If the area of the rectangle to be drawn is 12 square units, where should points C and D be located, if they lie vertically below A and B, to make this rectangle?

In order to find the probability start the construction of the possible relay team, if the team is made by any 4 swimmers then

if the first member is a girl and the other three needs to be boys, the number of possibilities are

then, divide in order to find the probability

The perimeter is the sum of the side lengths of a polygon. Now, let it be:

• l,: the length of the rectangle

• w,: the width of the rectangle

Considering the information given and the previous definition, we can write and solve the following system of equations.

We can use the substitution method to solve the system of equations.

Step 1: We combine like terms in Equation 2.

Step 2: We substitute the value of l from Equation 1 into Equation 2.

Step 3: We solve for w the resulting equation.

Step 4: We replace the value of w in Equation 1.

Thus, the solution of the system of equations is:

The length of the rectangle is 13 inches, and the width of the rectangle is 4 inches.

Let:

x = Number of points Juan earned on the second text

n = Total number of points of each test

First, let's find the total number of points of each test using the information provided:

Now, we can find how many points Juan earned on the second test:

Answer:

40 points

Plan 1:

Initial (fixed) fee: $60

Variable fee: $0.50 per mile

Plan 2:

Initial (fixed) fee: $0

Variable fee: $0.70 per mile

If we call x to the number of miles driven by Tony, then the cost of Plan 1 is:

P1 = 60 + 0.5x

The cost of Plan 2 is:

P2 = 0.7x

It's required to find the number of miles Tony should drive for both plans to cost the same, that is:

60 + 0.5x = 0.7x

Subtracting 0.5x:

60 = 0.7x - 0.5x

Operating:

60 = 0.2x

Dividing by 0.2:

x = 60 / 0.2

x = 300

Tony should drive 300 miles for both plans to cost the same.

Under that condition, both plans cost the same. Plan 1 cost:

P1 = 60 + 0.5*300

P1 = 60 + 150

P1 = $210

Plan 2 cost:

P2 = 0.7*300

P2 = $210

Both costs are equal

ANSWER:

C. $1,538.46

STEP-BY-STEP EXPLANATION:

To understand the question we must take into account that it is the gross payment, which is the payment received by the employee agreed with the company, without taking into account deductions or bonuses.

Therefore, we calculate it with the total payment divided by the amount of payments, like this:

So the correct answer is C. $1,538.46

Area of rectangle is given by:-

So the correct answer is

Remember that the sum of the interior angles is 180. Then, we have the following equation:

This is equivalent to:

solve for M-angle:

Then, te correct answer is :

he had 40 biscuits in the beginning

to solve this we can use a rule of three

so

Step 1

let x represents the total treats he had in the beginning , so

so, the proportion is

therefore,

he had 40 biscuits in the beginning

I hope this helps you

Looking at the sentences, we have that (1), (2) and (3) are questions that require just one specific answer (For (1) it's a name of a person, for (2) it's a value and for (3) it's also a single value).

But in sentence (4), there are more than one type of maple tree, so we can answer with each type of maple tree, stating the percentage of each type for example.

So the sentence that would be considered a statistical question is (4).

The restricted values of x for the following rational expression.

x = 0

x = -3/4

Restricted values are those values in a rational expression that bring the denominator to zero. When referring to "Market Value," the term "restricted value" denotes the property's value under the assumption that it is subject to a temporary governmental or private limit on rentals and tenant income levels. The denominator's real numbers that have a value of 0 are not included in the domain. The word "restrictions" refers to these values. Similar to how fractions are simplified, rational expressions can be too. Cancel the common factors after factoring the numerator and denominator. Place a zero as the denominator. Put the equation to rest. The restricted values are the answer or answers.

Rational expressions should first be multiplied, and then the numerator and denominator should be factored. Next, common factors should be cancelled. Notify yourself of the domain's limitations.

−5x– 8/x² + 4 = 0

- 5x - 8/[tex]x^{2}[/tex] = -4

x = 0

x = -3/4

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Answer:

Step-by-step explanation:

Maybe

2x times 11x

The area of the overlapping region is of: 6.25 units squared.

The area of a rectangle of length l and width w is given by the multiplication of the dimensions, as follows:

A = lw.

The dimensions of the right triangle as follows:

Hence the remaining leg on the overlapping region is:

4 - x, as AD = 4.

By symmetry, the other dimension of the overlapping region is also of:

4 - x.

Being also the hypotenuse of the right triangles.

The value of x can be found applying the Pythagorean Theorem as follows:

x² + 2² = (4 - x)²

x² + 4 = 16 - 8x + x²

8x = 12

x = 1.5.

Then the two dimensions of the shaded region are:

4 - 1.5 = 2.5.

Meaning that the area is of:

A = 2.5 x 2.5 = 6.25 units squared.

The figure is missing and is given by the image at the end of the answer.

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Answer:

look below

Step-by-step explanation:

Answer:

The y-intercept b for the derived equation is;

Explanation:

Given that the line passes through the point (4,-9) and has a slope of -1/2;

Applying the point-slope form of linear equation;

substituting the slope and the given point;

Comparing it to the slope intercept form of linear equation;

where;

m = slope

and b = y-intercept

Therefore, the y-intercept b for the derived equation is;

Test scores: 93 83 98 89 97 91 83 86 92 90 88 84 85 82 91

organizing the data: 82,83,83,84,85,86,88,89,90,91,91,92,93,97,98

(a) Complete the grouped frequency distribution for the data.

79 to 83 -> 3

84 to 88 -> 4

89 to 93 -> 6

94 to 98 -> 2

(b) Construct a histogram for the data.

the histogram can be constructed using the information obtained in point (a)

Answer:

Where's the chart?

Step-by-step explanation:

Answer;

Medain for morning is 25

Median for evening is 21.5

Explanation;

Here, we want to create frequency tables for each of the given groups

We start with the morning group

The frequency table for it is as follows;

Now, we proceed to the afternoon group

We have this as follows;

Lastly, we will want to get the median value of both groups

To do this, we need to re-arrange the values in the data set in ascending or descending order

For the purpose of this solution, we shall be using the ascending order mode. Then from here, we pick out the middle value

For the morning group, we have;

12, 19,21, 23,25,27,31,36,39

Since the numbers are 9, the middle number will be the 5th number since it leaves equal spread of values on the left and right

Thus, we have the median value as 25

The afternoon set, we have it as;

8,8,11,15,16,27,34,39,43,51

We proceed to choose the mid 5th values comig from both ends

We have this as;

We have these values as; 16 and 27

We add these and divide by 2

We have this as;

Given:

The accumulated value of investment is A = 13,407.58.

The invested amount is P = 12,000.00.

The time period is 4 years and 6 months.

Explanation:

The formula for the accumulated value at r rate of interest is compounded semi-annually.

Substitute the values in the formula to determine the value of r.

So the rate of interest is 2.48%.

We can use the definition:

Looking at the figure we can see the values:

But we don't have the hypotenuse value, we must use the Pythagorean theorem to find it

Now we have the hypotenuse we can find all values

In polar coordinates, the x variable is given as

So, we have the equation

By dividing both sides by cosine of thetat, we get

since

The above result is equivalent to:

• A ,Reflection

• A ,Vertical Shift 4 units down

1) Considering the parent function, i.e. the simplest form of a family of functions, in this case, to be:

2) Then we can state that this transformed function:

We can see the following transformations:

• A ,Reflection,, pointed out by the negative coefficient

• A ,Vertical Shift 4 units down

As we can see below, to better grasp it:

Tim should order approximately 6 pizza.

Division in mathematics is the process of dividing an amount into equal parts. For instance, we may split a group of 20 people into four groups of 5, five groups of 4, and so on. One of the four fundamental arithmetic operations, or how numbers are combined to create new numbers, is division. The other operations are multiplication, addition, and subtraction. Mathematicians use addition, subtraction, multiplication, and division as their four fundamental arithmetic operations. The division is one of these four operations that we employ most frequently in our daily work. It involves dividing a huge group into equally sized smaller units. Divide 25, for instance, by 5.

Given Data

Number of employees = 22

Slice of pizza one should get = 1/4

Dividing 22 by 1/4

[tex]\frac{22}{4}[/tex]

5 and [tex]\frac{1}{2}[/tex]

Tim should order approximately 6 pizza.

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Given,

The coordinates of the points are (2,6) and (7, 2).

Required:

The distance between the points and the midpoint of the points.

The distance between two points is calculated as,

Hence, the distance between the points is 6.4

The midpoint is calculated as,

Hence, the midpoint is (4.5,4).

Given,

x-3y=-3

2x+3y=-6

Plotting it in graph we have,

Since we have only one point of intersection so that would be only one solution.

The point of intersection is (-3,0)

Thus x=-3 and y=0

ANSWER

y = -3x + 3

EXPLANATION

We want to write the equation in slope-intercept form, which is the form:

y = mx + c

where m = slope; c = intercept

To do that, we have to use the point-slope method:

y - y1 = m(x - x1)

where (x1, y1) = point the line goes through

From the question:

m = -3

(x1, y1) = (0, 3)

So, we have that:

y - 3 = -3(x - 0)

y - 3 = -3x

=> y = -3x + 3

That is the equation of the line in slope-intercept form.

Answer:

x=-6. y=6. xy=-36

x=-2. y=-3. xy=6

x=1. y=2. xy=2

Factoring

Factor the expression:

Divide the expression into two halves:

Factor b^2 from the first group and xb from the second group:

Now find the greatest common multiple of 72 and 96:

72= 2*2*2*3*3

96=2*2*2*2*2*2*3

Now we take the common factors with their least number of repetitions:

GCF=2*2*2*3=24

Now we find the GCF of 90 and 120:

90=2*3*3*5

120=2*2*2*3*5

GCF=2*3*5=30

Taking the GCF of each group:

Now we finally take out 3z+4h from both groups:

This last expression can be further factored by taking out 6b from both terms:

This is the final expression factored as much as possible

6. Measure of angle 1 is 60 degrees because it congruent to angle 4 because they are opposed by the vertex

7. Measure of angle 3 is equal to 180 - angle 1 - angle 2 = 180 - 60 - 40 = 80 because these three angles sum 180 degrees

8. Measure of angle 5 is 40 degrees because it congruent to angle 2 because they are opposed by the vertex

9. Measure of angle 6 is equal to angle 3, because they are congruent, so it measures 80 degrees

10. Mesure of angle 7 is equal to the sum of angles 1 and 2 because they are congruent, so measure of angle 7 is 100

11. 80

12. 60

13. 120

14. 60

15. 120