Mr. Burn's class is taking a field trip to the planetarium. The trip will cost $27 for each
student. There are 18 students in his class. Which way do you think is a better way to
estimate the total cost of the trip: rounding or using compatible numbers? Explain.


PLEASE HELP

Answer:

x = sqrt (2), y = sqrt (2)

Step-by-step explanation:

Here is how we can approach this problem in a step by step solution:

*Also, if you knew that a 45-45-90 triangle's sides form a ratio of a, a, and sqrt (2) a, you could also use that and substitute in the values to solve. Both ways work! Hope this helps!!

The set of points between two points in a plane and the infinite number of points that continue beyond these points is called 'line'.

A line is what is formed when a collection of collinear points are joined in a one-dimensional plane.

A straight line is defined as a group of collinear points that never curves and can continue indefinitely in opposite directions.

A curved line is one that has a bend or curvature in its construction and is made up of collinear points.

A diagonal or slanted line is referred to as an oblique. It is not, however, vertical, horizontal, parallel, or perpendicular.

Any straight line that travels from left to right and right to left is referred to as a horizontal line. Simply put, a sleeping line is another name for a horizontal line.

Any straight line that runs from top to bottom and bottom to top is referred to be a vertical line. The vertical line too is referred to as a straight line in layman's terms.

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Answer:

Step-by-step explanation:

I’m having the same problem

Answer:

∠ABC =   52°

∠BCA =  48°

∠CAB = 80°

Step-by-step explanation:

Angle sum property of triangle: Sum of all the angles of a triangle is 180.

13x² + 12x² + 20x² = 180

Combine like terms,

                 45x²  = 180

                     x² = 180 ÷ 45

                     x² = 4

                     x = √4

                     x = ± 2

x = 2 ; -2

∠ABC = 13x² = 13*4 = 52°

∠BCA = 12x² = 12 *4 = 48°

∠CAB = 20x² = 20 *4 = 80°

The value of x is +2 and -2 and the angles will be given as ∠ABC = 52 ∠ACB = 48 and ∠CAB = 80.

The branch of mathematics sets up a relationship between the sides and the angles of the right-angle triangle is termed trigonometry.

Given that:-

∠ABC = 13x² ∠ACB = 12x² and ∠CAB = 20x²

The angles will be calculated as follows:-

13x² + 12x² + 20x² = 180

45x²  =  180

x²  =  4

x   =  ±2

The angles will be:-

∠ABC = 13x²  = 13 x ( 2² ) = 52

∠ACB = 12x²  = 12 ( 2² )    = 48

∠CAB = 20x²  = 20 ( 2² )  = 80

Therefore value of x is +2 and -2 the angles will be given as ∠ABC = 52 ∠ACB = 48 and ∠CAB = 80.

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Answer:

lost 120

Step-by-step explanation:

10% of 1200 is 120 so you subtract 120 from 1200

Answer:

120

Step-by-step explanation:

Loss = (Loss%)(C.P)

Loss = (10%)(1200)

Loss = (10/100)(1200)

Loss = 120

The solid that is the common interior base of the sphere x² + y² + z² = 80 and the paraboloid z = √(x² + y²/2) can be determined by finding the points of intersection between the two surfaces.

These points of intersection represent the boundary of the common interior region.

To find the common interior base of the given sphere and paraboloid, we need to find the points where the two surfaces intersect. By setting the equations of the sphere and the paraboloid equal to each other, we can solve for the coordinates (x, y, z) of the points of intersection.

By solving the equations, we can obtain the boundary of the common interior region, which represents the solid base shared by the sphere and the paraboloid.

To visualize the solid, it would be helpful to plot the surfaces and observe the region where they intersect. This will give a better understanding of the shape and dimensions of the common interior base.

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The maximum weight for which the toy will work properly is 39.5 lb

The spring is compressed a distance of 1.9 inches by the weight of a 25-pound child, the spring force, F = kx where

Making k subject of the formula, we have

k = F/x

Now F = weight of child = mg where

and x = compression = 1.9 in

So, k = F/x

k = mg/x

k = 25 lb × 32 ft/s²/1.9 in

k = 800 lbft/s²/1.9 in

k = 421.1 lb-f/in

The maximum force for a compression of 3 inches is

F = kx where

So, F = 421.1 lb-f/in × 3 in

F = 1263.3 lb-f

Since F = mg

The maximum weight m = F/g

= 1263.3 lb-f ÷ 32 ft/s²

= 39.48 lb

≅ 39.5 lb

So, the maximum weight for which the toy will work properly is 39.5 lb

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The lengths in the left side are proportional to the ones in the right side, with that we know that x = 10.

The lengths in the left side and the ones in the right side are proportional, such that the scale is k.

Then we can write:

21*k = 27

(x - 3)*k = (x - 1)

With the first equation, we can find the value of k, then we will get.

k = 27/21

Replacing that in the second equation we will get:

(x - 3)*27/21 = (x - 1)

Now we can solve this.

(x - 3)*27 = 21*(x - 1)

Now we can solve this for x.

27x - 81 = 21x - 21

27x - 21x = 81 - 21

6x = 60

x = 60/6 = 10

x = 10

That is the value of x.

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The cost of the total fuel consumed can be determined by the conversion of the Euro into Dollars. The total cost of the fuel is 383 USD.

Significant Figure

Significant figures are the number of digits in a value, often a measurement, that contribute to the degree of accuracy of the value. We start counting significant figures at the first non-zero digit. Calculate the number of significant figures for an assortment of numbers.

Euro and Dollars:

The cost of the total fuel consumed can be determined by the conversion of the Euro into Dollars.

Given here,

Total distance = 5000 km

Average fuel consumption = 6 lit per 100 km = 0.06 lit / km

Average fuel cost = 1.063 EUR/lit

1 EUR  = 1.2 USD

So, Total fuel consumption,

⇒ 5000 km × 0.06 lit /km

⇒ 300 lit

Thus, Total fuel cost,

⇒ 300 lit × 1.063 EUR/lit

⇒ 318.9 EUR

⇒ 318.9 EUR × 1.2 USD

⇒ 383 USD

Therefore, the total cost of the fuel is 383 USD

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The standard form of the equation of a line perpendicular to the line (3x + 6y = 5) and passing through the point (1, 3) is (2x - y = -1)

To determine the equation of a line perpendicular to the line (3x + 6y = 5) and passing through the point (1, 3), we can follow these steps:

1. Obtain the slope of the provided line.

To do this, we rearrange the equation (3x + 6y = 5) into slope-intercept form (y = mx + b):

6y = -3x + 5

y =\(-\frac{1}{2}x + \frac{5}{6}\)

The slope of the line is the coefficient of x, which is \(\(-\frac{1}{2}\)\).

2. Determine the slope of the line perpendicular to the provided line.

The slope of a line perpendicular to another line is the negative reciprocal of the slope of the provided line.

So, the slope of the perpendicular line is \(\(\frac{2}{1}\)\) or simply 2.

3. Use the slope and the provided point to obtain the equation of the perpendicular line.

We can use the point-slope form of a line to determine the equation:

y - y1 = m(x - x1)

where x1, y1 is the provided point and m is the slope.

Substituting the provided point (1, 3) and the slope 2 into the equation, we have:

y - 3 = 2(x - 1)

4. Convert the equation to standard form.

To convert the equation to standard form, we expand the expression:

y - 3 = 2x - 2

2x - y = -1

Rearranging the equation in the form (Ax + By = C), where A, B, and C are constants, we obtain the standard form:

2x - y = -1

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We need to know the radius of the circle. Unfortunately, we don't have that information in the diagram provided. Therefore, it's not possible to give a definitive answer without additional information. I'm sorry I couldn't provide a more helpful response, but if you have any further questions, please don't hesitate to ask.

It seems like you're asking about the circumference of a circle with the center labeled "O" and a point on the circle labeled "K". However, some details are missing to provide an accurate answer. To calculate the circumference, we need to know the radius (distance between O and K) or the diameter of the circle.

The circumference of a circle can be calculated using the following formula:
Circumference = 2 * π * radius
or Circumference = π * diameter

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Answer:

No, one of the angles has to be 90º for it to be a right triangle

Step-by-step explanation:

Answer:

no. it doesn't have a right angle.

Answer:

x = 2, because 16/8 = (8x)/8

Step-by-step explanation:

Devide both sides by the coefficient of variable

Answer:

um i really dont know but if i dont know the the answer to sum i put c but i recommend not doing that

Step-by-step explanation:

Answer:

The second option, 2 is a prime number, but not odd

Step-by-step explanation:

A prime number is a result of two other whole numbers multiplied by themselves. There is no whole number that you can multipy by itself to get 2 because 1 × 1 = 1 and 2 × 2 = 4. Therefore, it is a prime number. But, that does not mean it is an odd number because odd numbers are 1, 3, 5, 7, etc. and even numbers are 2, 4, 6, 8, etc.

Answer:

y = -x/3 -5

Step-by-step explanation:

when two lines are perpendicular, the relation between the slopes of the lines m1 and m2

m1m2 = -1

The general equation of a line is given as

y = mx + c where m is the slope and c is the intercept

Considering the given equation

6y-18x=12

6y  = 18x + 12

Divide through by 6

y = 3x + 2

comparing with y = mx + c,

m = 3

hence the slope of the perpendicular line m2

= -1/3

Given that the line passes through the point (0, -5)

Using the equation y - y1 = m(x - x1) to find the equation

y - - 5 = -1/3(x - 0)

y + 5 = -x/3

y = -x/3 -5

The quadratic equation 49x^2 + 14x + 4 can only be factorized as 49(x - (-7 + i√147) / 49)(x - (-7 - i√147) / 49)

To factorize 49x^2 + 14x + 4, we can use the quadratic formula:

x = (-b ± sqrt(b^2 - 4ac)) / 2a

where a = 49, b = 14, and c = 4. Substituting these values into the formula, we get:

x = (-14 ± √(14^2 - 4(49)(4))) / 2(49)

x = (-14 ± √(196 - 784)) / 98

x = (-14 ± √(-588)) / 98

x = (-14 ± 2i√147) / 98

x = (-7 ± i√147) / 49

So the solutions to the quadratic equation 49x^2 + 14x + 4 are x = (-7 + i√147) / 49 and x = (-7 - i√147) / 49.

To factorize the quadratic expression, we can use the fact that the solutions to the equation ax^2 + bx + c = 0 are given by:

x = (-b ± sqrt(b^2 - 4ac)) / 2a

In this case, a = 49, b = 14, and c = 4, so the solutions are:

x = (-14 ± sqrt(14^2 - 4(49)(4))) / 2(49)

x = (-14 ± sqrt(196 - 784)) / 98

x = (-14 ± sqrt(-588)) / 98

x = (-7 ± i√147) / 49

Therefore, we can write:

49x^2 + 14x + 4 = 49(x - (-7 + i√147) / 49)(x - (-7 - i√147) / 49)

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Every Wednesday, Wayne works out for 3/4 of an hour at the fitness center. Every Saturday, he goes to the fitness center again and exercises for 3 times as long. How much time does Wayne spend at the fitness center in all each week?

3 hours (or 180 minutes)

3/4 of an hour = 45 minutes

45 minutes × 3 = 135 minutes or 2 hours and 25 minutes

2 hours and 25 minutes + 45 minutes = 3 hours (180 minutes)

A block hangs in equilibrium from a vertical spring. The equilibrium position sags by 6.00 cm when adding a second identical block. The oscillation frequency of the two-block system is approximately 1.44 Hz.

To find the oscillation frequency of the two-block system, we can use Hooke's Law and the formula for the frequency of simple harmonic motion.

Hooke's Law states that the force exerted by a spring is directly proportional to the displacement from its equilibrium position. Mathematically, it can be expressed as:

F = -kx

where F is the force applied by the spring, k is the spring constant, and x is the displacement from the equilibrium position.

In the equilibrium position, the force exerted by the spring is balanced by the weight of the block(s), resulting in zero net force. Thus, we have:

mg = kx_eq

where m is the mass of one block, g is the acceleration due to gravity, and x_eq is the equilibrium displacement of the spring.

When a second identical block is added, the total mass becomes 2m. The equilibrium displacement increases to 2x_eq due to the additional weight. We are given that the equilibrium position sags by 6.00 cm, so we have:

2mg = k(2x_eq)

2mg = 4kx_eq

Dividing both sides by 2m, we get:

g = 2kx_eq / m

The angular frequency (ω) of the two-block system can be calculated using the formula:

ω = √(k / m)

The oscillation frequency (f) can be calculated as:

f = ω / (2π)

To find the oscillation frequency, we need to find k/m. From the equation above, we have:

k/m = (g / 2x_eq)

Substituting the given values, g = 9.8 m/s² and x_eq = 6.00 cm = 0.06 m:

k/m = (9.8 m/s²) / (2 * 0.06 m)

k/m = 81.67 N/m

Now, we can calculate the angular frequency and the oscillation frequency:

ω = √(81.67 N/m / m) = √(81.67 s⁻²) ≈ 9.04 rad/s

f = ω / (2π) ≈ 9.04 rad/s / (2π) ≈ 1.44 Hz

Therefore, the oscillation frequency of the two-block system is approximately 1.44 Hz.

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Answer:

A

Step-by-step explanation:

y = 1/4 × x - 2

x=8 => y=0. correct for B

x=12 => y= 1. correct for C

all other answer options fail for these 2 points.

Metric System is a decimal system of measurement that is based on the meter, kilogram, and second and is used in most countries around the world. It is also known as the International System of Units (SI).

The Metric System is the most common measuring system used in the world today. It is a decimal system based on the meter, kilogram, and second and is officially known as the International System of Units (SI). This system was initially developed in France in the late 18th century and is now used in most countries around the world. The Metric System is based on powers of 10 and each unit is related to the next unit by a factor of 10. For example, a kilometer is equal to 1000 meters, a milliliter is equal to 0.001 liters, and a centimeter is equal to 0.01 meters. The Metric System is used to measure length, area, mass, weight, temperature, and volume. It is used in many different industries and applications including science, engineering, medicine, and agriculture. The Metric System has become the international standard for scientific measurements and is accepted by most countries as the preferred system of measurement. The Metric System is also easier for students to learn and use than other systems of measurement.

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Answer:

m∠DAC = 21°

Step-by-step explanation:

Exterior Angle Theorem

The exterior angle of a triangle is equal to the sum of the two non-adjacent interior angles of the triangle.

Apply the Exterior Angle Theorem to triangle ACD and solve for x:

⇒ m∠DAC + m∠ACD = m∠ACH

⇒ (1 - 4x) + (2 - 15x) = 2x + 108

⇒ -4x - 15x + 1 + 2 = 2x + 108

⇒ -19x + 3 = 2x + 108

⇒ -19x + 3 = 2x + 108

⇒ -21x + 3 = 108

⇒ -21x = 105

⇒ x = -5

Substitute the found value of x into the expression for angle DAC:

⇒ m∠DAC = 1 - 4x

⇒ m∠DAC = 1 - 4(-5)

⇒ m∠DAC = 1 + 20

⇒ m∠DAC = 21°

Therefore, the measure of angle DAC is 21°.

1.False, 2.True, 3.False, and 4.False

This question uses probability theory, which is used to analyze the likelihood of different outcomes occurring. It is based on the idea that there is a certain probability that any given outcome will happen.

The given question steps by step explanations are as follows

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The correct answer for each row - 1.False, 2.True, 3.False, and 4.False

This question uses probability theory, which is used to analyze the likelihood of different outcomes occurring. It is based on the idea that there is a certain probability that any given outcome will happen.

In the given question,

It is less likely that Eleanor will choose a pair of gray socks than a pair of black socks: False - There are 14 pairs of gray socks and 8 pairs of black socks, so it is more likely that Eleanor will choose a pair of gray socks.

It is more likely that Eleanor will choose a pair of white socks than a pair of gray socks: True - There are 6 pairs of white socks and 14 pairs of gray socks, so it is more likely that Eleanor will choose a pair of white socks.

The most likely outcome is that Eleanor will choose a pair of black socks: False - There are 8 pairs of black socks and 14 pairs of gray socks, so it is more likely that Eleanor will choose a pair of gray socks.

The least likely outcome is that Eleanor will choose a pair of white socks: False - There are 6 pairs of white socks and 14 pairs of gray socks, so it is least likely that Eleanor will choose a pair of white socks.

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Answer: moderate, C, B

Step-by-step explanation:

A)  A shows a moderate negative correlation.  It is moderate because the scattered points are sort of close to the line so it has moderate/medium correlation.  It is also negative because it has a negative slope

B) C shows the strongest correlation because the points around the line are tight and close.

C)  B should not have been drawn.  The  correlation is very weak.  You do know where the line should be because the points are all over the place.

Courtney would take 8 hours to type a 50-page paper on her own. This is because the amount of time it takes to type a paper is directly proportional to the number of pages in the paper.

Kirsten and Courtney together took 6 hours to type 50-page paper. This means they both worked for 3 hours each.

Therefore, Courtney would take 8 hours to type a 50-page paper on her own.

Kirsten and Courtney worked together to type a 50-page paper in 6

hours. This means that each of them worked for 3 hours each. Thus, it would take Courtney 8 hours to type a 50-page paper on her own. To put it into perspective, she would need to work for double the time she worked with Kirsten to finish the paper alone. As such, it would take Courtney 8 hours to type a 50-page paper if she were to do it alone. This is because the amount of time it takes to type a paper is directly proportional to the number of pages in the paper. Consequently, Courtney would need to put in 8 hours of work to type a 50-page paper.

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Answer:

Step-by-step explanation:

This is not a square or rectangle because of the 94° angle

All sides are equal, it is a rhombus

Answer:

Step-by-step explanation:

-80