find the length of MN​

[tex]\bf{ (x^2-5x)(2x^2+x-3)}[/tex]

[tex]\bf{Distribute \ the \ sum \ group. }[/tex]

[tex]\bf{Expand \ the \ distribution \ of \ terms. }[/tex]

[tex]\bf{Remove \ parentheses. }[/tex]

[tex]\bf{Collect \ like \ terms. }[/tex]

[tex]\bf{Simplify}[/tex]

composite function J[P(W)=J(1/3w+4) represent paintings Jeremy completes in a year .

this equation means number of paintings= weeks(rate)

The function P takes a number of weeks as an argument and returns the number of paintings.

The function J takes some argument (unspecified) and returns a number of weeks per year.

The composite function that will give the number of paintings per year will be P(weeks per year) = P(J(y)).  

P(J(y)) = 1/3·J(y) +4 .

Looking at the units of the input and output of each of the functions is called "units analysis."

Unit analysis means using the rules of multiplying and reducing fractions to solve problems involving different units.

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Answer:

P[J(y)] = 1/3 (Jy) + 4

Answered the quiz and it's correct.

Answer:

68

Step-by-step explanation:

We know the sum of interior angles for a quadrilateral must equal 360, so we can create the following equation

[tex]55+117+120+x=360[/tex]

Simplify

[tex]292+x=360[/tex]

Subtract 292 from both sides

[tex]x=68[/tex]

Answer:

68

Step-by-step explanation:

The sum of the interior angles of a quadrilateral is 360.  The sum of the interior angles or a triangle is 180.  If you think about a rectangle, you can cut that up into two triangles, so 180 + 180 = 360.

Now subtract out the 3 angles that you know

360-55-117-120 = 68

The slope of tangent line at point(4, 2pi) is undefined.

For given question,

We have been given a polar equation r = 2 + 2cos(θ)

We need find dy/dx as well as the slope of tangent line at point(4, 2π).

We know that, for polar equation we use,

x = r cos(θ)   and  y = r sin(θ)

plug the given value of r into these equations we get:

⇒ x = r cos(θ)

⇒ x = (2 + 2cos(θ) ) ×  cos(θ)

⇒ x = 2(cos(θ) + cos²(θ))

⇒ x = 2cos(θ) + 2cos²(θ)

Similarly,

⇒ y = r sin(θ)

⇒ y = (2 + 2cos(θ) ) ×  sin(θ)

⇒ y =  2(sin(θ) + sin(θ)cos(θ))

⇒ y =  2sin(θ) + 2sin(θ)cos(θ)

Now we find derivative of x and y with respect to theta.

[tex]\Rightarrow \frac{dx}{d\theta} =-2sin(\theta)+2(-2cos(\theta)sin(\theta))\\\\\Rightarrow \frac{dx}{d\theta} =-2sin(\theta)-2sin(2\theta)[/tex]          .............(1)

Similarly,

[tex]\Rightarrow \frac{dy}{d\theta}=2cos(\theta)+2(cos^2(\theta)-sin^2(\theta))\\\\\Rightarrow \frac{dy}{d\theta}=2cos(\theta)+2(cos(2\theta))[/tex]          ..............(2)

Now we find dy/dx

⇒ dy/dx = (dy/dθ) / (dx/dθ)

From (1) and (2),

[tex]\Rightarrow \frac{dy}{dx} =\frac{2cos(\theta)+2cos(2\theta)}{-2sin(\theta)-2sin(2\theta)} \\\\\Rightarrow \frac{dy}{dx} =\frac{2(cos(\theta)+cos(2\theta))}{-2(sin(\theta)+sin(2\theta))}\\\\\Rightarrow \frac{dy}{dx} =-\frac{cos(\theta)+cos(2\theta)}{sin(\theta)+sin(2\theta)}[/tex]

We know that The slope of tangent line is given by dy/dx.

So, the slope is: [tex]m =-\frac{cos(\theta)+cos(2\theta)}{sin(\theta)+sin(2\theta)}[/tex]

Now we need to find the slope of tangent line at point(4, 2pi)

Substitute θ = 2π in above slope formula.

[tex]\Rightarrow m =-\frac{cos(2\pi)+cos(2\times 2\pi)}{sin(2\pi)+sin(2\times 2\pi)}\\\\\Rightarrow m=-\frac{1+cos(4\pi)}{0+sin(4\pi)}\\\\\Rightarrow m=-\frac{1+cos(4\pi)}{sin(4\pi)}[/tex]

⇒ m = ∞

The slope of tangent line at point(4, 2pi) is not defined.

This means, the tangent line must be parallel to Y-axis.

Therefore, the slope of tangent line at point(4, 2pi) is undefined.

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The value of a particular trigonometric expression that is cos 2θ under the third quadrant is -119/169

Given:

sin θ = -⁵/₁₃

This can be seen from the trigonometric identity.

cos 2θ = 1 - 2sin²θ

From trigonometric identities, we know that;

cos 2θ = 1 - 2sin²θ

Thus;

cos 2θ = 1 - 2(-⁵/₁₃)²

cos 2θ = 1 - 2(25/169)

cos 2θ = 119/169

since cos θ is negative in the third quadrant, then we have;

cos 2θ = -119/169

so; cos θ is negative in the third quadrant, so ;

cos 2θ = -119/169

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Answer:

5.5

Step-by-step explanation:

For the first fold, we cut the 11-inch side in half, resulting in an 8.5-by-5.5-inch piece. After the second fold, we have a 4.25 by 5.5 piece after halving the 8.5 inch side. The length is 5.5 inches.

Answer:

[tex]m=-3[/tex]

Step-by-step explanation:

Given points:
[tex](5,3),(8,-6)[/tex]

1. Find the slope

The slope of a line between two points equals the change in the points' y-coordinates (rise) over the change in their x-coordinates (run).

The coordinates of point 1 are: [tex]x_1=5,y_1=3[/tex]

The coordinates of point 2 are: [tex]x_2=8,y_2=-6[/tex]

To find the slope, plug the points' x and y-coordinates into the formula and combine to simplify:

[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

[tex]m=\frac{-6-3}{8-5}[/tex]

[tex]m=\frac{-9}{3}[/tex]

[tex]m=-3[/tex]

The equation is neither geometric nor arithmetic

The function is given as

f(x) = 2x^2 + 6x - 9

As a general rule, arithmetic functions or sequences have a common difference while geometric functions or sequences have a common difference

Set x = 0, 1 and 2

f(0) = 2(0)^2 + 6(0) - 9 = -9

f(1) = 2(1)^2 + 6(1) - 9 = -1

f(2) = 2(2)^2 + 6(2) - 9 = 11

Calculate the common difference (d)

d = 11 --1 = -1--9

d = 12 = 8 ---- false equation i.e. no common difference

Calculate the common ratio (r)

r = 11/-1 = -1/-9

d = -11 = 1/9 ---- false equation i.e. no common ratio

The above function is not an arithmetic function.

This is so because it does not have a common difference

Also, the function is not a geometric function.

This is so because it does not have a common ratio

Hence, the true statement about the function is (c) the equation is neither geometric nor arithmetic

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Answer:

7

Step-by-step explanation:

The length of the arc can be calculated via a simple proportion:

2 pi r : 360° = x : 45°

Where r is the radius of the circumference and x the length of the arc we want to know. Isolating the x:

x = (2 pi r : 360) * 45 = (2 pi * 9 : 180) * 45 = 18 pi : 360 * 45 = 18pi : 8 = 7

Last option, (-2,6) where the lines intercept / cross over each other.

Hope this helps!

It takes 1 hour 43 minutes to finish mowing the lawn.

The rate of work done by Gregory and Jennifer finish mowing the lawn in

1 hour 43 minutes.

According to the question

Gregory can mow the family's lawn in 3 hours, she mows at a rate of 1/3 of the lawn per hour(1/3 lawn/hour)

Jennifer can mow it in 4 hours, which means her rate is 1/4 lawn/hour.

Together , their rates are 1/3 + 1/4.

This equals 7/12 lawns/hr.

We want to know how many hours they have to mow in order to mow 1 lawn.

This can be represented by the equation : [tex]\frac{7}{12} \times x = 1[/tex]

To solve for x, we would divide both sides by 7/12.

This leaves us with x = 12/7 which is 1.714.

Convert 1.714 to minutes by multiplying 60.

This gives you a final answer of about 1 hour 43 minutes.

Hence, It takes 1 hour 43 minutes to finish mowing the lawn.

The rate of work done by Gregory and Jennifer finish mowing the lawn in

1 hour 43 minutes.

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The slope of the scenario is calculated as: -250.

Slope (m) = change in y / change in x = (y2 - y1)/((x2 - x1).

Given the points:

(4, 7,000) = (x1, y1)

(6, 6,500) = (x2, y2)

Plug in the values

Slope (m) = (6,500 - 7,000) / (6 - 4)

Slope (m) = (-500) / (2)

Slope (m) = -250

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Answer:

  b.  18

Step-by-step explanation:

The perpendicular bisector of a chord is a diameter of the circle. Conversely, if the diameter is perpendicular to a chord, it also bisects it.

  BC = BP +PC

  BC = 2×BP . . . . . . . BP = PC

  BP = BC/2 = 36/2 = 18 . . . . . . . divide by 2; substitute given values

The length of segment BP is 18 units.

The maximum value of P = x + 6y subject to the constraints is 9

The objective function is given as:

P = x + 6y

The constraints are given as:

2x + 4y ≤ 10

x + 9y ≤ 12

x≥0 y≥0

Rewrite 2x + 4y ≤ 10 and x + 9y ≤ 12 as equations

2x + 4y = 10

x + 9y = 12

Divide 2x + 4y = 10  through by 2

x + 2y = 5

Subtract x + 2y = 5 from x + 9y = 12

x - x + 9y - 2y = 12 - 5

Evaluate the difference

7y = 7

Divide by 7

y = 1

Substitute y = 1 in x + 2y = 5

x + 2(1) = 5

Solve for x

x = 3

So, we have

(x, y) = (3, 1)

Substitute (x, y) = (3, 1) in P = x + 6y

P = 3 + 6 * 1

Evaluate

P = 9

Hence, the maximum value of P = x + 6y subject to the constraints is 9

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Answer:

4

Step-by-step explanation:

revenue has to be greater than cost for a profit

revenue minus cost = profit

2x^2 – 20x + 70 - (–x^2 + 5x + 18) =

2x^2 – 20x + 70 + x^2 - 5x - 18 =

3x^2 – 25x + 52 ≤ 0

(x - 4) (3x - 13)  ≤ 0

x ≤ 4

x ≤ 13/3

since its multiple choice you can enter one of the answers where the x is to get the answer

if you don't know what the question is and are short on time this may help

again:

revenue has to be greater than cost for a profit

revenue minus cost = profit

cost is 2x^2 – 20x + 70

revenue is –x^2 + 5x + 18

cost is

2(4)^2 – 20(4) + 70 =

32-80+70 =

102-80 =

22

revenue is

–x^2 + 5x + 18

–(4)^2 + 5(4) + 18

-16+20+18

-16+38

22

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

cost is

2(5)^2 – 20(5) + 70 =

20

revenue is

–(5)^2 + 5(5) + 18

18

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

cost is

2(20)^2 – 20(20) + 70 =

470

revenue is

–(20)^2 + 5(20) + 18

-282

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

cost is

2(22)^2 – 20(22) + 70 =

598

revenue is

–(22)^2 + 5(22) + 18

-356

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

cost is

2(3)^2 – 20(3) + 70 =

28

revenue is

–(3)^2 + 5(3) + 18

24

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

cost is

2(2)^2 – 20(2) + 70 =

38

revenue is

–(2)^2 + 5(2) + 18

24

Answer:

±5

Step-by-step explanation:

-5k²+20k-30

if u look at the equation ±5 are the greatest common factors so we ±5(±k²±4k±6)

Finding the equivalent angle of [tex]\theta[/tex], the correct statements are given as follows:

Each angle on the second, third and fourth quadrants will have an equivalent on the first quadrant.

In this problem, the given angle is as follows:

[tex]\theta = \frac{5\pi}{4}[/tex]

It is on the third quadrant, as it is between pi and 1.5 pi, hence the equivalent on the first quadrant, also known as the reference angle, is given by:

[tex]\frac{5\pi}{4} - \pi = \frac{5\pi}{4} - \frac{4\pi}{4} = \frac{\pi}{4}[/tex]

The angle of 45º has equal sine and cosine, and tangent of 1, hence the correct statements are:

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Answer:

The measure of the reference angle is 45 degrees

tan(theta) = 1

Step-by-step explanation:

Answer:

Below in bold.

Step-by-step explanation:

Standard form is Ax + By = C

where A, B and C are integers  and A must be positive.

So the first 2 are already in standard form but the last 2 can be converted to standard form by multiplying each term by -1:

-12x+3y=27

= -1*-12x + -1*3y = -1*27

12x - 3y = -27   is the answer.

The last one is:

24x + 12y = -60.

The account be worth in 7 months is 375.725 .

Amount (A) is the total money paid back at the end of the time period for which it was borrowed. The total amount formula in case of simple interest can also be written as: A = P(1 + RT)

Here, A = Total amount after the given time period.

Given that,

P = $350, R = 1.05%, T = 7 month

The simple interest equation uses "t" as years, but is just cycles, using an APR rate.

now, if we never mind "t" as years and just use it as an interest cycle, then we can say the rate is 1.05% and the period is 7 cycles.

A = P(1 + RT)

   = 350(1+1.05%×7)

   = 350(1+0.0105×7)

   = 350(1+0.0735)

   = 350×1.0735

A  = $375.725

Hence, The account be worth in 7 months is 375.725 .

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Answer:

is 54, 45, 36, 27, 18

Step-by-step explanation:

Recursive formulas give us two pieces of information:

1. The first term of the sequence

2. The pattern rule to get any term from the term that comes before it

In the formula given,

n is any term number

f(n) is the nth term

This means

f(1) is the first term

f(f-1) is the term before the nth term

To find the first five numbers in this arithmetic sequence, we know the formula has given us these two pieces of information:

1. The first term is 54

2. The rule to get any term from its previous term is -9

So, we know the sequence for this formula is 54, 45, 36, 27, 18 because starting off with 54, then minus 9 from every sum gives us the following equations

54-9=45

45-9=36

36-9=27

27-9=18

The factorization of given cubic polynomial 6x³ - 11x² - 12x + 5 is:  

6x³ - 11x² - 12x + 5 = (x + 1)(x - [tex]\frac{5}{2}[/tex])(x - [tex]\frac{1}{3}[/tex])

For given question,

We have been given the cubic polynomial 6x³ - 11x² - 12x + 5

We need to factorize given cubic polynomial.

By the rational roots theorem, any rational zero of f(x) is expressible in the form ± [tex]\frac{p}{q}[/tex] for integers p, q with p a divisor of the constant term 5 and q a divisor of the coefficient 6 of the leading term.

Factors of p = 5: 1, 5

Factors of q = 6: 1, 2, 3, 6

That means that the only possible rational zeros are:

±{ [tex]\frac{1}{1} ,\frac{1}{2} ,\frac{1}{3} ,\frac{1}{6} ,\frac{5}{1} ,\frac{5}{2} ,\frac{5}{3} ,\frac{5}{6}[/tex] }

= ±{ [tex]1 ,\frac{1}{2} ,\frac{1}{3} ,\frac{1}{6} ,5 ,\frac{5}{2} ,\frac{5}{3} ,\frac{5}{6}[/tex] }

We need to find the exact zeros of given cubic polynomial.

For x = 1,

6(1)³ - 11(1)² - 12(1) + 5 = -12

This means, x = 1 is not a zero of given cubic polynomial.

For x = -1,

6(-1)³ - 11(-1)² - 12(-1) + 5 = 0

This means, x = -1 is a zero of given cubic polynomial and (x + 1) is a factor.

To factorize given cubic polynomial we use synthetic division.

The synthetic division (6x³ - 11x² - 12x + 5) ÷ (x + 1) is as shown in following image.

⇒ 6x³ - 11x² - 12x + 5 = (x + 1)(6x² - 17x + 5)

The factors of above quadratic polynomial 6x² - 17x + 5 are:

⇒ 6x² - 17x + 5 = (x - [tex]\frac{5}{2}[/tex])(x - [tex]\frac{1}{3}[/tex])

So, the factors of given cubic polynomial are:

⇒ 6x³ - 11x² - 12x + 5 = (x + 1)(x - [tex]\frac{5}{2}[/tex])(x - [tex]\frac{1}{3}[/tex])

Therefore, the factorization of given cubic polynomial 6x³ - 11x² - 12x + 5 is:  6x³ - 11x² - 12x + 5 = (x + 1)(x - [tex]\frac{5}{2}[/tex])(x - [tex]\frac{1}{3}[/tex])

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Answer:

Confidence Level z*-value

90% 1.645 (by convention)

95% 1.96

98% 2.33

99% 2.58

Step-by-step explanation:

the difference in sample means is 0.1, and the upper end of the confidence interval is 0.1 + 0.1085 = 0.2085 while the lower end is 0.1 – 0.1085 = –0.0085.

Kathy has 22 more Euros than British pounds.

Linear equation is an algebraic equation that is a representation of the straight line. Linear equations are composed of variables and constants. These equations are of first-order, that is, the highest power of any of the involved variables i.e. 1. It can also be considered as a polynomial of degree 1. Linear equations containing only one variable are called homogeneous equations. The corresponding variable is called the homogeneous variables.

For instance,

300 / 2 = 150 dollars.

150 /1.64 = 91.46 British pounds

150 /1.32 =113.64 Euros

113.64 - 91.46 =22.18 ≅ 22

Thus Kathy has 22 more Euros than British pounds.

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the solution of the system of linear equations is:

x = 6/11

y = -4/11

Here we have the system of equations:

To solve the system, we can see that y is already isolated in both sides, then we get:

(-5/2)*x + 1 = 3x - 2

Now we can solve this for x:

(-5/2)*x + 1 = 3x - 2

2 + 1 = 3x + (5/2)*x

3 = (6/2)*x + (5/2)*x

3 = (11/2)*x

(2/11)*3 = x

6/11 = x

To get the value of y, we evaluate any of the lines in x = 6/11

y = 3*(6/11) - 2 = 18/11 - 2 = 18/11 - 22/11 = -4/11

Then the solution of the system of linear equations is:

x = 6/11

y = -4/11

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The measure of angle < APD = 98°. That is option D

Angle APB = 62°

Angle DPC = 102°

But length AD = BC

Therefore, angle APD = BPC

Also, the angle at a point = 360°

The sum of the angles given = 102 + 62 = 164°

The remaining angle = 360 - 164 = 196°

Therefore angle APD = 196/2 = 98°

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Answer:

$9600 saving / year

Step-by-step explanation:

1/5 of $21000 = 21000 / 5 = $4200 / month on rent

3/7 of $21000 = (21000 / 7) x 3 = $9000 / month on food (shocking right :) food is expensive)

1/3 of $21000 = 21000 / 3 = $7000 on other expenses / month

total savings/month = salary/month - rent/month - food/month - other expenses/month

total savings/month = 21000 - 4200 - 9000 - 7000

total savings/month = $800

BUT the question asks for savings per year. therefore, we must multiply the savings per month by total months per year (12)

800 x 12 = $9600

the person's total savings per year, with a salary of $21000 per month, is equal to $9600 per year