Mathematics College

Rewrite the polynomial .22 – 52 + 6 as 2? + m2 + n2 +6, where m. n = 6 and m +n=-5. What are the values of m and n?

Answers

Answer 1

Answer:

m = -2 and n = -3

Explanation

Given the polynomial

x^2 - 5x + 6

Rewrite as x^2 +mx + nx + 6

x^2 - 2x - 3x + 6

Compare

mx = -2x

m = -2

Similarly;

nx = -3x

n = -3

Hence m = -2 and n = -3

Related Questions

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The value of a stock decreases by an average of 10 dollars each week. Which of the following represents the total average decrease in the stock after 8 weeks?

Answers

The stock witness an total average decrease in stock of $80 in the 8 weeks

How to determine the total average decrease in the stock

The given parameters are:

Average decrease per week = 10 dollars

Also, we have the number of weeks to be

Number of Weeks = 8 weeks

So, the total average decrease in the stock is calculated using the following equation

Total = Average decrease per week x Number of weeks

Substitute the known values in the above equation

So, we have the following equation

Total = 10 x 8

Evaluate the products in the above equation

So, we have the following equation

Total = 80

Hence, the total average decrease in the stock is $80

Answers

4x -2 = 3(x-3)

4x - 2 = 3x - 9

bring like terms together

4x-3x = -9 +2

x = -7

Jenny is designing a pen for a cow in the shape of a right triangle. Because of space limitation on the farm, the first side of the pen should measure 10 feet and form a right angle with the second side, which should be 14 feet long. How many feet of fencing does Jenny need to make the whole pen? Round to the nearest tenth.

Answers

Answer:

Step-by-step explanation:

14 x 10 is 140.

Since a triangle is just half a square, we multiply the two sides we have and then divide it.

140 ÷ 10 = 70.

Answer = 70.

P.S If it is correct, pls give Brainliest, thanks!

1. What is the domain of the graph?84-8O{x | -3 SXS3)all real numbers{x | xs-3 or x 2 3}y 1-3 sy s 3)

Answers

From the graph below, the domain is

[tex]x\colon\text{ x }\leq\text{ -3 or x }\ge\text{ 3}[/tex]

P(6, -3); y =1/2 x + 2
Write an equation for the line in point-slope form.

Answers

Equation for the line in point-slope form is 5x + 6y = 6.

What is point slope form?

The equation of a straight line that passes through a particular point and is inclined at a specific angle to the x-axis can be found using the point slope form.

Given Data

P(6, -3)

y =1/2 x + 2

When the equation has been solved for y, the line in slope intercept form with slope = m = 1/2 = the coefficient of the x term is represented by the equation y= (1/2)x + 2. 2 represents the y coordinate of the location (0, 2) where the line intersects the y axis as the y intercept.

So, the points are (6,-3) and (0,2)

Formula

y₂ - y₁ = m(x₂ - x₁)

slope of the line (m) = [tex]\frac{x-x}{y-y}[/tex]₁¹

m= [tex]\frac{2-(-3)}{0-6}[/tex]

m = -[tex]\frac{5}{6}[/tex]

Equation

y- (-3) = -[tex]\frac{5}{6}[/tex](x- 6)

y +5 = -[tex]\frac{5}{6}[/tex]x + 6

y + 5 = -[tex]\frac{5+36 }{6}[/tex]

6y + 30 = -5x + 36

5x + 6y = 6

Equation for the line in point-slope form is 5x + 6y = 6.

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What is the length of a rope if the mass of a rope is 4.25

Answers

Using a regression calculator, the line of best fit for the given set of data is:

[tex]y=0.34121x+0.168088[/tex]

where y = mass of the rope and x = length of the rope.

To estimate the length of the rope if its mass is 4.25 kilograms, let's replace "y" in the equation above with 4.25, and then solve for x.

[tex]4.25=0.34121x+0.168088[/tex]

Subtract 0.168088 on both sides of the equation.

[tex]4.25-0.168088=0.34121x+0.168088-0.168088[/tex][tex]4.081912=0.34121x[/tex]

Then, divide both sides of the equation by 0.34121.

[tex]\frac{4.081912}{0.34121}=\frac{0.34121x}{0.34121}[/tex][tex]\begin{gathered} 11.963049=x \\ 11.96\approx x \end{gathered}[/tex]

Therefore, the length of the rope having a mass of 4.25 kilograms is approximately 11.96 meters.

A tank has 120 gallons of water and is being drained at a rate of 1/2
gallon each second. Another tank has 100 gallons of water and is being drained at a rate of 1/4
gallon each second. Which equation could be used to determine x, the number of seconds, when the two tanks have the same amount of water?

Answers

It will take 80 seconds for both tank 1 and tank 2 to have the same amount of water

Water in the tank 1 = 120 gallons

Drainage rate of tank 1 = 1/2 gallon each second

Water in tank 2 = 100 gallons

Drainage rate of tank 2 = 1/4 gallon each second

Let x represent the number of seconds it will take for both tanks to have the same amount of water

Formulating the equation we get the following:

Water in tank 1 - Drainage rate of tank 1*x = Water in tank 2 - Drainage rate of tank 2*x

120 - 1/2x = 100 - 1/4x

20 = 1/2x - 1/4x

20 = 1/4x

x = 80

So, it will take 80 seconds

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Please explain the steps you would take to solve this derivative (gr 12 calc)

Answers

First step, derivative of the constant:

[tex]f^{\prime}(x)=\frac{1}{2}\frac{d(e^{-3x^2+tan(3x+5)})}{dx}[/tex]

Second step, the chain rule:

[tex]\begin{gathered} =\frac{1}{2}e^{-3x^2+tan(3x+5)}*\frac{d(-3x^2+tan(3x+5))}{dx} \\ =\frac{1}{2}e^{-3x^2+tan(3x+5)}*\frac{(-6x+sec^2(3x+5)*3)}{} \end{gathered}[/tex]

Where we applied that the derivative of tangent is the secant^2.

Hence the answer is:

[tex]\frac{1}{2}e^{-3x^2+tan(3x+5)}*\frac{(-6x+3sec^2(3x+5))}{}[/tex]

Predict the amount of tips that would be collected if 100 customers were served at the restaurant on a given day Explain your reasoning. Answer is $178 explain your answer thank you! 40 points if answered correctly!!

Answers

Answer:

$194.69

Step-by-step explanation:

The best way to predict the amount of tips is using this formula:

[tex]100(\frac{Tips(total)}{Customers(total)} )[/tex]

This finds the average tip per customer with all of the data, and multiplies it by 100 to get the predicted amount of tips for 100 customers.

Plugging in the data from the table gives you this equation:

[tex]100(\frac{1174}{603} )[/tex]

This equals $194.69.

Describe a series of transformations Matt can perform to decide if the two windows are congruent

Answers

Answer:

See below

Step-by-step explanation:

Rotate rectangle A 90 ° clockwise with the center being the lower right hand corner. Then translate down and right until rectangle A in over rectangle B

Does anyone understand this geometry question

Answers

Answer:

This is an isosceles right triangle, so

x = 45°.

What system of linear inequalities is shown in the graph?

Enter your answers in the boxes.

Answers

Answer: [tex]y < \frac{1}{3}x+2, y < -2x+2[/tex]

Step-by-step explanation:

The equations of the lines are [tex]y=\frac{1}{3}x+2[/tex] and [tex]y=2-2x[/tex].

Since the line [tex]y=\frac{1}{3}x+2[/tex] has a dotted boundary and is shaded below, it represents the inequality [tex]y < \frac{1}{3}x+2[/tex].

Since the line [tex]y=2-2x[/tex] has a dotted boundary and is shaded below, it represents the inequality [tex]y < 2-2x[/tex].

six times the sum of four and a number is 7. what is the number?

Answers

Step-by-step explanation:

6×(4 + x) = 7

24 + 6x = 7

6x = -17

x = -17/6 = -2.833333333... = -2 5/6

Write the equation of the perpendicular bisector of XY if endpoint X is at (-9,1) and endpoint Y is at (3,5). A) y = -X B) y = 3x - 6 C) y = -3x - 6 D) y = 3x + 12

Answers

A perpendicular bisector is a segment which intersects another segment on its midpoint and with a right angle.

First, we have to find the midpoint between X(-9,1) and Y(3,5), as follows

[tex]\begin{gathered} M=(\frac{-9+3}{2},\frac{1+5}{2}) \\ M=(\frac{-6}{2},\frac{6}{2}) \\ M=(-3,3) \end{gathered}[/tex]

This means the perpendicular bisector must pass through (-3,3). Now, with the given points we find the slope of XY

[tex]\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1} \\ m=\frac{5-1}{3-(-9)}=\frac{4}{3+9}=\frac{4}{12} \\ m=\frac{1}{3} \end{gathered}[/tex]

Then, we apply the rule of perpendicularity to find the slope of the perpendicular bisector.

[tex]\begin{gathered} m_1\cdot m=-1 \\ m_1=\frac{-1}{m} \\ m_1=-\frac{1}{\frac{1}{3}}=-3 \end{gathered}[/tex]

Now, we use the slope-point formula to find the equation for the perpendicular bisector.

[tex]y-y_1=m(x-x_1)[/tex]

Where we replace the slope -3 and the point (-3,3).

[tex]\begin{gathered} y-3=-3(x-(-3)) \\ y-3=-3x-9 \\ y=-3x-9+3 \\ y=-3x-6 \end{gathered}[/tex]Therefore, the right answer is C.

Daniyar paid his April FlashCard bill in full. His May bill shows an average daily balance of $270.31 and a monthly periodic rate of 1.65%. What is the finance charge on Daniyar's May statement?

Answers

The finance charge on Daniyar's May statement is $4.45.

What is finance charge?

The cost of consumer credit expressed as a dollar amount is the financing charge. It includes any fee imposed by the creditor as an incident to or a requirement of the credit extension that is directly or indirectly payable by the customer. It excludes any fee that would be paid in an equivalent cash transaction.

The finance charge is equal to the product of the average daily balance and the monthly periodic rate.

So,

$270.31 x 1.65%

= $270.31 x 0.0165

= $4.45

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Please help!

The volume of a sphere is 36 in³. What is the surface area?

Answers

Answer:

Step-by-step explanation:

V = 4/3.pi.r^3

36 = 4/3 pi r^3

8.6 = r^3

r = 2 in

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

Area of sphere :

A = 4.pi.r^2

A = 4 . Pi . 2^2

A = 16 Pi

A = 50.26 in

45. Write an inequality that represents the graph. Explain it step by step please.

Answers

Answer: x < -4

Step-by-step explanation:

➜ First thing we notice is the open circle. This means we will use either < or >

➜ The next thing we notice is that the values are pointing to the left of the circle, this means we will be using <

➜ The last part we notice is that the dot is on -4. This is the value we'll use to write our inequtliy.

The last thing to do is to write the inequality using the parts we pointed out above:

x < -4

I need help with this question but no one is helping me! Can someone please help me

Answers

Answer:

the probability is 2/8

Step-by-step explanation:

Two buses leave Dallas at the same time traveling in opposite directions. One bus travels at 59 mph and the other at 54 mph. How soon will they be 791 miles apart?

Answers

Let t be the time, in hours, elapsed till the buses are 791 miles apart, then we can set the following equation:

[tex]59mph\cdot t+54\text{mph}\cdot t=791\text{ miles.}[/tex]

Solving the above equation for t we get:

[tex]\begin{gathered} 113\text{ mph}\cdot t=791miles, \\ t=\frac{791}{113}\text{hours,} \\ t=7\text{ hours.} \end{gathered}[/tex]

Answer: 7 hours.

Find the mean, mode, and range Mean_______ show all workRange_______show all workExplain how you find thisMode_________

Answers

To answer this question, it is a good practice to order the data in ascending order as follows:

[tex]9,\: 10,\: 10,\: 10,\: 10,\: 11,\: 11,\: 11,\: 11,\: 11,\: 11,\: 12,\: 12,\: 12,\: 12,\: 12,\: 13,\: 13,\: 13,\: 14,\: 14,\: 15,\: 15,\: 15,\: 15,\: 15,\: 15,16,17,17[/tex]

We need to check for the total number of data. In this case, we have 30 observations.

Finding the mean

To find the mean, we need to find the sum of all the observations and then divide this result by the total of observations (30). Then, we have:

[tex]\frac{9+\: 10+\: 10+10+\: 10+\: 11+\: 11+\: 11+\: 11+\: 11+\: 11+\: 12+\: 12+\: 12+\: 12+\: 12+\: 13+\: 13+\: 13+\: 14+\: 14+15+\: 15+\: 15+15+15+_{}15+16+17+17}{30}[/tex]

Then, the value for the mean is:

[tex]\text{mean}=\frac{382}{30}=12.73333333\ldots[/tex]Finding the range

The range is the result of subtracting the greatest number and the lowest number in the data:

[tex]\text{Range}=17-9=8[/tex]Finding the mode

The mode is the observation that is repeated the most (appears the most).

We can see that we have two values that appear six times in the list: 11 and 15.

Therefore, we can see that there is not a unique element, so there is no mode.

In summary, we have:

• Mean = 12.73333...

• Range = 8

• Mode = None.

HELP ME WITH IS PROBLEM THANK YOU

Answers

The given algebraic expression would be equivalent to the expression [tex]\dfrac{1}{4(x)^\frac{2}{9} }[/tex] which is the correct answer would be an option (B)

What is the algebraic expression?

Algebraic expressions are mathematical statements with a minimum of two terms containing variables or numbers.

The given algebraic expression is:

[tex](64x^{\frac{2}{3} })^{-\frac{1}{3} }[/tex]

Apply the property of a⁻ˣ = 1/aˣ in the above term,

[tex]\dfrac{1}{ (64x^{\frac{2}{3} })^{\frac{1}{3} }}[/tex]

Here 64 = 4×4×4 = 4³

[tex]\dfrac{1}{ (4^3x^{\frac{2}{3} })^{\frac{1}{3} }}[/tex]

Apply the cube root property and Multiply the exponent of the variable x to 1/3

[tex]\dfrac{1}{ 4x^{\frac{2}{3} }^\times^{\frac{1}{3} }}[/tex]

Apply the multiplication operation to the exponent of the variable x to get the solution.

[tex]\dfrac{1}{4(x)^\frac{2}{9} }[/tex]

Hence, the correct answer would be an option (B)

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Select the reason why these triangles are similar. If they are not, select "Not similar". 88 3 2 88 B. SAS A. AA D. Not similar C. SSS

Answers

From the given figure

The 2 triangles have one equal angle of measure 88

The side of length 3 and the side of length 1 have a ratio 3: 1

The side of length 6 and the side of length 2 have a ratio 6: 2, when we divide both terms of the ratio by 1, it becomes 3: 1

That means we have one equal angle and two proportional sides

Since the angle is between the proportional sides, then

The 2 triangles are similar by the SAS postulate

Answer B

Need help with a geometry problem. it is a scalene triangle with a parallel line through it which is x+1. the base is going to be 3x-2 and is parallel with x+1. on the right of x+1 there should be 12 at the top then 20 will split it . I need to solve for x

Answers

[tex]\begin{gathered} \Rightarrow\frac{12}{x+1}=\frac{32}{3x-2} \\ \Rightarrow12(3x-2)=32(x+1) \\ 36x-24=32x+32 \\ 36x-32x=32_{}+24 \\ 4x=56 \\ x=14 \end{gathered}[/tex]

5 Guess my rule: X Y 1 9 IN min OUT

Answers

1) Looking at that table, we can pick the points

(1,9) (3,23)

2) Note that every time x increases by 2 units y increases by 14

3) Considering this a linear function we can find the rule by plugging in

23-9/3-1=14/2 = 7

9=7(1)+b

9=7 +b

2 =b

So we can write the rule as y =7x+2

This is my practice review me I have unlimited attempts. I need help with this question

Answers

Let x represent the number of pounds of coffee that she bought.

From the information given,

cost per pound of coffee = $8.73

Cost of x pounds of coffee = 8.73 * x = 8.73x

Initial amount that she had = $90

After spencing $8.73x, the amount left is $63.81. This means that

90 - 8.73x = 63.81

8.73x = 90 - 63.81

8.73x = 26.19

x = 26.19/8.73

x = 3

She bought 3 pounds of coffee

Prime Factorization

(See attachment for more info)

Thank you.

Answers

the fraction is info

Please answer correctly and explain how you got it please don't have but it would help.

Answers

Answer: Linear

Step-by-step explanation:

Each time [tex]x[/tex] increases by [tex]1[/tex], [tex]y[/tex] decreases by [tex]8[/tex]. Since the value of y changes at a constant rate, the relationship is linear.

From the diagram below, if the sides AD = 3 and DC = 27, and BD = X + 3, find x.

Answers

Given:

• AD = 3

• DC = 27

• BD = x + 3

Let's solve for x.

To solve for x, apply the altitude formula:

[tex]\frac{AD}{BD}=\frac{BD}{DC}[/tex]

Where BD is the altitude.

Cross multiply:

[tex]BD^2=AD*DC[/tex]

Plug in the values and solve for x:

[tex]\begin{gathered} (x+3)^2=3*27 \\ \\ (x+3)^2=81 \end{gathered}[/tex]

Take the square root of both sides:

[tex]\begin{gathered} \sqrt{(x+3)^2}=\sqrt{81} \\ \\ x+3=9 \\ \\ \text{ Subtract 3 from both sides:} \\ x+3-3=9-3 \\ \\ x=6 \end{gathered}[/tex]

Therefore, the value of x is 6 .

ANSWER:

d. 6

vinny has decided to order high tops in black and white at a 5.8 ratio. he beleives he will need a total of 169 pairs. how many black high tops will he order

Answers

Answer:

65 pairs

Step-by-step explanation:

Black makes up 5/(5+8) = 5/13 of the total order, so ...

(5/13)(169 pairs) = 65 pairs

Vinny will order 65 pairs of black high tops.

Which expression is equivalent to the given expression? \frac{\left(ab^{2}\right)^{3}}{b^{5}}

Answers

The expression which is equivalent to the given expression; (ab²)³/b⁵ as given in the task content is; a³b.

Which expression is equivalent to the given expression; (ab²)³/b⁵ as in the task content?

It follows from the task content that the expression which is equivalent to; (ab²)³/b⁵ be determined.

Hence, since the given expression is; (ab²)³/b⁵.

By first applying the power of power law of indices; we have;

(ab²)³/b⁵ = a³b⁶/b⁵.

Also, by applying the quotient of powers rule of indices; we have;

a³ b^(6 - 5)

= a³b¹

= a³b

Ultimately, the expression which is equivalent to; (ab²)³/b⁵ as required in the task content is; a³b.