The number of miles driven varies directly with the number of hours in the car. Billy drives 171 miles in 3 hours, so he could drive _____ miles in 4.5 hours.

Answer:  The required distance between the two points R and T is 1.1 units.

Step-by-step explanation:  Given that point R is at (3, 1.3) and Point T is at (3, 2.4) on a coordinate grid.

We are to find the distance between the two points R and T.

Distance formula :

The distance between the two points A(a, b) and B(c, d) is given by

[tex]d=\sqrt{(c-a)^2+(d-b)^2}.[/tex]

Therefore, the distance between the points R and T is given by

[tex]d=\sqrt{(3-3)^2+(2.4-1.3)^2}=\sqrt{0^2+1.1^2}=\sqrt{1.1^2}=1.1.[/tex]

Thus, the required distance between the two points R and T is 1.1 units.

The distance is 1.1 units, which is the distance between point R is at (3, 1.3) and Point T is at (3, 2.4) on a coordinate grid.

It is defined as the formula for finding the distance between two points. It has given the shortest path distance between two points.

We have two points such that:

R (3, 1.3) and T (3, 2.4)

The distance formula for finding the distance between two points is:

If the points are [tex]\rm (x_1, y_1) \ \ and \ \ (x_2, y_2)[/tex]

[tex]\rm D = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

Here:

[tex]\rm x_1= 3\\\rm y_1= 1.3\\\rm x_2= 3\\\rm y_2= 2.4\\[/tex]

Then,

[tex]\rm D = \sqrt{(3-3)^2+(2.4-1.3)^2}[/tex]

[tex]\rm D = \sqrt{(1.1)^2}[/tex]

D = √1.21

D = 1.1 units

Thus, the distance is 1.1 units, which is the distance between point R is at (3, 1.3) and Point T is at (3, 2.4) on a coordinate grid.

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Answer:

The answer is A!!!

Step-by-step explanation:

The number produces an irrational number when multiplied by 0.4 would be C) 3π.

Irrational numbers are those real numbers that are not rational numbers.

Know that all natural numbers are integers, and all integers are rational numbers. That means natural numbers are not irrational.

π is irrational, and so is 3π

The expression 3π +0.4 is an irrational term as well.

If x is irrational and y is rational, then x + y is the irrational term.

Thus, choice C is the answer.

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Solving this problem is just pretty straight forward. We simply have to get the ratio of distance and time to get the speed. that is:

speed = distance / time

speed = 100 m / 10.94 s

speed = 9.14 m/s

Final answer:

Gail Devers' average speed during her Olympic win in the 100-meter dash with a time of 10.94 seconds is calculated to be approximately 9.14 meters per second using the formula speed = distance/time.

Explanation:

In 1996, Gail Devers won the 100-meter dash in the Olympic Games with a time of 10.94 seconds. To find her average speed in meters per second, we use the formula:

s = d / t

where s is speed, d is distance, and t is time. Given that the distance (d) is 100 meters and the time (t) is 10.94 seconds, we can calculate the average speed:

s = 100 m / 10.94 s ≈ 9.14 m/s

Therefore, Gail Devers' average speed during her Olympic 100-meter dash victory was approximately 9.14 meters per second.

A percentage increase can be calculated by first finding the difference between the new and original values, then dividing that difference by the original value. The result is then multiplied by 100 to get the percentage increase. This method can also help calculate inflation rates and various other mathematical problems.

To calculate a percentage increase, you need to understand the basic principles of mathematics. Using the context provided, we can define calculating a percentage increase in the following way:

For example, suppose the original price for a basket of goods was $20 and the new price is $25. First, find the difference: $25-$20 = $5. This is the increase. Then, divide the increase ($5) by the original price ($20) to get 0.25. Multiply by 100 and you get a 25% increase.

This method can be applied to many scenarios including calculating the rate of inflation. There are also online calculators and computers that can assist in finding these percentages quickly.

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Answer:

Step-by-step explanation:

Rotate 180° about the point (2, -4) -- maps the figure onto itself.

A figure is mapped onto itself when the transformation results in the original pre-image for the image.

Answer: C is the answer

Step-by-step explanation:

Rotate 180° about the point (2, -4) -- maps the figure onto itself. A figure is mapped onto itself when the transformation results in the original pre-image for the image.

The question deals with a sequence of movements of a golf ball falling and rebounding, which forms a geometric series. To find the total distance traveled by the ball on its 10th descent, we calculate the sum of the first 19 terms of this geometric progression.

The student is asking about a geometric series problem, which involves a golf ball being dropped from a height and rebounding to a fraction of that height. The sequence of the distances covered by the ball forms a geometric progression.

Let's denote the initial height the ball is dropped from as a, which is 30 ft. The rebound height is one-fourth of the descent, so the rebound ratio, or common ratio r, is 1/4. The ball travels the initial height a plus the rebound distance each time it hits the pavement. This series continues with each rebound being one-fourth of the previous fall. We want to find the total distance traveled by the ball as it hits the pavement on its 10th descent.

The total distance traveled D after the ball hits the pavement for the 10th time is the sum of the first 10 terms of this geometric sequence. Using the formula for the sum of the first n terms of a geometric series, [tex]S_n = a(1-r^n)/(1-r)[/tex], where n is the number of terms, we can calculate the total distance.

For 10 descents, we have n = 19 since each descent and rebound except

the last descent counts as two movements:
[tex]S_{19} = 30(1-(1/4)^{19})/(1-(1/4))[/tex]
[tex]S_{19} = 30(1-(1/4)^{19})/(3/4)[/tex]
By calculating [tex]S_{19[/tex], we find the total distance traveled when the ball hits the pavement on its 10th descent.

Final answer:

To find (g-h)(-4), we calculate g(-4) as -9 and h(-4) as -15. Subtracting the latter from the former results in -9 + 15, which equals 6.

Explanation:

To find (g-h)(-4), we need to calculate the value of g at -4 and the value of h at -4, and then subtract the value of h from g.

The functions are defined as G(a)=2a-1 and h(a)=3a-3. Let's compute these step-by-step:

Calculate g(-4):

G(-4) = 2(-4) - 1

= -8 - 1

= -9

Calculate h(-4):

h(-4) = 3(-4) - 3

= -12 - 3

= -15

Calculate (g-h)(-4):

= g(-4) - h(-4)

= -9 - (-15)

= -9 + 15

= 6

Therefore, (g-h)(-4) equals 6.

Answer:

r = 13

Step-by-step explanation:

The radius of a circle that its center at the origin, and passes through point (5, -12) is 13 units

The given parameters are:

The length of the radius is calculated using:

[tex]r = \sqrt{(x - a)^2 + (y - b)^2}[/tex]

So, we have:

[tex]r = \sqrt{(5 - 0)^2 + (-12 - 0)^2}[/tex]

Evaluate

[tex]r = \sqrt{169}[/tex]

Solve the square root

r = 13

Hence, the radius is 13 units long

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Answer:

[tex]-4x^2y^3[/tex]

Step-by-step explanation:

We have been given an expression [tex]\sqrt[3]{-64x^6y^9}[/tex]. We are asked to simplify our given expression.

Applying radical rule [tex]\sqrt[n]{-a}=-\sqrt[n]{a}[/tex], when n is odd, we will get:

[tex]-\sqrt[3]{64x^6y^9}[/tex]

We can rewrite terms of our given expression as:

[tex]-\sqrt[3]{(4)^3(x^2)^3(y^3)^3}[/tex]

Using radical rule [tex]\sqrt[n]{a^n}=a[/tex], we will get:

[tex]-4x^2y^3[/tex]

Therefore, simplified form of our given expression is [tex]-4x^2y^3[/tex].

The required number is 380,303.

It is required to find nearest ten thousands of the number.

What is "Rounding" ?

Rounding means making a number simpler but keeping its value close to what it was.

Given that:

We have to find the nearest ten thousands of the number  380.303.

We know that to round a number to the nearest 10,000, check the thousands digit to decide whether to round up or round down. If the thousands are 5000 or more, round up. If they are 4999 or less, round down. 45,000 to the nearest 10,000 is 50,000.

So, the number is less than 5000 so, round down or unchanged.

Therefore, the required number is 380,303.

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The measures of all three angles are 15, 30, and 135 degrees respectively.

The angle sum property of a triangle states that the sum of the interior angles of a triangle is 180 degrees.

Let the smallest angle be represented as x,

one angle = 2x

largest angle = 9x

Therefore, x + 2x + 9x = 180° (by angles sum in a triangle)

12x = 180°

x = 15°

Then 2x = 15° x 2

= 30°

Also, 9x = 15° x 9

= 135°

Hence, The smallest angle is 15° and the one angle is 30°.

The largest angle is 135°.

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Answer:

36

Step-by-step explanation:

When the cube is rolled two times

Let (a,b) denote a possible outcome of rolling the cube twice , with a the number on the top of the first roll and b the number on the top of the second roll

(1,1) (1,2) (1,3) (1,4) (1,5) (1,6)

(2,1) (2,2) (2,3) (2,4) (2,5) (2,6)

(3,1) (3,2) (3,3) (3,4) (3,5) (3,6)

(4,1) (4,2) (4,3) (4,4) (4,5) (4,6)

(5,1) (5,2) (5,3) (5,4) (5,5) (5,6)

(6,1) (6,2) (6,3) (6,4) (6,5) (6,6)

There are 36 possibilities for (a,b).

It can be obtained from the multiplication principle: there are 6 possibilities for a, and for each outcome for a, there are 6 possibilities for b.

So, the total number of outcomes (a,b) is [tex]6 \times 6 =36[/tex]

Hence the total number of possible outcomes is 36

When the cube is rolled two times, there are a total of 36 possible outcomes.

Use the concept of probability defined as:

Probability is the ratio of:

The number of favorable outcomes to the total number of outcomes for an event's taking place.

Given that,

A six-sided number cube is used, with numbers 1-6 labeled on each face.

Each number is used exactly once on the cube.

The cube is rolled two times.

The objective is to determine the number of possible outcomes when rolling the cube two times.

To find the number of possible outcomes when a six-sided number cube is rolled two times:

Use a simple principle called the multiplication principle.

Since there are six possible outcomes for each roll,

The total number of outcomes for rolling the number cube two times is found by multiplying the number of outcomes for each roll together.

So, if you roll the number cube two times,

There would be 6 outcomes for the first roll and 6 outcomes for the second roll.

Multiplying them together gives us a total of 36 possible outcomes.

Hence,

The answer is 36 possible outcomes when the cube is rolled two times

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54 / 2 2/3 =

54/1 / 8/3 =

54/1 x 3/8 = 162/8 = 20 1/4 miles per month