uppose that a, b, and c are collinear points. b is the midpoint of ac . the coordinate of a is -8, and the coordinate of b is -2.5. what is the coordinate of c?

Answer:

The equation for the speed of the train is: 162 = 3x

I think the speed of the train is 54 miles per hour

Step-by-step explanation:

We know that:

y = distance in miles

x = speed of train (miles/hour)

t = time traveled from the departing station (hours)

The equation: y = xt is given, we can therefore substitute the give values:

y = xt or tx

162 = 3x (This would be the equation)

Now we can find x by diving 3 on both sides of "="

162/3 = x

54 = x (This would be the speed of train)

Hope this helps!

The volume of the cylinder is given by the equation V = 8,167.14 yards³

A cylinder is a three-dimensional shape consisting of two parallel circular bases, joined by a curved surface. The center of the circular bases overlaps each other to form a right cylinder. The volume of a cylinder is

Volume of Cylinder = πr²h

Surface area of cylinder = 2πr ( r + h )

where r is the radius of the cylinder

h is the height of the cylinder

Given data ,

Let the volume of the cylinder be represented as V

Now , the equation will be

The height of the cylinder h = 9 yards

The diameter of the cylinder d = 34 yards

So , the radius of the cylinder r = d/2 = 17 yards

And , Volume of Cylinder = πr²h

Substituting the values in the equation , we get

Volume of Cylinder = ( 3.14 ) x ( 17 )² x 9

On simplifying the equation , we get

Volume of Cylinder = ( 3.14 ) x 2,601

Volume of Cylinder = 8,167.14 yards³

Hence , the volume of cylinder is 8,167.14 yards³

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Answer:

the second one

Step-by-step explanation:

the independent number is the y intercept (where it touches the y-axis which would make the y-intercept 2) and the slope is 1/2 if you use rise/run. so it seems as if the equation is written in y=mx+b form. so the answer is y=1/2x+2

To find the average rate of change of a function from x1 to x2, you need to calculate the difference in the function's values at x1 and x2, and divide it by the difference in the x-values. The formula for average rate of change is (f(x2) - f(x1)) / (x2 - x1).

The average rate of change measures the average rate at which a function is changing over a given interval. To calculate it, you subtract the function's values at the starting point (x1) and ending point (x2), and then divide it by the difference in the x-values. This gives you the average rate of change for the interval from x1 to x2.

Example: Let's say we have a function f(x) = 2x + 3. To find the average rate of change from x1 = 1 to x2 = 4, we substitute these values into the formula: (f(4) - f(1)) / (4 - 1). Simplifying, we get (11 - 5) / 3 = 6 / 3 = 2. Therefore, the average rate of change of the function from x1 = 1 to x2 = 4 is 2.

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The x-intercepts of the function g(x) = 8x² - 10x - 3 can be found by setting g(x) equal to zero and solving for x. The x-intercepts represent the points where the graph of the function intersects the x-axis.

To find the x-intercepts, we set g(x) = 0:

8x² - 10x - 3 = 0

To solve this quadratic equation, we can use factoring, completing the square, or the quadratic formula. In this case, factoring is not straightforward, so we can use the quadratic formula:

x = (-b ± \(\sqrt{(b^2 - 4ac)}\)) / (2a)

For the given equation, a = 8, b = -10, and c = -3. Plugging these values into the quadratic formula, we have:

x = (-(-10) ± \(\sqrt{((-10)^2 - 4(8)(-3))}\)) / (2(8))

Simplifying further:

x = (10 ± √(100 + 96)) / 16

x = (10 ± √196) / 16

x = (10 ± 14) / 16

This gives us two possible solutions:

x1 = (10 + 14) / 16 = 24 / 16 = 3/2 = 1.5

x2 = (10 - 14) / 16 = -4 / 16 = -1/4 = -0.25

Therefore, the x-intercepts of the function g(x) are x = 1.5 and x = -0.25.

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Answer:

Step-by-step explanation:

Plot 213, −56, and −312 on the number line.

Perfect squares are numbers gotten by squaring whole numbers. Therefore, 5 exmaples of perfect squares are

4(2^2)

9(3^3)

16(4^4)

25(5^5)

49(7^7)

So 5 perfect squares are 4, 9, 16, 25, 49

use the following property:

so:

Answer:

Our calculator limits your interest deduction to the interest payment that would be paid on a $1,000,000 mortgage. Interest rate: Annual interest rate for this

Step-by-step explanation:

Answer:

C=78

Step-by-step explanation:

first add 72 and 30 you get 102 then subrtract 102 from 180 and youll get your answer of 78

The value of the scalar product M ⋅

M is given by answer 4, a2 + 2ab + b2.

Therefore, the value of the scalar product M ⋅

N is given by answer 6, ad + bc.

What is a scalar product?

A scalar product is a type of binary operation in algebra that combines two vectors in a scalar value.

It is also known as the dot product.

This product is defined as the product of the magnitude of two vectors multiplied by the cosine of the angle between them.

In a scalar product, the order of multiplication does not matter, but the properties of multiplication do hold.

How to calculate a scalar product?

The scalar product of two vectors A and B is given by the formula:

A . B = |A||B| cosθ

where, |A| and |B| are the magnitudes of vectors A and B, and θ is the angle between them.

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The temperature at 6000 feet will be 32.1°F.

This question uses the theory of adiabatic lapse rate, which is the rate at which air temperature changes as it ascends or descends in the atmosphere. The moist adiabatic lapse rate is typically about 6°C/km (3.5°F/1000 ft) when the air is saturated, but it can vary due to the local atmospheric conditions.

Step 1: Calculate the temperature change per 1000 feet.

Change in temperature = 1.4°F

Step 2: Calculate the total change in temperature.

Total change = 1.4°F x 6 (6000 feet divided by 1000 feet) = 8.4°F

Step 3: Subtract the total change from the temperature on the ground.

Temperature at 6000 feet = 50.9°F - 8.4°F = 32.1°F

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Answer:

ΔABC ~ ΔEDF

Step-by-step explanation:

ΔABC ~ ΔEDF

Given:

∠A = ∠E

∠B = ∠D

So,

We say that;

∠C = ∠F

By AAA;

Rule

ΔABC ~ ΔEDF

To calculate the probability of two separate events using the ratio method, we must first understand the odds associated with each event. The odds are expressed as a ratio, with the first number representing the chances of success and the second number representing the chances of failure. For example, the odds of an event happening might be 3:2, which indicates that there is a 3/5 chance of success.

Once the odds for each event are known, we can calculate the probability of both events occurring by multiplying the odds of each event together. So, for example, if the odds of Event A are 3:2 and the odds of Event B are 4:5, the probability of both events occurring is 3/2 * 4/5 = 6/10. This means that there is a 6 in 10 chance of both events occurring.

To sum up, calculating the probability of two separate events using the ratio method is fairly simple. Just look at the odds associated with each event and multiply them together to get the probability of both events occurring.

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The value of c in the quadratic equation given is 32.

Given a quadratic equation of the form 3x² + bx + c = 0 has roots of 6 plus or minus square root of 2, we know that the quadratic equation can be written as:

3(x - (6 + √2))(x - (6 - √2)) = 0

Expanding this product gives:

3[(x - 6 - √2)(x - 6 + √2)] = 0

Using the difference of squares, we can simplify this expression to:

3[(x - 6)² - (√2)²] = 0

3(x - 6)² - 6 = 0

Multiplying out the squared term, we get:

3x² - 36x + 102 - 6 = 0

Simplifying, we get:

3x² - 36x + 96 = 0

Dividing both sides by 3, we get:

x² - 12x + 32 = 0

Therefore, the value of c is 32.

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Answer: B

Step-by-step explanation:

The odds in favor of obtaining a number divisible by 3 or 4 in a single roll of a die are 7:5 or 7/5.

The probability of obtaining a number divisible by 3 or 4 in a single roll of a die can be found by adding the probabilities of rolling 3, 4, 6, 8, 9, or 12, which are the numbers divisible by 3 or 4.

There are six equally likely outcomes when rolling a die, so the probability of obtaining a number divisible by 3 or 4 is:

P(divisible by 3 or 4) = P(3) + P(4) + P(6) + P(8) + P(9) + P(12)

P(divisible by 3 or 4) = 2/6 + 1/6 + 1/6 + 1/6 + 1/6 + 1/6

P(divisible by 3 or 4) = 7/12

The odds in favor of an event is the ratio of the probability of the event occurring to the probability of the event not occurring. Therefore, the odds in favor of obtaining a number divisible by 3 or 4 in a single roll of a die are:

Odds in favor = P(divisible by 3 or 4) / P(not divisible by 3 or 4)

Odds in favor = P(divisible by 3 or 4) / (1 - P(divisible by 3 or 4))

Odds in favor = 7/5

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Answer:

OOOOOOOOHHH SHUTE BROTHER SORRY WISHED I COULD HELP but im blonde so sowwy

Answer:

1/2.

Step-by-step explanation:

There seem to be a couple prominent points on the line. We can use two of them to find the slope.

(0, 75)

(30, 90)

(90 - 75) / (30 - 0) = 15 / 30 = 3 / 6 = 1/2.

Hope this helps!

Answer:

x=14 y=37

Step-by-step explanation:

The correct answer is D. Translation 2 units right and 4 units up

A) (x, y) -> (x - 3, y - 3): This represents a translation 3 units left and 3 units down.
B) (x, y) -> (x - 2, y - 4): This represents a translation 2 units left and 4 units down.
C) (x, y) -> (x - 3, y + 3): This represents a translation 3 units left and 3 units up.
D) Translation 2 units right and 4 units up: This represents a translation with the given direction and magnitude.
E) Translation 3 units left and 3 units down: This represents a translation with the given direction and magnitude.
To determine which statements describe the translation from point A to point B, you would need to analyze the graph and compare it to the translations provided in the options.

If the graph shows, for example, a movement 3 units left and 3 units down, then the correct statements would be A) and E).

Starting from point A, we can see that we need to move to the right by 2 units and up by 4 units to reach point B.

Therefore, the translation from point A to point B is:

(x, y) -> (x + 2, y + 4)

Option D "Translation 2 units right and 4 units up" correctly describes the translation. Option E "Translation 3 units left and 3 units down" does not correctly describe the translation, as it moves in the opposite direction.

Therefore, the correct answer is D.

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Question: In a sale, the price of a book is reduced by 25%. The price of the book in the sale is £12. Work out the original price of the book

Answer: £16

Step-by-step explanation:

To determine the original price of the book, we can use the fact that the sale price is 75% (100% - 25%) of the original price. Let's denote the original price as x.

75% of x = £12

To solve for x, we can set up the equation:

0.75x = £12

To isolate x, we divide both sides of the equation by 0.75:

x = £12 / 0.75

x = £16

Therefore, the original price of the book was £16.

The student's average speed was approximately 52.5 km/h, where he drove a distance of 14.0 km in 16.0 minutes.

The student drove a distance of 14.0 km in 16.0 minutes. To find the average speed, we need to convert the time to hours and then use the formula:

Average speed is a measure of the total distance traveled divided by the total time taken. It represents the average rate at which an object or person covers a certain distance over a given period of time.

Mathematically, average speed is calculated using the formula:

Average speed = Total distance traveled / Total time taken

First, convert 16.0 minutes to hours:

16.0 minutes * (1 hour / 60 minutes) = 0.2667 hours

Now, calculate the average speed:

Average speed = 14.0 km / 0.2667 hours ≈ 52.5 km/h.

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Answer:

28

Step-by-step explanation:

Use the pythagorean theorem and solve for a:

a² + b² = c²

a² + 21² = 35²

a² + 441 = 1225

a² = 784

a = 28

So, the missing length is 28.

The equation of the hyperbola is (y - 1)^2 / 16 - (x - 2)^2 / 65 = 1

To find the equation of the hyperbola, we need to determine its center, vertices, and foci.

Given:
Vertices: (2, 5) and (2, -3)
Foci: (2, 10) and (2, -8)

The center of the hyperbola is the midpoint between the vertices, which can be found by averaging their x-coordinates and y-coordinates:

Center: (2, (5 + (-3))/2) = (2, 1)

The distance between the center and the vertices is denoted by "a". In this case, the distance is the absolute value of the difference between the y-coordinates of the center and one of the vertices:

a = |1 - 5| = 4

The distance between the center and the foci is denoted by "c". In this case, the distance is the absolute value of the difference between the y-coordinates of the center and one of the foci:

c = |1 - 10| = 9

The relationship between "a", "b", and "c" in a hyperbola is given by the equation:

c^2 = a^2 + b^2

Solving for "b^2", we have:

b^2 = c^2 - a^2
= 9^2 - 4^2
= 81 - 16
= 65

Now we have all the necessary information to write the equation of the hyperbola in standard form:

For a horizontal hyperbola:

(x - h)^2 / a^2 - (y - k)^2 / b^2 = 1

For a vertical hyperbola:

(y - k)^2 / a^2 - (x - h)^2 / b^2 = 1

Since the given foci have the same x-coordinate, the hyperbola is vertical. Plugging in the values:

(y - 1)^2 / 4^2 - (x - 2)^2 / √65 = 1

Simplifying, we have:

(y - 1)^2 / 16 - (x - 2)^2 / 65 = 1

Therefore, the equation of the hyperbola is:

(y - 1)^2 / 16 - (x - 2)^2 / 65 = 1

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The following is an excerpt from A First Training in Probability by Sheldon Ross. (74) = 35 is the right response.

Total moves required are 7, as follows:

Three steps up as well as four steps right.

Remember that perhaps the number of paths equals the number of arranged 7-tuples with 3 U's and 4 R's. As instance, the word URRURRU indicates to travel up, right, up, right, right, up.

There are 7 ways to arrange these letters, 7 ways to arrange the corresponding Us, and 7 ways to arrange the comparable Rs, for a total of 7!3!4! (74).

For each NxN grid, we may write the following as a generalization of our formula: It should be noted that there's a simpler method of writing this: D = N! / (K! * (N-K))! additionally known as the binomial coefficient.

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The factor of the given expression 4(a+b) - x(a+b) is (a+b)(4-x)

A factor of an expression is an expression that divides another expression without leaving a reminder. A factor of a number or an expression can be found using various methods.

The given expression is 4(a+b) - x(a+b).

Finding the factor of this expression is a one-step process.

To find the factor of the given expression, take out the common term from the expression, and the factor is obtained.

4(a+b) - x(a+b)

Take (a+b) as a common term, we get

(a+b)(4-x)

Thus, the factor is obtained.

Hence, the factor of the expression 4(a+b) - x(a+b) is (a+b)(4-x).

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