which point is the vertex of the quadratic function f(x)=x^2-6x+8

Answer:

domain and range below

Step-by-step explanation:

domain: [-5,1) or 1>x≥-5

range: [-4,7) or -4≥x<7

these are due to the domain being the possible x-values and range being the possible y-values.

hope this helps! comment below my response if you need further clarification.

Answer:

1.91h

Step-by-step explanation:

0.06h+h+0.85h

1.91h

Answer:

The first one asdfghjkfruyctdf

Step-by-step explanation:

Answer:

I put in y = 2-x. I believe that was the equation you asked a table for. If it is another equation please tell me or just download or look up Desmos. Desmos helps create graphs and tables. I hope this helps. Have a great rest of your day!

The probability that the balls are the same color is x + 10/60

Where x is the number of blue balls there are in the second urn.

Given,

The quantity of blue balls in the second urn will be called x. The number of red balls would be 20 - x given that there are 20 balls in this urn.

In order to find the probability that the balls are the same colour, we must assume that they are both either blue OR red. (Since we're using "or," we can infer that we'll add the probabilities of both outcomes.

1) P(both balls are blue) = P(both balls are the same colour) + P ( both balls are red).

2) Next, we'll determine the probability that both balls are blue (this will require multiplication because we need both ball 1 and ball 2 to be blue):

P(ball 1 is blue) x P = P(both balls are blue) (ball 2 is blue)

P(both blue balls) = = (1/6)* (x/20) = x/120

3) The procedure is the same as when both balls are blue to get the probability that both balls are red.

P(ball 1 is red) x P = P(both balls are red) (ball 2 is red)

When both balls are red, P(both are red) = = (1/6) * (20-x)/20 = 20- x/12

4) Returning to point 1 and substituting:

P(the same color of both balls) = x/120 + (20 - x)/120

= 2x + 20/120

= x + 10/60

That is,

The probability of the balls having the same color are x + 10/60.

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Answer:

Anything to the power of 0 equals 1, even 1 billion.

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Answer:

Terrence made $30 more than Teresa.

Step-by-step explanation:

Giving the following information:

Terrence earns $450 per week.

Teresa earns $300 per week plus a 6% commission on the total sales of books she sells.

First, we need to structure the total income formula for each:

Terrence= 450

Teresa= 300 + 0.06*x

x= sales

Now, for $2,000 sales of books:

Terrence= $450

Teresa= 300 + 0.06*2,000= $420

Answer:

A. y = 1.5x - 1

B. y = 1.5x

Step-by-step explanation:

Answer:

45

Step-by-step explanation:

rate : 9 minutes per mile

5 x 9 = 45

Answer:

45 minutes

Step-by-step explanation:

18= 2miles

18/2= 9 minutes  (1 mile)

18+18+9= 45

The correct answer is B. $1,000. According to a survey conducted by Bankrate in 2019, 48% of Americans reported having less than $1,000 in savings.

This can be calculated using the following formula:

Percentage of Americans with less than $1,000 in savings = (Number of Americans with less than $1,000 in savings / Total number of Americans surveyed) x 100

Using the data from the survey, the formula can be expressed as follows:

Percentage of Americans with less than $1,000 in savings = (11,094 / 23,064) x 100 = 48.1%

This means that nearly half of all Americans reported having less than $1,000 in savings. This is a concerning statistic, as it indicates that many Americans are not preparing adequately for financial emergencies.

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The number after rounding off the given decimal number is

20283.

Rounding means making a number simpler but keeping its value close to what it's original value. The result is less accurate, but easier to use.

Given is the decimal number as -

20282.93

The given number is -

20282.93

20282.9           {3 < 5}

20283              {9 > 5}

Therefore, the number after rounding off the given decimal number is

20283.

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Answer:

its not there bud

Step-by-step explanation:

Answer:

The correct answer is B.

Step-by-step explanation:

The value of the expression 2³/2³ is 1.

This is because 2³ (or 2 raised to the power of 3) is equal to 8, and 8 divided by itself is always equal to 1.

In other words, when you have the same base number in both the numerator and denominator of a fraction, you can simply cancel out those numbers and the result is 1.

So, 2³/2³ simplifies to 8/8, which is equal to 1.

Therefore, the correct answer is B.1.

Exponential function is a mathematical function of the following form: \(`f(x) = a^x`,\)where a > 0, a ≠ 1 and x is any real number.
These functions have important applications in science, engineering, and mathematics, particularly in growth and decay phenomena. In the question, we are to identify the exponential functions among the options given

\(`(a) v(x)=x^π`, `(c) h(x)=(√π)^x`, `(d) k(x)=(-π)^x`, and `(e) m(x)=π^x`.\)

Therefore, these functions are the exponential functions.Explanation for each option:

a) `v(x)=x^π`This function is not an exponential function because it is not in the form \(`a^x`\).

b) `t(x)=πx`

This function is not an exponential function because it is not in the form `

\(a^x`.c) `h(x)=(√π)^x`\)

This function is an exponential function because it is in the form `

a^x`, where a = √π. Thus, \(a^x`.c) `h(x)=(√π)^x`\)

d)

\(`k(x)=(-π)^x\)`This function is an exponential function because it is in the form\(`a^x`\), where a = -π.

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The greatest common factor of 4m³ + 12xm² - 8m² - 24xm is 4m. The factorization gives 4m(m + 3x)(m - 2)

An equation is an expression that shows the relationship between two or more numbers and variables.

An independent variable is a variable that does not depends on other variable while a dependent variable is a variable that depends on other variable.

Given the equation:

4m³ + 12xm² - 8m² - 24xm

The greatest common factor is 4m, hence:

= 4m(m² + 3xm - 2m - 6x)

= 4m(m(m - 2) + 3x(x - 2))

= 4m(m + 3x)(m - 2)

The greatest common factor of 4m³ + 12xm² - 8m² - 24xm is 4m. The factorization gives 4m(m + 3x)(m - 2)

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The original bag had 10 + 2 = 12 ping pong balls.

Let's denote the number of ping pong balls in the original bag as "n". If we take away two balls from the bag, we will have "n-2" balls left to arrange in an equilateral triangle.

The number of balls in an equilateral triangle can be found by the formula:

Tn = (n(n+1))/2

where Tn is the nth triangular number, i.e. the sum of the first n positive integers.

For an equilateral triangle, the number of balls on each side is equal to Tn, so we have:

Tn = (n(n+1))/2

Solving for n, we get,

n^2 + n - 2Tn = 0

Using the quadratic formula, we can solve for n:

n = (-1 + sqrt(1 + 8Tn)) / 2

Now we want to find the value of n such that the difference between the number of balls in the two equilateral triangles is 11. Let's denote the number of balls in the second equilateral triangle as "m". We have:

m - Tn = 11

Using the formula for Tn, we can express m in terms of n:

m = Tn + n + 1

Substituting this expression for m into the equation above, we get:

Tn + n + 1 - Tn = 11

Simplifying, we get:

n + 1 = 11

Therefore, n = 10.

Thus, the original bag had 10 + 2 = 12 ping pong balls.

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Answer:

20

Step-by-step explanation:

it equals 19.99 but if you round it equals to 20

Answer:

I think the answer is A but I am not for sure

Step-by-step explanation:

Answer:

x=3

Step-by-step explanation:

4x-9=3

4x=3+9

4x=12

x=12/4

x=3

Answer:

x=3

Step-by-step explanation:

1) 4x-9 = 3

2) 4x=12

3) x=3

Check it:

4(3)-9=3

12-9=3 checks :)

Answer:

5200 people

Step-by-step explanation:

1. Divide 100 by 5 (How many sets of 5 are there in 100)

100/5 = 20

2. Multiply 260 by 20 (To find the number of people, you need to find 100%)

260*20 = 5200

Answer:

5200

Step-by-step explanation:

Answer:

-15

Step-by-step explanation:

(y2 - y1)/( x2 - x1) = (4-64)/(3+1) = -60/4 = -15

Answer:

The solution(s) to a system of equations is the point(s) of intersection.

To find the solution, equate the equations and solve for x to find the x-coordinate:

\(\implies f(x)=g(x)\)

\(\implies 3x+2=[x-1]+1\)

\(\implies 3x+2=x\)

\(\implies 2x=-2\)

\(\implies x=-1\)

Now substitute the value of x into one of the equations to find the y-coordinate of the solution:

\(f(-1)=3(-1)+2=-1\)

So the solution to this system of equations is (-1, -1)

Therefore, (1, 5) is NOT a solution to the system of equations.

Let's check

\(\\ \rm\rightarrowtail y=3x+2\)

\(\\ \rm\rightarrowtail 5=3+2\)

\(\\ \rm\rightarrowtail 5=5\)

Verified

And

\(\\ \rm\rightarrowtail y=[x-1]+1\)

\(\\ \rm\rightarrowtail 5=1-1+1\)

\(\\ \rm\rightarrowtail 5\neq 1\)

No

Recall the definition of absolute value:

• |x| = x if x ≥ 0

• |x| = -x if x < 0

So you need to consider 4 different cases (2 absolute value expressions with 2 possible cases each).

(i) Suppose 2x + 3 < 0 and x - 2 < 0. The first inequality says x < -3/2 and the second says x < 2, so ultimately x < -3/2. Then

|2x + 3| + |x - 2| = 6x

-(2x + 3) - (x - 2) = 6x

-2x - 3 - x + 2 = 6x

-3x - 1 = 6x

9x = -1

x = -1/9

But -1/9 is not smaller than -3/2, so this case provides no valid solution.

(ii) Suppose 2x + 3 ≥ 0 and x - 2 < 0. Then x ≥ -3/2 and x < 2, or -3/2 ≤ x < 2. Under this condition,

|2x + 3| + |x - 2| = 6x

(2x + 3) - (x - 2) = 6x

2x + 3 - x + 2 = 6x

x + 5 = 6x

5x = 5

x = 1

This solution is valid because it does fall in the interval -3/2 ≤ x < 2.

(iii) Suppose 2x + 3 < 0 and x - 2 ≥ 0. Then x < -3/2 or x ≥ 2. So

|2x + 3| + |x - 2| = 6x

-(2x + 3) + (x - 2) = 6x

-2x - 3 + x - 2 = 6x

-x - 5 = 6x

7x = -5

x = -5/7

This isn't a valid solution, because neither -5/7 < -3/2 nor -5/7 ≥ 2 are true.

(iv) Suppose 2x + 3 ≥ 0 and x - 2 ≥ 0. Then x ≥ -3/2 and x ≥ 2, or simply x ≥ 2.

|2x + 3| + |x - 2| = 6x

(2x + 3) + (x - 2) = 6x

2x + 3 + x - 2 = 6x

3x + 1 = 6x

3x = 1

x = 1/3

This is yet another invalid solution since 1/3 is smaller than 2.

So there is one solution at x = 1.

Q6: Approximately 68.3% of the cherry tomatoes sold by Berkeley Bowl fall within the specified diameter limits of 20 mm to 32 mm.

Q7: To achieve half of the Six Sigma Quality, the standard deviation of the process should be approximately 0.22 mm for Berkeley Bowl's cherry tomatoes.

In Q6, we can use the concept of the normal distribution to determine the percentage of tomatoes within the specification limits. Since the average diameter is 26 mm and the standard deviation is 3 mm, we can assume a normal distribution and calculate the percentage of tomatoes within one standard deviation of the mean. This corresponds to approximately 68.3% of the tomatoes falling within the specified limits.

In Q7, achieving Six Sigma Quality means that the process has a very low defect rate. In this case, half of the Six Sigma Quality means reducing the variability in diameter to half the acceptable range.

The acceptable range is 32 mm - 20 mm = 12 mm. To achieve half the range, the standard deviation should be approximately half of 12 mm, which is 6 mm. Since the standard deviation is given as 3 mm, the process would need to be improved to reduce the standard deviation to approximately 0.22 mm for it to meet half of the Six Sigma Quality.

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Step-by-step explanation:

\( - 4( - 6 + 2) \)

\( - 4( - 4) = + 16\)

Answer: A)-16

Step-by-step explanation:

If the sum of three numbers is 20 , then the product of all the three numbers is 28  .

In the question ,

the sum of three numbers is given as = 20 ,

let the three numbers be x₁ , x₂ and x₃ .

So , x₁ + x₂ + x₃ = 20 ,

the first number is 4 times the sum of other two ,

that is , x₁ = 4(x₂ + x₃) ;

and the second number is 7 times the third ,

that is , x₂ = 7x₃

Substituting the values from above in the sum equation ,

we get ,

4(x₂ + x₃) + 7x₃ + x₃ = 20

4(7x₃ + x₃) + 7x₃ + x₃ = 20

32x₃ + 8x₃ = 20

40x₃ = 20

x₃ = 1/2

So , x₂ = 7/2 and

x₁ = 4(7/2 + 1/2) = 32/2 = 16

So ,the product is = 16×(7/2)×(1/2)

= 28 .

Therefore , the product is 28 .

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Let's solve each of the given parts one by one.1. Use the definition of "big Oh" to prove that n2​ is O(n). (3 marks). The definition of Big Oh states that for a given function f(n) to be O(g(n)), if and only if there exist positive constants c and n0 such that:f(n) ≤ c*g(n), for all n >= n0Given f(n) = n2​ and g(n) = n, we need to show n2​ is O(n). So, we need to find a positive constant c and n0 such that:n2​ ≤ c*n, for all n >= n0.

Let's solve the inequality:n2​ ≤ c*n⇒ n ≤ c(when n is positive)Hence, for any value of c>=1 and n0 = 1, the above inequality will always hold. Therefore, n2​ is O(n).2. Let f(n) and g(n) be positive functions such that f(n) is O(g(n)). Use the definition of "big Oh" to prove that f(n)×g(n) is O(g2(n)), where g2(n)=g(n)×g(n). (3 marks)Solution:Given f(n) is O(g(n)). So, there exist positive constants c and n0 such that:f(n) ≤ c*g(n), for all n >= n0Now, we need to show that f(n)×g(n) is O(g2(n)), where g2(n)=g(n)×g(n)We can write, f(n)×g(n) ≤ c*g(n)×g(n) ≤ c*g2(n), for all n >= n0Thus, by the definition of Big Oh, we can say that f(n)×g(n) is O(g2(n)).3.

Use the definition of "big Oh" to prove that n3+4n4​ is not O(n3).Solution:We need to prove that there does not exist any constant c such that n3+4n4​ <= c*n3 for all n >= n0.By taking the limit of the ratio of the two functions as n approaches infinity, we can show that n3+4n4​ grows faster than n3. So, the ratio of n3+4n4​ to n3 is greater than or equal to 4 for all values of n greater than 1.We can write:n3+4n4​/n3 >= 4 for all n > 1Therefore, n3+4n4​ is not O(n3).Hence, we have proved that n3+4n4​ is not O(n3).

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Answer: The entered points belong to a vertical line. There is no slope.

Equation: x = -3.

Step-by-step explanation:

In a case whereby Adam traveled out of town for a regional basketball tournament. He drove at a steady speed of 72.4 miles per hour for 4.62 hours. The exact distance Adam traveled was miles Adam traveled a distance of about 335 miles.

The distance traveled in a unit of time is called speed. It refers to a thing's rate of movement. The scalar quantity known as speed is the velocity vector's magnitude. It has no clear direction.

Speed = Distance/ time

speed =72.4 miles

time=4.62 hours

Distance =speed * time

= 72.4 *4.62

Distance = 334.488 miles

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complete question;

Adam traveled out of town for a regional basketball tournament. He drove at a steady speed of 72.4 miles per hour for 4.62 hours. The exact distance Adam traveled was miles. Rounding decimals to the nearest whole number, Adam traveled a distance of about miles.

plug the givwn values in the equatiom y=mx+b

y = -2/9x -10

ANSWER: \(y = \frac{-2}{9} x - 10\)

EXPLANATION:

1. Know what the slope-intercept form is:

\(y = m x + b\)

where:

\(y = ycoordinate\\m = slope\\x = x coordinate\\b = y intercept\)

2. Plug in what you know

\(y = \frac{-2}{9} x + (-10)\)

+ and - is equal to - so

\(y = \frac{-2}{9} x - 10\)