A farmer plants the same amount every day, adding up to 2 1/4 acres at the end of the year. If the year is 3/4 over, how many acres has the farmer planted?

Let's assume that each van and each bus can carry "x" number of students.

Let's assume there are "x" students in each van and each bus. Therefore, the total number of students in High School A's senior class is 8x + 8x = 16x. We know that the total number of students in High School A's senior class is 240, so we can set up an equation:

16x = 240

Solving for x, we get:

x = 15

So, each van and each bus had 15 students in it for High School A's senior class.

Similarly, for High School B, the total number of students is 4x + 1x = 5x. We know that the total number of students in High School B's senior class is 54, so we can set up an equation:

5x = 54

Solving for x, we get:

x = 10.8

Since the number of students must be a whole number, we can round up to 11. Therefore, each van and each bus had 11 students in it for High School B's senior class.

Therefore, the total number of students in High School A's senior class is 1x + 6x = 7x. We know that the total number of students in High School A's senior class is 372, so we can set up an equation:

7x = 372

Solving for x, we get:

x = 53

Therefore, each van and each bus can carry 53 students for High School A's senior class.

Similarly, for High School B, the total number of students is 4x + 12x = 16x. We know that the total number of students in High School B's senior class is 780, so we can set up an equation:

16x = 780

Solving for x, we get:

x = 48.75

Since the number of students must be a whole number, we can round up to 49. Therefore, each van and each bus can carry 49 students for High School B's senior class.

Let's assume that the price of one senior citizen ticket is "s" and the price of one child ticket is "c". Therefore, we can set up two equations based on the given information:

\(3s + 9c = 75\)

\(8s + 5c = 67\)

We can solve these equations simultaneously to find the values of "s" and "c". One way to do this is to multiply the first equation by 8 and the second equation by 3, so that we can eliminate "c" and solve for "s":

\(24s + 72c = 600\)

\(24s + 15c = 201\)

Subtracting the second equation from the first, we get:

57c = 399

Solving for "c", we get:

c = 7

Substituting this value into one of the original equations, we can solve for "s":

\(3s + 9(7) = 75\)

\(3s + 63 = 75\)

\(3s = 12\)

\(s = 4\)

Therefore, one senior citizen ticket costs $4 and one child ticket costs $7.

Let's assume that the speed of the boat in still water is "b" and the speed of the current is "c".

Therefore, we can set up two equations based on the given information:

\(336 = (b + c) * 12\)

\(336 = (b - c) * 14\)

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Answer:

x=35

y=145

z=25

Step-by-step explanation:

(do first)x:

55 + 90 = 145

180-145=35

(do last)y:

25+10=35

180-35=145

(do second)z:

65+90=155

180-155=25

Answer:

x = 35, y = 145, z = 25

Step-by-step explanation:

All triangles' angles have a sum of 180°. Because we know this, we can solve the first triangle easily.

180 = x + 90 + 55

180 = x + 145

35 = x

Angles x and y are what we call suplementary angles. This means they have a sum of 180°.

180 = 35 + y

145 = y

Once again, we know that triangles have a sum of 180°. So the next triangle should now be easy to solve.

180 = 10 + 145 + z

180 = 155 + z

25 = z

The longest line segment that may be drawn in one of these pieces is l and l^2 is 108.

Diameter is 12cm and radius is 6cm.

Central angle of one arc = 360 deg / 3 = 120 deg

I^2 = 108.

A circle is a figure composed of a given point, that is, every point on a plane that lies at a given distance from  the center. Equivalently, it is a curve describing points moving along a plane such that the distance from a given point is constant. The distance between a point on a circle and its center is called the radius. In general, the radius should be a positive number. This article is about circles in Euclidean geometry, specifically the Euclidean plane unless otherwise noted.

A line segment is a line segment that can connect two points. It is endless and extends endlessly in both directions. If you mark two points A and B on it and select these segments separately, they will be straight segments.

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Answer:

C  \(\frac{48}{70}\)

Step-by-step explanation:

Option C - \(\frac{48}{70}\) is incorrect because when multiplying the numerator and denominator of the fraction \(\frac{7}{10}\) by 7, you’re suppose to get \(\frac{49}{70}\).

Hence, section PL measures about 18.03 cm in length (rounded to the nearest hundredth digit).

The length of a one-dimensional object, such as a line, curve, or straight segment, is measured by the fundamental physical quantity known as length. It is a way to gauge the separation between two points or the size of an object along a specific axis. The International System of Units (SI) uses metres as the unit of length (m). One of the most important ideas in geometry is length, which is used to describe the characteristics of geometric forms and shapes. For instance, the length of a circle is the distance around its circumference, whereas the length of a line segment is the distance between its endpoints.

given

(A) We must first determine the length of chord PQ in order to determine the length of segment PM. Since LM is the perpendicular bisector of PQ in the figure, PM is equal to MQ. PQ's length is 20 cm, so PM and MQ's lengths are each 50 percent of that, or:

PM=MQ=20/2=10 cm

Sqrt(PM2 + LM2) = PL

(d) When we enter the values from parts (a) and (c), we obtain:

Sqrt(10 + 15) = PL

Sqrt(100 + 225) = PL

Sqrt = PL (325)

PL ≈ 18.03 cm

Hence, section PL measures about 18.03 cm in length (rounded to the nearest hundredth digit).

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Answer:

graph?

Step-by-step explanation:

Answer:  you forgot to show the answer choices but

When you have a linear equation, the x-intercept is the point where the graph of the line crosses the x-axis.

Hope this helps :)

Rectangles' volumes are calculated using the formula length times width times height. The volume of one tennis ball is 372,057.

With four sides, four corners, and four right angles (90°), a rectangle is a closed 2-D object. The opposing sides of a rectangle are equal and parallel. Books, doors, table tops, blackboards, and other everyday objects are a few examples of rectangles. Having four right angles, a rectangle is a quadrilateral. a form having four equal-length sides. Four right angles and two sets of parallel sides make up the form. A rectangle is a four-sided polygon with internal angles that are all exactly 90 degrees. Each corner or vertex is a right angle intersection of the two sides. In contrast to squares, rectangles have equal-length opposite sides.

You may calculate how many tennis balls fit inside a rectangular limousine by dividing its volume by that of a tennis ball, assuming that the vehicle is empty of its wheels, engine, seats, and trunk. Thus, if you divide 1,555,2000 by 4.18, you get 372,057.45, or 372,057 tennis balls. If the limousine has seats or isn't a rectangle, you can calculate the volumes of those objects and deduct them from the rectangle's volume to determine the actual volume of the vehicle. Next, divide by the tennis ball's volume and round down.

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First, I'd find the volume of one tennis ball using the equation for sphere volume, 4/3πr³, where π = 3.14 and r = the radius of the tennis ball. If the tennis ball is 2 inches in diameter, its radius is 1 inch. The equation is (4/3)π(1)³ = 4.18 cubic inches. Next, I find the cubic inches of the limo. The equation for the volume of rectangles is length times width times height. Assuming a limo has a length of 360 inches, height of 60 inches, and width of 72 inches, the volume of the limo is 1,555,2000 inches.

Answer:

336m^2

Step-by-step explanation:

The triangle area is half of base times height so: 1/2*8*12=48m^2

There are 4 triangles so 48*4=192

Then the square base area is side times side so: 12*12=144m^2

Then surface area of model is 192m^2+144m^2=336m^2

Answer:

336 m²

Step-by-step explanation:

We can find the surface area of this pyramid by finding the surface area of one of the sides, multiplying it by 4 (as there are 4 sides to the pyramid) then adding it to the surface area of the base.

Each side of this (excluding the base) is a triangle, and to find the area of a triangle we use the equation \(\frac{b \cdot h}{2}\).

\(\frac{12 \cdot 8}{2}\)

\(\frac{96}{2}\)

48.

So, one side of this is 48. Multiplying it by 4 gets us 192.

Now we have to add the area of the base. The area of the bass is a square with side lengths of 12, so we can square 12 to get the area of the bass. 12² = 144.

Now let's add these numbers:

192+144 = 336

So, 336 m² is what this comes out to.

Hope this helped!

Answer:

The equation to solve for x is 8x - 14 = 5x + 34

The value of x is 16

Step-by-step explanation:

Let us use the angles between the parallel lines to find x

∵ Lines l and m are parallel

∴ ∠(8x - 14)° and ∠(5x + 34)° are alternate exterior angles

∵ The alternate exterior angles are congruent

∴ ∠(8x - 14)° ≅ ∠(5x + 34)°  

→ Equate them

∴ 8x - 14 = 5x + 34

∴ The equation to solve for x is 8x - 14 = 5x + 34

Let us solve it to find x

∵ 8x - 14 = 5x + 34

→ Subtract 5x from both sides

∵ 8x - 5x - 14 = 5x - 5x + 34

∴ 3x - 14 = 34

→ Add 14 to both sides

∴ 3x - 14 + 14 = 34 + 14

∴ 3x = 48

→ Divide both sides by 3 to find x

∴ \(\frac{3x}{3}=\frac{48}{3}\)

∴ x = 16

∴ The value of x is 16

Answer:

x=\(\sqrt{2}\)/4 and x=-\(\sqrt{2}\)/4

Step-by-step explanation:

One method of solving is using the Quadratic Formula: -b ±\(\sqrt{b^{2}-4ac }\)/2a, with a=8, b=0, and c=-1.

After plugging these values in you get -0±\(\sqrt{0^2-(4*8*-1)}\)/2*8

After simplifying you get ±\(\sqrt{32}\)/16

Because 32 is 2^5, you can simplify it to 4\(\sqrt{2}\), which makes the equation ±4\(\sqrt{2}\)/16, or ±\(\sqrt{2}\)/4.

Answer:

16>2.3b

Step-by-step explanation:

1.5+0.8=2.3

Substitute b as 1. Which would still keep it as 2.3.

Answer:

3/2 pi radians

Step-by-step explanation:

To change to radians. multiply by pi/180

270 * pi/180

3/2 pi

Answer:

p = \(-\frac{15}{2}\), p = \(\frac{17}{2}\)

Step-by-step explanation:

1. Subtract 15 from both sides:

- |2p -1| = -16

2. Divide both sides by -1:

\(\frac{-|2p - 1|}{-1} = \frac{-16}{-1}\)

|2p - 1| = 16

3. Apply the absolute value rule (If |u| = a, a > 0, then u = a, or u = -a)

2p - 1 = 16  or  2p - 1 = -16

4. Solve for the positive and negative intervals:

2p - 1+1 = 16+1

2p = 17

\(\frac{2p}{2} = \frac{17}{2}\)

p = \(\frac{17}{2}\)

2p - 1+1 = -16+1

2p = -15

\(\frac{2p}{2} = \frac{-15}{2}\)

p = \(\frac{-15}{2}\)

hope this helps!

The solution to the equation is θ = -0.3218 + kπ.

To solve the equation tan(θ) = -1/3, we can use the inverse tangent function (arctan) to find the angle θ.

Step 1: Take the inverse tangent (arctan) of both sides of the equation:

arctan(tan(θ)) = arctan(-1/3)

Step 2: Simplify the left side using the identity: arctan(tan(θ)) = θ

θ = arctan(-1/3)

Step 3: Use a calculator or reference table to find the value of arctan(-1/3).

arctan(-1/3) ≈ -0.3218 (rounded to four decimal places)

Therefore, the solution to the equation tan(θ) = -1/3 is:

θ ≈ -0.3218 + kπ, where k is any integer.

Correct Question :

Solve the given equation. let k be any integer. round terms to two decimal places where appropriate.) tan(θ)= − 1/3.

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Answer:

The negative regions of a function are those intervals where the function is below the x-axis. It is where the y-values are negative (not zero). y-values that are on the x-axis are neither positive nor negative. The x-axis is where y = 0.

Step-by-step explanation:

hope this helps :)

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

\(\diamond\large\textsf{\textbf{\underline{Given question:-}}}\)

        -0.5=-m/6. what is m?

\(\diamond\large\textsf{\textbf{\underline{\underline{Answer and how to solve:-}}}}\)

    ❖  First, multiply both sides by 6 to get rid of the fraction:-

 ▪︎ -0.5*6=-m/6*6

On the RHS, the 6's cancel:-

◆-0.5•6=-m

➪  \(\it{-3=-m}\)

 ➪ \(\it{3=m}\)

❒So we conclude that the value of m is 3.

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

Answer:

m = 3

Step-by-step explanation:

⇒ -0.5 = - m/6

Divide both sides by -1.

⇒ -0.5/-1 = -m/(6 × -1)

⇒ 0.5 = m/6

Multiply both sides by 6.

⇒ 0.5 × 6 = m/6 × 6

⇒ m = 3

Answer:

1.6 kilometers

Step-by-step explanation:

Umm... sorry...

I can't think of an explanation.

I memorized the answer (because I do track and field)

Well, feel free to tell me if I did anything wrong! :)

Answer:

1539/4 (improper fraction) or 384 3/4 (simplified fraction)

Step-by-step explanation:

To find the improper fraction, write 384.75 as a fraction:

384.75/1

Then, since you have 2 decimal places after the ., multiply the entire fraction by 100:

38475/100

Next, find the GCF, which is 25, and simplify this fraction to find the final improper fraction:

1539/4

To find the simplified fraction, we already have the whole number, 384, so we have to convert 0.75 to a fraction which is 3/4, because 0.75 is 3/4 of 100:

384 3/4

Hope this helps :)

Answer:

3(b + 4) = 2

Step-by-step explanation:

There are 720 ways the first three positions of the order of finish can occur assuming no ties in a race with 10 horses.

To calculate the number of ways the first three positions can occur, we use the permutation formula:

nPr = n! / (n - r)!

where n is the total number of objects and r is the number of objects we are choosing.

In this case, we have 10 horses and we want to choose the first three positions, so we get:

10P3 = 10! / (10 - 3)! = 10! / 7! = (10 x 9 x 8) / (3 x 2 x 1) = 720

Therefore, there are 720 ways the first three positions of the order of finish can occur assuming no ties.

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The length of AC is approximately 10.85 cm.

To find the length of AC, we can use the Pythagorean theorem.

According to the Pythagorean theorem, in a right triangle where c is the hypotenuse (the side opposite the right angle) and a and b are the other two sides, the relationship between the lengths of the sides is:

c^2 = a^2 + b^2

In this case, we can use AB as one of the legs of the right triangle and BC as the other leg, with AC being the hypotenuse. So we have:

AC^2 = AB^2 + BC^2

AC^2 = (10.2 cm)^2 + (3.7 cm)^2

AC^2 = 104.04 cm^2 + 13.69 cm^2

AC^2 = 117.73 cm^2

To find the length of AC, we take the square root of both sides:

AC = sqrt(117.73 cm^2)

AC ≈ 10.85 cm

Therefore, the length of AC is approximately 10.85 cm.

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Answer:

y = 4(x - 3)² - 5

Step-by-step explanation:

Given the vertex, (3, -5), and the other point, (4, -1):

Substitute these values into the vertex form of the quadratic equation:

y = a(x - h)² + k

where:

(h, k) = vertex

a = determines the direction of which the graph opens (if a > 1, the graph opens up; a < 1, the graph opens down). The value of a also determines the width of the parabola.  If 0 < a < 1, the graph will be wide; if a > 1, the graph will be narrow.

h = indicates a horizontal translation.

k = indicates a vertical translation.

Next, substitute the values of the vertex, (3, -5), and the other given point, (4, -1) into the vertex form and solve for the value of a:

y = a(x - h)² + k

-1 = a(4 - 3)² - 5

-1 = a( 1 )² - 5

-1 + 5 = a1 - 5 + 5

4 = a

Therefore, the equation of the given graph is: y = 4(x - 3)² - 5.  

Note:

If the  equation needs to be in standard form, ax² + bx + c, simply expand the binomial factors in the vertex form, and combine like terms.  Doing so will result in the following standard form: y = 4x² - 24x + 31.

Answer:

option 4

Step-by-step explanation:

Answer:

e. 8/00 ggg： What sum of money amounts to Rs. 8700 in 3 years at the rate of 24% per annum? [Ans: Rs. 5058.14]

Step-by-step explanation:

Answer:

y = -2x + 9

Step-by-step explanation:

Answer:

-5.6666.... is a rational number and 3.25 is a rational number but not integer too. the rest you got all right, good job.

hope that answers your question

dont hesitate to comment if you need some explanation about this topic

The equation of the hyperbola in standard form is y²/64 – x²/36 = 1.

The general form of equation of hyperbola:

y²/a²  - x²/b² = 1

From the vertex coordinates of (2, 8), we have that; a = ± 8.

From the focus coordinates (2, 10), the y-coordinate of it is; c = 10 .

Use pythagoras theorem to find b:

c² = a² + b²

100 = 64 + b²

b² = 100-64

b² = 36

b = 6

The equation of the hyperbola is:

y²/64 – x²/36 = 1.

Therefore, the equation of the hyperbola in standard form is y²/64 – x²/36 = 1.

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