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We know that

• There are two true/false questions.

• There are two multiple-choice questions with three choices each.

In the true/false questions, there are 4 ways to answer since each question has only two choices.

In the multiple-choice questions, there are 6 ways to answer since there are 3 choices per question.

The width of the given rectangle is 2x²-3x+3.

Given that, area of rectangle = [tex]6x^4-8x^3+9x^2-3x-12[/tex] and the length of rectangle = 3x-4.

The area can be defined as the amount of space covered by a flat surface of a particular shape. It is measured in terms of the "number of" square units. The formula to find the area of a rectangle = Length × Width.

Now, (3x-4) × width = [tex]6x^4-8x^3+9x^2-3x-12[/tex]

⇒ Width = [tex]\frac{6x^4-8x^3+9x^2-3x-12}{3x-4}[/tex]

3x-4|[tex]6x^4-8x^3+9x^2-3x-12[/tex]|2x³-3x+3

       [tex]6x^4[/tex] - 8x³

      _________________

                 0+9x²-3x-12

                 (-) 9x²+12x
      _________________

                      0+9x-12

                     (-) 9x(+)12

        _________________

                              0

So, width = 2x²-3x+3

Therefore, the width of the given rectangle is 2x²-3x+3.

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Answer:

The natural numbers, whole numbers, and integers are all subsets of rational numbers

Step-by-step explanation:

hope it helps

have a good day

Explanation.

The question wants us to determine the circumference of the circle.

Circumference of a circle simply means the perimeter of a circle, and the formula to be used is

To solve this problem we have to remember that diagonals of a parallelogram bisect each other. This means that they intersect in the midle point of each other. From this we can conclude that

Once we have our equations we can solve them. Let's find x

Now, let's find y

Then x=18 and y=9,

Measure of CAB is 84.4, by using supplementary angle theory.

In geometry, two angles are referred to as supplementary angles if their sum is 180 degrees. For instance, if A + B = 180°, then A and B are considered supplementary angles. Complementary angles always result in a straight angle when combined (180 degrees).

Angles that add up to a precise 90 degree angle are said to be complementary. For instance, 30 degrees and 60 degrees are complementary angles.

We have given, CAB= 4x+14 and DAB = 6x-18

Both are supplementary angle

Therefore, CAB + DAB = 180

4x+14+6x-18=180

10x-4=180

10x=176

x=17.6

hence, CAB = 4(17.6)+14 = 84.4

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Given data:

The box is given.

The given expression can be written as,

Thus, the option (c) is correct.

The graph that represents the system of inequalities is the graph attached below.

The graph that would represent the system of inequalities must be two lines that intersect each other and have the exact slope and y-intercept of each of the lines on the graph.

Determine the slope and y-intercept of each of the inequalities, and also determine their boundary lines based on which inequality sign they have.

The line that represents the inequality, y ≥ ½x + 1, will be a solid line that has a slope of ½, and a y-intercept of 1.

The second line that represents the inequality, y ≥ -x - 2, will be a dashed line that has a slope of 1, and a y-intercept of -2.

Therefore, the graph that represents the features stated above for both lines is shown in the diagram below.

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Answer:

(0, -2)

Step-by-step explanation:

Add the x value and divide by 2

[tex]\frac{13-13}{2}[/tex] = [tex]\frac{0}{2}[/tex] = 0

Add the y value and divide by 2

[tex]\frac{-14 + 10}{2}[/tex] = [tex]\frac{-4}{2}[/tex] = -2

For this type of probability question, there are different ways to solve the same question but let's analyze the situation and calculate as simple as possible.

For our question, there are two parts, the first one first is the probability to pick someone who is a woman. Once there are 60 people of which 30 are women, it means this probability is 30/60. Let's keep this probability.

Now let's move on to the second part. The situation where we pick someone who is without a date. once there are 60 people and all 30 women have a date and 16 men also have a date it means 30 + 16 - 60 = 14 people does not have a date. So the probability to pick someone without a date is 14/60.

Now once we have analyzed the two parts of the question, and we have two probabilities all we need is to sum our probabilities, as follows:

But why do we sum and do not multiply? Because we use the proposition OR at "Find the probability of picking someone at random and getting a person who is a woman OR without a date" If the proposition was AND we would have multiplied both probabilities.

Answer:

I say w is equal to 4, because:

4 divided by 2 = 2

2 + 4 = 6

6 > 5

Step-by-step explanation:

Hope it helps! =D

In order to solve this system of equations, we can add both equations, this way we can find the value of y and then the value of x:

So the solution to this system is (3, 1).

Answer:

6  2/3 inches

Step-by-step explanation:

2 inches / 6 feet   * 20 feet = 6 2/3 inches

Using the congruency of the triangle we can prove all the conditions.

The dimensions of the sides and angles of two or more triangles determine whether they are congruent. A triangle's size and shape are determined by its three sides and three angles, respectively. Two triangles are said to be congruent if pairings of corresponding sides and corresponding angles are equal. They are the exact same size and form.

D is the midpoint of AC

so AB = BC

and also AD = CD

so the triangle ADB is congruent to triangle CDB

Therefore,

angle ADB = angle CDB

angle ABD = angle CBD

angle BAD = angle BCD

Using congruency of the triangle.

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Solution: X-value of vertex=-3

Y-value of vertex=-4

Zeros of the parabola: X=-5 and x=-1

Analysis

We can find the x-coordinate of the vertex, calculating -b/2a. First, we identify the a and b values of y=ax^2+bx+c of your quadratic equation.

b=6

a=1

Now, let's find the zeros of the parabola. We factorize the quadratic equation:

Answer:

2S-a1n/n

Step-by-step explanation:

S = n(a1 + an)/2

2S = n(a1 + an)

2S = na1 + nan

nan = 2S - na1

an = (2S - n a1)/n

Given the equation:

y = 828000 - 2700x

Where y is the value of the building and x is the number of months of use.

Let's find when the value of the building will be $666,000.

To find when the value will be $666,000, substitute 666000 for y in the equation and solve for x.

y = 828000 - 2700x

666000 = 828000 - 2700x

Subtract 828000 from both sides:

666000 - 828000 = 828000 - 828000 - 2700x

-162000 = -2700x

Divide both sided by -2700:

The value of the building will be $666,000 after 60 months.

Now, let's convert from months to years.

Where:

12 months = 1 year

Therefore, the value of the building will be $666,000 after 5 years.

ANSWER:

5 years.

Answer:

74.52

Step-by-step explanation:

[tex]P(10)=0.018(10)^3-0.294(10)^2+3.074(10)+55.180 \\ \\ =74.52[/tex]

Given:

m∠C = 70°

m∠CDE = 130°

Question 1:

To find ∠CDB, let's use the exterior angle theorem.

The exterior angle theorem states that the sum of 2 opposite interior angles is equal to the exterior angle.

Thus,

m∠C + m∠B = 130

70 + m∠B = 130

Subtract 70 from both sides:

70 - 70 + m∠B = 130 -70

m∠B = 60°

Now, use the triangle angle sum theorem to find ∠CDB.

The triangle angle sum theorem states that the sum of interior angles in a triangle is 180°

∠CDB = 180 - 70 - 60 = 50°

∠CDB = 50°

Question 2:

∠CBA = ∠C + ∠CDB

∠CBA = 70 + 50 = 120°

∠CBA = 120°

ANSWER:

∠CDB = 50°

∠CBA = 120°

Answer

∛20 is between 2 and 3.

Explanation

The question asks us to find the cube root of 20.

∛20

The key to doing this without the calculator is to take the cube of numbers and the one that has 20 in between them is the answer.

1³ = 1

2³ = 8

3³ = 27

We can see that 20 is between 8 and 27.

So,the cube root of 20 has to be betwen 2 and 3.

The other way to do this with the calculator is to actually find the cube root of 20

∛20 = 2.71

Which is between 2 and 3.

Hope this Helps!!!

The distance remaining is given by the equation d = 270 - 60t

Speed is the ratio of distance travelled to time taken. It is given by:

Speed = distance / time

Let d represent the distance from Las Vegas to Los Angeles and t represent the remaining time after departure.

A car travels from Las Vegas to Los Angeles at about 60 mi/h. The distance from Las Vegas to Los Angeles is 270 miles.

Hence distance remaining is:

d = 270 - 60t

The distance remaining is d = 270 - 60t

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The two inlet pipes can fill the tank in 4 hours and 10 hours.

The work done by the inlet pipes per hour is calculated to be:

The outlet pipe drains the tank in 2 hours. The work done will be:

Therefore, if both inlet pipes and the outlet pipes are opened at the same time, the work done by the pipes combined will be:

Since the work done to fill the tank is negative, it means that the tank will never get full as it empties faster than it fills up.

The number of lineups possible is the combination of selecting 5 songs from 8 songs.

8C5 = 56.

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Answer:

68

Step-by-step explanation:

Answer:  Table A has a proportional relationship

See the diagram below

==================================================

Explanation:

Table A has a proportional relationship because all the points are on the same straight line. That line in this case is y = 2x

Whatever x is, multiply it by 2 and you'll get the y value

Example: If x = 4, then y = 2*x = 2*4 = 8 which gives the point (4,8)

Another phrase for "proportional relationship" is "direct variation".

We have the next two points:

- (1/2,5)

- (5/2,9)

And we must use the point-slope formula to write an equation of a line in slope-intercept

First, we need to calculate the slope of the line using the point-slope formula

Where (x1, y1) and (x2, y2) are the two points

Now, replacing the points

Now, we must replace the slope and one of the two points in the point-slope formula:

Replacing m = 2 and (1/2, 5)

Finally, we must simplify to obtain the slope-intercept form

ANSWER:

y = 2x + 4

By Angle-Angle theorem similarity ΔABC is similar to ΔA'B'C'.

Given two triangles are ABC and A'B'C'.

Dilation is the process of resizing or transforming an object. It is a transformation that makes the objects smaller or larger with the help of the given scale factor. The new figure obtained after dilation is called the image and the original image is called the pre-image.

1) Triangle ABC is reduced to triangle A'B'C'

∠ABC=∠A'B'C'=90°

∠BAC=∠B'A'C'

So, by AA similarity

ΔABC≈ΔA'B'C'

2) Triangle ABC is enlarged to triangle A'B'C'

∠ABC=∠A'B'C'

∠BAC=∠B'A'C'

So, by AA similarity

ΔABC≈ΔA'B'C'

Therefore, by Angle-Angle theorem similarity ΔABC is similar to ΔA'B'C'.

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