what would happen if everyone wasnt on earth? (please be creative)

5 "Always." Consecutive angles of a rectangle are always congruent.

6 "Never." A parallelogram is not always a square.

7 "Sometimes." In a rhombus, the diagonals are always perpendicular bisectors of each other, but they are not always congruent.

8 "Always." A rectangle has congruent sides, but not necessarily all four sides.

9 Given: ABCD is a parallelogram

To prove: AABC = ACDA

Proof:

AB || DC (definition of parallelogram)

AD || BC (definition of parallelogram)

∠ABC = ∠CDA (alternate interior angles)

AC = AC (reflexive property)

∠BCA = ∠DAC (alternate interior angles)

Therefore, AABC = ACDA (ASA congruence theorem)

10 Given: TRAP is an isosceles trapezoid

To prove: AAPR ARTA

TR = AP (definition of isosceles trapezoid)

∠APT = ∠ATR (alternate interior angles)

∠PAR = ∠RTA (alternate interior angles)

∠PAR = ∠APT (angles at a point)

Therefore, AAPR ARTA (AA congruence theorem)

Consecutive angles of a rectangle are always congruent. This is a property of rectangles that is true for every rectangle.

A square is a specific type of parallelogram that has all four sides congruent and all four angles right angles.

A rectangle has two pairs of opposite sides that are congruent, but the adjacent sides may have different lengths. This is a defining characteristic of rectangles, and it is always true for every rectangle.

The ASA congruence theorem states that two triangles are congruent if two angles and the included side of one triangle are congruent to the two angles and the included side of the other triangle. In this case, ∠ABC and ∠CDA are congruent by (3), AC is congruent by (4), and ∠BCA and ∠DAC are congruent by (5). Therefore, AABC = ACDA by the ASA congruence theorem.

The AA congruence theorem states that two triangles are congruent if two angles of one triangle are congruent to two angles of the other triangle, and the side between those angles is congruent in both triangles

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Answer:

$1,093.67 = $1,100 rounded to th next $100

Step-by-step explanation:

Final investment value

$1,093.67

Total interest earned

$273.67

Initial balance

$820.00

Total monthly deposits

$0.00

Effective Annual Rate (APY)

1.816%

The formula used in the compound interest calculator is A = P(1+r/n)^(nt)

A = the future value of the investment

P = the principal investment amount

r = the interest rate (decimal)

n = the number of times that interest is compounded per period

t = the number of periods the money is invested for

Answer:

1100

Step-by-step explanation:

To describe the temperatures for the week, we can apply the following statistical tools:

a) Find the mean, median, mode, and range.

c) Construct a line graph.

d) Construct a stem and leaf plot.

We can describe temperatures using measures of central tendencies (especially the mean, median, and mode).

The mean temperature is the average, which shows the overall trend in temperature changes.  It is computed by adding up the temperatures for the period and diving by the number of data values.

In addition, the median gives the middle value when the data set is ordered in ascending or descending orders. Similarly, the mode gives the highest temperature occurrence within the period. It may not be useful here.

We can estimate the difference between the highest and lowest temperature for the week with the range.

A line graph (showing connecting lines) and a stem-and-leaf plot (like a bar graph) can graphically describe the temperatures for the week.

Thus, we can use Options A, C, and D to describe the temperature.

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What could you do to describe the following data, showing temperatures for the week? (Check all that apply.)

Mon - 65°

Tues - 67°

Wed - 66°

Thur - 70°

Fri - 72°

Sat - 68°

Sun - 69°

a) Find the mean, median, mode, and range.

b) Survey people about the weather.

c) Construct a line graph.

d) Construct a stem-and-leaf plot.

Answer:

where is the figure? to calculate the surface area

The direct labor cost included in the Preble Company's flexible budget for March is $819,000.

To find the direct labor cost included in the company's flexible budget for March, we shall estimate the actual direct labor cost incurred during the period.

Given:

Actual production and sales =n26,600 units

Actual direct labor rate = $13.00 per hour

Actual direct labor hours worked = 63,000 hours

Direct labor cost = Actual direct labor rate × Actual direct labor hours worked

Direct labor cost = $13.00/hour × 63,000 hours

Direct labor cost = $819,000

Hence, the direct labor cost included in the company's flexible budget for March would be $819,000.

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Answer:

Kindly check explanation

Step-by-step explanation:

Given the data:

Speed(Km/hr)___No of players__Relative freq

10--13.9_________4______4/612 = 0.0065359

14-17.9_________ 7______7/612 = 0.0114379

18-21.9________20_____20/612 = 0.0326797

22-25.9_______ 83_____83/612 = 0.1356209

26-29.9_______319____319/612 =0.5212418

30-33.9______ 179_____179/612 = 0.2924836

The percentage of players that had a top speed between 22 and 25.9 km/h was : 0.1356209 × 100 = 13.56%

c. The percentage of players that had a top speed less than 13.9 km/h was: 0.0065359 × 100 = 0.65%

Answer:

12) A ( 9, 11, 13, 15)

13) A ( o , a)

14) A  (b ∈ ( a, b, c, d, e, f))

15) C ( -364)

16) D (-1°C)

17) B (Negative)

18) C (26 feet)

19) B (7)

Step-by-step explanation:

12) All of these are odd numbers greater than 7

13) These are the only vowels in "MONDAY"

14) Point B cannot belong in a set that already has B

15) -9876 + 9512 = -364

16) 4 - 5 = -1

17) ex: -2 + (-2) = -4

18) -20 + 12 - 18 = -26

19) 3(5) + 4(-2) = 15 - 8 = 7

-Chetan K

The area of the square with a side length of 3.1 meters is 9.61 square meters.

To find the area of a square, we need to multiply the length of one side by itself. In this case, the square has a side length of 3.1 m.

Area of a square = side length × side length

Substituting the given side length into the formula:

Area = 3.1 m × 3.1 m

To perform the calculation:

Area = 9.61 m²

It's worth noting that when calculating the area, we are working with squared units. In this case, the side length is in meters, so the area is expressed in square meters (m²). The area represents the amount of space enclosed within the square.

Remember, to find the area of any square, you simply need to multiply the length of one side by itself.

The area of the square with a side length of 3.1 meters is 9.61 square meters.

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Applying the function, it is found that the object was dropped from a height of 256 feet.

--------------------

The time it takes for the object to hit the ground is given by:

\(t(h) = \sqrt{\frac{h}{4}}\)

--------------------

\(t(h) = \sqrt{\frac{h}{4}}\)

\(8 = \sqrt{\frac{h}{4}}\)

\((\sqrt{\frac{h}{4}})^2 = 8^2\)

\(\frac{h}{4} = 64\)

\(h = 4(64) = 256\)

The object was dropped from a height of 256 feet.

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Answer:

1,024

Step-by-step explanation:

Answer: 2

Step-by-step explanation:

Let the constant be \(a\). Then, it follows that:

\(\frac{100+a}{60+a}=\frac{180+a}{100+a}\\\\(100+a)^2=(60+a)(180+a)\\\\a^2 +200a+10000=a^2 +240a+10800\\\\200a+10000=240a+10800\\\\40a=-800\\\\a=-20\\\\\therefore r=\frac{100-20}{60-20}=2\)

Rounding to the nearest hundredth, the area is approximately 151.976 cm².

The formula for the area of a sector is:

A = (θ/360) x πr²

where θ is the central angle in degrees, r is the radius, and π is pi (3.14).

Plugging in the given values, we get:

A = (144/360) x 3.14 x 11^2

A = 0.4 x 3.14 x 121

A = 151.976

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A diagram of parallelogram MNOP is attached below

We have side MN, || side OP, and side MP || NO

Using the rule of angles in parallel lines, ∠M and ∠P are supplementary as well as ∠M and ∠N.

Since ∠M+∠P = 180° and ∠M+∠N=180°, we can conclude that ∠P and ∠N are of equal size.

∠N and ∠O are supplementary by the rules of angles in parallel lines

∠O and ∠P are supplementary by the rules of angles in parallel lines

∠N+∠O=180° and ∠O+∠P=180°

∠N and ∠P are of equal size

we deduce further that ∠M and ∠O are of equal size

Hence, the correct statement to complete the proof is

∠M ≅ ∠O; ∠N ≅ ∠P

The area of the triangle is 52.32 square units

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

The triangle (see attachment)

The base of the triangle is calculated as

base = 12 * tan(36)

The area of the triangle is then calculated as

Area = 1/2 * base * height

Where

height = 12

So, we have

Area = 1/2 * base * height

Substitute the known values in the above equation, so, we have the following representation

Area = 1/2 * 12 * tan(36) * 12

Evaluate

Area = 52.32

Hence, the area of the triangle is 52.32 square units

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The mean absolute deviation (MAD) for the given data is 1/20. This means that, on average, each data point in the set differs from the mean by 1/20.

To find the mean absolute deviation (MAD) of a set of data, we need to calculate the average difference between each data point and the mean of the data set. Here's how we can calculate it for the given data:

Step 1: Find the mean (average) of the data set.

Mean = (1/4 + 5/8 + 3/8 + 3/4 + 1/2) / 5 = 2/5

Step 2: Calculate the difference between each data point and the mean.

Differences: |1/4 - 2/5|, |5/8 - 2/5|, |3/8 - 2/5|, |3/4 - 2/5|, |1/2 - 2/5|

Step 3: Calculate the absolute value of each difference.

Absolute Differences: 1/20, 1/40, 1/40, 1/20, 1/10

Step 4: Find the average of the absolute differences.

MAD = (1/20 + 1/40 + 1/40 + 1/20 + 1/10) / 5 = 1/20

The MAD provides a measure of the average amount of variation or dispersion in the data set. In this case, a MAD of 1/20 indicates that the data points are relatively close to the mean, with most values falling within 1/20 of the mean value.

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Answer:

The answer is in the picture below

Step-by-step explanation:

Hope this helps!

Figure number four in the image shows △MNP reflected over the y-axis to form △M`N`P`. The correct option is D.

The reflection operator geometrically repositions image elements, or pixel values, in such a way that they are reflected about a user-specified image axis or image point and placed in a new position in a matching output image.

In the given image option fourth is showing the correct reflection of the triangle △MNP over the y-axis to the form △M`N`P'.

It is observed that every point of the triangle MNP is at the same distance from the y-axis as every point of the triangle M'N'P'.

Therefore, figure number four in the image shows △MNP reflected over the y-axis to form △M`N`P`. The correct option is D.

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Answer: .1036

Step-by-step explanation:

The area of the label needed to cover the face of the box is 144 in².

To find the Area if Face we need to find the length and breadth of the rectangular faces first.

using distance formula the distance between (-6,5) & (6,5) is 12

and distance between (-6,-4) & (6,-4) is also 12.

Hence this is a rectangular box with both length and breadths as 12.

Area of the face = Length × Breadth

Area= 12×12

Area = 144 in²

What is Distance Formula?

The distance formula can be used to calculate the separation between two points on the xy-plane. The co-ordinate of a point is represented as an ordered pair (x, y), where the x-coordinate (or abscissa) is the distance from the x-axis and the y-coordinate (or ordinate) is the distance from the y-axis.

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Answer:

144 in2

Step-by-step explanation:

Answer:

Step-by-step explanation:

Everything to know about a and b!

Graph the parabola using the direction, vertex, focus, and axis of symmetry.

Direction: Opens Up

Vertex: (0, −5)

Focus: (0, \(-\frac{19}{4\\}\)−)

Axis of Symmetry: x = 0

Directrix: y = \(-\frac{21}{4}\)

For Part b

Table:

x    |     y

______

−2      −1

−1      −4

0       −5

1        −4

2       −1

9514 1404 393

Answer:

  (b)  x -3 ≥ 0

Step-by-step explanation:

The square root function will return non-negative values, so the inequality √(x-3) ≥ 0 gives no new information. What is required is that the argument of the square root function be non-negative:

  x -3 ≥ 0

Answer:

slope is 2 or 2/1 and y intercept is -7

Step-by-step explanation:

y=mx+b

mx= slope

b= y intercept

The range is the best measure of variability for this data, and its value is 4.

The line plot displays the number of roses purchased per day at a grocery store, with the data values ranging from 0 to 4 (since there are no dots above 4).

The best measure of variability for this data is the range, which is the difference between the maximum and minimum values in the data set. In this case, the minimum value is 0 and the maximum value is 4, so the range is:

Range = Maximum value - Minimum value = 4 - 0 = 4

Therefore, the range is the best measure of variability for this data, and its value is 4.

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\(zeros \begin{cases} x=0\implies &x=0\\ x=9\implies &x-9=0\\ x=9\implies &x-9=0 \end{cases}\qquad \implies a(x)(x-9)(x-9)=\stackrel{y}{0} \\\\\\ \stackrel{\textit{with a coefficient of 1}}{1(x)(x-9)(x-9)=y}\implies x(x-9)^2=y\implies x(x^2-18x+81)=y \\\\\\ ~\hfill {\Large \begin{array}{llll} x^3-18x^2+81x=y \end{array}}~\hfill\)

Answer:

0

Step-by-step explanation:

Look at the graph, for x because it is going right continously but it is going towards 0 on the y-axis.

Think of it this way it that line kept going rightward for infinite amounts what would the y value get close to? 0.

In given graph of function, When x → ∞, f(x)=0

Option D is correct.

From the given graph of function,

It is observed that, x- axis is the asymptote of the function.

Since, graph of function never intersect the x- axis.

When x → ∞, f(x)=0

Therefore, option D is correct.

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1) Let's solve this Linear System of equations

y=-5x-13

x+2y=-23

2) Using the method of Substitution on the 2nd equation

x +2(-5x-13) = -23

x -10x -26= -23

-9x -26 =-23 Add 26 to both sides

9x=-23+26

9x = 3

x= 3/9

x= 1/3

y=-5(1/3) -13

y=-5/3 -13

y=-44/3

3) So there is one solution to that Linear System, different than those points (-1,-8) (4,10).

Answer: (6,11π/6).

Step-by-step explanation:We need to find the radius r and the angle θ. Remember that r2=x2+y2, so

because of the signs of x and y, our angle is in quadrant IV. Therefore, we find that θ=11π/6.

So the final answer is (6,11π6).

A formula for the function g(x) obtained when the graph of f(x) = 1/x is shifted down 7 units and to the right 5 units is g(x) = 1/(x - 5) - 7.

In Mathematics, the translation a geometric figure or graph to the right simply means adding a digit to the value on the x-coordinate of the pre-image or function.

In Mathematics, a horizontal translation to the right is modeled by this mathematical expression g(x) = f(x - N) while a vertical translation to the negative y-direction (downward) is modeled by this mathematical expression g(x) = f(x) - N.

Where:

By translating the graph of f(x) = 1/x down 7 units and 5 units to the right , we have:

g(x) = f(x - 5) - 7

g(x) = 1/(x - 5) - 7

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Using the relation between velocity, distance and time, it is found that:

Velocity is distance divided by time, that is:

\(v = \frac{d}[t}\)

Flying against the wind, an airplane travels 2520 kilometers in 4 hours, that is:

\(v - v_w = \frac{2520}{4}\)

\(v - v_w = 630\)

\(v = 630 + v_w\)

Flying with the wind, the same plane travels 9450 kilometers in 9 hours, hence:

\(v + v_w = \frac{9450}{9}\)

\(v + v_w = 1050\)

\(v = 1050 - v_w\)

Hence, solving for the wind's speed:

\(630 + v_w = 1050 - v_w\)

\(2v_w = 420\)

\(v_w = \frac{420}{2}\)

\(v_w = 210\)

For the plane, we have that:

v = 1050 - 210 = 840.

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Answer:

2

Step-by-step explanation:

8gallons=16 cup

8x16=128

62+2=64

128÷2=64

Step-by-step explanation:

median :

first, arrange the numbers

= 9,11,13,37,48

then, determine the middle

= 13

mean :

mean = total numbers ÷ numbers

mean = (9 + 11 + 13 + 37 + 48) ÷ 5

= 118 ÷ 5

= 23.6

Answer:

the answer is 100

Step-by-step explanation:

the number greater than 2 : 3,4,5,6

so 4/6 x 150 = 2/3 x 150 = 100