Find the vertex of the quadratic function f(x)=x^2-6x+1

Answer:

To calculate the percent error, we need to find the absolute difference between the correct value and the measured value, divide that by the correct value, and then multiply by 100 to get a percentage.

The absolute difference between the correct value and the measured value is:

$38.07 - $38.06 = $0.01

Dividing this by the correct value ($38.07) gives:

$0.01 / $38.07 ≈ 0.0002626

Multiplying by 100 gives the percent error:

0.0002626 x 100% ≈ 0.02626%

Therefore, the percent error in the student's calculation is approximately 0.02626%.

The percent error in the student's calculation is 2.63%.

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The factored representation of the quadratic function 2x² - 10x - 48 is given as follows:

2(x - 8)(x + 3).

The quadratic function for this problem is defined as follows:

2x² - 10x - 48

The leading coefficient of 2 is common to all the terms of the expression, hence the expression can be simplified as follows:

2x² - 10x - 48 = 2(x² - 5x - 24).

The term with the square of x can be simplified as follows:

x² - 5x - 24 = (x - 8)(x + 3).

Meaning that x = 8 and x = -3 are the roots of the quadratic function, hence, considering the leading coefficients and the linear factors, the simplified expression is given as follows:

2x² - 10x - 48 = 2(x - 8)(x + 3).

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The factorization of the quadratic equation is:

y = 2*(x + 3)*(x - 8)

Here we have the quadratic equation:

2x^2 - 10x - 48

To factorize it, we need to find the roots of the quadratic, to do so we need to solve the equation:

y = 2*x^2 - 10*x - 48 = 0

2x^2 -10x - 48 = 0

Dividing by 2 in both sides we will get:

(2x^2 - 10x - 48)/2 = 0/2

x^2 - 5x - 24 = 0

Now we can use the quadratic formula to get the roots:

[tex]x = \frac{5 \pm \sqrt{(-5)^2 - 4*1*-24} }{2} \\\\x = \frac{5 \pm 11}{2}[/tex]

The roots are:

x = (5 + 11)/2 =8

x = (5 - 11)/2 = -3

Then the factorization will be:

y = 2*(x - (-3))*(x - 8)

y = 2*(x + 3)*(x - 8)

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We can suggest the following three themes for a math and science week, combining the two fields and exploring current events and issues:

Here are a few steps you can follow to find a theme:

By following the steps above, you can figure out a theme for yourself. If you wish, use one of the themes already suggested above.

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Answer: $289.52

Step-by-step explanation: We will solve the problem by first finding the number of cubic centimeters in the bar, then finding the number of grams, then converting that number of grams to a price.

We are given the dimensions of the silver bar. With this, we can find how many cubic centimeters are in the bar. Cubic centimeter is a three-dimensional unit and we are given the three dimensions. We simply multiply the dimensions by each other to find the # of cubic centimeters since this would be the same as (cm^1)^3. This gives a unit in cm^3. 4*10*1 is  40 or 40 cm^3.

We are also given that there are 10.49 g/cm^3 meaning in each cm^3 of silver, there are 10.49 grams. We can multiply the # of cm^3 by 10.49 to find the #of grams. 10.49*40 is 419.6 or 419.6 grams.

Finally, we are given that each gram is worth 69 cents or $.69. We simply multiply the # of grams by this value to find the total price. .69*419.6 is 289.52. This is the answer in dollars.

Hope this helps! These types of problems all just come down to unit conversion so focus on what units are being used.

the answer is "EF = 3.16". According to condition of Similar triangles.

How to solve these problem?

To solve this problem, we will use the property of similar triangles, which states that corresponding angles of similar triangles are equal, and their corresponding sides are proportional.

First, we need to find the ratio of the sides of the two triangles. We can do this by dividing the length of one side of triangle ABC by the corresponding side of triangle DEF. Let x be the length of EF, then:

AB/DE = BC/EF = CA/DF

Substituting the given values, we get:

11/4.4 = 7.9/x = 7.6/(DE + x)

Solving for x, we get:

x = 3.16

Therefore, EF = 3.16.

Hence, the answer is "EF = 3.16".

Note that we can also check our answer by verifying that the corresponding sides of the two triangles are proportional using the ratios we found:

AB/DE = 11/4.4 = 2.5

BC/EF = 7.9/3.16 = 2.5

CA/DF = 7.6/(4.4+3.16) = 2.5

Since the ratios are all equal, we can conclude that the triangles are similar.

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Sine function in which the amplitude is 2 and its graph has 3 complete cycles on the interval is 2sin3x

The sine function in trigonometry is the ratio of the hypotenuse's length to the opposite side's length in a right-angled triangle.

Y= A sin( B( X-C))+ D Or  Y= A cos( B( X-C))+ D

where,

A is the value of the amplitude

B is the number of cycles between 0 and 2 pi since B is the graph's period, or (2π).

C is the graph's horizontal movement.

D is the graph's vertical movement.

amplitude=2

number of cycle in the interval=3

Example:

Y= 2 sin 3X

it has an amplitude of 2

There are three cycles of sin between 0 and 2 π

Hence, y=2sin3x  is the sine function in which the amplitude is 2 and its graph has 3 complete cycles on the interval.

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the cοrrect expressiοns are, 1)Thirteen times a number squared - D)

2)A number times eleven plus thirty-three - A) 11n + 33

3) Twelve less than a number - C) y - 12

4)The quοtient οf a number and twenty - B) p ÷ 20

Mathematical expressiοns cοnsist οf at least twο numbers οr variables, at least οne arithmetic οperatiοn, and a statement. It's pοssible tο multiply, divide, add, οr subtract with this mathematical οperatiοn. Unknοwn variables, integers, and arithmetic οperatοrs are the cοmpοnents οf an algebraic expressiοn. There are nο symbοls fοr equality οr inequality in it.

Here we need to convert given statement into expression. Then,

1)thirteen times a number squared

=> 13[tex]\times b^2[/tex] = [tex]13b^2[/tex]

2) a number times eleven plus thirty-three

=> 11 times of number+ 33

=> 11*n+33

=> 11n+33

3) twelve less than a number

=> number -12

=> y-12

4)The quotient of a number and twenty

=> p/20

=> p ÷ 20

Hence the correct expressions are,

1)Thirteen times a number squared - D) [tex]13b^2[/tex]

2)A number times eleven plus thirty-three - A) 11n + 33

3) Twelve less than a number - C) y - 12

4)The quotient of a number and twenty - B) p ÷ 20

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The names of the column headers in the table indicates that the function c(x) = q(x) ÷ m(x), where q(x) and m(x) are whole numbers, indicates that the function c(x) is a rational function.

Rational functions are functions that consists of a ratio of polynomial functions. A rational function, f(x), consists of the functions g(x) and h(x), such that f(x) = g(x)/h(x), where h(x) ≠ 0.

The input variable of the functions is; x

The functions in the question are; q(x) and m(x)

The function c(x) is; c(x) = q(x) ÷ m(x)

The function c(x) is composed of two functions q(x) and m(x), that are together presented as a fraction, which indicates that c(x) is a rational function.

The type of function represented by the function c(x) is therefore;

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The value equivalent tο the expressiοn "4 times 3 cubed" is 108.

Algebraic expressiοn can be defined as cοmbinatiοn οf variables and cοnstants. An algebraic expressiοn is a mathematical phrase that can cοntain numbers, variables, and mathematical οperatiοns such as additiοn, subtractiοn, multiplicatiοn, and divisiοn.

It is a cοmbinatiοn οf numbers, variables, and symbοls arranged in a meaningful way tο represent a mathematical statement οr relatiοnship.

The expressiοn "Fοur times Three cubed" means that we shοuld first cube the number 3, and then multiply the result by 4.

Tο cube 3, we multiply it by itself three times :

[tex]3^3 = 3 * 3 * 3 = 27[/tex]

Next, we multiply this result by 4:

4 * 27 = 108

Therefοre, the value equivalent tο the expressiοn "4 times 3 cubed" is 108.

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Answer: 9x * 1024x or

9126x if you need it that way

Step-by-step explanation: 3x to the power of 2 is 3x3 which is 9

4x to the power of 5 is 4x4x4x4 which is a bit harder but the answer comes out to 1024

4x4 = 16

16x4 = 64

64x4 = 256

256x4 = 1024

Answer:80

Step-by-step explanation:

if 79.9 Is 99% of the unknown number the other 1% would be 80

The range of the function for the given domain is {-12, 0, 3}.

What is function?

In mathematics, a function is a relationship between two sets of elements, called the domain and the range, such that each element in the domain is associated with a unique element in the range. In simpler terms, a function is a set of rules that takes an input value and produces a corresponding output value.

If the domain of f(x) is {-2,0,1}, we can evaluate the function for each value in the domain:

When x = -2:

f(-2) = -(-2)² + 4(-2) = -4 - 8 = -12

When x = 0:

f(0) = -(0)² + 4(0) = 0

When x = 1:

f(1) = -(1)² + 4(1) = 3

Therefore, the range of the function for the given domain is {-12, 0, 3}.

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Answer: $1.03

Step-by-step explanation:

4.10 x 1/4 = 1.025

Therefore , the solution of the given problem of unitary method comes out to be the additional choices are not exclusive to Inditex's value chain and are frequently used by other businesses in the sector.

By combining what was learned and implementing this variable technique, which also includes all supplemental information from two people who used a particular tactic, the task can be finished. In other words, if the desired result occurs, either the entity specified expression in the computation will be acknowledged, or both of the expression's crucial processes will actually skip the colour. A refundable fee of Rupees ($1.01) may be needed for forty pens.

Here,

The fact that goods are delivered straight to warehouses distinguishes Inditex SA's value chain from other companies.

As a result, lead periods are shortened and inventory costs are kept to a minimum during the quick and effective distribution of goods to retail stores. Fast fashion is this method, and it has been a major factor in Inditex's success in the fashion sector.

The additional choices are not exclusive to Inditex's value chain and are frequently used by other businesses in the sector.

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The value of x is equal to 35° and the measure of the angle between points AY, m∠AND is equal to 80°.

From the question, we observe that the larger angle between m∠ANY consists of the two angles between m∠AND and m∠YND, so we shall sum the two small angles and equate the result to the larger angle to solve for the value of x as follows:

2x + 10 + 30 = 110°

2x + 40 = 110

2x = 110 - 40 {subtract 40 from both sides}

2x = 70

x = 70/2 {divide through by 2}

x = 35°

so we can evaluate for the angle between m∠AND as follows:

m∠AND = 2(35) + 10

m∠AND = 70 + 10

m∠AND = 80°

In conclusion, the value of x is equal to 35° and the measure of the angle between points AY, m∠AND is equal to 80°.

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Answer:

Step-by-step explanation:

Hope this helps

As a result, y = 200 + 160[tex]e^{(0.4t)}[/tex] is the answer to the provided differential equation with starting conditions of y = 40 and t = 0.

A mathematical statement that shows the equivalence of a couple of equations is what an equation at algebra means. For instance, the equation 3x + 5 = 14 consists of the two expressions 3x + 5 and 14, which are split by the 'equal' symbol.

The given differential equation is:

dy/dt = 0.4(y - 200)

To solve this differential equation, we need to separate the variables and integrate:

dy/(y - 200) = 0.4 dt

Integrating both sides, we get:

ln|y - 200| = 0.4t + C

where C is the constant of integration.

To determine the value of C, we use the initial condition that y = 40 when t = 0:

ln|40 - 200| = 0.4(0) + C

ln|-160| = C

C = ln(160)

Thus, the equation becomes:

ln|y - 200| = 0.4t + ln(160)

Taking the exponential of both sides, we get:

|y - 200| = [tex]e^{(0.4t+ln(160))}[/tex] = 160[tex]e^{(0.4t)}[/tex]

Simplifying, we get:

y - 200 = ±160[tex]e^{(0.4t)}[/tex]

y = 200 ± 160[tex]e^{(0.4t)}[/tex]

Using the initial condition that y = 40 when t = 0, we can determine the value of the constant of integration:

40 = 200 ± 160[tex]e^{(0.4(0))}[/tex]

40 = 200 ± 160

Solving for the two possible values of y, we get:

y = 360 or y = 40

Therefore, the solution to the given differential equation with the initial condition y = 40 and t = 0 is:

y = 200 + 160[tex]e^{(0.4t)}[/tex]

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Answer:

Step-by-step explanation:

6

Therefore , the solution of the given problem of unitary method  comes out to be attempt to refrain from taking on needless debt, such as credit card debt.

By multiplying the data received using this type of variable nanosection throughout add to the output of the two individuals who applied the unilateral strategy, the task can be completed. Fundamentally, this implies that whenever an intended result expression occurs, either the stated entity is recognised or, in fact, the pigment of both large-scale productions is skipped. For forty pens, a variable charge of Inr ($1.01) may have been required.

Here,

There are four essential actions one can take to maintain control over their finances:

1) Make and stick to a budget: A budget is a plan for your financial spending over a specific time frame, typically a month. To make sure you are not overpaying, it is crucial to make a budget and adhere to it.

2) Keep track of your spending: By keeping tabs on your spending, you can spot potential areas of overspending and modify your budget as necessary.

3) Save money for emergencies: Having money set aside to cover unforeseen costs, such as vehicle repairs or medical bills, can prevent you from incurring debt.

4) Avoid taking on needless debt: Attempt to refrain from taking on needless debt, such as credit card debt.

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Therefore , the solution of the given problem of function comes out to be the interval's edges, rounded to four decimals, are -1.3233 and 0.7838.

The math lesson includes a variety of subjects, such as math, integers, but one's subdivisions, as well as architecture, construction, and that both real but rather fictitious geographic locations. A work covers the connections between different variables that all work together to produce the same result. A utility is made up of a variety of distinctive components that cooperate to create distinctive results for each input.

Here,

First, we assess f(x) at the interval's endpoints:

=> f(-3) = 2(-3)^3 - 7(-3) + 4 = -43

=> f(3) = 2(3)^3 - 7(3) + 4 = 44

There must be at least one root in each of the gaps between (-3, r) and (r, 3), where r is the function's root, because the function changes sign at x = -3 and x = 3. To find the function's roots numerically,

we can use the bisection technique or Newton's method.

We can plot the function using a graphing calculator or computer software and see that there is one root in the range (-3, -2), one root in the range (-2, 0), and one root in the range (-3, -2). (0, 3).

Consequently, the periods where the function is positive on the range (-3, 3) are as follows:

=> (-3, -1.3233) and (0.7838, 3) (0.7838, 3)

The interval's edges, rounded to four decimals, are -1.3233 and 0.7838.

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The 90% of the standard normal distribution has z-scores between -1.645 and 1.645, the lowest 5% has z-scores between -1.645 and 1.645, and the middle 50% of the standard normal distribution has z-scores between -0.6745 and 0.6745.

The probability density function f(x) for the continuous random variable X taken into account in the system defines the normal distribution. It is a function who's integral over a range (let's say, x to x + dx), when taking into account values between x and x + dx, yields the probability of the random variable X.

The mean and variance of a typical normal distribution are both 0. An alternative term for this is a z distribution.

Yes, the z-scores for the specified standard normal areas are shown here:

Middle 50%: The middle 50% of a standard normal distribution can be found between the 25th and 75th percentiles. We can determine the z-scores associated with those percentiles using Excel's NORM.S.INV () function as follows:

The z-score for the 25th percentile is -0.6745 (percentile).

The z-score for the 75th percentile is 0.6745.

The middle 50% of the ordinary normal distribution is thus represented by z-scores that vary from -0.6745 to 0.6745.

Minimum 5%: The lower 5% of the standard normal distribution are represented by the region to the left of the 5th percentile. We can determine the z-score associated with that percentile by using Excel's NORM.S.INV () function as follows:

-1.645 is the z-score assigned to the fifth percentile.

Hence, -1.645 is the z-score that represents the bottom 5% of the standard normal distribution.

Middle 90%: The middle 90% of the standard normal distribution is the region between the 5th and 95th percentiles. We can determine the z-scores associated with those percentiles using Excel's NORM.S.INV () function as follows:

-1.645 is the z-score assigned to the fifth percentile.

The 95th percentile's corresponding z-score is 1.645.

The middle 90% of the standard normal distribution is thus represented by z-scores that vary from -1.645 to 1.645.

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Hope this helps.

Answer:In an arithmetic sequence, the difference between consecutive terms is constant. Let us denote the common difference by d.

We know that a2 = -5, which means that the second term of the sequence is -5. Using the formula for the nth term of an arithmetic sequence, we can write:

a2 = a1 + d

-5 = a1 + d

We also know that a6 = 7, which means that the sixth term of the sequence is 7:

a6 = a1 + 5d

7 = a1 + 5d

We now have two equations with two unknowns (a1 and d), which we can solve for using substitution or elimination.

Substituting -5 = a1 + d into 7 = a1 + 5d, we get:

7 = -5 + 6d

12 = 6d

d = 2

Substituting d = 2 into -5 = a1 + d, we get:

a1 = -7

So the arithmetic sequence is: -7, -5, -3, -1, 1, 3, ...

The 5th term of this sequence is -1

Step-by-step explanation:

Answer:    -2(x-1)(4x-3)

Step-by-step explanation:   because im just that guy

Answer:

The probability of selecting a blue or green ball on the first draw is 2/3 or approximately 0.67.

Step-by-step explanation:

The probability of selecting a blue or green ball on the first draw can be calculated by adding the probability of selecting a blue ball to the probability of selecting a green ball.

The probability of selecting a blue ball on the first draw is the number of blue balls divided by the total number of balls in the bag:

P(blue ball) = 6/(6+5+4) = 6/15 = 2/5

Similarly, the probability of selecting a green ball on the first draw is:

P(green ball) = 4/(6+5+4) = 4/15

Therefore, the probability of selecting a blue or a green ball on the first draw is:

P(blue or green ball) = P(blue ball) + P(green ball)

                                    = 2/5 + 4/15

                                    = 2/3 = 0.67

So, the probability of selecting a blue or green ball on the first draw is 2/3 or 0.67

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Answer:

sin -1/2   cos sqrt3/2

Step-by-step explanation:

UNIT CIRCLE

Answer:

Pls mark as brainliest

Step-by-step explanation:

To solve this problem, we can use the concept of present value of money. We want to find the equal payments that will settle the obligations in 5 and 11 months, respectively, and we know the amounts and due dates of the obligations.

Using a 6% interest rate, we can find the present value of each obligation on each comparison date, and then solve for the unknown equal payments.

Comparison date is 11 months hence:

The present value of $10,000 due in 3 months at a 6% interest rate is:

PV1 = $10,000/(1 + 0.06 * 3/12) = $9,703.70

The present value of $20,000 due in 7 months at a 6% interest rate is:

PV2 = $20,000/(1 + 0.06 * 7/12) = $19,003.22

To settle these obligations with two equal payments, we can set up the equation:

PV1/(1 + 0.06 * 8/12) + PV2/(1 + 0.06 * 4/12) = x + x/(1 + 0.06 * 6/12)

where x is the size of each payment.

Simplifying the equation, we get:

9703.70/1.04 + 19003.22/1.02 = 2.5x

Solving for x, we get:

x = $8,102.67

Therefore, each payment should be $8,102.67.

Comparison date is now:

The present value of $10,000 due in 3 months at a 6% interest rate is:

PV1 = $10,000/(1 + 0.06 * 3/12) = $9,703.70

The present value of $20,000 due in 7 months at a 6% interest rate is:

PV2 = $20,000/(1 + 0.06 * 7/12) = $19,003.22

To settle these obligations with two equal payments, we can set up the equation:

PV1 + PV2/(1 + 0.06 * 4/12) = x + x/(1 + 0.06 * 6/12)

where x is the size of each payment.

Simplifying the equation, we get:

9703.70 + 19003.22/1.02 = 2.5x

Solving for x, we get:

x = $8,556.54

Therefore, each payment should be $8,556.54.

Comparison date is 3 months:

The present value of $10,000 due in 3 months at a 6% interest rate is:

PV1 = $10,000

The present value of $20,000 due in 7 months at a 6% interest rate is:

PV2 = $20,000/(1 + 0.06 * 4/12) = $19,508.67

To settle these obligations with two equal payments, we can set up the equation:

PV1/(1 + 0.06 * 8/12) + PV2 = x + x/(1 + 0.06 * 6/12)

where x is the size of each payment.

Simplifying the equation, we get:

10000/1.04 + 19508.67 = 2.5x

Solving for x, we get:

x = $8,433.13

Therefore, each payment should be $8,433.13.

The correct answer is Option B, The amount Jonathan is paid for each hour over 10.

The expression { 7 . 5 x ; 0 ≤ x ≤ 10 75 + 9 ( x − 10 ); x > 10 } gives the amount of money Jonathan is paid each week based on the number of hours he works, x. The first part of the expression, 7.5x, applies when x is between 0 and 10, inclusive. The second part of the expression, 75 + 9(x - 10), applies when x is greater than 10.

So, the term 9(x - 10) represents the amount he is paid for each hour over 10. When Jonathan works more than 10 hours, he is paid a flat rate of $75 for the first 10 hours, and then an additional $9 for each hour over 10. Therefore, if Jonathan works x hours and x is greater than 10, then he is paid 9(x - 10) dollars for each hour over 10.

Therefore, the correct answer is B. the amount he is paid for each hour over 10.

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