strong, negative association.

The association between variables can be classified either as positive or as negative, as follows:

In the context of this problem, it is found that of the students that take art class, the majority do not play a sport, while among those who do not take art class, the majority play a sport, hence there is a strong and negative association between the two variables.

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Given the following question:

Your answers are the first and second options.

The food collected on first day,

The food collected on second day,

The total amount of food collected can be calculated as,

Therefore, the total amount of food collected so far is 7 11/12 pounds.

Answer:

b) 28

c) 52

Step-by-step explanation:

f(2) = -2³ + 7(2)² - 2(2) + 12

= -8 + 28 - 4 + 12

= 28

f(-2) = -(-2)³ + 7(-2)² - 2(-2) + 12

= 8 + 28 + 4 + 12

= 52

Given:

Adding a negativen number is the same as subtracting that number, so:

Since both denominators (bottom number ) are equal we can subtract the numerators ( top numbers)

Answer:

We want to graph the following inequality system

First, we need to solve both inequalities. To solve the first one, we subtract 8 from both sides

To solve the second one, we multiply both sides by 7.

Now, our system is

We can combine those inequalities into one.

The number x is inside the interval between 1 and 7. Graphically, this is the region between those numbers(including them).

Question:

Solution:

An equation of the circle with center (h,k) and radius r is:

This is called the center-radius form of the circle equation.

Now, in this case, notice that the center of the circle is (h,k) = (-3,3) and its radius is r = 3 so that the center-radius form of the circle would be:

To obtain the general form, we must solve the squares of the previous equation:

this is equivalent to:

this is equivalent to

this is equivalent to:

so that, the general form equation of the circle would be:

thus, the correct answer is:

CENTER - RADIUS FORM:

GENERAL FORM:

The answer would be the product of the number of 3 freshman groups by 2 sophomores groups.

The number of 3 freshman groups is given by

The number of 2 sophomore groups is given by

Now, doing their product

We have 1764 different committees of three freshman and two sophomores.

We have that the volume of the spheres have a ratio of 8:27.

This means that the relation between linear measures, like the radii, will be the cubic root of that ratio

Solution

- The base is a regular hexagon. This implies that it can be divided into equal triangles.

- These equal triangles can be depicted below:

- If each triangle subtends an angle α at the center of the hexagon, it means that we can find the value of α since all the α angles are subtended at the center of the hexagon using the sum of angles at a point which is 360 degrees.

- That is,

- We also know that regular hexagon is made up of 6 equilateral triangles.

- Thus, the formula for finding the area of an equilateral triangle is:

- Thus, the area of the hexagon is:

- With the above formula we can find the length of the regular hexagon as follows:

- The formula for the volume of a hexagonal pyramid is:

- Thus, the volume of the pyramid is

1) We need to differentiate the following functions:

Note that we had to use some properties like the Product Rule, and the Chain Rule.

b) We can start out by applying the Quotient Rule:

Thus, these are the answers.

SOLUTION

Now putting x = -3 into f(x) or y, we have that

The value of n is 36

The simplified answer of the composite function is as follows:

Composite functions is a function that depends on another function.  A composite function is created when one function is substituted into another function.

In other words, a composite function is generally a function that is written inside another function.

Therefore,

f(x) = 2x

g(x) = 3x²

Hence, the composite function can be simplified as follows:

(f + g)(x) = f(x) + g(x)  = 2x + 3x²

(f - g)(x) = f(x) - g(x)  = 2x - 3x²

(f. g)(x) = f(x) . g(x) = (2x)(3x²) = 6x³

(f / g)(x) = f(x) / g(x) = 2x / 3x² = 2 / 3x

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Explanation: To understand this problem we need to know that there are two different types of probability. The experimental probability and the theoretical probability.

- The experimental probability occurs once you conduct the experiment and after the experiment, you calculate the probability using the result of the experiment.

- The theoretical probability occurs before the experiment. Once you have information about the situation so you calculate the probability the get a specific result before trying.

Step 1: For this question, once we have a number cube with faces 1,2,3,4,5 and 6 and we want to know the experimental probability to get a 5 once you roll the cube 300 times you would need to get in real life a number cube and to roll it 300 times. After this experiment we would get all the results of each time we roll it and we would know how many times (from 300 times) we got a number 5. After that, we would use the following formula

Once the get this result we finish the question.

Given the area of the rectangle is given by the following expression:

The area of the rectangle is the product of the length by the width

So, we will factor the given expression

To factor the expression, we need two numbers the product of them = 6

and the sum of them = 5

So, we will factor the number 6 to find the suitable numbers

6 = 1 x 6 ⇒ 1 + 6 = 7

6 = 2 x 3 ⇒ 2 + 3 = 5

So, the numbers are 2 and 3

The factorization will be as follows:

So, the answer will be the possible dimensions are:

Given:

Rachel sold 4 houses.

Heather sold 4 houses.

Kaitlin sold 12 houses.

Lena sold 11 houses.

Deshaun sold 3 houses.

Required:

a) We need to find which agent sold the most houses.

b) We need to find the number of houses Lna soldemore than Heather.

c) We need to find the number of agents who sold fewer than 4 houses.

Explanation:

a)

The greatest number of houses sold =12 houses.

Kaitlin sold 12 houses.

Answer:

The agent Kaitlin sold the most houses.

The agent sold 12 houses.

b)

Lena sold 11 houses.

Heather sold 4 houses.

The difference between 11 and 4 is 11-4 =7.

Answer:

Lena sold 7 housmore than Heather

1) Two triangles are similar if they have congruent angles and proportional sides (for each corresponding leg).

2) So let's check whether there are similar triangles by setting a proportion:

3) So yes they are similar, i.e. ΔCAB ~ΔHGJ

Let me write here an example of a common number/term in both numerator and denominator that we can cancel.

In the above example, we are able to cancel out the common number 4 because they are stand alone numbers. We can divide 4 by 4 and that is 1. Hence, the answer is just xy.

Another example:

In the above example, we are able to cancel out (x + 2) because this term is a common factor to both numerator and denominator.

In the example, we can also see that -1 is a common number however, we cannot cancel it out because the number -1 is not a standalone factor. It is paired with other number/variable. (x - 1) and (2x - 1) are both factors but are not the same, that is why, we are not able to cancel that.

Another example:

As we can see above, (x + 2) is a common term however, we cannot cancel it. We can only cancel common terms if they are common factors of both numerator and denominator. (Notice the plus sign in the middle. )

The term (x + 2) above is not a factor of the numerator and denominator, hence, we cannot cancel it.

Step-by-step explanation:

13.

a/7 + 5/7 = 2/7

a/7 = 2/7 - 5/7 = -3/7

a = -3

14.

6v - 5/8 = 7/8

6v = 7/8 + 5/8 = 12/8

v = 12/8 / 6 = 2/8 = 1/4

15.

j/6 - 9 = 5/6

j - 54 = 5

j = 5 + 54 = 59

16.

0.52y + 2.5 = 5.1

0.52y = 5.1 - 2.5 = 2.6

y = 2.6/0.52 = 5

17.

4n + 0.24 = 15.76

4n = 15.76 - 0.24 = 15.52

n = 15.52/4 = 3.88

18.

2.45 - 3.1t = 21.05

-3.1t = 21.05 - 2.45 = 18.6

t = 18.6/-3.1 = -6