The variables A, B, and C represent polynomials where A = x2, B = 3x + 2, and C = x - 3. What is AB - C in simplest form?

Answer:

96

Step-by-step explanation:

80÷100×120

96 ,, , ,; , ,

Answer:

(0.8) (120)

Step-by-step explanation:

\(80\% \: of \: 120\\\\ = \frac{80}{100} \times 120 \\ \\ = (0.8)(120)\\\\=96\)

The acceleration of a particle moving along a straight line is given by a = 6t. If, when t = 0, its velocity, v, is 1 and its position, s, is 3, then at any time t: s = t³ + t + 3. The correct answer is C.

We know that acceleration is the derivative of velocity and velocity is the derivative of position. So, integrating the given acceleration a = 6t with respect to time we get, v = 3t² + C1 where C1 is a constant of integration.

Given that when t = 0, v = 1, so substituting these values in the above equation, we get 1 = 3(0)² + C1, which implies C1 = 1.

Now, integrating the velocity v = 3t² + 1 with respect to time we get, s = t³ + t + C2 where C2 is a constant of integration.

Given that when t = 0, s = 3, so substituting these values in the above equation, we get 3 = 0³ + 0 + C2, which implies C2 = 3.

Therefore, the position of the particle at any time t is given by s = t³ + t + 3.

Hence, the correct option is (C) s = t³ + t + 3.

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Answer:

The proper linear equation is written in following form: y = mx + b (where m is slope, and b is y-intercept). Since we already have the slope, we need to find the y-intercept, b

So we plug in what we have:

y = mx + b

-1 = (-3)(6) + b, where we solve for b

-1 = -18 + b

b = 17

Finally, the equation of the line that passes through point (6, -1) and has a slope of -3 is y = -3x + 17

120% can be expressed as a decimal by dividing it by 100: 120 / 100 = 1.2 So, 120% of 5x can be expressed as: 1.2 * 5x = 6x The expression simplifies to 6x.

Algebraic expressions are the idea of expressing numbers using letters or alphabets without specifying their actual values. The basics of algebra taught us how to express an unknown value using letters such as x, y, z, etc. These letters are called here as variables. An algebraic expression can be a combination of both variables and constants. Any value that is placed before and multiplied by a variable is a coefficient. An algebraic expression in mathematics is an expression which is made up of variables and constants, along with algebraic operations (addition, subtraction, etc.).These expressions are represented with the help of unknown variables, constants and coefficients. The combination of these three (as terms) is said to be an expression.

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Step-by-step explanation:

The purple triangle would be an equilateral triangle because all three sides are equal.

The pink triangle would be an isosceles triangle because only two sides are equal.

We are looking for the value of t when d(t) equals 250. So:

\(d(t)=250\\-16t^2+400t=250\)

So let's solve for t. The best way to do this is by using the Quadratic Formula. This evaluates quadratic equations. Quadratic equations are trinomials with a degree of two.

\(x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\-16t^2+400t=250\\-16t^2+400t-250=250-250\\-16t^2+400t-250=0\\\\t=\frac{-400\pm\sqrt{400^2-4(-16)(-250)}}{2(-16)}\\t=\frac{-400\pm\sqrt{160000-4(4000)}}{-32}\\t=\frac{-400\pm\sqrt{160000-16000}}{-32}\\t=\frac{-400\pm\sqrt{144000}}{-32}\\t=\frac{-400\pm379.47}{-32}\\t=\frac{-20.53}{-32},\frac{-779.47}{-32}\\t=0.641,24.36\)

So the projectile will be at a height of 250ft at 0.641 seconds and 24.36 seconds.

Answer:

2 distance

Step-by-step explanation:

you solve it and see it's easy know first try I will do it

The value of the given expression is 0.So, the correct option is (d) None of these.

To simplify the given expression, let's focus on each term individually and then combine them.

First, let's simplify the expression 3/1 - b/3:

3/1 - b/3 = 9/3 - b/3 = (9 - b)/3

Next, let's simplify the expression a/1 - b/3:

a/1 - b/3 = 3a/3 - b/3 = (3a - b)/3

Now, let's simplify the expression -a/1 + b/3:

-a/1 + b/3 = -3a/3 + b/3 = (-3a + b)/3

Finally, let's simplify the expression -3/1 + b/3:

-3/1 + b/3 = -9/3 + b/3 = (-9 + b)/3

Now, let's combine all the simplified terms:

(9 - b)/3 + (3a - b)/3 + (-3a + b)/3 + (-9 + b)/3

We can group the terms with similar variables:

[(9 + (-9))/3] + [(3a + (-3a))/3] + [(b - b)/3] + [(-b + b)/3]

Simplifying each grouped term further:

[0/3] + [0/3] + [0/3] + [0/3]

Since all the grouped terms result in 0/3, the overall expression simplifies to:

0 + 0 + 0 + 0 = 0

Therefore, the value of the given expression is 0.

So, the correct option is (d) None of these.

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The binary search tree to be complete means all the nodes has its own subtree with maximum zero or two children.

In the binary search tree data structure which is composed of some nodes have following characteristics :

The given question is incomplete, I answer the question in general according to my knowledge:

What does it mean for a binary search tree to be complete?

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Answer:

She can buy a 12000$ car

--heart if helped or brain me ;3--

Answer:

450%

Step-by-step explanation:

Answer:

its is (b) turns the oven on

Answer:

D

Step-by-step explanation:

I did the test

Answer:

-15

Step-by-step explanation:

if its just asking for what number would represent a loss of 15 it would be negative 15

i dont know if there's more to the problem or not

Answer:

-15

Step-by-step explanation:

This is because whatever much water was in the tank is now decreasing by 15, therefore, you can write it as -15,

hope this helps!

The net change of the function f(t) = t^2 - 3t between t = 4 and t = 4 + h is h^2 + 5h, and the average rate of change over this same interval is h + 5.

The net change of a function is the overall change in its output value over a given interval. In this case, we are given the function f(t) = t^2 - 3t and asked to determine the net change and average rate of change between t = 4 and t = 4 + h.
To find the net change, we need to evaluate the function at the two endpoints and subtract the smaller value from the larger value. Thus, we have:
f(4 + h) - f(4) = [(4 + h)^2 - 3(4 + h)] - [4^2 - 3(4)]
= [16 + 8h + h^2 - 12 - 3h] - [16 - 12]
= h^2 + 5h
Therefore, the net change of the function between t = 4 and t = 4 + h is given by h^2 + 5h.
Next, we need to find the average rate of change of the function over this same interval. The average rate of change is the slope of the line connecting the two endpoints of the interval. We can find this slope by using the formula:
average rate of change = (f(4 + h) - f(4)) / h
Plugging in the expression for f(t), we get:
average rate of change = [(4 + h)^2 - 3(4 + h) - (4^2 - 3(4))] / h
= (h^2 + 5h) / h
= h + 5
Therefore, the average rate of change of the function between t = 4 and t = 4 + h is given by h + 5.
In summary, the net change of the function f(t) = t^2 - 3t between t = 4 and t = 4 + h is h^2 + 5h, and the average rate of change over this same interval is h + 5.

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The time needed for light to travel 42000 Km is 0.14 second.  

Given that,

The speed of the light is = 3 × 10⁸ m/s

Distance travelled by light is = 42000 km = 42 × 10⁶ m [since 1 km = 10³ m]

We have to find the time needed to travel the distance 42000 km by the light.

We know that from the velocity formula,

Speed = Distance/Time

Time = Distance/Speed

Time = (42 × 10⁶)/(3 × 10⁸) = 14 × 10⁻² = 0.14 second.

Hence the time needed for light to travel 42000 Km is given by 0.14 second.  

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Answer:

y = - \(\frac{1}{6}\) x + 3

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = 6x + 3 ← is in slope- intercept form

with slope m = 6

given a line with slope m then the slope of a line perpendicular to it is

\(m_{perpendicular}\) = - \(\frac{1}{m}\) = - \(\frac{1}{6}\) , then

y = - \(\frac{1}{6}\) x + c ← is the partial equation of the perpendicular line

to find c substitute (- 6, 4 ) into the partial equation

4 = 1 + c ⇒ c = 4 - 1 = 3

y = - \(\frac{1}{6}\) x + 3 ← equation of perpendicular line

Answer:

2 4 6 8 10

Step-by-step explanation:

i think 2sssssssss

Answer:

|12|

|-12|                                    

im pretty sure thats it

- - - - - - - - - - - - - - - - - - - - - - - -

Hello! Explanation below!

- - - - - - - - - - - - - - - - - - - - - - - -

Ideally, we should break apart the number for this problem. So, here goes nothing. :)

500 / 8 = 62.5

20 / 8 = 2.5

8 / 8 = 1

Now, add your products.

62.5 + 2.5 + 1 = 66

- - - - - - - - - - - - - - - - - - - - - - - -

Good luck!

~pinetreee

The RTS of the isoquant is 1000K, indicating the rate at which labor can be substituted for capital while maintaining constant production. The labor to capital cost ratio is 0.5. To minimize the cost of producing q units per hour, the specific value of q is needed to find the optimal combination of K and L along the expansion path, represented by the cost function C(K, L) = 40K + 20L.

The RTS (Rate of Technical Substitution) measures the rate at which one input can be substituted for another while keeping the production level constant. To determine the RTS, we need to calculate the derivative of the production function with respect to L, holding q constant.

Given the production function q = 1000KL, we can differentiate it with respect to L:

d(q)/d(L) = 1000K

Therefore, the RTS of the isoquant for production level q is 1000K.

The ratio of labor to capital cost can be calculated by dividing the labor cost by the capital cost.

Labor cost = $20/hour

Capital cost = $40/machine/hour

Ratio of labor to capital cost = Labor cost / Capital cost

                              = $20/hour / $40/machine/hour

                              = 0.5

The ratio of labor to capital cost is 0.5.

To find the combination of K and L that minimizes the cost of producing q units per hour, we need to set up the cost function and take its derivative with respect to both K and L.

Let C(K, L) be the total cost function.

The cost of capital is $40 per machine per hour, and the cost of labor is $20 per hour. Therefore, the total cost function can be expressed as:

C(K, L) = 40K + 20L

To produce q units per hour at minimal cost, we need to find the values of K and L that minimize the total cost function while satisfying the production constraint q = 1000KL.

The expansion path of the firm represents the combinations of K and L that minimize the cost at different production levels q.

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The proof of "if group G has exactly one subgroup H of order k, then H is normal in G" is explained below.

If a "group-G" has exactly one subgroup H of order k, we want to show that H is normal in G. This means that for any element g in G, when we conjugate H by g, we get H again.

To prove this, we consider the left cosets of H in G. A left coset of H is formed by taking an element g in G and multiplying it with each element of H. Since H is the only subgroup of order k, each left coset has k elements.

Now, we take any element-g from G. Since the left cosets partition G, g must be in one of these left cosets, which we can write as gH.

When we conjugate H by g, we get gHg⁻¹. This means we multiply each element of H by g and then multiply the result by g⁻¹, the inverse of g.

Since G is a group, this multiplication follows the group's properties.  When we multiply any element of H by g and then by g⁻¹, the result is still an element of H.

Because of this, we can conclude that for any element g in G, the conjugate of H by g (gHg⁻¹) is still a subset of H.

Therefore, H is normal in G.

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The given question is incomplete, the complete question is

If a group G has exactly one subgroup H of order k, prove that H is normal in G.

Jiri's age is 20.

To find Jiri's age, we can set up a system of equations based on the given information.

Let's assume Pamela's age is P and Jiri's age is J.

According to the problem, Pamela's age is three times Jiri's age: P = 3J.

The sum of their ages is 80: P + J = 80.

Now we can solve this system of equations to find Jiri's age.

We can substitute the value of P from the first equation into the second equation:
3J + J = 80.

Combining like terms, we get:
4J = 80.

Dividing both sides of the equation by 4, we find:
J = 20.

Therefore, Jiri's age is 20.

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Answer:

Radius is 4

Step-by-step explanation:

Answer:

I think answer's G. I'm really sorry if it's wrong. You rock!

Step-by-step explanation:

Hope this helps

Answer:

C. is the only one that makes sense, but the real answer is (-15, 0)

(っ◔◡◔)っ ♥ Hope It Helps ♥

The parameter of interest in this situation is whether or not the die rolls fives more often than it should.

In this situation, the parameter of interest is the probability or proportion of times that the die rolls a five in the long run. The experimenter suspects that the die is not weighted correctly and wants to determine if it rolls fives more frequently than the expected probability of 1/6 (approximately 0.167) for a fair six-sided die.

To test the die, the experimenter rolls it 60 times and records the number of times it lands on a five, which turns out to be 16. To calculate the proportion, the number of times the die rolled a five (16) is divided by the total number of rolls (60), resulting in a proportion of approximately 0.267, or 26.7%.

This observed proportion of 26.7% raises suspicion that the die might be biased towards rolling fives. However, it is important to note that this is a sample proportion based on a relatively small number of rolls. To draw more robust conclusions about the fairness of the die, a larger sample size would be needed. Statistical tests, such as hypothesis testing, can also be employed to determine the likelihood of the observed proportion occurring by chance alone and to make more definitive statements about the fairness of the die.

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The parameter of interest is the proportion of times the die rolls a five. By comparing the observed proportion to the expected proportion, we can determine if the die is weighted correctly.

The parameter of interest in this situation is the proportion (percentage) of times that the die rolls a five in the long run.

To determine if the die is rolling fives more often than it should, we compare the observed proportion of fives rolled (16/60) to the expected proportion of 1/6. If the observed proportion is significantly different from the expected proportion, then it suggests that the die is not weighted correctly.

In this case, the observed proportion of 26.7% is higher than the expected proportion of 16.7%, indicating that the die may indeed be rolling fives more often than it should.

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The simple interest equation for this problem is given as follows:

A = 500 + 10t.

The equation that gives the balance of an account after t years, considering simple interest, is modeled as follows:

A(t) = P(1 + rt).

In which the parameters of the equation are listed and explained as follows:

The parameter values for this problem are given as follows:

P = 500, r = 0.02.

Hence the equation is given as follows:

A = 500(1 + 0.02t)

A = 500 + 10t.

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All formulas that model the sequence​ include the following:

E. aₙ =  aₙ₋₁ - 13.8, where a₁ = -7.4

F. aₙ =  6.4 - 13.8n

In Mathematics and Geometry, the nth term of an arithmetic sequence can be calculated by using this equation:

aₙ =  a₁ + (n - 1)d

Where:

Next, we would determine the common difference of the given sequence by using the following formula;

Common difference, d = a₂ - a₁

Common difference, d = -21.2 - (-7.4)

Common difference, d = -13.8.

For the nth term of this arithmetic sequence, we have:

aₙ =  a₁ + (n - 1)d

aₙ =  -7.4 + (n - 1)-13.8

aₙ =  -7.4 - 13.8(n - 1)

aₙ =  -7.4 - 13.8n + 13.8

aₙ =  6.4 - 13.8n

aₙ =  aₙ₋₁ - 13.8, where a₁ = -7.4

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The stationary probability distribution is:

\(\pi = ((a^2)/(a^2 + B^2 + aB), (aB)/(a^2 + B^2 + aB), (B^2)/(a^2 + B^2 + aB))\)

To find the stationary probability distribution of the continuous-time Markov chain with jump rates q(i, i+1) = B for i=0,1 and q(i,i-1) = a for i=1,2, we need to solve the balance equations:

π(0)q(0,1) = π(1)q(1,0)

π(1)(q(1,0) + q(1,2)) = π(0)q(0,1) + π(2)q(2,1)

π(2)q(2,1) = π(1)q(1,2)

Substituting the given jump rates, we have:

π(0)B = π(1)a

π(1)(a+B) = π(0)B + π(2)a

π(2)a = π(1)B

We can solve for the stationary probabilities by expressing π(1) and π(2) in terms of π(0) using the first and third equations, and substituting into the second equation:

π(1) = π(0)(B/a)

π(2) = π(0)(\((B/a)^2)\)

Substituting these expressions into the second equation, we obtain:

π(0)(a+B) = π(0)B(B/a) + π(0)((\(B/a)^2)a\)

Simplifying, we get:

π(0) = \((a^2)/(a^2 + B^2 + aB)\)

Using the expressions for π(1) and π(2), we obtain:

π = (π(0), π(0)(B/a), π(0)(\((B/a)^2))\)

\(= ((a^2)/(a^2 + B^2 + aB), (aB)/(a^2 + B^2 + aB), (B^2)/(a^2 + B^2 + aB))\)

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We can find :

14 , 1/2s in 7,

16, 3/8s in 6 and

6 , 5/16s in 1 7/8

A fraction is a part of a whole number. The number is expressed as a quotient, in which the numerator is divided by the denominator. In a simple fraction, both are integers In a proper fraction, the numerator is less than the denominator.

dividing 7 by 1/2

7÷1/2= 14

dividing 6 by 3/8

6÷ 3/8= 16

dividing 15/8 by 5/16

15/8÷ 5/16= 6

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