sketch the curve by using the parametric equations to plot points. indicate with an arrow the direction in which the curve is traced as t increases.

The supplied roots' polynomial equation is x³-7x²+20x-24=0.

A polynomial equation is one in which a polynomial is set to zero. It is an equation composed of variables, non-negative integer exponents, and coefficients, as well as operations and an equal sign. It has various exponents. The highest one represents the equation's degree. To be a polynomial equation, the variable in the equation must contain only non-negative integer exponents. Specifically, variable exponents should be non-negative and neither negative nor fractional.

Given that, solution polynomial equation of the least degree has roots of 3, 2+2i, and 2-2i.

Now, x=3, x=2+2i and x=2-2i

x-3, x-2-2i and x-2+2i

So, the polynomial equation is (x-3)(x-2-2i)(x-2+2i)=0

=(x-3)(x(x-2-2i)-2(x-2-2i)+2i(x-2-2i))=0

=(x-3)(x²-2x-2xi-2x+4+4i+2xi-4i-4i²)=0

=(x-3)(x²-2x-2x+4-4i²)=0

=(x-3)(x²-4x+4+4)=0 (∵i²=-1)

=(x-3)(x²-4x+8)=0

=x(x²-4x+8)-3(x²-4x+8)=0

=x³-4x²+8x-3x²+12x-24=0

= x³-7x²+20x-24=0

The supplied roots' polynomial equation is x³-7x²+20x-24=0.

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-10

By BODMAS Method

8 + 3*4 ÷ -2*3

8 + 3* [tex]\frac{4}{-2}[/tex] *3

8 + 3*-2*3

8 +(-18)

-10

The order of operations (BODMAS) in mathematics and computer programming refers to a set of rules that represent standards for which operations to carry out first in order to evaluate a specific mathematical expression.

For instance, since the advent of contemporary algebraic notation, multiplication has been given a higher priority than addition in mathematics and most computer languages.

As a result, 1 + (2 × 3) = 7, rather than (1 + 2) × 3 = 9. is the value assigned to the expression 1 + 2 × 3. BODMAS was first used in the 16th and 17th centuries when addition and multiplication were given priority. BODMAS could only is used as a superscript to the right of their base.

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If Brandon works at the waterpark on the weekends. Last Saturday, he worked 7 11/12 hours. On Sunday, he worked 84% of the hours he worked on Saturday, The total hours that he would have to work on the weekend is 6.65 hours

The total numbers of hours that was worked can be solved by

7 11/12 hours * 84%

= 95 / 12 * 84 / 100

= 7980 /1200

= 6.65

Therefore we can  say that if Brandon works at the waterpark on the weekends. Last Saturday, he worked 7 11/12 hours. On Sunday, he worked 84% of the hours he worked on Saturday, The total hours that he would have to work on the weekend is 6.65 hours

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Answer:

6 hours and 39 minutes is the correct answer.

Step-by-step explanation:

So, set up your problem...

STEP 1: 84% out of 100%, or 84/100

STEP 2: 7 11/12 is a mixed number, so to make solving easier, make it an improper fraction: 95/12

- 7 11/12

- 7 × 12 = 84 + 11 = 95

- Keep the denominator (12)

- 95/12 is now an improper fraction.

STEP 3: Multiply 95/12 × 84/100 = 6.65

STEP 4: Convert to hours...

- Note that 6.65 hours and 6:65 is not the same. 6.65 hours with the decimal point is 6.65 hours in terms of hours. 6:65 with the colon is 6 hours and 65 minutes.

- Start by dividing up what is before and after the decimal point. 6 = hours, .65 = fractional hours

- To convert from 6.65 decimal hours to hours and minutes, we need to convert the .65 fractional hours to minutes.

- Since there are 60 minutes in an hour, you multiply the .65 fractional hours by 60 to get minutes. .65 × 60 = 39 minutes.

So, in conclusion, the correct answer to your question is... 6 hours and 39 minutes.

Hope this helps! Have an amazing rest of your day! Please award me Brainliest!! :)

From the numeric value of the formula, the tuition and fees for the school year ending in 2010 was of $26,270.

The numeric value of a function is found replacing each instance of x by the value that we want to find.

For this problem, the cost function is given by:

T(x) = 26x² + 806x + 15610.

In which x is the number of years after 2000.

Hence the cost in 2010 will be given by:

T(10) = 26(10)² + 806(10) + 15610 = $26,270.

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Answer: 15

Step-by-step explanation:

The distance from point X to line p is 2√17 units.

We are given the point X as:

X = ( - 2 , 5 )

We need to find the distance of X from the line p.

We will do this by using the distance formula:

Distance = √ (y₂ - y₁)² + (x₂ - x₁)²

Distance = √ (- 2 - 0) ² - (5 - ( - 3))  ²

= √ ( - 2) ² - (5 + 3) ²

= √ ( - 2) ² - (8) ²

= √ 4 + 64

= √ 68

= 2 √17 units

Therefore, the distance from point X to line p is 2√17 units.

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Your question was incomplete. Please find the content below:

Find the distance from point X to line p. An image of a point X, a line p, and three segments joining the point and the line. Question 12 options:

A. 2 √34 units

B. √85 units

C. 2 √17 units

D. √17 units

If a satellite flies 114550 miles in 22.91 hours, then it will flies 34850 miles in 6.97 hours

Given,

The total distance flies by the satellite = 114550 miles

Time taken = 22.91 hours

Speed of the satellite = Distance / Time taken

[tex]\frac{114550}{22.91} =5000[/tex] miles per hour

The total distance flown by the satellite in 6.97 hours

Distance = Speed × Time

= 5000×6.97

=34850 miles

Hence, if a satellite flies 114550 miles in 22.91 hours, then it will fly 34850 miles in 6.97 hours

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Answer:

k=-13

Step-by-step explanation:

-2 = k+7/3

Multiply 3 to both sides.

-2 = k+7/3

-6=k+7

Subtract 7 from both sides.

-13=k

k equal -13.

Hope this helps!

Please mark as brainliest if correct!

Answer:

Step-by-step explanation:

−2=k+7/3

≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡

k+7/3=−2

k+7/3−7/3    =   −2−7/3

k=    −13/3

the image (new coordinate) after the translation is (-2.5, 9.8)

Here we have a rule (also called a transformation or an operator) that works as:

T(x, y) = (x - 7.5, y + 6.8)

So we decrease the x-value by 7.5 and increase the y-value by 6.8. This is a translation of 7.5 units to the left and 6.8 units upwards.

Now, our point is (5, 3), if we apply that transformation we will get:

T(5, 3) = (5 - 7.5, 3 + 6.8) = (-2.5, 9.8)

That is the image after the translation.

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Answer: b=7.5

Step-by-step explanation:

b+5=20-b

b+b+5=20-b+b     ==> add b on both sides to put b on only one side of the equation

2b+5=20

2b=15

b=7.5

93.7 feet is the distance from the bottom of the slide to the bottom of the ladder.

Let us consider the distance from the bottom of the ladder to the bottom of the slide "x" (the unknown we want to find).

The ladder's length is 35 feet, and the slide's length is 100 feet.

According to the Pythagorean theorem:

c² = a² + b²

where c is the hypotenuse (the ladder's length), and a and b are the two other sides of the right-angled triangle (the distances we want to find).

In this case, the equation becomes:

35²= x² + 100²

Solving for x:

1225 = x² + 10000

x² = 10000 - 1225

x² = 8775

Taking the square root of both sides to find "x":

x = √8775

x = 93.7 feet

So, the distance from the bottom of the slide to the bottom of the ladder is 93.7 feet.

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Answer:

BC = 13

Step-by-step explanation:

x + 10 + x + 14 = 22

2x + 24 = 22

2x = -2

x = -1

BC = x + 14 = -1 + 14 = 13

Part A: The equation of least squares regression line is

ŷ = 0.4684X + 64.69888

Part B: The residual that we have here is - 1.382

Part C: Residual refers to the difference between the observed value and the predicted value

Sum of X = 102.5

Sum of Y = 695

Mean X = 10.25

Mean Y = 69.5

Sum of squares (SSX) = 33.625

Sum of products (SP) = 15.75

Regression Equation = ŷ = bX + a

b = SP/SSX = 15.75/33.63 = 0.4684

a = MY - bMX = 69.5 - (0.47*10.25) = 64.69888

ŷ = 0.4684X + 64.69888

Residual = observed - predicted

The observed = 68

The predicted = 0.4684 x 10 + 64.69888

= 4.684 + 64.69888

= 69.382

residual = 68 - 69.382

= -1.38

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Answer:

(-3,3/2)

Step-by-step explanation:

It's easy just add the abscissa and ordinate individually and divide the obtained abscissa and ordinate by 2

The length of DNA in Scientific notation (standard form) = 34[tex]e^{-8}[/tex] meters

Also, the significant figure in the measurement = 1

In this question, we have been given the length of human DNA.

The genetic information of almost every living thing is stored in a tiny strand called DNA.

Human DNA is 3.4 x 10-8 meter long.

We need to write the length in standard form.

3.4 x 10-8 meter

= 3.4 x 10 ^ (-8)

= 3.4 x 0.00000001

= 0.000000034

= 0.00000003

Here Significant Figures = 1

Decimals = 8

And the length in Scientific Notation = 34[tex]e^{-8}[/tex] meters

Therefore, the length of DNA in Scientific notation (standard form) = 34[tex]e^{-8}[/tex] meters

Also, the significant figure in the measurement = 1

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Answer:

y=120

z=20

Step-by-step explanation:

angle below y is 60° because of corresponding angles

y=180-60=120

y+(4z-20)=180(angles in a straight line)

120+4z-20=180

100+4z=180

4z=180-100

4z=80

z=80/4

z=20°

The postulate that proves that the triangles are congruent is: SAS congruence postulate.

The SAS congruence postulate states that when two triangles have a pair of included congruent angles, and two pairs of corresponding sides that are congruent, then both triangles are congruent.

In the triangles given, we have:

Two pairs of corresponding sides that are congruent - BL ≅ PF and BG ≅ PX

A pair of included congruent angles - <B ≅ <P.

This means both triangles are congruent by SAS.

Therefore, the postulate that proves that the triangles are congruent is: SAS congruence postulate.

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Answer:

100

Step-by-step explanation:

Answer:if they choose the family tickets its 15% off the regular ticketts individually

Step-by-step explanation:

Answer:

e foot

Step-by-step explanation:

Answer:

How far down the wall did

the ladder

Step-by-step explanation:

Answer:D

Step-by-step explanation:

The number of items that must be sold for the company to make a profit is 757.

Calulation of number of items sold:

R = 195x

C = 160x + 18000

Here R means the revenue

And, C means the cost

Now

We know that

Profit = R - C

Profit = Revenue - cost

=195x - (160x + 18000)

= 195x - 160x - 18000

= 35x -18000

Now solve the above equation

So,

35x - 18000 = 8500

x=757

Therefore,

x = 757

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Answer:

Step-by-step explanation:

x - 3y = 10

5x + y = 2

x - 3y = 10

15x + 3y = 6

16x = 16

x = 1

5 + y = 2

y = -3

(1, -3)

Answer:

ain't no way you need help my bou

Using a system of equations, the expression, in terms of x, for the total number of students at the college is:

T = 11x.

A system of equations is when multiple variables are related, and equations are built to find the values of each variable, according to the relations given in the problem

For this problem, considering the Venn diagram, we have that:

Thus the total number of students in the college is given by:

T = A + B + x.

1/2 of the students who learn the piano also learn the guitar, hence:

A = x.

Thus the number of students who play the piano is:

A + x = x + x = 2x.

5 times as many students learn the guitar as learn the piano, hence:

B + x = 5(2x)

B + x = 10x

B = 9x.

Hence:

T = A + B + x

T = x + 9x + x

T = 11x.

The expression, in terms of x, for the total number of students at the college is:

T = 11x.

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The correct statements regarding the given bar graph are as follows:

A bar graph shows the number of times that each observation appears in the data-set.

The first correct statement is:

Mickton had more rainy days in July than in January, November, and December combined in 2012 and 2013.

As:

30 + 29 > 8 + 5 + 11 + 7 + 10 + 4

The second correct statement is:

There were 13 rainy days in February 2013.

Due to the blue bar in Feb.

The third correct statement is:

The month with the greatest difference in the number of rainy days between 2012 and 2013 was December.

Difference of 10 - 4 = 6 days, which is the biggest.

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{x, y, z} = { -16/13, -10/13, -28/13}.

The algebraic expression for the phrase "the quotient of y and 6" is y / 6

The difference of -3 - 4 is -7.

The algebraic expression of the following phrase "the quotient of y and 6" is as follows:

Quotient is a quantity produced by the division of two numbers.

Therefore, the algebraic expression for the phrase "the quotient of y and 6" is y / 6

The difference of -3 - 4 can be calculated as follows:

The difference of -3 - 4 is -7.

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The indicated computation of (4 x 10^4) (2 x 10^3) in decimal notation is 80000000

The expression is given as

(4x10 to the power of 4) (2x10 to the power of 3) =

Rewrite properly, as:

(4 x 10^4) (2 x 10^3) =

Evaluate the product of 4 and 2

So, we have

(4 x 10^4) (2 x 10^3) = 8 x 10^4 x 10^3

Evaluate the product of 10^4 and 10^3 using the law of indices

So, we have

(4 x 10^4) (2 x 10^3) = 8 x 10^7

Evaluate the product of 8 and 10^7

So, we have

(4 x 10^4) (2 x 10^3) = 80000000

Hence, the indicated computation of (4 x 10^4) (2 x 10^3) in decimal notation is 80000000

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