ABCD is a parallelogram.
The diagonals of ABCD intersect at O.
OA = a and OB = b
a) Express the vector CA in terms of a.
b) Express the vector AB in terms of a and b.
c) Express the vector BC in terms of a and b.

The missing reasons for the proof are given as follows:

1) AB/DB = CB/EB - Given

2) ∠ABC ≅ DBE - Opposite Angles

3) ΔABC ~ ΔDBE - Angle - Side - Side Postulate.

The Angle-Side-Side (ASA) Postulate states that if two angles and a side of one triangle are congruent to two angles and the corresponding side of another triangle, then the two triangles are congruent.

In other words, if two triangles have the same orientation and their corresponding angles and sides match in size, the two triangles are identical. The ASA Postulate can be used to determine the congruence of triangles and to prove theorems and solve problems in geometry and related fields.

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The value of x is given as follows:

x = 10.

In a parallelogram, the consecutive angles are supplementary, meaning that the sum of their measures is of 180º.

The measures of the consecutive angles for the parallelogram in this problem are given as follows:

6x and 12x.

Hence the value of x is obtained as follows:

6x + 12x = 180

18x = 180

x = 180/18

x = 10.

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The solution is given below.

A table in which the rows represent the categories for one category variable, the columns represent the categories of a second category variable and each cell displays the frequency (or proportion) resulting for that row and column combination for the two variables.

here, we have,

1. Positive association - direct relationship: increase = increase and vice versa

2. Scatterplot - scattered data

3. Bivariate data - two variables

4. Two-way table - displays two variables into rows and columns

5. Two-way relative frequency table - shows the relative frequencies in the table

6. Association - how sets of data are related

7. Negative association - reverse relationship: increase = decrease and vice versa

8. Relative frequency - frequency of a specific data value divided by the total number of data values

9. No association - no relationship

10. Strength of association

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The amount of free space inside the cylindrical container would be

92 cm³.

A cylinder is a three-dimensional solid object having two similarly circular bases that are joined by a curving surface that is positioned a certain distance from the center.

Examples of cylinders are toilet paper rolls and cold beverage cans.

The volume of a cylinder is πr²h.

We know, The volume of a cylinder is πr²h and the volume of a

sphere is (4/3)πr³.

Therefore, The amount of empty space that will be there is the volume the spherical balls subtracted from the volume of the cylinder which is,

= [tex][\pi{(2)^2\times10] - [(\frac{4}{3})\pi(2)^3] cm^3[/tex]

= [tex]40\pi - (32/3)\pi cm^3[/tex].

= [tex]92 cm^3[/tex].

Q. A toy company sells 3-packs of sphere-shaped bouncy balls the height of the cylindrical package is 10 cm and the radius of each ball is 2 cm, If the company ships the three bouncy balls in a cylindrical container like the one shown, how many empty space will there be in the container?

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The explicit function of the sequence is a(n) = 2(5)^n-1

The definition of the function is given as

2, 10, 50, 250, 1250

The above definitions imply that we simply multiply 5 to the previous term to get the current term

Using the above as a guide,

So, we have the following representation

a(1) = 2

Common ratio, r = 5

So, we have

a(n) = a * r^n-1

This givs

a(n) = 2(5)^n-1

Hence, the sequence is a(n) = 2(5)^n-1

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The measure of angle 3 from the diagram is 115 degrees

The given figure is a line geometry. An angle is defined as the point where two lines meet.

Given that the measure of <5 is 115 degrees, the measure of <3 is calculated as shown below:

m<3 = m<5 = 115 degrees

This angles are equal since they are alternate exterior angles.

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Answer:

D

Step-by-step explanation:

9(4x + 8) ← multiply each term in the parenthesis by the 9 outside

= 36x + 72

Answer:

indicates the relationship of two variables whenever one variable changes.

Step-by-step explanation:

In a case whereby Mr. Ahmed has 31 students in his class. There are 14 boys and 17 girls.

From the question we were told that there are 14 boys in the class wehereby there the whole class has 31 students

Then we can conclude that te  ratio of the part-to-whole relationship for boys= 14/31.

From the question, there are 17 girls in the class, then we can conclude that  the ratio of the part-to-whole relationship for girls = 17/31.

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complete question:

Mr. Ahmed has 31 students in his class. There are 14 boys and 17 girls.

The ratio

describes the part-to-whole relationship for boys.

The ratio

describes the part-to-whole relationship for girls.

The linear equation represented by the graph is y = 8x.

A linear equation is a mathematical equation that describes a straight line in a two-dimensional space. It can be written in the form of:

y = mx + b

where y and x are variables, m is the slope of the line, and b is the y-intercept of the line (the point where the line crosses the y-axis).

The slope, represented by "m", describes the steepness of the line, while the y-intercept, represented by "b", is the point where the line intersects with the y-axis.

Linear equations can also be written in other forms, such as the standard form:

Ax + By = C

where A, B, and C are constants, and x and y are variables. In this form, the equation describes a line in terms of its x and y intercepts.

Linear equations are used in a variety of fields, including mathematics, physics, engineering, economics, and more. They are useful for describing and predicting relationships between variables that exhibit a linear pattern.

The equation represented by the graph is a linear equation in the form of y = mx + b, where m is the slope and b is the y-intercept.

To find the slope, we can use the formula:

m = (y2 - y1)/(x2 - x1)

Let's choose the first two points (0.5, 4) and (1, 8):

m = (8 - 4)/(1 - 0.5) = 8

So, the slope is 8.

To find the y-intercept, we can use the point-slope form of the equation:

y - y1 = m(x - x1)

Let's choose the point (0.5, 4) and the slope we just found:

y - 4 = 8(x - 0.5)

y - 4 = 8x - 4

y = 8x

So, the linear equation represented by the graph is y = 8x.

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Answer: [tex]370.08 m^2[/tex]

Step-by-step explanation: Lets do the easy part first. We see that there is a proven square in the center of the figure with side lengths of 12. The area formula is [tex]l*w[/tex] and since its a sqaure we can just multiply a side length by itself.

[tex]12*12 = 144[/tex]

^^ Thats the area of the square.

We now have to do the more difficult part which is finding the area of the semi circles. I combined the semi circles to form 2 circles with diameter 12. Now we know that the area of a circle is [tex]\pi r^2[/tex] and that the diameter is [tex]2r[/tex] so we just divide 12 by 2 to get the radius which is 6. Now we use the area formula and multiply it by 2 because there are 2 circles.

[tex]A = 2(3.14)(6^2)[/tex]

which is

[tex]226.08[/tex]

Now add it to the area of the square to get the area of the figure.

[tex]226.08+144 = 370.08[/tex]

put units and thats it!

Answer:

y = -x - 1

Step-by-step explanation:

y = mx +c

y = -x + c [ m = slope]

As the line passes through (4,-5)

-5 = -4 + c [Substituting value of x and y]

c = -1 [Solving the above equation]

The value of r is 2.134

in the equation, we would first

add 2.4

to both sides:

5.2r - 2.4 + 2.4 = 8.7+ 2.4

5.2r = 11.1

now we will

divide both sides by 5.2

to isolate the variable "r"

[tex]\frac{5.2r}{5.2} = \frac{11.1}{5.2}[/tex]

1r = 2.13461538

thus, the value of r = 2.134 approximately

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x=6 is the solution to the equation 18 - x - x - x = 0.

Two or more expressions with an Equal sign is called as Equation.

One way to build a subtraction equation using the indicated expression is:

18 - x - x - x = 0

Add the like terms

18 - 3x = 0

Now let us solve for x

we can isolate x on one side of the equation by subtracting 18 from both sides:

-3x = -18

Divide both sides by -3 to find the value of x:

x = 6

Therefore, a solution to the equation 18 - x - x - x = 0 is x = 6.

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The diameter of the circle is 396 units

The diameter is the length of the line through the center that touches two points on the edge of the circle.

A diameter is twice the radius of a circle.All diameters are segment but not all segments are diameter.

length of an arc = tetha/360 × πd

l = 80/360 × π d

88π = 80/360 × π d

80d = 88× 360

80d = 31680

divide both sides by 80

d = 31680/ 80

d = 396 units

therefore the diameter of the circle is 396 units

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A x=3 hope it helps-parker have a nice day

Answer:

The total cost of putting on the play is $500 for theater rental + $500 for actors + $750 for set decorations and costumes = $1750.

To reach the break-even point, the revenue from ticket sales needs to equal the total cost, so $1750 = $25 x (number of tickets sold).

Solving for the number of tickets sold, we can divide both sides by $25: $1750 / $25 = (number of tickets sold).

This gives us: 70 = number of tickets sold.

Therefore, Mr. Curry needs to sell 70 tickets to reach the break-even point.

Step-by-step explanation:

Answer:

Total distance flown = 5.2 miles

Step-by-step explanation:

The path of the helicopter is that of a right triangle with the first stretch of 2 miles as one leg and the other stretch 90° left as the other leg.

The return trip direct to starting point is the hypotenuse of the right triangle

By the Pythagorean theorem if c is the hypotenuse and a, b are the two legs

c² = a² + b²

Letting a = 2mi and b= 1mi,

c² = 2² + 1²

c² = 4 + 1

c² = 5

c = √5  (only positive square root considered)

c =2.236 mi

c = 2.236 mi to the nearest tenth

Total distance = 2 + 1 + 2.236

= 5.236

= 5.2 mi to the nearest tenth

The total number of sixth graders surveyed is 600 sixth graders

The given diagram is a pie chart with different percent of pet owned by sixth graders.

We need to determine the number of sixth grader surveyed if 30 sixth graders own birds.

Number of birds = 5% of the total sixth graders

Substitute the given parameters

30 = 0.05 * T

T = 30/0.05

T = 600

Hence is 30 sixth graders own birds, then 600 sixth graders were surveyed.

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The correct response is C. 0.0036 Square degrees The field of vision of the Hubble Space Telescope is only 0.006 degrees, which is around 100 times less than that of the Micro Observatory telescopes. But it has a 100 times better angular resolution!

Skywatchers can readily view planets with just a modest or medium-sized telescope. How much of our solar system is visible will wow you! Additionally, you don't need a completely dark sky to see all of the planets in our solar system; a telescope can still make Venus, Mars, Jupiter, and Saturn easily visible even when viewed in a city. From $100 to well over $10,000, a telescope can be purchased. In 2022, you can anticipate that a good telescope for visual observing will start around $300 and a telescope capable of deep-sky astrophotography would start around $800. With a 25x telescope, even the tiniest telescope should be able to see Saturn's rings.

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Large telescopes often have small fields of view. For example, the Hubble Space Telescope's (HST's) advanced camera has a field of view that is roughly square and about 0.06 degree on a side. Calculate the angular area of the HST's field of view in square degrees.

A. 0.006 Square degrees

B. 0.36 Square degrees

C. 0.0036 Square degrees

D. 0.06 Square degrees

One possible true statement regarding the data is that there is a significant outlier in the dataset, which is the value of 1,820,000.

An outlier is an observation that is significantly different from other observations in the dataset, and it can have a big impact on the results of statistical analyses, such as the mean or the median.

In this case, the outlier value of 1,820,000 is much larger than the other values, which range from 45,000 to 65,000.

It is possible that this value represents a different type of house, or that it has some unique characteristics that make it much more expensive than the other houses on Hill Street.

Therefore, if we are interested in analyzing the prices of houses on Hill Street, it may be important to remove the outlier value before conducting any statistical analysis.

P.S: Your question is incomplete, so I gave you a general overview on how to interpret data.

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The angle of elevation is 66.50 degrees

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

Rise = 46 ft

Length = 20 ft

The angle of elevation, x is calculated as

tan(x) = 46/20

Evaluate

tan(x) = 2.3

Take the arc tan of bth sides and evaluate

x = 66.50

Hence, the angle is 66.50 degrees

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Answer:

x=1; y=4

Step-by-step explanation:

for this system, you could use either substitution or elimination

i'll solve it both ways

SUBSTITUTION:

5x+y=9 becomes y=-5x+9

10x-7y=-18; substitue y from y=-5x+9

10x-7(-5x+9)=-18

10x+35x-63=-18

45x=45

x=1

substitue x into y=-5x+9

y=-5(1)+9

y=4

ELIMINATION

5x+y=9

10x-7y=-18

multiple the top equation by 7 to get 35x+7y=63

now, 7y and -7y cancel out

add the two equations to get 45x=45

x=1

substitute into 5x+y=9

5(1)+y=9

y=4

The apothem is the perpendicular distance from the center of a regular polygon to any one of its sides.

The apothem of a regular polygon is the perpendicular distance from the center of the polygon to any one of its sides because it serves as a measure of the inradius, or the radius of the circle inscribed within the polygon. In a regular polygon, all sides are congruent and all interior angles are equal, so the apothem is the same for all sides.

To see this, imagine drawing radii from the center of the polygon to each vertex, and then drawing the perpendicular bisector of each side. These perpendicular bisectors will all intersect at the same point, which is the center of the polygon. The apothem is the length of the line segment connecting this center point to any one of the sides of the polygon.

The apothem is useful in finding the area of a regular polygon. By using the formula for the area of a regular polygon in terms of the apothem and the number of sides, one can find the area of a regular polygon without having to find the exact shape of the polygon.

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To find 10 percent of 20000, you can multiply 20000 by 0.1, which gives you the answer of 2000.

0.1 × 20000 = 2000.

Here's the explanation of the calculation: When we want to find a certain percentage of a number, we can convert the percentage into a decimal by dividing it by 100. In this case, 10% is equivalent to 10/100, which simplifies to 0.1. Then, we can multiply 20000 by 0.1 to find the answer, which is 2000. In summary, to find 10% of a number, we can convert the percentage into a decimal by dividing it by 100, and then multiply the decimal by the original number.

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Julie is correct. If n=0 then you would get the fraction [tex]\frac{0}{0}[/tex] which is indeterminant (or undefined) since a zero is present in the denominator.

The area of the field is 900√10 m².

Pythagorean theorem states that for a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

We can apply this theorem only in a right triangle.

Example:

The hypotenuse side of a triangle with the two sides as 4 cm and 3 cm.

Hypotenuse side = √(4² + 3²) = √(16 + 9) = √25 = 5 cm

We have,

Quadrilateral ABCD.

The longer diagonal connects vertices A and C, and let E and F be the feet of the perpendiculars from vertices B and D to the longer diagonal AC.

From the figure,

BE = 20 m

DF = 30 m

AE = EC = 120/2 = 60 m

Now,

The area of the quadrilateral.

The area of a trapezoid.

= (sum of parallel sides) x (height) / 2

Using the Pythagorean theorem,

AB² = AE² + BE²

60² + 20² = 4000

AB = √(4000)

AB = 20 √10

And,

CD² = CE² + DF²

CD² = 60² + 30²

CD² = 4500

CD = √(4500)

CD = 15 √20

Now,

Area = AB + CD x 1/2 x AC

= 20√10 + 15√20 x 1/2 x 120

= 900√10

Therefore,

The area of the field is 900√10 m².

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Yes, both tests can be reported to denote a significant difference. The T-test is used for normally distributed data, whereas the Mann-Whitney U test is used for non-normally distributed data.

Yes, both the Student's T-test and the Mann-Whitney U test can be used to denote a significant difference. The Student's T-test is used to compare the means of two normally distributed samples and determine if the difference in means is statistically significant. The Mann-Whitney U test is used to compare the means of two non-normally distributed samples and determine if the difference in means is statistically significant. Both tests are used to test the null hypothesis that the means of the two samples are the same. If the null hypothesis is rejected, it can be concluded that the difference between the means is statistically significant. Both tests provide a measure of the strength of the evidence against the null hypothesis, which can be used to determine if the difference between the means is significant.

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Answer:

The length of side x in the given triangle is 12 m.

Step-by-step explanation:

To calculate length x in the given triangle, use the Area Sine Rule.

[tex]\boxed{\begin{minipage}{7.6 cm}\underline{Area Sine Rule} \\\\$A=\dfrac{1}{2}ab \sin C$\\\\where:\\ \phantom{ww}$\bullet$ $C$ is the angle. \\ \phantom{ww}$\bullet$ $a$ and $b$ are the sides enclosing the angle. \\\end{minipage}}[/tex]

The given values are:

Substitute the given values into the formula:

[tex]\implies 42=\dfrac{1}{2} \cdot 14 \cdot x\cdot \sin30^{\circ}[/tex]

Multiply 1/2 · 14 = 7:

[tex]\implies 42=7x\sin30^{\circ}[/tex]

Divide both sides of the equation by 7:

[tex]\implies 6=x\sin30^{\circ}[/tex]

Calculate sin30°:

[tex]\implies 6=\dfrac{1}{2}x[/tex]

Multiply both sides of the equation by 2:

[tex]\implies 12=x[/tex]

Therefore, the length of side x in the given triangle is 12 m.