Sketch the graph of the following equation: y=-3x-5​

Answer:

A. W

Step-by-step explanation:

Because their is a rhythm and pattern

Anderson could provide 0.5x2 + 4x + 8 = 0 has exactly one real root if the discriminant is 0,

Any equation that can be rewritten in standard form as where x represents an unknown, a, b, and c represent known numbers, and where a 0 is true is a quadratic equation. As there is no ax2 term when a = 0, the equation is linear rather than quadratic.

A polynomial's discriminant is a quantity that depends on the coefficients and enables for some root attributes to be inferred without actually computing them. It is actually a polynomial function of the original polynomial's coefficients.

0.5x^2 + 4x + 8 = 0

The discriminant is computed utilizing:

d = b^2 - 4ac

Thus, we have:

d = 4^2 - 4 * 0.5 * 8

Evaluate

d = 0

The equation has only one real root since the discriminant is 0,

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[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]

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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Answer:50%

Step-by-step explanation:  It doesn't matter how many questions there are because for each question, you have a 50% chance of getting it right. So, the probability is 50%.

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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The number of hours spent repairing televisions. after how many hours does he break even is 7 hours

These are equations that contains several equations with unknowns. Given the function that modelled the revenue generated from television repair as;

y = 25 + 30x

where:

x is the number of hours spent repairing televisions.

If his overhead cost, in dollars, is modelled by the equation y=5x^2−10, the company breaks even when;

25 + 30x = 5x^2 -10

Divide through by 5

5 + 6x = x^2 - 2

Equate to zero to have:

x^2 - 6x  -2 - 5 = 0

x^2 - 6x - 7 = 0

x^2 - 7x + x - 7 = 0
x(x-7)+1(x-7) =0

x = -1 and 7

Hence the number of hours spent repairing televisions. after how many hours does he break even is 7 hours

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1. Sea level (0 m) - 100%

2. Mid-level elevation (4,500 m) - 57%

3. Peak (8,850 m) - 33%

Identify the elevation and the percentage of oxygen available at each elevation.

Elevation has a significant impact on the amount of oxygen in the atmosphere. The oxygen level increases with decreasing height and decreases with increasing elevation. Thus, we have a situation where the oxygen concentration is highest at sea level or 0 elevations. The oxygen level drops dramatically when we ascend to greater elevations, say 4,500 m, making breathing difficult. Even at higher altitudes, such as 8,850 m, the oxygen level will drop significantly, making it necessary for a person to undergo extensive training and carry oxygen to survive.

1. Sea level (0 m) - 100%

2. Mid-level elevation (4,500 m) - 57%

3. Peak (8,850 m) - 33%

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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

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

Hope this helps!

The percentage reduction of the price of the video game from 60 to 45 was 25%.

The percentage reduction refers to the fractional reduction in the price of the video game.

This implies that a percentage is a fraction of a value.  Percentages are calculated over 100.

A percentage is, therefore, a number or ratio expressed as a fraction of 100, often denoted using the "%" sign.

The old price of the video game = 60

The new price of the video game = 45

Reduction in price = 15 (60 - 45)

Percentage reduction = 25% (15/60 x 100)

Thus, the percentage reduction of the price of the video game from 60 to 45 was 25%.

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Answer: D. 5 choose 3

Step-by-step explanation:

The 'C' stands for Choose

and you read left to right, leaving you with "5 choose 3"

It looks like the function might be defined by

[tex]f(x) = \begin{cases} 3a{}x + b & \text{if } x > 1 \\ 11 & \text{if } x = 1 \\ 5a{}x - 2b & \text{if } x < 1 \end{cases}[/tex]

To ensure continuity at [tex]x=1[/tex], we need both one-sided limits to exist and have the same value.

[tex]\displaystyle \lim_{x\to1^-} f(x) = \lim_{x\to1} (5a{}x - 2b) = 5a - 2b[/tex]

[tex]\displaystyle \lim_{x\to1^+} f(x) = \lim_{x\to1} (3a{}x + b) = 3a + b[/tex]

Both limit values must be equal to [tex]f(1) = 11[/tex], so that

[tex]\begin{cases} 5a - 2b = 11 \\ 3a + b = 11 \end{cases}[/tex]

Eliminating [tex]b[/tex], we have

[tex](5a - 2b) + 2 (3a + b) = 11 + 2\cdot11 \implies 11a = 33 \implies \boxed{a=3}[/tex]

Solving for [tex]b[/tex], we get

[tex]5\cdot3 - 2b = 11 \implies -2b = -4 \implies \boxed{b=2}[/tex]

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.

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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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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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 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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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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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.

The quantity of meat and cheese sold by the deli according to the description accounts in the task content are; 4.5 and 2.5 pounds respectively.

The quantity of meat sold by the deli as represented by the variable X in the task content can be calculated by solving the systems of equations.

The quantity of cheese sold by the deli as represented by the variable y in the task content can be calculated by solving the systems of equations.

Consequently, solving the system of equations by means of substitution, we have;

y = (30.50-4x)/5

Hence, we have;

11x + 14((30.50-4x)/5) = 84.50

x = 4.5 pounds of meat and

y = 2.5 pounds of cheese.

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The idea that group work theories are appropriate for all clients all the time is a myth (Third option).

About Group Process:

The term "group process" describes how people collaborate within an organization to complete tasks. Typically, organizations invest a lot of time and effort into defining and achieving goals, but little thought is usually given to how those goals are affecting the most valuable resource of a group - its people.

Since different clients have different demands and priorities, group work might not be suitable for many, but not for all. Different types of clients require different types of collaboration, type of group or individuals, and working strategies that work for their goals the best.

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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

the location of the g point is 3.

Two ratios are set to be equal in an equation called a proportion. You might express the ratio as 1: 3 for instance, if there is 1 boy and 3 girls.

Point G Partition the directed line segment form d to f into a

5:4 ratio

so,

g - d = (5/9) x (f - d)

We have that d = -2 and f = 7, Therefore

g - d = (5/9) x (f - d)

g + 2 = (5/9) x (7 + 2)

g + 2 = 5

g = 3

Therefore the location of the g point is 3.

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Answer: OPTION D

Step-by-step explanation:

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]