A fish tank is being drained at a constant rate. The graph shows the linear relationship between the volume of water in the fish tank in liters and the time in minutes the tank has been draining.

Answer:

(3z)^3

Step-by-step explanation:

27 = 3 * 3 * 3 = 3^3

3^3 z^3   = (3z)^3

According to the graph of the function the real zeros of the functions are (-0.33, 0)

Real zeros of the function

Based on the graph methods, the real zero of a function is where the graph of the function crosses the x‐axis; that is, the real zero of a function is the x‐intercept(s) of the graph of the function.

Given,

Here we have the function f(x) = -9x² - 6x - 1

Now, we have to plot the graph for the function by using the graphing calculator and then we have to find the real zeros of the function.

Here we have to take the expression and input it in the graphing calculator.

Then we get the graph like the following.

Now, we have to identify the real zeros of the function through this plotted graph.

The real zeros of the function means the x intercept points of the graph.

Here we have the x intercepts is (-0.33,0)

Therefore, the real zeros on the function are (-0.33 , 0)

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The sales Sam need to make $733.50 per week before taxes is $3475.

Given, Sam is paid $14 per hour plus 6% of sales.

If he worked 37.5 hours in one week, what would his sales need to make

$733.50 per week before taxes = ?

Let the sales be represented by x

Amount made from no of hours worked :

= $14 × 37.5 hours

=$525

Sales made = 6% of x

=0.06x

Total = 0.06x+$525

=$733.50

0.06x=733.50-$525

=$208.5

x=$3,475

Hence we get the required answer.

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The multiple of 2, 5, and 7, such that the sum of the 3 digits is 10 is:

630

We want to find a number that is a multiple of 2, 5 and 7, such that the sum of the 3 digits is 10. (such that the number is not 280)

So our number N is of the form:

N = a*(2*5*7)

Where a is an integer.

N = a*70

Here we just need to find the value of a such that the sum of the 3 digits of the outcome is equal to 10.

For example, if a = 2 then:

N = 2*70 = 140

The sum gives 1 + 4 + 0 = 5

Now we jut need to keep trying values of a.

Eventually, we will get to:

if a = 9 then:

N = 9*70 = 630

The sum gives: 6 + 3 + 0 = 10

So this is our number.

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There are 12.3553 square miles are in 32 square kilometers.

What is square miles and square kilometers?

A square mile is equivalent to 2.59 square kilometres. A square mile must be multiplied by a factor of 2.59 in order to be converted to a square kilometre. For instance, 3 square miles are equivalent to 7.77 square kilometers when multiplied by 2.59, or square meters.

We have to find how many square miles are in 32 square kilometers.

Since, 1 square mile = 2.59 square kilometer

Suppose x square miles = 32 square kilometer

Consider, the ratio

[tex]\frac{1}{x} = \frac{2.59}{32} \\x = \frac{32}{2.59}\\ x=12.3553[/tex]

Therefore, 12.3553 square miles are in 32 square kilometer.

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Answer:

D = 30/7; R =32/7

Step-by-step explanation:

First, we need to find the scale of the number line.  We can see that there are 7 ticks between 4 and 5.  Thus, we can use (5-4)/7 to find the scale which is 1/7.  

Since D is two ticks away from 4, we can use the equation:

[tex]4+2(\frac{1}{7})=D\\ 4+\frac{2}{7}=D\\ 4\frac{2}{7}=D\\ 4*7=28+2=\frac{30}{7}=D[/tex]

Since R is two ticks away from D or 30/7, we can use a similar equation:

[tex]\frac{30}{7}+2(\frac{1}{7})=R\\ \frac{30}{7}+\frac{2}{7}=R\\ \frac{32}{7}=R\\ 4\frac{4}{7}=R[/tex]

Your problem doesn't tell us whether we need to we use improper or mixed fractions, but I've included both for you.

Answer:

gpaph C.

Step-by-step explanation:

graph 'C' represents the provided function. Its equation is

[tex]y=-\frac{5}{2}x +4.[/tex]

A graph which represents the solutions of p + 1 < -1 or p - 5 > 7 is shown in the image attached below.

In Mathematics, an interval notation simply refers to a set of real numbers which consist of all the real numbers that represents a continuous function and lies between two set of numbers.

This ultimately implies that, an interval notation should be used for writing all of the subsets of a real number line (graph) as shown below:

For the first interval, we have:

p + 1 < -1

p < -1 - 1

p < -2

Therefore, in interval notation, we have:

p = {∞, -2}

For the second  interval, we have:

p - 5 > 7

p < 7 + 5

p < 12

Therefore, in interval notation, we have:

p = {12, ∞}

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The number of days which it would take 1000 people to sign the petition as required in the task content is; 4.35 days.

It follows from the task content that the number of days which it would take Jan to get 1000 signatures on the petition be determined.

Since it is given in the task content that 230 people sign the petition each day.

It therefore follows from proportion that the number of days needed for 1000 people to sign the petition is;

= 1000/230

= 4.3478 days.

Hence, the number of days which it would take 1000 people to sign the petition is approximately; 4.35 days.

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Answer:

I believe this should be it,

Step-by-step explanation:

344.8572

Answer of the following questions:

As given in the question,

For a coordinate plane,

Line passes through the points (-6, 8) and (2,6).

Slope of the line = ( y₂ - y₁)/ (x₂ - x₁)

                          = ( 6 - 8) / (2- (-6))

                          = -2 /8

                          = -1/4

Slopes of the parallel line are always equal.

Equation of the line parallel to the given line and passes through (-2, -4)

is given by:

y -(-4) = (-1/4)(x -(-2))

⇒y + 4 = -x/4-1/2

⇒ y = -x/4 -9/2

y-intercept of the line which is parallel to the given line and passes through (-2, -4) is given by:

x = 0

y = -9/2 is the y-intercept.

Therefore,  answer of the questions for the given condition :

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Simplifying

-7x2 + 5x + -18 = 0

Reorder the terms:

-18 + 5x + -7x2 = 0

Solving

-18 + 5x + -7x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by

-7 the coefficient of the squared term:

Divide each side by '-7'.

2.571428571 + -0.7142857143x + x2 = 0

Move the constant term to the right:

Add '-2.571428571' to each side of the equation.

2.571428571 + -0.7142857143x + -2.571428571 + x2 = 0 + -2.571428571

Reorder the terms:

2.571428571 + -2.571428571 + -0.7142857143x + x2 = 0 + -2.571428571

Combine like terms: 2.571428571 + -2.571428571 = 0.000000000

0.000000000 + -0.7142857143x + x2 = 0 + -2.571428571

-0.7142857143x + x2 = 0 + -2.571428571

Combine like terms: 0 + -2.571428571 = -2.571428571

-0.7142857143x + x2 = -2.571428571

The x term is -0.7142857143x.  Take half its coefficient (-0.3571428572).

Square it (0.1275510204) and add it to both sides.

Add '0.1275510204' to each side of the equation.

-0.7142857143x + 0.1275510204 + x2 = -2.571428571 + 0.1275510204

Reorder the terms:

0.1275510204 + -0.7142857143x + x2 = -2.571428571 + 0.1275510204

Combine like terms: -2.571428571 + 0.1275510204 = -2.4438775506

0.1275510204 + -0.7142857143x + x2 = -2.4438775506

Factor a perfect square on the left side:

(x + -0.3571428572)(x + -0.3571428572) = -2.4438775506

Answer:

A decimal or consecutive tenths decimals. Also 0.1 away from each other.

Step-by-step explanation:

They have decimal endings: .1 and .2

And are 0.1 away.

As per the proportionally concept, the missing value in the table is 240

and in 18 minute Kenny type 720 words.

Proportionality:

If two objects are proportional to each other, then it means that as one object increases the other will also increase and the ratio of the quantities is the same for all values.

Given,

Kenny is practicing for a typing test to obtain a job as paralegal. The number of words he can type is proportional to the number of minutes he types.

Here we need to find if the test is 18 mins long how many word will Kenny be able to type and the missing value in the table.

Here we have assume that if number of words typed is proportional to number of minutes

So, it can be written as Word typed α number of minutes

As in the equation form of the relation is,

Word typed = k * number of minutes

where k refers constant of proportionality

So, first we have to find the value of k, in order to solve this,

For, that we have to take the following,

=> 120 = k * 3

=> k = 120/3

Therefore, k = 40

So, if test is 18 minutes long, then the number of words is calculated as,

=> Word typed = k * 18

=> Word typed = 40 * 18

=> Word typed = 720

And the missing value of the table is,

=> words = 40 * 6

=> words = 240

Therefore, the number of words in 6 minutes is 240.

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The solution in set builder notation is given by = {y:3>y≥-1}

Given the inequalities are,

y-1<2 ............(i)

y+2 ≥ 1 ..............(ii)

Solving the first inequality we get,

y-1 < 2

y-1+1 < 2+1, adding 1 to both sides

y < 3

Solving second inequality we get,

y+2 ≥ 1

y+2-2 ≥ 1-2

y ≥ -1

So the range is 3>y≥-1

So the solution in set builder notation is = {y:3>y≥-1}

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Answer:

Step-by-step explanation:

89,83,91,92,93,x

n=6

average=91

total=91*6=546

89+83+91+92+93+x=546

448+x=546

x=546-448=98

Answer:

Step-by-step explanation:

1)

Let Andre's grade needs to be a x on his next test

Hence,

[tex]\displaystyle\\\frac{89+83+91+92+93+x}{6} =91\\\\\frac{448+x}{6} =91[/tex]

Multiply both parts of the equation by 6:

[tex]448+x=91(6)\\\\448+x=546\\\\448+x-448=546-448\\\\x=98[/tex]

2)

[tex]\displaystyle\\\frac{1000+1181+1191+1200+1268+1328+2584+x}{8} =1344\\\\\frac{9752+x}{8}=1344[/tex]

Multiply both parts of the equation by 8:

9752+x=1344(8)

9752+x=10752

9752+x-9752=10752-9752

x=$1000

3)

302, 293, 218, 330, 199, 253, 288

Arrange this series:

199, 218, 253, 288, 293, 302, 330

[tex]\displaystyle\\a)\ the \ median = \$288\\\\b) \ the\ mean =\frac{199+218+253+288+293+302+330}{7} \\\\=\frac{1883}{7} \\\\=\$269\\c)\\\\\frac{1883+x}{8} =269+5\\\\\frac{1883+x}{8} =274[/tex]

Multiply both parts of the equation by 8:

1883+x=274(8)

1883+x=2192

1883+x-1883=2192-1883

x=$309

According to the given square root value, the resulting value of the expression 2√4 × √9 is 12

Square root:

Square root refers any number that is equal to a number, which when squared gives the original number.

Given,

Here we have the expression 2√4 × √9.

Now, we have to find the value of the expression.

While we looking the given expression we have identified that the value of the square roots are

√4 = √(2 x 2) = 2

Similarly, the value of

√9 = √(3 x 3) = 3

So, now we have to replace the root with these values, then we get,

=> (2 x 2) x 3

=> 4 x 3

=> 12

Therefore, the resulting value is 12.

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The equation, [tex]g(x) = \sqrt{\frac{1}{4}x }-2[/tex], represents the transformation formed by horizontally stretching the graph of [tex]f(x) = \sqrt{x}[/tex]  by a factor of 4 and then vertically shifting the graph 2 units down.

What is transformation of graph?

The process of algorithmically producing a new graph from an original graph is known as graph transformation, sometimes known as graph rewriting. It has several uses, including software engineering, layout algorithms, and image.

Consider, the given function [tex]f(x) = \sqrt{x}[/tex].

If horizontally stretching the graph by 4 units then, the graph  becomes,

[tex]f(x) = \sqrt{\frac{x}{4} }[/tex].

If vertically shifting the graph 2 units, then the graph becomes,

[tex]h(x) = \sqrt{\frac{x}{4} } - 2[/tex].

Hence, the transformed form of the graph is, [tex]h(x) = \sqrt{\frac{x}{4} } - 2[/tex].

So, the third option is correct.

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Answer:

The answer is B false

Step-by-step explanation:

The domain of the given function is the hours or time taken whereas the range will be the concentration and greatest concentration of the medication that a patient will have in their body is 8 mg/L.

What is Domain of a function?

Inputs are assigned outputs by functions. The collection of all potential inputs for a function is its domain. For instance, the domain of f(x)=x2 and g(x)=1/x are all real integers with the exception of x=0.

Therefore, The domain of the given function is the hours or time taken.

What is range of a function?

The collection of potential output values for a function is known as its range.

Therefore, the range of the function is concentration.

B) Graph of the function is attached and we can see from the graph that greatest concentration of the medication that a patient will have in their body is 8 mg/L.

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Answer:

  (f∘g)(x) = 5x -16

Step-by-step explanation:

You want the simplified form of the composition (f∘g)(x) when f(x)=5x-6 and g(x)=x-2.

The notation (f∘g)(x) is a shorthand way to write f(g(x)). The composition operator (ring operator) works right to left, meaning that g(x) is evaluated first, then the result is used as an argument to the function f.

Functions are evaluated in the usual way.

  f(g(x)) = f(x-2) = 5(x-2) -6 = 5x -10 -6 = 5x -16

  (f∘g)(x) = 5x -16

The dimensions of the shape will be 175 meters and 87.5 meters

The largest area that can be enclosed is 15312.5m².

Based on the information given, the equation to illustrate this will be:

2x + y = 350

y = 350 - 2x

Note that area = length × width

= x × y

We'll substitute the value into the equation. This will be:

A = x × (350 - 2x)

A(x) = 350x - 2x²

Differentiating the area, x will be 87.5

Width = 87.5m

Since y = 350 - 2x

= 350 - 2(87.5)

= 350 - 175

= 175

Length = 175m

Area = Length * Width

= 175 × 87.5

= 15312.5m²

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The slope is, 1/4.

And the y - intercept is (0, -1).

What is slope and y-intercept?

A number that describes a line's direction and steepness is known as the slope or gradient of a line in mathematics.

A y-intercept, also known as a vertical intercept, is a point in analytical geometry where the graph of a function or relation meets the y-axis of the coordinate system, employing the convention that the horizontal axis represents a variable x and the vertical axis represents a variable y. Thus,

x = 0 is satisfied at these sites.

Let the x - intercept is 4.

The x - intercept is the point on x - axis, when y = 0.

So, the x - intercept is (4, 0).

The y - intercept is -1.

y-intercept is the point on the y - axis, when x is zero.

So, the y - intercept is (0, -1).

Here we have two points (4, 0) and (0, -1).

By using these points we can find the slope.

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

[tex]m = \frac{-1-0}{0-4}= \frac{-1}{-4} = \frac{1}{4}[/tex]

Hence, the slope is 1/4 and the y - intercept is (0, -1).

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Answer:

y=-1/2x+4

y=2x+5

y=x+2

Step-by-step explanation:

1. The equation of the line is y = - 4 / 9 x + 25 / 9.

2. The equation of the line is y = 5 /3 x -  14 / 3

3. The equation of the line is  y = x + 2

The equation of a line can be represented in slope intercept form as follows:

y = mx + b

where

Therefore, the equation of the line can be found as follows:

1.

(4, 1)(-5, 5)

m = 5 - 1 / -5 -4

m = 4 / -9

m = - 4 / 9

Let's find y-intercept

1 = - 4 / 9(4) + b

1 + 16 / 9 = b

b =  9 + 16 / 9

b = 25 / 9

Hence, thee equation of the line is  y = - 4 / 9 x + 25 / 9

2.

(-2, -8)(4, 2)

m = 2 + 8 / 4 + 2

m = 10 / 6

m = 5 / 3

Let's find y-intercept

2 = 5 / 3 (4) + b

2 - 20 / 3 = b

b =  6 - 20/ 3

b = - 14 / 3

Therefore, the equation of the line is y = 5 /3 x -  14 / 3

3.

(0, 2)(-2, 0)

m = 0 - 2 / -2 -0

m = - 2 / -2

m = 1

Let's find y-intercept

2 = 1(0) + b

b = 2

Therefore, the equation of the line is y = x + 2

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Answer:

[tex]y=80(1.1)^x[/tex]

Step-by-step explanation:

Please, tell me if I did this wrong as I'm not really sure of this. Thx

The rocket reaches its maximum height at 2.25 second(s) after launch

The maximum height reached by the object is 88 feet.

The function is given as

h(t) = -16t² + 72t + 7

Differentiate the above function

So, we have the following representation

h'(t) = -32t + 72

Set to 0

-32t + 72 = 0

So, we have

32t = 72

Divide by 32

t = 2.25

Hence, the time is 2.25 seconds

In (a), we have

t = 2.25

Substitute t = 2.25 in h(t) = -16t² + 72t + 7

h(2.25) = -16(2.25)² + 72(2.25) + 7

Evaluate

h(2.25) = 88

Hence, the maximum height is 88 feet

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The measures of  the angles formed by the common transversal to the parallel lines are;

1. Angle 1 = 87°

Angle 2 = 100°

2. Angle 1 = 78°

Angle 2 = 78°

Parallel lines are lines that have the same slope but pass throuh different points.

The diagram consists of parallel lines that have a common transversal, therefore;

1. The 87° angle and the Angle 1 are alternate interior angles, therefore;

87° ≅ Angle 1

87° = Angle 1

The 87° angle and the Angle 2 are same side interior angles

Therefore;

87° + Angle 2 = 180°

Angle 2 = 180° - 80° = 100°

Angle 2 = 100°

2. The 78° angle and the Angle 1 are corresponding angles, therefore;

78° ≅ Angle 1

Angle 1 = 78° (by the definition of congruency)

Angle 1 and Angle 2 are vertical angles

Therefore, Angle 1 is congruent to Angle 2 by vertical angle theorem

Angle 1 = Angle 2 by definition of congruency

Angle 1 = 78° = Angle 2

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Answer:

1

Step-by-step explanation:

anything to the power of 0 is equal to 1

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