2. The area of a garden plot can be represented by
the expression 85.2z - 58.8. The garden will be
divided into six sections for planting six different
vegetables. The sections will be equal in area.
Write an expression that represents the area of
each section.

Using the proportions of the side lengths of the pair of similar triangles, we have:

1. x = 35

2. x = 20; y = 23.3

3. x = 11

4. x = 9

5. x = 10

Triangles that are similar to each other, will have side lengths that are proportional to each other.

Therefore, using proportions, we would have:

1. x/14 = 40/16

Cross multiply:

16x = 40 * 14

16x = 560

x = 560/16

x = 35

2. x/12 = 15/9

9x = 12 * 15

9x = 180

x = 20

y/14 = 15/9

9y = 210

y = 23.3

3. (x + 5)/24 = 36/54

Cross multiply:

54(x + 5) = 36 * 24

54x + 270 = 864

54x = 864 - 270

54x = 594

x = 11

4. 20/28 = 15/(2x + 3)

Cross multiply:

20(2x + 3) = 28 * 15

40x + 60 = 420

40x = 420 - 60

40x = 360

x = 9

5. 24/28 = x + 8 / 3x - 9

Cross multiply:

24(3x - 9) = 28(x + 8)

72x - 216 = 28x + 224

72x - 28x = 216 + 224

44x = 440

x = 10

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The equation of the polynomial function graphed is given as follows:

y = -0.125(x³ + x² - 14x - 24).

From the graph, the roots of the polynomial are given as follows:

Considering the roots, the linear factors of the polynomial are given as follows:

Applying the Factor Theorem, the function, as a product of it's linear factors, is given as follows:

y = a(x + 3)(x + 2)(x - 4).

y = a(x² + 5x + 6)(x - 4)

y = a(x³ + x² - 14x - 24).

When x = 0, y = 3, hence the leading coefficient a is obtained as follows:

-24a = 3

a = -0.125.

Hence the function is:

y = -0.125(x³ + x² - 14x - 24).

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Answer: The outlier is $95 and the plot is D.

Step-by-step explanation:

          An outlier is the data value that's much larger or much smaller than the other data values. Here, that is $95.

          Excluding this value, our smallest is $15 and the largest is $60. We plot a dot at both of these points.

          The middle dot is the median. To find this, we will arrange the values in order and find the middle value. (We are excluding $95.) After doing this process, we see the middle dot is at 39.

    $15, $20, $38, $60, $45, $40, $35, $50

    $15, $20, $35, $38, $40, $45, $50, $60

    ----, ----, ----, $38, $40, ----, ----, ----

                    [tex]38 + 40 = 78, \;\;78 / 2\;\;\boxed{= 39}[/tex]

          This means we have dots at 15, 39 and 60, leading us to answer D.

Answer:

Step-by-step explanation:

5 times -4 is -20, so the equation becomes -20 - r + 1 = -37

-20 plus 1 equals -19, so the equation is now -19 - r = -37

Then you add 19 to both sides to isolate r

-r = -18

To get a positive r, divide or multiply both sides by -1, and you get r = 18

[tex]5(-4)-r+1=-37[/tex]

Simplify:

[tex]-20-r+1=-37[/tex]

Combine Like Terms:

[tex](-r)+(-20+1)=-37[/tex]

[tex]-r-19=-37[/tex]

Add 19 to both sides:

[tex]-r-19+19=-37+19[/tex]

[tex]-r=-18[/tex]

Divide both sides by -1:(To remove the negative from the variable r)

[tex]\dfrac{-r}{-1}=\dfrac{-18}{-1}[/tex]

[tex]\boxed{r=18}[/tex]

Answer: 97%

Step-by-step explanation:

If for the 3 exams, the mean was 83% and the first two were 76%, that means..

76 + 76 = 152 (divided by two = 76%/current mean)

In order to get an average of 83%, Colin has to have a score that is higher than 76% and somewhat closer to above 90%.

By doing trial and error (testing different percents between 76% and 80%),  you can come to the conclusion that, 76% + 76% + 97% = 249 / 3 = 83

Answer:

284 + 28d

Step-by-step explanation:

Because she has 284 it is known

She plans to obtain 28/day

Therefor, it should be 248+28d

The volume of the solid obtained by rotating about the x-axis the region enclosed by the curves is 32π/5 cubic units.

In this problem, we are asked to find the volume of a solid obtained by rotating a region enclosed by curves about the x-axis. We will use integration to calculate the volume.

First, let's sketch the region and the solid we need to find the volume of.

The region is enclosed by the curves

=> y = 16 /(x² + 16), y = 0, x = 0, and x = 4.

When we rotate this region about the x-axis, we get a solid with a hole in the center, shaped like a donut.

To find the volume of this solid, we can use the method of cylindrical shells.

We start by taking a thin strip of the region, parallel to the y-axis, and of width dy. This strip has height y, and we rotate it about the x-axis to get a cylindrical shell of thickness dy and radius x.

The volume of this cylindrical shell is given by the formula V = 2πxy dy, where x is the distance from the y-axis to the edge of the shell.

To express x in terms of y, we can solve for x in the equation

y = 16 /(x² + 16).

y(x² + 16) = 16

x² = 16/y - 16

x = √(16/y - 16)

Now we can substitute x into the formula for V to get:

V = 2πx(16/(x² + 16)) dy

[tex]= 2\pi(16/y - 16)^{1/2}(16/y) dy \\\\= 32\pi(y - y^{3/2}) dy[/tex]

To find the total volume, we integrate this expression from y = 0 to y = 1 (since the maximum value of y is 16/16 = 1):

[tex]\int_0^1 32\pi(y - y{(3/2)}) dy = 32\pi/5[/tex]

Therefore, the volume of the solid obtained by rotating the region about the x-axis is 32π/5 cubic units.

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Answer: Option 1

Step-by-step explanation:

I'd say the easiest way would be to find the prize per oz in both options

Option 1: $1.10/12oz = approx 0.092 (so around 9 pennies)

Option 2: $0.98/10oz = 0.098 (also 9 pennies but still slightly more than option 1)

You can check by choosing a random number of oz and multiplying them by the price to see which costs more

ex: 120 oz

option 1 : 10 x 1.10 = $11

option 2: 12 x 0.98 = $11.76

The fractions greater than 5/8 are 6/8, 7/8 and 8/8

Fractions greater than 5/8

Using the number line as a guide, we have the following:

Fractions greater = 6/8, 7/8 and 8/8

Fractions less than 3/8

Using the number line as a guide, we have the following:

Fractions less = 1/8 and 2/8

Fractions greater than 3/8

Using the number line as a guide, we have the following:

Fractions greater = 4/8, 5/8, 6/8, 7/8 and 8/8

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Answer:

Step-by-step explanation:

To prove that sin(51) + sin(81) - cos(21) = 0, we can use the trigonometric identity:

sin(A + B) = sin(A)cos(B) + cos(A)sin(B)

We can rewrite 51 and 81 as the sum of two angles:

51 = 45 + 6

81 = 90 - 9

Using the above identity, we can write:

sin(51) = sin(45 + 6) = sin(45)cos(6) + cos(45)sin(6) = (2/2)sin(6) + (2/2)cos(6) = sin(6) + cos(6)

and

sin(81) = sin(90 - 9) = sin(90)cos(9) - cos(90)sin(9) = 0 + (-1)sin(9) = -sin(9)

Finally,

sin(51) + sin(81) - cos(21) = sin(6) + cos(6) - sin(9) - cos(21) = (sin(6) + cos(6)) - (sin(9) + cos(21))

We know that sin(90 - x) = cos(x) and cos(90 - x) = sin(x), so we can rewrite the right-hand side as:

(sin(6) + cos(6)) - (cos(90 - 9) + sin(90 - 21)) = (sin(6) + cos(6)) - (cos(9) + sin(69))

We also know that sin(180 - x) = -sin(x) and cos(180 - x) = -cos(x), so we can rewrite the right-hand side as:

(sin(6) + cos(6)) - (cos(9) + -sin(111)) = (sin(6) + cos(6)) - (-sin(111) + cos(9))

Since sin(6) + cos(6) = sin(6 + 90) = sin(96) and -sin(111) + cos(9) = sin(69 - 180) = -sin(111), we can simplify the expression further to:

sin(6) + cos(6) - (-sin(111)) + cos(9) = sin(96) + cos(9)

Since sin(x + y) = sin(x)cos(y) + cos(x)sin(y), we can write:

sin(96) + cos(9) = sin(60)cos(36) + cos(60)sin(36) = (2/2)sin(36) + (√3/2)cos(36) = sin(36) + (√3/2)cos(36)

Finally, since sin(2x) = 2sin(x)cos(x), we can write:

sin(36) + (√3/2)cos(36) = 2sin(18)cos(18) + (√3/2)cos(36) = 2(√2/2)(√2/2) + (√3/2)(√2/2) = (√2 + √6)/2 + (√6/2) = (√2 + √6)

So, sin(51) + sin(81) - cos(21) = (√2 + √6) ≠ 0.

Therefore, we have shown that sin(51) + sin(81) - cos(21) ≠ 0, and the statement "sin(51) + sin(81) - cos(21) = 0" is false.

Answer: it’s C. My dear <3

Step-by-step explanation: hope this helps (btw I’m just being nice so don’t ask)

The initial balance of the account was approximately $3541.83.

This can be illustrated by using basic math: if you have $100 and it earns 5% interest each year, you'll have $105 at the end of the first year. You will wind up with $110.25 at the conclusion of the second year.

We can utilise the compound interest formula to find a solution to this issue:

A = P(1 + r/n)ⁿⁿ

In this case, we have P = the initial balance of the account, r = 0.23 (23% expressed as a decimal), n = 4 (since interest is compounded quarterly), t = 3 years, and A = $6258. We can solve for P by rearranging the formula:

P = A / (1 + r/n)ⁿⁿ

Substituting the values we know, we get:

P = 6258 / (1 + 0.23/4)⁴ˣ³

Simplifying this expression gives:

P = 6258 / 1.76757

P ≈ $3541.83

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The total area of the figure is 258cm². Thus, option 3 is corect.

Given:

shorter side: 18 centimeters

perpendicular height : 4 centimeters

portion from a point to a vertical line created by two vertices : 3centimeters

height : 12 centimeters

from figure we know that,  it is the vertex's height as well as the length of the sides to multiply together and we also have to divide since there is 5 sides

So , after multiplying the vertex height and sides and dividing it by the 5 , we get 258 cm²

Hence , the total area of the figure is 258cm².

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Answer:

7 degrees C

Step-by-step explanation:

To solve this question, we can start by ordering the temperatures from least to greatest:

4, 1, 0, -2, -1, -3, 1, -2, 3, -1  --> -3, -2, -2, -1, -1, 0, 1, 1, 3, 4

the lowest temperature would be -3 in this list, and the highest temperature in this list would be 4. We can find the difference in temperature using subtraction:

4-(-3) = 4+3=7

The difference is 7 degrees C.

Answer:

Step-by-step explanation:

The satellites Sputnik, Yeltsin, and Plekov are in a great circle, which is a circular path on the surface of a sphere that passes through the center of the sphere. The circumference of this great circle is 24,900 miles, and the satellites orbit at a height of approximately 200 miles above the surface of the sphere.

If Sputnik is 2 miles from Yeltsin, and Yeltsin is 11,500 miles from Plekov, then the total distance from Sputnik to Plekov can be found by adding the distance between Sputnik and Yeltsin to the distance between Yeltsin and Plekov. So, the total distance is 2 miles + 11,500 miles = 11,502 miles.

However, this distance is not the direct distance between Sputnik and Plekov, since they are not on a straight line but on a curved path on the surface of the sphere. To find the actual distance between Sputnik and Plekov, we can use the formula for the great-circle distance between two points on a sphere, which is:

d = acos(sin(lat1) * sin(lat2) + cos(lat1) * cos(lat2) * cos(long2 - long1)) * R

where lat1 and lat2 are the latitudes of the two points, long2 - long1 is the difference in longitudes of the two points, R is the radius of the sphere, and acos is the inverse cosine function.

Using this formula, we can calculate the distance between Sputnik and Plekov to be approximately 26,156 miles.

The height of each elevator at this time is, -2.5 m, negative means below ground level.

The distance covered by the object is equal to the product of the speed at which the object is moving and time taken for covering the distance.

Distance = Time × Speed

To find how long it would take each elevator to reach ground level, we can set h = 0 in the given expressions for their travel times:

Elevator A:  

= 0.8h + 16

= 0.8(0) + 16

= 16 seconds

Elevator B:  

= -0.8h + 12

= -0.8(0) + 12
= 12 seconds

Therefore, elevator A would take 16 seconds and elevator B would take 12 seconds to reach ground level at this time.

To find at what height the elevators pass each other, we can set their travel times equal to each other and solve for h:

0.8h + 16 = -0.8h + 12

1.6h = -4

h = -2.5

Now, we can substitute value of h in the expression

Elevator A:

= 0.8(-2.5) + 16

= 14 seconds

Elevator B:

= -0.8(-2.5) + 12

= 14 seconds

Therefore, the elevators would pass each other 14 seconds after they both start moving towards each other.

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The complete question:

Elevators A building has two elevators that both go above and below ground.

At a certain time of day, the travel time it takes elevator A to reach height h in meters is 0.8h+16 seconds.

The travel time it takes elevator B to reach height h in meters is -0.8h+12 seconds.

How long would it take each elevator to reach ground level at this time? If the two elevators travel toward one another, at what height do they pass each other? How long would it take?

Answer:

£3549

Step-by-step explanation:

The value of the car depreciates by 35% each year, so we can calculate the depreciation for 2006 as follows:

Depreciation for 2006 = 0.35 * £5460 = £1911

The value of the car at the end of 2006 is:

£5460 - £1911 = £3549

Answer:

The depreciation rate:

Step-by-step explanation:

Step 1: Total depreciation = 35% x 2 years = 70%

Step 2: Find the value of the car at the end of 2006:

Value at the end of 2006 = 5460 x (100 - 70)/100 = 1638

Therefore, the value of the car at the end of 2006 was £1638.

The equation to represent the function is y = 6x + 10 where y is the height of the drone in meters and x is the time in seconds. so the drone rises 6 meters per second.

The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.

Let us  find the rate of change, we can divide the total change in the height of the drone by the time taken for the change.

rate of change = (change in height) / (time taken)

(40 m - 10 m/ (5 s - 0 s)= 30 m/5 s=6m/s

The drone rises 18 m every 3 s

rise per second = 18 m / 3 s = 6 m/s

This means that the initial height of the drone is 10 meters, since it takes 3 seconds for the drone to rise to a height of 28 meters

Therefore, the equation to represent the function is:

y = 6x + 10

where y is the height of the drone in meters and x is the time in seconds.

Therefore, the drone rises 6 meters per second.

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If you get a new job, outline the forms you will have to deal with to file your taxes. The form has to fill in Form W-9 sent by the employer and given use to file your taxes.

The company determines what information to include in the Form 1098 or Form 1099 based on the information provided on the Form W-9.

Information about taxpayers is gathered using Form W-9 to assist with informational reporting to the IRS.

Although it is utilised in other contexts as well, the Form W-9 is most frequently employed when working with businesses that employ independent contractors.

The form requests that a taxpayer enter their name, residence, tax bracket, and withholding specifications.

Therefore, from the following conditions are:

1. Outline the forms you will need to file your taxes if you get a new job. Form W-9 must be completed and returned to the employer in order to file your taxes.

A W-2 will be given to you detailing your profits. New employees are frequently required to complete a Form W-4 rather than a Form W-9 in order to supply their company with information about their taxpayers.

2. Gross income is all income from whatever source derived that is not excluded or deferred from income. AGI is gross income minus "for AGI" deductions. Taxable income is AGI minus "from AGI" deductions.

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Answer:

Nintendo's revenue was $21 billion

Step-by-step explanation:

A measurement which is closest to the volume of the cylinder in cubic cm is 158.87 cubic cm.

Mathematically, the volume of a cylinder can be calculated by using this formula:

Volume of a cylinder, V = πr²h

Where:

Next, we would determine the radius of the base of the cylinder:

Circumference of a circle = 2πr

10 = 2πr

Radius, r = 1.59 cm.

Substituting the given parameters into the volume of a cylinder formula, we have the following;

Volume of a cylinder, V = 3.142 × (1.59)² × 20

Volume of a cylinder, V = 158.87 cubic cm.

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Answer:

-2x^4+4x^3+8x

Step-by-step explanation:

please check the answer given

According to the posed question, the rectangular prism's surface area would be 90 cm2.

What is a Rectangular Prism's Surface Area?

The total surface area of a rectangular prism's rectangular faces is alluded to as the prism's surface area. There are two distinct types of it: lateral surface area and total surface area. In contradiction to the lateral surface area, which only includes the lateral faces and omit the base areas, the total surface area of a rectangular prism refers to the area among all six faces.

Given, W = 3 cm, L = 6 cm, and H = 3 cm

surface area = 2 (WL + LH + HW)

                     = 2 (18 + 18 + 9)

                      = 2× 45 = 90 cm².

Consequently, the rectangular prism's surface area is 90 cm².

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Answer:

Therefore, z = 1 + i.

Step-by-step explanation:

Given that the argument of z + 1 is pi/6 and the argument of z - 1 is 2*pi/3, we can use the fact that the argument of a complex number is equal to the angle between the positive x-axis and the line connecting the origin to the complex number in the complex plane.

Let's call the complex number z = a + bi. Then, z + 1 = a + (b + 1), and z - 1 = a - (b - 1).

Using the argument values given, we have:

arg(z + 1) = pi/6, so the line connecting the origin to z + 1 makes an angle of pi/6 with the positive x-axis.

arg(z - 1) = 2pi/3, so the line connecting the origin to z - 1 makes an angle of 2pi/3 with the positive x-axis.

From the above information, we can sketch the complex plane and find the location of the complex number z. We then have two equations for a and b in terms of the argument of the complex numbers:

a = (z + 1 + z - 1)/2 = 1

b = (z + 1 - z - 1)/2 = 1

Therefore, z = 1 + i.

In the given figure angle CBF and angle CEF are supplementary angles. So Option C is correct.

An angle is a mathematical term, which we can define, when two straight lines or rays meet at a common endpoint. The common point is called the vertex of an angle. The word angle comes from a Latin word named ‘angulus,’.

Given that,

A figure which contains one trapezium BCEF

And in this portion angle CBF and angle BCE are  opposite angles

and opposite angles are supplementary angles,

Hence, the pairs of angles are ∠CBF & ∠CEF

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The term that best describes the point W in the triangle is given by the following option:

B. Orthocenter.

The orthocenter is the point where all three altitudes of a triangle will intersect.

An altitude is a line which passing through one of the three vertices of the triangle and is perpendicular to the opposite side relative to this vertex.

Hence point W is the orthocenter of triangle XYZ.

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The length of side AB within quadrilateral ABCD is 14.301 meters.

In this problem we find a geometric system formed by a quadrilateral and two diagonals, whose parameters are listed below:

CD = 20 m

m ∠ BCD = 20°

m ∠ ACB = 40°

m ∠ ADC = 45°

m ∠ ADB = 50°

The missing side can be found by combining law of sine and law of cosine:

Law of sine

20 / sin 65° = BD / sin 20°

BD = 7.548

20 / sin 75° = AD / sin 60°

AD = 17.932

Law of cosine

AB = √(AD² + BD² - 2 · AD · BD · cos ADB)

AB = √(17.932² + 7.548² - 2 · 17.932 · 7.548 · cos 50°)

AB = 14.301

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