Mathmatics please help me

Answer:

60

Step-by-step explanation:

The solution to the system of inequalities in interval notation is [-2, 1].

Based on the information provided in the image below, we have the following system of inequalities;

-12 < 3x - 6

-3 ≥ 3x - 6

By adding 6 to both sides of the equation (inequality), we have;

-12 < 3x - 6

-12 + 6 < 3x - 6 + 6

-6 < 3x

-2 < x

x > -2 (flip)

-3 ≥ 3x - 6

-3 + 6 ≥ 3x - 6 + 6

3 ≥ 3x

1 ≥ x

x ≤ 1

Therefore, the solution to the system of inequalities is given by:

-2 < x ≤ 1

In interval notation, we have [-2, 1].

Read more on inequality here: https://brainly.com/question/30665021

#SPJ1

Missing information:

The question is incomplete and the complete question is shown in the attached picture.

Answer:

Step-by-step explanation:

Answer:

8/12 and 9/12

Step-by-step explanation:

Let's assume David's average speed is S km/h.

A) To find David's average speed, we can use the formula: Speed = Distance / Time.

David completed the race in 5 hours, so his speed is S km/h. Therefore, we have:

S = Distance / 5

B) Ken's average speed is 9.8 km/h less than David's average speed, which means Ken's average speed is (S - 9.8) km/h.

Ken took 7 hours to complete the race, so we have:

S - 9.8 = Distance / 7

Now, we can solve the system of equations to find the values of S and Distance.

From equation (1): S = Distance / 5

Substitute this into equation (2):

Distance / 5 - 9.8 = Distance / 7

Multiply both sides of the equation by 35 to eliminate the denominators:

7 * Distance - 35 * 9.8 = 5 * Distance

7 * Distance - 343 = 5 * Distance

Subtract 5 * Distance from both sides:

2 * Distance - 343 = 0

Add 343 to both sides:

2 * Distance = 343

Divide both sides by 2:

Distance = 343 / 2 = 171.5 km

Therefore, the distance of the cycling race is 171.5 kilometers.

To find David's average speed, substitute the distance into equation (1):

S = Distance / 5 = 171.5 / 5 = 34.3 km/h

So, David's average speed was 34.3 km/h.\(\)

Answer:

A) 34.3 km/h

B) 171.5 km

Step-by-step explanation:

Since Ken's average speed is said to be 9.8km/h less than David's average speed, and we know that Ken's average speed is dependent on him traveling for 7 hours, then we have our equation to get the distance of the cycling race:

\(\text{Ken's Avg. Speed}=\text{David's Avg. Speed}\,-\,9.8\\\\\frac{\text{Distance}}{7}=\frac{\text{Distance}}{5}-9.8\\\\\frac{5(\text{Distance})}{7}=\text{Distance}-49\\\\5(\text{Distance})=7(\text{Distance})-343\\\\-2(\text{Distance})=-343\\\\\text{Distance}=171.5\text{ km}\)

This distance for the cycling race can now be used to determine David's average speed:

\(\text{David's Avg. Speed}=\frac{\text{Distance}}{5}=\frac{171.5}{5}=34.3\text{ km/h}\)

Therefore, David's average speed was 34.3 km/h and the distance of the cycling race was 171.5 km.

Answer:

x=−3.207703,−1.142291,2.183328

Step-by-step explanation:

x−6x3−13x2+34x+48=0

−6x3−13x2+35x+48=0

1. Use cubic formula.

x=−3.207703,−1.142291,2.183328

The initial value where x=0, y is 12.74 and the exponential function is

y = 12.74(0.7)×.

Option D is correct.

The formula f(x) = \(a^x\) defines an exponential function, where x is the input variable as an exponent. The exponential curve is determined by the exponential function and the value of x.

The quantity drops rapidly at first, then slowly in Exponential Decay. The rate of change slows over time. As time passes, the rate of change slows.

We know the formula for an exponential function is

y= a \(b^x\)

where a is initial value and b is growth factor.

Now, we have to find the growth factor as

We can observe from the table that the values of y decrease as x increases.

That is an example of an exponential decay function.

In an exponential decay function, the value of a growth/decay factor b is always smaller than 1.

Thus, the initial value a= 12.74 and growth factor b=0.7 that is less than 1.

Learn more about exponential function here:

https://brainly.com/question/10451996

#SPJ7

Answer:

Option A 8 units left and 6 units up

Number of 20-cent coins in the box are 33.

1. Let's assume the number of 20-cent coins to be x and the number of 50-cent coins to be y.

2. We can set up two equations based on the given information:

  - x + y = 54   (since the total number of coins in the box is 54)

  - 0.20x + 0.50y = 20.70   (since the total value of all the coins is $20.70)

3. We can multiply the second equation by 100 to get rid of the decimals:

  - 20x + 50y = 2070

4. Now, we can use the first equation to express y in terms of x:

  - y = 54 - x

5. Substitute the value of y in the second equation:

  - 20x + 50(54 - x) = 2070

6. Simplify and solve for x:

  - 20x + 2700 - 50x = 2070

  - -30x = -630

  - x = 21

7. Substituting the value of x back into the first equation:

  - 21 + y = 54

  - y = 33

8. Therefore, there are 21 20-cent coins and 33 50-cent coins in the box.

For more such questions on Number, click on:

https://brainly.com/question/30752681

#SPJ8

To find f(g(x)), we need to substitute g(x) into the function f(x). Given that g(x) = x - 4, we substitute it into f(x) as follows:

\(f(g(x)) = f(x - 4) = (x - 4)^2 + 4\)

To simplify this expression, we can expand the square:

\(f(g(x)) = (x - 4)(x - 4) + 4\\ = x^2 - 8x + 16 + 4\\ = x^2 - 8x + 20\)

Therefore, f(g(x)) simplifies to\(x^2 - 8x + 20.\)

Next, let's find g(f(x)). We substitute f(x) into the function g(x):

\(g(f(x)) = g(1/x^2 + 4) = 1/x^2 + 4 - 4\\ = 1/x^2\)

Hence, g(f(x)) simplifies to 1/x^2.

In summary, f(g(x)) simplifies to\(x^2 - 8x + 20\), and g(f(x)) simplifies to 1/x^2.

For more such questions on functions

https://brainly.com/question/10439235

#SPJ8

Answer:

The equation is: \(\frac{x+3}{7-x} = 4\)

The solution is:   x = 5

Step-by-step explanation:

Let's write the statement given in math form using "x" to represent the unknown:

"a number is added to the numerator of 3/7 and the same number is subtracted from the denominator, the result is 4"

\(\frac{x+3}{7-x} = 4\)

This is then the equation that represents the statement, and now for the solution  of the problem: solving for the unknown.

\(\frac{x+3}{7-x} = 4\\x+3=4\,(7-x)\\x+3=28-4x\\x+4x=28-3\\5x=25\\x=5\)

Answer:

3+x

-------- = 4

7-x

x=5

Step-by-step explanation:

3+x

-------- = 4

7-x

Multiply each side by (7-x)

3+x = 4(7-x)

Distribute

3+x = 28 - 4x

Add 4x to each side

3+x+4x= 28-4x+4x

3 +5x = 28

Subtract 3 from each side

5x = 28-3

5x= 25

Divide by 5

5x/5 = 25/5

x = 5

The values of x after solving the quadratic equation x²+14x-1 , using completing the square method is -√50-7 or +√50-7.

A Quadratic equations is second-degree algebraic expressions and is of the form ax² + bx + c = 0.

Uisng the method of completing the square to solve the equation below, we following the steps.

Equation ⇒ x²+14x-1 = 0

Step 1:

Take the constant to the other side of the equation

Step 2:

Find half the coefficient of x, square, and  add it to both side of the equation.

There,

Step 3:

Express the trinomial on the left side as a square of binomial

Step 4:

Take the square root of both side.

Step 5:

Make x the subject of the equation by moving 7 to the other side of the equation

Step 6:

Seperate the expression for each value of x

Hence, the value of x is  -√50-7 or +√50-7.

Learn more about quadratic equation here: https://brainly.com/question/25841119

#SPJ1

Answer:

13.5 or if in fraction 27÷2

Step-by-step explanation:

1.5 = m ÷ 9

1.5 × 9 = m (since you're finding m,shift the 9 to the left.So divide becomes multiply)

27/2 (27÷2) or 13.5 = m

The biconditional statement for the given conditional statement would be:

2x = 18 if and only if x = 9.

The given conditional statement "If 2x = 18, then x = 9" can be represented symbolically as p → q, where p represents the statement "2x = 18" and q represents the statement "x = 9".

To form the biconditional statement, we need to determine if the converse of the conditional statement is also true. The converse of the original statement is "If x = 9, then 2x = 18". Let's evaluate the converse statement.

If x = 9, then substituting this value into the equation 2x = 18 gives us 2(9) = 18, which is indeed true. Therefore, the converse of the original statement is true.

Based on this, we can write the biconditional statement:

2x = 18 if and only if x = 9.

The biconditional statement implies that if 2x is equal to 18, then x must be equal to 9, and conversely, if x is equal to 9, then 2x is equal to 18. The biconditional statement asserts the equivalence between the two statements, indicating that they always hold true together.

In summary, the biconditional statement is a concise way of expressing that 2x = 18 if and only if x = 9, capturing the mutual implication between the two statements.

for such more question on conditional statement

https://brainly.com/question/27839142

#SPJ8

The coordinate point of N'is (-2,5)

Answer:

b

Step-by-step explanation:

just trust me

A \({ \purple{ \sf{polynomial}}}\) is defined as an expression which is composed of variables, constants and exponents, that are combined using mathematical operations such as addition, subtraction, multiplication and division (No division operation by a variable).

Answer:

ALGUIEN PARA COJER?

TENGO 20 PERRO

Answer:

c

Step-by-step explanation:

Answer:

55/4 or 13.75 or 13 3/4

Step-by-step explanation:

it just is

Answer:

55/4

Step-by-step explanation:

keep the first fraction, change the division to multiplication then flip the second fraction. Then you do that and find it in simplest form homes

Answer:

the square root of 32 times square root of 7 equals the square root of 32 times square root of 7 equals 3 times square root of 7

Step-by-step explanation:

im a mathaholic :0

Answer:

it is not likey bc inless the class have over 2 mil ppl in it itis doouptfull

Step-by-step explanation:

The probability that a student is a graduate student given they are a history major is approximately 0.16.

The likelihood or chance that an event will occur is quantified by probability. A number between 0 and 1, where 0 denotes that the occurrence is impossible and 1, denotes that the event is certain, is generally used to express it.

We are given the following information:

Total number of students who are history major: 463

Total number of graduate students: 261

Number of graduate students who are history major: 73

We can use the formula for conditional probability to find the probability that a student is a graduate student given that they are a history major:

P(graduate | history) = P(graduate and history)/P(history)

P(graduate | history) = 73/463

P(graduate | history) ≈ 0.1575 (rounded to the nearest hundredth)

Therefore, the probability that a student is a graduate student given they are a history major is approximately 0.16.

To know more about probability visit:

https://brainly.com/question/29221515

#SPJ1

In order to explain why -4 - 2 equals -8, let's start with the equation 0.2 = 0. By analyzing this equation, we can uncover the reason behind this seemingly counterintuitive result.

1. Begin with the equation 0.2 = 0.

2. Subtract 0.2 from both sides of the equation to isolate the variable: 0.2 - 0.2 = 0 - 0.2.

  This simplifies to 0 = -0.2.

3. Observe that the right side of the equation, -0.2, is a negative number.

4. Recall that subtracting a negative number is equivalent to adding its positive counterpart. Therefore, -0.2 is the same as +0.2.

5. Rewrite the equation as 0 = +0.2.

6. Notice that 0 on the left side of the equation is equal to 0 + 0, since any number added to zero remains unchanged.

7. Substitute 0 + 0 for 0 in the equation: 0 + 0 = +0.2.

8. Simplify the equation to 0 = +0.2.

9. Finally, recognize that a positive number cannot equal zero. Hence, the equation 0 = +0.2 is false.

10. As a result, the original equation 0.2 = 0 is invalid.

11. Therefore, the logical consequence is that any subsequent deductions based on this invalid equation would also be incorrect.

12. Consequently, -4 - 2 does not equal -8, as per the explanation derived from the flawed equation.

To summarize, by analyzing the equation 0.2 = 0, we can determine that subsequent deductions based on this equation are incorrect. Hence, -4 - 2 does not equal -8.

For more such questions on counterintuitive, click on:

https://brainly.com/question/17004386

#SPJ8

Answer: 18.78 cubic feet

Step-by-step explanation:

The detailed analysis is attached below.

Answer:

B

Step-by-step explanation:

The radius of the circle is 13, the center is at (7, 0, 0), and the plane containing the circle is the xy-plane.

The radius of the circle can be determined using the Pythagorean theorem, which states that the square of the hypotenuse is equal to the sum of the squares of the other two sides. In this case, the hypotenuse (the radius) is the length from the origin (the center of the circle) to the point on the circle given by the equation, which we can calculate using the formula r(t) =\((7i + (12cos t)j + (12sin t)k)\). Plugging this into the Pythagorean theorem and solving for the radius gives us the radius of the circle: \(r = √(7^2 + 12^2) = 13\).

The center of the circle can be determined by looking at the equation r(t). We can see that the x-coordinate is 7, the y-coordinate is 12cos t, and the z-coordinate is 12sin t. We can also see that all of these values are constant, which means that the center of the circle is at the point (7, 0, 0).

Finally, the plane containing the circle can be determined by looking at the equation r(t). We can see that the x-coordinate is 7, the y-coordinate is 12cos t, and the z-coordinate is 12sin t. This tells us that the plane containing the circle is the xy-plane.

The radius of the circle is 13, the center is at (7, 0, 0), and the plane containing the circle is the xy-plane.

Learn more about Pythagorean theorem here:

https://brainly.com/question/14930619

#SPJ4

Answer:

19/20 , 1 1/4 , 1 4/5

Step-by-step explanation:

1.8 = 1 4/5 (fraction)

1.8 converts to 18/10. This can be simplified twice, firstly by making it 9/5 since both 18 and 10 are divisible by two, but can be simplified further to 1 4/5

1.25 = 1 1/4 (fraction)

1.25 converts to 125/100. This can be simplified to 5/4 or 1 1/4

0.95 = 19/20 (fraction)

0.95 converts to 95/100. This can be simplified to 19/20

Ascending Order (smallest to largest)

smallest - 19/20

middle - 1 1/4

largest - 1 4/5

I believe this is the right answer, but haven't done fractions in a while so may want to double check to make sure