Two buses, 385 miles apart, are traveling directly toward each other on the same road. One is averaging 60 mph and the other averages 50 mph. After how long will they meet?

The values of x for which the function f(x) = x³ + 3x² - 9x + 7 is increasing are (-∞, -3) and (1, +∞).

To find the values of x for which the function f(x) = x³ + 3x² - 9x + 7 is increasing, we need to take the derivative of the function and determine where the derivative is positive.

f(x) = x³ + 3x² - 9x + 7

f'(x) = 3x² + 6x - 9

To find where f(x) is increasing, we need to find the values of x where f'(x) > 0.

3x² + 6x - 9 > 0

Simplifying this inequality, we get

x² + 2x - 3 > 0

Factoring the left side of the inequality, we get

(x + 3)(x - 1) > 0

The critical points of f(x) occur when f'(x) = 0 or when the denominator of f'(x) is undefined. The denominator of f'(x) is always defined, so we only need to find where f'(x) = 0

3x² + 6x - 9 = 0

Dividing both sides by 3, we get

x² + 2x - 3 = 0

Factoring the left side of the equation, we get

(x + 3)(x - 1) = 0

So the critical points of f(x) are x = -3 and x = 1.

Now we can use a sign chart to determine the intervals where f'(x) > 0.

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The given question is incomplete, the complete question is:

What are all values of x for which the function f is defined by f(x)= x³ +3x² -9x +7 is increasing?

An angle in a rectangular coordinate system is in standard position if its vertex is at the origin of the plane, the initial side of the angle is on the positive x-axis, and the terminal side of the angle is in one of the four quadrants. The angle is measured in a counterclockwise direction from the positive x-axis and is considered positive if it lies in the counterclockwise direction and negative if it lies in the clockwise direction.

The position of an angle is measured from the reference line called the initial side, which is the positive x-axis, and it ends at the terminal side, which is the side where the angle is located. An angle in a rectangular coordinate system is in a standard position if its vertex is at the origin of the plane. An angle is said to be in a standard position if its vertex is located at the origin of the coordinate system.

To summarize, an angle in a rectangular coordinate system is in standard position if its vertex is at the origin of the plane, the initial side of the angle is on the positive x-axis, and the terminal side of the angle is in one of the four quadrants. The position of an angle is measured from the reference line called the initial side, which is the positive x-axis, and it ends at the terminal side, which is the side where the angle is located.

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If the odds of a horse winning a race are 2 to 1, then the probability of this horse winning the race is approximately 2/3 or 0.6667.  This can be calculated as 1 divided by the sum of the odds plus 1.

The odds of a horse winning a race are typically expressed in the form of "a to b", where a represents the number of favorable outcomes (winning) and b represents the number of unfavorable outcomes (losing). In this case, the odds are 2 to 1, which means there are 2 favorable outcomes (winning) for every 1 unfavorable outcome (losing).

To convert odds to probability, we use the following formula:

Probability = a / (a + b)

In this case, the probability of the horse winning the race can be calculated as:

Probability = 2 / (2 + 1) = 2 / 3 ≈ 0.6667

Therefore, the probability of the horse winning the race is approximately 2/3 or 0.6667.

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The volume of water filled in the bath tub is 6 feet × 2 feet × 2.2 feet = 26.4 cubic feet. You need 11.83 minutes in the shower to use as much water as the bath.

The volume of water filled in the bath tub is 6 feet × 2 feet × 2.2 feet = 26.4 cubic feet.

The amount of water used in shower = flow rate × time = 2.23 gallons/minute × 8 minutes = 17.84 gallons

Let's convert gallons to cubic feet: 1 cubic foot = 7.5 gallons

17.84 gallons = 17.84/7.5 cubic feet = 2.378 cubic feet

The volume of water used in the shower is 2.378 cubic feet. The volume of water used for taking a bath is 26.4 cubic feet.

To calculate how many minutes one would need in the shower to use as much water as the bath, divide the volume of water used in taking a bath with the amount of water used per minute in the shower as shown:

26.4/2.23=11.83 min

Therefore, one needs 11.83 minutes in the shower to use as much water as the bath.

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It is answer choice (C). 7 and 8!

Really hope this helped! brainliest would be very appreciated!

~HAPPY DAYZ~

Answer: table C or 3

Step-by-step explanation:

If you graph it on paper then it creates a straight line, where the others do not.

This means that if a dataset follows a normal distribution, around 68% of the observations will fall within one standard deviation above and below the mean.

According to the empirical rule (also known as the 68-95-99.7 rule), approximately 68% of normally distributed data lies within one standard deviation of the mean.

what is mean?

The mean, also known as the average, is a measure of central tendency in statistics. It is calculated by summing up all the values in a dataset and dividing the sum by the number of values.

For a given set of data points x1, x2, x3, ..., xn, the mean (μ) is computed as:

μ = (x1 + x2 + x3 + ... + xn) / n

where n is the total number of data points.

The mean represents the "typical" or "average" value of the data and is often used as a measure of central location. It is sensitive to extreme values, as they can significantly impact the calculated mean.

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Answer:

j=15

Step-by-step explanation:

Let's set up an equation:

2j+7=37

Subtract both sides by 7

2j=30

Divide both sides by 2

j=15

Answer:

15

Step-by-step explanation:

37=2j+7

so subract 7 from both sides

30=2j

then divide by 2 on each side

j=15

Answer:

a season

Step-by-step explanation:

From the given figure the value of x is 6 and the measure of angle 3 is 57°.

From the given figure, m∠4=(20x+3)° and m∠6=(9x+3)°.

Angles in parallel lines are angles that are created when two parallel lines are intersected by another line called a transversal.

22). From the given figure

m∠4+m∠6=180° (Coointerior angles sum is equal to 180°)

(20x+3)°+(9x+3)°=180°

⇒ 29x+6=180

⇒ 29x=174

⇒ x=6

m∠4=(20x+3)°=123°

m∠3+m∠4=180° (Adjacent angles sum is equal to 180°)

m∠3+123=180

m∠3=57°

23). From the given figure

m∠3=m∠6 (Alternate interior angles are congruent)

x+10 = 4x-20

⇒ 3x=30

⇒ x=10

Now, m∠6=4x-20

=20

m∠6+m∠8=180° (Adjacent angles sum is equal to 180°)

20+m∠8=180°

⇒ m∠8=160

Therefore, from the given figure the value of x is 6 and the measure of angle 3 is 57°.

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The possible values of calls recieved by Huzan is more than 1645 and calls made is less than 2370.

What is Inequalities of equations ?

Mathematical expressions with inequalities are those in which the two sides are not equal. Contrary to equations, we compare two values in inequality. Less than (or less than or equal to), larger than (or greater than or equal to), or not equal to signs are used in place of the equal sign.Inequality simply means that two things aren't equal. One of the items could be inferior to, superior to, greater than, or equivalent to the other things.
p ≠ q means that p is not equal to qp < q means that p is less than qp > q means that p is greater than qp ≤ q means that p is less than or equal to qp ≥ q means that p is greater than or equal to q
Different kinds of inequality exist. Important inequities include the following: the inequalities of polynomials
Inequalities in absolute values
Logic-based disparities
Calls made by Hazar = 2370
Calls recieved by Hazar = 1645Let the number of Calls by Huzan be x.
And the number of calls recieved by Huzan be y.
Then the inequalities arex< 2370 and y> 1645
The possible values of calls recieved by Huzan is more than 1645 and calls made is less than 2370.

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Answer:

3x^3 - 2x^2

Step-by-step explanation:

This is the answer because for the equation 3x^3 - 2x^2, nothing further can be done to this equation since there are no like terms.

5/6x + 7 = 17

Subtract 7 from both sides:

5/6x = 10

Divide both sides by 5/6:

X = 10/ 5/6

When dividing a number by a fraction flip

The fraction over and multiply:

X = 10 x 6/5

Simplify

X = (10x6)/5

X = 60/5

X = 12

The answer is x = 12

Answer:

\(\boxed {x = 12}\)

Step-by-step explanation:

Solve for the value of \(x\):

\(\frac{5}{6}x + 7 = 17\)

-Subtract both sides by \(7\):

\(\frac{5}{6}x + 7 - 7 = 17 - 7\)

\(\frac{5}{6}x = 10\)

-Multiply both sides by \(\frac{6}{5}\), which is the reciprocal of \(\frac{5}{6}\):

\(x = 10 \times (\frac{6}{5})\)

\(x = \frac{10 \times 6}{5}\)

\(x = \frac{60}{5}\)

-Divide \(60\) by \(5\):

\(x = \frac{60}{5}\)

\(\boxed {x = 12}\)

Therefore, the value of \(x\) is \(12\).

By Using the table to work out the values of a , b , c , and d. X y = 2 x + 1 − 3 a − 2 − 3 − 1 b 0 1 1 c 2 d a = b = c = d =

Therefore, The solutions are : a = -3, b = 0, c = 6, d = 9

Equation:

In mathematics, an equation is an expression that indicates equality of two expressions by connecting them with the equal sign = . The word "equation" and related words in other languages ​​can have slightly different meanings. For example, in French an equation is defined as containing one or more variables, whereas in English a well-formed formula consisting of two expressions connected by an equal sign is an equation.

Given:

This table;

x             y = 3x+3

-3                -6

-2                 a

-1                  b

0                 3

1                  c

2                 d

To Find:

Values of a, b, c and d

Consider the 2nd row,

x = -2, y = a

Putting the values in the equation,

we get,

   a = 3(-2) + 3

⇒ a = -3

Consider the 3rd row,

x = -1, y = b

Putting the values in the equation,

we get,

   b = 3(-1) + 3

⇒ b = 0

Consider the 5th row,

x = 1, y = c

Putting the values in the equation,

   c = 3(1) + 3

⇒ c = 6

Consider the 6th row,

x = 2, y = d

   d = 3(2) + 3

⇒ d = 9

The final answer is,

a = -3, b = 0, c = 6, d = 9.

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Answer:

as the last two months have a few minutes in a factory and we have a few minutes away and will also send the

The remainder would be 12 as per the remainder theorem if the function P is defined by P(x) = x³ +7x² - 26x - 72.

A polynomial is defined as a mathematical expression that has a minimum of two terms containing variables or numbers. A polynomial can have more than one term.

Let   P(x) = x³ +7x² - 26x - 72  ...(i)

Divisor = (x+9)

Apply remainder theorem,

x + 9 = 0

x = -9

Substitute the value of x = -9 in equation (i),

⇒ P(-9) = (-9)³ +7(-9)² - 26(-9) - 72

⇒ P(-9) = (-729) +7(81) - 234 - 72

⇒ P(-9) = -729 + 567 - 234 - 72

⇒ P(-9) = -468

Therefore, the remainder would be -468.

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Answer:

d = 13

Step-by-step explanation:

3 = w - 10

(plus 10 on both sides to get)

13 = w OR w = 13

therefore the answer is 13.

Answer:

x = 13

Step-by-step explanation:

3 = w - 10

Add 10 on both sides:

13 = w

Check:

3 = 13 - 10

3 = 3

So it is true that is x = 13.

Hope this helps!

It reaches a high of 51.8 degrees Fahrenheit. There is a 59.4 degree F range. 12.6 degrees Fahrenheit is the standard deviation. The average temperature is 33.8°F. The median temperature is 35.6 °F. IQR is 60.8 degrees Fahrenheit.

The study of statistics focuses on gathering, organizing, organizing, analyzing, interpreting, and presenting data. It is customary to start with a statistical population or a statistical model to be researched when applying statistics to a scientific, industrial, or social problem. The study of gathering, analyzing, interpreting, presenting, and organizing data in a particular way is the focus of the mathematic branch known as statistics. The process of gathering data, classifying it, presenting it in a way that makes it understandable, and then conducting additional analyses of the data is known as statistics.

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Answer:

-13

Step-by-step explanation:

3y-10

Let y = -1

3(-1)-10

Multiply

-3-10

Combine

-13

Answer:

7 nickles

8 dimes

4 quarters

Step-by-step explanation:

q

d = 2q

n = q+3

25q + 10d + 5n = 215

25q + 10(2q) + 5(q + 3) = 215

25q + 20q + 5q - 15 = 215

50q = 200

q = 4

d = 2q = 8

n = q + 3 = 7

4000 N  is the work done .

In math, what is a distance?

The length of the segment of the line that connects the supplied two points determines the distance between them. The length of the shortest line segment connecting a point to a line represents the distance between them.

                               Distance is the sum of an object's movements, regardless of direction. Regardless of an object's starting or ending point, distance can be defined as the amount of ground it has traveled.

m = 80 kg

d = 5m

g = 10 m/s²

work done = force × distance

                   = mgh

                    =  80 × 10 × 5

                    =  4000 N

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Answer:

She bought 3 DVDs because $17.06 is 1/4 of $68.24

Answer:

2 friends

Step-by-step explanation:

use decimals 2.5 and 1.25 divide them and you will get 2

The value of x for this problem is given as follows:

x = 5.

Hence the angle measures are given as follows:

We have that angles A and D are congruent for this problem, meaning that they have the same measure.

Hence the value of x is obtained as follows:

7x - 3 = 5x + 7

2x = 10

x = 5.

Hence the angle measures are given as follows:

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Answer:

1(hr):33(min):45(sec)

Step-by-step explanation:

According to the distributive property:

\( \alpha ( \beta + \gamma ) = \alpha \beta + \alpha \gamma \)

So, applying this to our equation:

\(7(x + 3y) = 7 \times x + 7 \times 3y \\ 7(x + 3y) = 7x + 21y\)

The volume of the canister is 339.1 cubic inches.

The volume of a cylinder is calculated by using the formula V=πr²h, where r is the radius of the cylinder and h is the height of the cylinder.

The radius of the cylinder is half of the diameter, so the radius of the canister is 3 inches.

Using the formula, we can calculate the volume of the canister as follows:

V = π×3²×12

V = 108×3.14

V = 339.1 cubic inches

Therefore, the volume of the canister is 339.1 cubic inches.

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By mathematical induction, we have proved that for any positive integer n, 4 evenly divides 11n - 7n.

WHat is Divisibility?

Divisibility is a mathematical property that describes whether one number can be divided evenly by another number without leaving a remainder. If a number is divisible by another number, it means that the division process results in a whole number without any remainder. For example, 15 is divisible by 3

To prove that 4 evenly divides 11n - 7n for any positive integer n, we can use mathematical induction.

Base Case:

When n = 1, 11n - 7n = 11(1) - 7(1) = 4, which is divisible by 4.

Inductive Step:

Assume that 4 evenly divides 11n - 7n for some positive integer k, i.e., 11k - 7k is divisible by 4.

We need to prove that 4 evenly divides 11(k+1) - 7(k+1), which is (11k + 11) - (7k + 7) = (11k - 7k) + (11 - 7) = 4k + 4.

Since 4 evenly divides 4k, and 4 evenly divides 4, it follows that 4 evenly divides 4k + 4.

By mathematical induction, we have proved that for any positive integer n, 4 evenly divides 11n - 7n.

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