Draw the dilation image A'B'C'D' of the trapezoid ABCD with the center of the dilation at the point P and the scale factor -2.

If the length of the rectangle be (3x+2) units and width (4x+10)units then the area of the rectangle be \($x=-\frac{2}{3}, x=-\frac{5}{2}$$\).

The region enclosed by an object's shape is referred to as the area. The area of the shape is the area that the figure or any other two-dimensional geometric shape occupies in a plane.

A rectangle's sides determine its area. In essence, the length and breadth of the rectangle multiplied together gives the area of the rectangle.

Let the length of the rectangle be (3x + 2) units and width of the rectangle be (4x + 10)units.

Area of rectangle = length × breadth

= (3x +2) × (4x +10)

simplifying the above equation, we get

= (3x) × (4x +10) + 2(4x +10)

= 12x² + 30x +8x +20

12x² + 38x + 20 = 0

simplifying the above equation, we get

By using quadratic equation, then

\($x_{1,2}=\frac{-38 \pm \sqrt{38^2-4 \cdot 12 \cdot 20}}{2 \cdot 12}$$\)

simplifying the above equation, we get

\($$\begin{gathered}x_{1,2}=\frac{-38 \pm 22}{2 \cdot 12}\end{gathered}$$\)

Separate the solutions, we get

\($$\begin{aligned}& x_1=\frac{-38+22}{2 \cdot 12}, x_2=\frac{-38-22}{2 \cdot 12} \\& x=\frac{-38+22}{2 \cdot 12}:-\frac{2}{3} \\& x=\frac{-38-22}{2 \cdot 12}:-\frac{5}{2}\end{aligned}$$\)

The solutions to the quadratic equation are:

\($x=-\frac{2}{3}, x=-\frac{5}{2}$$\)

The complete question is:

Find the area of rectangle with length (3x+2) units and width (4x+10)units.

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Two lines are parallel if and only if their slopes are the same, that is:

To find the slope of the original line we write it in slope-intercept form.

Then:

Comparing the two equations we notice that the slope of the line is -5.

Therefore the parallel line has equation:

Answer:

C

Step-by-step explanation:

In slope intercept form y=mx+b

m is your rate of change/ slope

since the slope is +5

This means that your rate of change, in this case elevation, is 5 feet per minute.

As for b which is your y intercept, the -30 can be represented by the point (0,-30) on a graph it would be -30ft below the x axis. Meaning that if the diver lets say is the point he is 30 feet below sea level and acsending at a rate of 5 feet per minute.

Answer:

38.88in²

Step-by-step explanation:

Area of shaded region = Area of square - Area of semi circle

First lets find the area of the square and semi circle

Area of square = s²

Where s = side length

Here we have a given side length of 8in

So s = 8

This means area = 8² = 64in²

Area of semicircle = (πr²)/2

Where r = radius

Here, the side length of the square and the diameter of the semicircle is shared meaning they are congruent. This means the diameter of the semicircle = 8in

To convert from diameter to radius we simply divide by 2

So radius = 8 / 2 = 4

Now we have Area = (πr²)/2

==> plug in r = 4 and π = 3.14

Area = (3.14(4)²))/2

==> simplify exponent

Area = (3.14(16))/2

==> multiply 3.14 and 16

Area = 50.24/2

==> simplify division

Area = 25.12in²

Area of shaded region

We now subtract the two areas

Area of shaded region = Area of square - Area of semi circle

Area of square = 64in² and Area of semicircle = 25.12in²

Area of shaded region = 64in² - 25.12in² = 38.88in²

Answer:

Well its basically 3 x 4 = 12, so for every lamb add four legs until you get to three

Step-by-step explanation:

Answer:

Step-by-step explanation:

To find Jonas's total score after 9 holes of golf, we add up all the individual scores:

+2 + 1 - 1 + 0 + 0 - 1 + 3 + 4 - 1 = 7

Jonas's total score after 9 holes is 7.

Since the total score is positive (above zero), Jonas's score is above par.

Answer:

Step-by-step explanation:

Answer:

23.45 meters

Step-by-step explanation:

To solve, you do 3.35*7, which gives you 23.45

Answer:

\(42a^{2}\)

Step-by-step explanation:

Split them into sections!

First, \(3a\) x \(5a\) = \(15a^{2}\)

Next, \((3a+3a+3a)(3a)\) = \(9a\) x \(3a\) = \(27a^{2}\)

Add \(15a^{2}\) and  \(27a^{2}\) to get \(42a^{2}\)

Hope I helped!

Answer:

Alternative Depreciation System May Be Required.

Step-by-step explanation:

The Alternative Depreciation System (ADS) straight-line method must be used in certain situations, rather than the standard MACRS method.  ADS must also be used if your business use of listed property drops to 50 percent or less for a year.

we have the following:

They are related in the way taht if we replace, in both equations it gives the same result:

The calculated measure of m∠PNM is 87 degrees

from the question, we have the following parameters that can be used in our computation:

The circle

Where, we have

PM = 360 - 64 - 122

Evaluate

PM = 174

Next, we have

m∠PNM = 1/2 * 174

So, we have

m∠PNM = 87

Hence, the measure of m∠PNM is 87 degrees

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Answer:

Step-by-step explanation:

Well, since the length of a month can vary in the number of days, this answer can also vary.

For example, February is only 28 days long, while December is 31 days long.

That being said, the average length of all 12 months is 30.436875 days, so if Denny left to another country on June 20th, he would most likely be back   July 19th of July 20th.

I hope this helps!

Answer:

The answer is 48.

Step-by-step explanation:

None.

The difference in the addition of both fractions is that they have different lowest common multiples.

We want to add the fraction expression given as:

¹/₂ + ¹/₄

Taking the Lowest common multiple of 8, we have:

(4 + 2)/8 = 6/8

However, for the second fraction expression, we have:

¹/₂ + ¹/₃

Taking the lowest common multiple which is 6, we have:

(3 + 2)/6 = 5/6

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Answer:

10:14

15:21

20:28

Step-by-step explanation:

Construct the histogram for the percentage increase in the starting salary by using 10 as the class width.

Answer Output using MINITAB software is given below at the end of answer (bar graph)

Frequency:

The frequencies are calculated by using the tally mark and the range of the starting salary is grouped and the range is from 40 to 120. Here the number of times each percentage increase repeats is the frequency of that particular class.

The width of class is 10.

Make a tally mark for each value in the corresponding revenue class and continue for all values in the data.

The number of tally marks in each class represents the frequency, f of that class.

Similarly, the frequency of remaining classes for the percentage increase is given below at the end of the answer.

The data represents the median starting salary, the mid-career salary, and the percentage increase from starting salary to mid-career salary for the 20 college degrees with the highest mid-career salary.

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A perfect square refers to a number that is the result of multiplying an integer by itself. In this case, 6^1 is equal to 6.

However, 6 is not a perfect square because it cannot be obtained by multiplying an integer by itself. The perfect squares up to 6^1 would be 1^2 = 1 and 2^2 = 4.

The simplified boolean expression for F5 is F5 = P OR (NOT R). In this expression, P represents one boolean variable, and (NOT R) represents the negation of another boolean variable R. The OR operator combines the two variables, resulting in the final boolean expression F5.

To simplify the boolean expression F5 = (P AND Q) OR (R AND NOT P), we can apply Boolean algebra rules to reduce it to its simplest form.

Step 1: Apply De Morgan's laws

NOT (R AND NOT P) can be simplified as (NOT R) OR P.

Step 2: Distributive property

F5 = (P AND Q) OR ((NOT R) OR P)

Step 3: Apply associative property

F5 = (P AND Q) OR (P OR (NOT R))

Step 4: Apply absorption law

F5 = P OR (P OR (NOT R))

Step 5: Apply idempotent law

F5 = P OR (NOT R)

By simplifying the expression, we have reduced it to its simplest form while preserving its logical meaning. The simplified expression can be used to analyze and evaluate logical circuits or systems where the variables P and R are used.

Remember, boolean algebra allows us to manipulate and simplify complex logical expressions by applying various rules and properties. These simplifications help in understanding and analyzing logical operations in digital systems and circuits.

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The question probable may be:

Consider the boolean variables P, Q, and R. Determine the boolean expression for the variable F5 using the given variables:

F5 = (P AND Q) OR (R AND NOT P)

Using the boolean variables P, Q, and R, can you simplify the expression F5 to its simplest form by applying Boolean algebra rules?

Answer:

3

Step-by-step explanation:

x=3

4÷12=3

3*4=12

So the answer is 3

Answer:

If I am not mistaken, the equation is:

6x + 5

So the terms are:

The coefficient is:

The variable is:

The constant is:

I hope this helps! Your question was a bit unclear...

- sincerelynini

The difference (faculty-student) in the sample proportions of those who think that students should have five minutes to switch classes usually varies by roughly 0.096 from the actual difference in proportions.

A low standard deviation shows that the values tend to be close to the mean (also known as the expected value) of the set, whereas a high standard deviation suggests that the values are spread out over a broader range.

The standard deviation is a measure of variance or dispersion in statistics.

So, the sampling distribution's standard deviation is calculated as follows:

\(\begin{aligned}& \sigma_{\mathrm{F}}-\sigma_{\mathrm{s}}=\sqrt{\frac{0.37 \times(1-0.37)}{28}+\frac{0.89 \times(1-0.89)}{100}} \\& \sigma_{\mathrm{F}}-\sigma_{\mathrm{s}}=0.096\end{aligned}\)

The actual proportional difference between those who believe five minutes is not enough time for pupils to switch courses and those who believe this is generally 0.096.

Therefore, the difference (faculty-student) in the sample proportions of those who think that students should have five minutes to switch classes usually varies by roughly 0.096 from the actual difference in proportions.

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Correct question:

n a large high school, 37% of the teachers believe that five minutes is not enough time for students to change classes. However, 89% of the students believe that five minutes is not enough time for students to change classes. Let p hat Subscript Upper F and p hat Subscript Upper S be the sample proportions of teachers and students, respectively, who believe that five minutes is not enough time for students to change classes. Suppose 28 teachers and 100 students are selected at random and asked their opinion on the amount of time students have to change class. Which of the following is the correct shape and justification of the sampling distribution of p hat Subscript Upper F Baseline minus p hat Subscript s ?

Using arithmetic progression, number of logs in 6th row are 33.

We can use the information that each row has 5 fewer logs than the row below it to create a sequence of the number of logs in each row. Let's call the number of logs in the first row "a" (which we know is 58 logs). Then, the number of logs in the second row will be "a - 5", the number of logs in the third row will be "(a - 5) - 5" or "a - 10", and so on.

So, we have the sequence of the number of logs in each row as:

a, a - 5, a - 10, a - 15, a - 20, ...

To find the number of logs in the 6th row, we need to find the 6th term in this sequence. We can use the formula for the nth term of an arithmetic sequence:

an = a₁ + (n - 1)d

where an is the nth term, a1 is the first term, n is the number of the term we want to find, and d is the common difference between terms (which is -5 in this case, since each row has 5 fewer logs than the row below it).

Substituting the given values, we get:

a₆ = a₁ + (6 - 1)(-5)

= a - 25

So, the number of logs in the 6th row is a - 25. Since we know that a is 58 logs, we can substitute and simplify:

a - 25 = 58 - 25 = 33

Therefore, the answer is (b) 33.

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Answer:

3ft 11 in

Step-by-step explanation:

1 foot equals 12 inches, 12 × 3 = 36 = 3 feet + 11 inches = 47 inches = 3ft 11in

Answer:

Answer down below

Step-by-step explanation:

h (3x-4)

= \(\frac{1}{3x-4+2}\)

= \(\frac{1}{3x-2}\)

Step-by-step explanation:

the area of a triangle is always :

baseline × height / 2

the height is the line from the vertex opposite of the line we choose to be baseline to the baseline in a right (90°) angle.

and yes, that applies also to heights that actually land outside the triangle, like in this example.

so, the baseline here is 11, the height is 7.

the area is :

11 × 7 / 2 = 77/2 = 38.50

Answer:

\(a_{61}=-972\)

Step-by-step explanation:

Arithmetic Sequences

The arithmetic sequences are identified because any term n is obtained by adding or subtracting a fixed number to the previous term. That number is called the common difference.

The equation to calculate the nth term of an arithmetic sequence is:

\(a_n=a_1+(n-1)r\)

Where

an = nth term

a1 = first term

r   = common difference

n  = number of the term

We are given the first terms of a sequence:

-12, -28, -44,...

Find the common difference by subtracting consecutive terms:

r = -28 - (-12) = -16

r = -44 - (-28) = -16

The first term is a1 = -12. Now we calculate the term n=61:

\(a_{61}=-12+(61-1)(-16)\)

\(a_{61}=-12-60*16=-12-960\)

\(\mathbf{a_{61}=-972}\)

largest 4 digit number : 9999

smallest 4 digit numbers : 1000

Difference = 9999 - 1000 = 8999

Answer:

If you need further explanation, comment on this

In first situation= =given angle + x=sum of angle of triangle. =110°+x=180°=70° X=70° Similarly, 2. condition can be solved i.e-x=144° There you go! Have a awesome day.