Choose the system of inequalities that best match the graph below.

Answer:

f = 4 [tex]\frac{5}{37}[/tex]

Step-by-step explanation:

divide 1000 on both sides.

f = 4.135 repeating (the 135 is repeating.)

Put the .135135135... over 999 because it is repeating. F becomes 4[tex]\frac{135}{999}[/tex]

Simplify. f = [tex]4\frac{5}{37}[/tex]

Answer:

Step-by-step explanation:

The graph of the given f(x) shows you what you need to know. Nothing cancels. Two answers are going to be true: one for x<3 and one for x>6.

From the graph, you can see that for x>6 the graph is decreasing. That makes B incorrect.

You can also see that for x < 6 The bottom parabola shape is decreasing which makes A true.

Finally at least one of C or D has to be true. As you can see, they both are depending on which shape you look at.  

The correct answer is B: f(x) is increasing for all x > 6.

To determine the intervals of increase and decrease for the function f(x), we can analyze the critical points and the behavior of the derivative. The derivative of f(x) is given by:

f'(x) = [(x² - 9x + 18)'(x + 6) - (x + 6)'(x² - 9x + 18)] / (x² - 9x + 18)²

Simplifying the derivative and finding the critical points, we get:

f'(x) = (x² - 3x - 18) / (x² - 9x + 18)²

Setting the numerator equal to zero and solving for x, we find the critical points:

x² - 3x - 18 = 0

(x - 6)(x + 3) = 0

x = 6 or x = -3

Analyzing the intervals created by the critical points and using test points, we find that f(x) is increasing for all x > 6. Therefore, the correct answer is B: f(x) is increasing for all x > 6.

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Answer: 4/9

Step-by-step explanation:

Parallel lines have equivalent slopes.

As line 'l' and line 'm' are parallel to each other ,then the slope of line 'm' is also 4/9.

Parallel lines have the same slope. The slope of line segments is identical because they are all similarly inclined with respect to the positive x-axis. If 'l', and 'm' are the slopes of two parallel lines,

then l = m

Slope-intercept notation for lines may be expressed as y=mx+b.

In this notation, b denotes the location of the line's y-axis intercept, and slope(m) indicates the slope of the line.

The slope of 'l'=4/9

The slope of the two parallel lines is the same.

Therefore, the slope of the parallel line "m" = 4/9.

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Step-by-step explanation:

hope you can understand

Answer:

Samantha is 8 years and Maurice is 17 years

Step-by-step explanation:

First represent Samantha's brother's age with a variable, x.

Secondly, find Samantha's age. since shes 9 years younger, then it will be her brother's age which is x minus 9

Thirdly, in ten years, they will all age hence 10 will be added to all their ages.

Fourthly, once 10 has been added to their after 10 years, rhen we realise Maurice age will be 1.5 timess Samantha's age... Then you solve the resulting equation.

Answer:

[tex]\large \boxed{ \tt{y = - 2x + 5}}[/tex]

Step-by-step explanation:

From the y-intercept og [tex][0,5][/tex], travel five unit south over two unit east. Doing so will get yoy to the endpoint of [tex][1,3][/tex], which tells you that the rate of change is [tex] - 2[/tex], Therefore, your equation, in Solpe Intercept Form , is [tex]y = - 2x + 5[/tex]

[tex] \\ [/tex]

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[tex] \huge\mathbb{ \underline{SOLUTION :}}[/tex]

[tex]\leadsto[/tex] Using the slope-intercept form:

▪ [tex] \bold{y = mx + b}[/tex]

▪ [tex] \bold{y = mx + 5}[/tex]

Finally, we are going to use any point of the line. In this case, I am going to take the point (2, 1). Substituting,

[tex] \sf \longrightarrow{1 =m*2+5}[/tex]

[tex] \sf \longrightarrow{1 - 5 = 2m}[/tex]

[tex] \sf \longrightarrow{ m= - \dfrac{4}{2} = - 4 }[/tex]

[tex]\huge \mathbb{ \underline{ANSWER:}}[/tex]

[tex]\large\boxed{\sf y = 2x + 5}[/tex] ✓

The equation gives the measure of the central angle 7/5 times 3 60/2 π.

An angle with its vertex at the center of a circle and with sides that are radii of the circle.

radius= 5 feet.

Circumference of circle,

= 2πr

=2*3.14*5

= 31.4 feet.

Arc length = 7.

Then, the part of circle 7 feet arc have

=7/31.4

=0.2229

Also, 0.2229 * 360 = 80.244°

In radian,

80.244° = 1.4 radians

Hence, 7/5 times 360/2 π.

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Answer:

No. (-1/2) is not an integer

Integers involve all the no. +ve and -ve. which can be written without fraction. ie whole no. are counted as integers.

(-1/2) is a fraction

The range would be all real numbers such that 0 ≤ y ≤ 40.

The complete question is

Raj’s bathtub is clogged and is draining at a rate of 1.5 gallons of water per minute. The table shows that the amount of water remaining in the bathtub, y, is a function of the time in minutes, x, that it has been draining. What is the range of this function? all real numbers such that y ≤ 40 all real numbers such that y ≥ 0 all real numbers such that 0 ≤ y ≤ 40 all real numbers such that 37.75 ≤ y ≤ 40\

A function is an algebraic expression which relates an independent variable with a dependent variable.

It always comes with a defined range and domain.

Draining rate is at 1.5 gallons per minute

That would be y = 1.5x +c

at x = 0 , y = 40

Therefore the equation is y = 1.5x + 40

and from the data

It can be interpreted that as the time increases the water is draining

The range would be all real numbers such that 0 ≤ y ≤ 40.

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C would be the correct answer, I just did the test and got the answer correct.

Answer:

34791112

Step-by-step explanation:

Please check the attached for the explanation.

The next number for given sequence is 34791112.

The given sequence is 2,2,5,12,62,749,46450,......

An arithmetic sequence is a sequence of numbers where the differences between every two consecutive terms is the same.

Each number in the sequence is of the form Number3 × Number2 + Number1 = Number4

5×2+2=12

12×5+2=62

62×12+5=749

749×62+12=46450

So, the required number is

46450×749+62=34791112

Therefore, the next number for given sequence is 34791112.

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Answer:

80

Step-by-step explanation:

we know that 1 percent of 30 is just 30 / 10 which is 3. Is 6 a multiple of 3? yes it is. 6 / 3 = 2. that means 6 is 20 percent of 30 but it hasn't been decreased by 6, it is 6. meaning that the answer is 100 - 20 which is 80

Answer:

  B.) The only solution is (4, - 1/2)

Step-by-step explanation:

To solve this system of equations using the substitution method, we need to use one equation to find an expression for one of the terms or variables that can be substituted for that term or variable in the other equation.

__

Here, it is convenient to use the second equation to write an expression for x:

  x -2 = -4y

  x = 2 -4y . . . . add 2 to both sides

Using this expression for x, we can write the second equation as ...

  3x +2y = 11

  3(2 -4y) +2y = 11 . . . . . substitute for x

  6 -10y = 11 . . . . . . . . eliminate parenthses

This 2-step equation can be solved in the usual way:

  -10y = 5 . . . . . . . subtract the constant to isolate the variable term

  y = -5/10 = -1/2 . . . . . divide by the coefficient of the variable

  x = 2 -4(-1/2) = 2 +2 = 4 . . . . . find the corresponding x-value

The only solution is (x, y) = (4, -1/2).

The only solution is (x, y) = (4, -1/2). so, the correct option is B.

A system of equations is two or more equations that can be solved to get a unique solution. the power of the equation must be in one degree.

we have the system of equations;

3x+2y=11

x−2=−4y

By the substitution method;

use the second equation to write an expression for x:

 x -2 = -4y

 x = 2 -4y

substitute

 3x +2y = 11

 3(2 -4y) +2y = 11

 6 -10y = 11

solve

 -10y = 5

 y = -5/10 = -1/2

 x = 2 -4(-1/2)

x = 2 +2 = 4

Thus, The only solution is (x, y) = (4, -1/2). so, the correct option is B.

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By working with percentages we will see that the down payment is of $11,010 and the first monthly payment is of $275.25

First, the total cost is $110,100.

And we know that you initially pay the 10% of that, so the amount that you pay initially is:

P = 0.10* $110,100 = $11,010

So the down payment is of $11,010

The rest is financed over 30 years, so the rest is:

$110,100 - $11,010 = $99,090

Dividing by the number of months:

N = ( $99,090)/(30*12)  = $275.25

And there is an interest of the 9%, then the amount that you pay on month x is given by:

[tex]P(x) = $275.25*(1.09)^{x-1}[/tex]

Currently (on the first month, so x = 1)

Your pay will be of $275.25

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The value of x is calculated with the help of a similar triangle is 24.

A triangle is a three-sided polygon with three angles. The angles of the triangle add up to 180 degrees.

In a triangle, if there is a parallel line with any side of the triangle, then the line divides the other sides in the same ratio.

Then we have

x / 12 = 32 / 16

     x = 24

Then the value of x is 24.

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Answer:

The correct answer is option B i.e. (7.6, 8.8)

The length along a line or line segment between two points on the line or line segment.

Let the coordinates of the treasure be (x, y).

Let  d₁ =  distance from the rock to the treasure.

Let  d₂ =  distance from the tree to the treasure.

    d₁ = [tex]\sqrt{x^2 + (y-2)^2}[/tex]

    d₂ = [tex]\sqrt{(16-x)^2 + (21-y)^2}[/tex]

We want d₁/d₂ = 5/9 in order to locate the treasure.

Note that 5/9 = 0.556 (approx)

Test (11.4, 14.2)

d₁ = 14.8, d₂ = 8.2, d₁/d₂ = 1.8           Incorrect

Test (7.6, 8.8)

d₁ = 8.2,  d₂ = 14.8,  d₁/d₂ = 0.554    Correct

Test (5.7, 7.5)

d₁ = 6.13,  d₂ = 16.98, d₁/d₂ = 0.36   Incorrect

Test (10.2, 12.6)

d₁ = 12.8,  d₂ = 10.2, d₁/d₂ = 1.255   Incorrect

Thus, The correct answer is option B i.e.  (7.6, 8.8).

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The attraction that reaches a greater height and what it represent in terms of the context  is:

Ferris wheel

(x – 100)2 + (y – 75)2 = 4,900

y max= 75+70

y max=145 ft

Sling shot

y = –3x² + 48x – 30

dy/dx=-6+48=0

x=48/6

x=8

Hence:

y max = –3(8)² + 48(8) – 30
y max = –3×64+48(8)-30

y max = –192+384-30

y max =162 ft

Therefore slingshot reaches a greater height at  162 ft and Ferris wheel reaches a greater height at 145 ft.

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Step-by-step explanation:

this is first an arithmetic sequence with the first term A1=3(1)+1=4 And the 12th term A12=3(12)+1=37. Then use this formula

S12=12/2 ×(4+37)

=6×41

=246

Using the Poisson distribution, the probabilities are given as follows:

A. 0.0888 = 8.88%.

B. 0.1354 = 13.54%.

C. 0.8646 = 86.46%.

In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by:

[tex]P(X = x) = \frac{e^{-\mu}\mu^{x}}{(x)!}[/tex]

The parameters are:

Item a:

10 hours, 2 calls per hour, hence the mean is given by:

[tex]\mu = 2 \times 10 = 20[/tex].

The probability is P(X = 20), hence:

[tex]P(X = x) = \frac{e^{-\mu}\mu^{x}}{(x)!}[/tex]

[tex]P(X = 20) = \frac{e^{-20}20^{20}}{(20)!} = 0.0888[/tex]

Item b:

1 hour, hence the mean is given by:

[tex]\mu = 2[/tex]

The probability is P(X = 0), hence:

[tex]P(X = x) = \frac{e^{-\mu}\mu^{x}}{(x)!}[/tex]

[tex]P(X = 0) = \frac{e^{-2}2^{0}}{(0)!} = 0.1354[/tex]

Item c:

The probability is:

[tex]P(X \geq 1) = 1 - P(X = 0) = 1 - 0.1354 = 0.8646[/tex]

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Answer:

y= 4x - 10

Step-by-step explanation:

y-6 = 4(x - 4)

y - 6 = 4x -16

+6. +6

y= 4x - 10

Answer:

Step-by-step explanation:

→ Find the gradient

( -3 --4 ) ÷ ( 0 --3) = 1/3

→ Write into format

y = 1/3x + c

→ Substitute in a coordinate pair

-3 = 0 + c

→ Solve for c

c = -3

→ Write into format

y = 1/3x - 3

Answer:

FROM THE CALCULATIONS THE ANSWER IS B!

Step-by-step explanation:

Revin imediat...... ✨.

Answer:

[tex] {5}^{ \frac{1}{12} } = \sqrt[12]{5} [/tex]

Step-by-step explanation:

[tex] \frac{ \sqrt[3]{5} }{ \sqrt[4]{5} } = {5}^{ \frac{1}{3} } \div {5}^{ \frac{1}{4} } = {5}^{ \frac{4}{12} } \div {5}^{ \frac{3}{12} } = {5}^{ \frac{1}{12} } = \sqrt[12]{5} [/tex]

THIS IS THE ANSWER: 5 to the power of one-twelfth (Take a look at the image if this does not make sense) :))

:))

:)))   HAPPY SLAPPY!!!!

:))))

"UPDATE" : This was correct on my test. Also I realized to see the image in this answer keep your cursor on the side of your screen, not on the image :D

Answer:

[tex]\tan(\beta)[/tex]

Step-by-step explanation:

For many of these identities, it is helpful to convert everything to sine and cosine, see what cancels, and then work to build out to something.  If you have options that you're building toward, aim toward one of them.

[tex]{\tan(\theta)}={\dfrac{\sin(\theta)}{\cos(\theta)}[/tex]    and   [tex]{\sec(\theta)}={\dfrac{1}{\cos(\theta)}[/tex]

Recall the following reciprocal identity:

[tex]\cot(\theta)=\dfrac{1}{\tan(\theta)}=\dfrac{1}{ \left ( \dfrac{\sin(\theta)}{\cos(\theta)} \right )} =\dfrac{\cos(\theta)}{\sin(\theta)}[/tex]

So, the original expression can be written in terms of only sines and cosines:

[tex]\sin(\beta)\tan(\beta)\sec(\beta)\cot(\beta)[/tex]

[tex]\sin(\beta) * \dfrac{\sin(\beta) }{\cos(\beta) } * \dfrac{1 }{\cos(\beta) } * \dfrac{\cos(\beta) } {\sin(\beta) }[/tex]

[tex]\sin(\beta) * \dfrac{\sin(\beta) \!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!{---}}{\cos(\beta) \!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!{---}} * \dfrac{1 }{\cos(\beta) } * \dfrac{\cos(\beta) \!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!{---}} {\sin(\beta) \!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!{---}}[/tex]

[tex]\sin(\beta) *\dfrac{1 }{\cos(\beta) }[/tex]

[tex]\dfrac{\sin(\beta)}{\cos(\beta) }[/tex]

Working toward one of the answers provided, this is the tangent function.

The one caveat is that the original expression also was undefined for values of beta that caused the sine function to be zero, whereas this simplified function is only undefined for values of beta where the cosine is equal to zero.  However, the questions states that we are only considering values for which the original expression is defined, so, excluding those values of beta, the original expression is equivalent to [tex]\tan(\beta)[/tex].

Step-by-step explanation:

Very easy the value are given apply the value for X and y

5.7y-5.2=y/2.5

Add 5.2 to both sides:

5.7y = y/2.5 + 5.2

y/2.5 = 0.4y

5.7y = 0.4y + 5.2

Subtract 0.4y from both sides:

5.3y = 5.2

Divide both sides by 5.3:

y = 5.2/5.3

y = 0.98113

Answer:

y = 0.981

Step-by-step explanation:

Given expression:

Solution:

Subtract 0.4y from both sides:

Add 5.2 to both sides:

Divide both sides by 5.3:

Hence, y = 0.981.

The book does nick shelve in 2 hours is 60.

Given coordinates:

(0, 0), (2, 60) and (4, 120).

If we look at the coordinates (2, 60)

The value corresponds to 2 hours is 60.

Hence, the book nick shelves in 2 hours is 60.

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Answer:

(-2,7)

Step-by-step explanation:

x=7-3y

2(7-3y)+4y=8

14-6y +4y=8

14-2y=8

-2y = -6

y=3

x + 3(3) = 7

x + 9 = 7

x = -2

(-2,7)

Answer: -2,3

Step-by-step explanation: