Rewrite the equation shown in slope-intercept form. Identify the slope of the equation, the x intercept and the y-intercept. Then graph the equation. Make sure to show all your work in the
spaces provided.

Answer: Side of an empty cubicle carton = 9 cm.

Now as we know that volume of the cube is the cube of its side.

So the volume of an empty cubicle carton having side 9 cm, V = (9)3=729 cm3.

Now we have to find out can 1000 cubes of side 1cm fit in it.

So the volume of the cube of side 1 cm is, V’ = (1)3=1 cm3

So the volume of the 1000 such cubes = 1000 (1) = 1000 cubic centimeters.

Now if the ratio of the volume of the empty cubicle carton to the volume of 1000 cubes of 1 cm is greater than 1 then we can will 1000 cubes of side 1 cm into an empty cubicle carton otherwise not.

So the ratio of the volume of the empty cubicle carton to the volume of the 1000 cubes is,

⇒VV′=7291000=0.729 < 1

So as we see that the ratio is less than one so we cannot fit 1000 cubes of side 1 cm into an empty cubicle carton of side 9 cm.

Step-by-step explanation:

I really hope this works!

                                      Hope you Have a Great Day!! :)

If the three sides of the triangle is (x + 5), (2x - 3), (21 - x), then the perimeter of the triangle is 23 + 2x

The perimeter of the triangle is the summation of all three sides of the triangle

Perimeter = a + b + c

= (x + 5) + (2x - 3) + (21 - x)

= 2x + 23

= 23 + 2x

Therefore, if the three sides of the triangle is (x + 5), (2x - 3), (21 - x) then the perimeter of the triangle  23 + 2x.

Any two-dimensional figure's perimeter is determined by the space surrounding it. By adding the lengths of the sides, we can determine the perimeter of any closed shape.

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Gianna washes 15 cars in 5 hours as her rate of washing cars is 3 cars per hour.

What is unitary method?

The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.

According to the given question:

Gianna can wash 6 cars in 2 hours

Therefore, in 1 hour she can wash 6/2 cars which is 3 cars.

Gianna's rate of washing cars is 3 cars per hour

Hence by unitary method, Gianna at this rate can washes 5 x 3 cars that is 15 cars.

Gianna washes 15 cars in 5 hours as her rate of washing cars is 3 cars per hour.

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The maximum average BAC during the first 6 hours is about 0.177 mg/ml.

What is average ?

The middle number in a group of numbers is the average value, which is determined by dividing the sum of all the values by the variety of values.                                  

                                          When determining the average for a set of data, we add up all the values and divide this sum by the total number of values.

The maximum is found where the derivative of C(t) is zero.

 dC/dt = 1.35e^(-2.802t) -(1.35t)2.802e^(-2.802t) = 0

Solving for t gives ...

 t = 1/2.802

So, the maximum C(t) is ...

 C(1/2.802) = 1.35/2.802e^(-1) ≈ 0.177 . . . . . mg/mL

The maximum average BAC during the first 6 hours is about 0.177 mg/mL.

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We can write the given statement as inequality as -

-(x/9) < 12

Linear inequalities are defined as expressions in which two linear expressions are compared using the inequality symbols.

Reversal property : If (a > b) then (b < a) and  if (a < b) then (b > a).

Law of Trichotomy : The "Law of Trichotomy" says that - only one of the following is true : (a < b) or (a = b) or (a > b).

The general equation of a straight line is y = mx + c

Other possible equations of lines are -

We have the following statement -

"the quotient of a number and three minus twelve is less than 12".

We can write the inequality as -

-(x/9) < 12

Therefore, we can write the given statement as inequality as -

-(x/9) < 12

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The football field is longer than soccer field.

A mathematical expression is made up of terms (constants and variables) separated by mathematical operators. A mathematical equation is used to equate two expressions. Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem. Conversion of units is the conversion between different units of measurement for the same quantity, typically through multiplicative conversion factors.

We have a soccer field that is 105 meters long and a football field is 120 yards long.

In one yard, we have -

1 yard = 0.9144 meters

Then, in 120 yards, we will have -

120 x 0.9144 = 109.728 meters

Now, 109.728 meters > 105 meters.

Therefore, the football field is longer than soccer field.

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The composition of the function are as follows:
(g ∘ g) (x) = 4x + 16
(f ∘ g) (x) = 16x + 64
f [g(7)] = 6x - 28
g [f(3)] = -30x - 10

What is a Composite Function?
If we are given two functions, we can compose one function into the other to produce a third function. The steps needed to complete this operation are the same as those needed to solve any function for any given value. These are referred to as composite functions.

We have,

i] f(x) = 8x  and
g(x) = (2x+8)

(g ∘ g) (x) = g[g(x)]
Substitute x with (2x+8) in the function g(x) = (2x+8).
= 2((2x+8))+8
= 4x + 16

(f ∘ g) (x) = f [g (x)]
Substitute x with (2x+8) in the function f(x) =  8x.
(f ∘ g) (x) = 8(2x+8)  
= 16x + 64

ii]  f(x) = 6x + 2 and g(x) = x -5
f [g(7)] = 6(x-5) + 2  
= 6x - 28

g [f(3)] = (6x + 2 ) - 5
= -30x - 10

Hence, the composition of the function is:
(g ∘ g) (x) = 4x + 16
(f ∘ g) (x) = 16x + 64
f [g(7)] = 6x - 28
g [f(3)] = -30x - 10

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The blanks are filled as below

Collinear points are those that are situated along a single straight line.

Collinear points are those that are on a line either close to or far from another point, it can be more than two points.

While coplanar points imply lying on the same plane

In the diagram,

E, F, and G are collinear points

D, B, E, F, and G are coplanar points

A, B, and C are another collinear points

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The equivalent expression of (6x² - 9x) - (2x -3) is 6x² - 11x + 3

Two expressions are said to be equivalent if they have the same value irrespective of the value of the variable(s) in them.

In other words, equivalent expressions are expressions that have similar value or worth but do not look the same.

To find equivalent expression we can simplify the expression.

Therefore,

(6x² - 9x) - (2x -3)

open the brackets

6x² - 9x - 2x + 3

combine like terms

Therefore,

(6x² - 9x) - (2x -3) = 6x² - 11x + 3

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Tamar raise $15

What is division ?

One of the four fundamental arithmetic operations, or the process by which two or more numbers are added together to create a new number, is division. Multiplication, addition, and subtraction round out the list of operations.

A group is divided into equal portions when it is divided. For a game or activity, division can be used to divide a class into equal groups. It can also be used to divide a pizza among friends in equal pieces. Divided into partitive and quotative, there are two forms of division.

There are 2 ways one by writing equation and the other by using logic

1. by using equation

3*x=45

x=45/3

 = 15

2. Logically

If Jack has $45 which is 3 times Tamara's we can reverse the statement:

45/3

=15

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[tex]tan(\alpha - \beta) = \cfrac{tan(\alpha)- tan(\beta)}{1+ tan(\alpha)tan(\beta)} \\\\[-0.35em] ~\dotfill\\\\ cos(\alpha )=\cfrac{\stackrel{adjacent}{3}}{\underset{hypotenuse}{5}}\qquad \textit{let's find the opposite} \\\\\\ \textit{using the pythagorean theorem} \\\\ c^2=a^2+b^2\implies \sqrt{c^2 - a^2}=b \qquad \begin{cases} c=hypotenuse\\ a=adjacent\\ b=opposite\\ \end{cases}[/tex]

[tex]\pm\sqrt{5^2 - 3^2}=b\implies \pm 4=b\implies \stackrel{IV~Quadrant}{-4=b}~\hfill tan(\alpha)=\cfrac{\stackrel{opposite}{-4}}{\underset{adjacent}{3}} \\\\[-0.35em] ~\dotfill[/tex]

[tex]tan(\alpha - \beta) \implies \cfrac{\stackrel{tan(\alpha)}{-\frac{4}{3}}- \stackrel{tan(\beta)}{\frac{4}{3}}}{1+ \stackrel{tan(\alpha)}{\left( -\frac{4}{3} \right)}\stackrel{tan(\beta)}{\left( \frac{4}{3}\right)}}\implies \cfrac{~~ \frac{-8 }{3 } ~~}{1-\frac{16}{9}}\implies \cfrac{~~ \frac{-8 }{3 } ~~}{\frac{-7}{9}} \\\\\\ \cfrac{-8}{3}\cdot \cfrac{9}{-7}\implies \cfrac{24}{7}\implies {\Large \begin{array}{llll} 3\frac{3}{7} \end{array}}[/tex]

Answer: $21.33

Step-by-step explanation: 50 - 28.67 = 21.33

Answer:

√130

Step-by-step explanation:

                              |

          ?                  |         7

                              |

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

            9

a² + b² = c²

7² + 9² = c²

49 + 81 = c²

130 = c²

√130 = √c²

√130 = c

I hope this helps!

According to the Alternate Interior Angles Theorem, when two parallel lines are cut by a transversal, the resulting alternate interior angles are congruent.

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The graph y = - 0.5x + 12 has a slope of - 0.5 and decreases in nature.

We know lines have various types of equations, the general type is

Ax + By + c = 0, and the equation of a line in slope-intercept form is

y = mx + b.

Where slope = m and b = y-intercept.

the slope is the rate of change of the y-axis with respect to the x-axis and the y-intercept is the (0,b) where the line intersects the y-axis at x = 0.

Given, harper created a graph of a line by y = - 0.5x + 12.

∴ The graph will have a slope of - 0.5 which is decreasing in nature.

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Answer:

one number is 8 and other is 4

Step-by-step explanation:

So we can say x+y=12.

And 3x+5y=44

For x+y=12, we can subtract x to get: y=12-x

Plug that in to get 3x+5(12-x)=44

3x+60-5x=44

Subtract 44: -2x+16=0

2x=16

x=8

12-8=4.

Answer: the space shuttle

Step-by-step explanation:

The Height of trees are equal after 4 years and the height is 54 inches.

A linear equation is a equation which draws straight line on the plot

when plotted.

Given,

Height of tree A at the time of planting = 38 inches

Height of tree B at the time of planting = 22 inches

Each year  tree A grow = 4 inches

Each year  tree B grow = 8 inches

Let's make an equation for the height of the trees,

H = 38 +4t

H = 22+8t

Now the time when height of both the trees will equal

38 + 4t = 22 + 8t

4t = 16

t = 4

Hence , After 4 years the height of both the trees will equal and the height of both the trees after 4 years will be 54 inches.

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Answer:

[tex]x=1.45[/tex]

Step-by-step explanation:

[tex]2\left(x-4 \frac{1}{2} \right)=-6.1 \\ \\ 2\left(x-\frac{9}{2} \right)=-6.1 \\ \\ 2x-9=-6.1 \\ \\ 2x=2.9 \\ \\ x=1.45[/tex]

The perimeter of the quadrilateral is 46 units, so the correct option is d.

The perimeter is equal to the sum of the lengths of all the sides of the quadrilateral.

Remember that the length of a segment whose endpoints are (x₁, y₁) and (x₂, y₂) is:

L = √( (x₁ - x₂)^2 + (y₁ - y₂)^2)

The length between the first two vertices: (−6, −2), (0, −10)

L₁ = √( (-6 - 0)^2 + (-2 + 10)^2) = 10

The length between the second two vertices:  (0, −10), (5, 2)

L₂ = √( (0 - 5)^2 + (-10 - 2)^2) = 13

The length between the third two vertices:  (5, 2), (−1, 10)

L₃ = √( (5 + 1)^2 + (2 - 10)^2) = 10

The length between the fourth two vertices:  (−1, 10), (−6, −2)

L₄ = √( (-1 + 6)^2 + (10 + 2)^2) = 13

Then the perimeter is:

P = 10 + 13 + 10 + 13 = 46

The correct option is D.

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Answer:

y^2

Step-by-step explanation:

a^m/a^n = a^(m - n)

y^5/y^3 = y^2

the diameter to allow an elongation of 0. 38 mm therefore required diameter is 7.65 mm

Given the data in the question;

F = 11100 N

l₀ = 310 mm = 0.31 m

E = 207 GPa = 207 × 10⁹ N/m²

Δl = 0.38 mm = 0.0005 m

So, lets assume the deformation is elastic;

d₀ = √(  [4l₀F] / [πEΔl] )

we substitute

d₀ = √(  [4 × 0.38 × 11100] / [π × (207 × 10⁹) × 0.0005]] )

d₀ = √( 10123.2 / 172787595.947 )

d₀ = √( 5.85875 × 10⁻⁵ )

d₀ = 0.007654 m

d₀ = ( 0.007654 × 1000 )mm

d₀ = 7.65 mm

Therefore, required diameter is 7.65 mm

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Probability of people less than 19 year old = 0.5343

Probability of people greater than 10 year old = 0.8116

What is probability?

Mathematical descriptions of the likelihood that an event will occur or that a statement is true are referred to as probabilities. A number between 0 and 1 represents the probability of an event, with 0 roughly denoting impossibility and 1 denoting certainty.

People under age 10 = 253

People between the age of 10-18 = 466

People between the age of 19-30 = 174

People above the age of 30 = 450

Total no. of people = 1343

a) people less than 19 years old = 253+466 = 719

probability of people<19 year old = P(age<19) = 719/1343 = 0.5354

b) people of age greater than 10 = 466+174+450 = 1090

probability of people >10 year old = P(age>10) = 1090/1343 = 0.8116

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1) 16.7% probability of rolling 10+.

2) 50% probability an odd number is rolled.

3) 7 is the most likely total result.

These are all the possible outcomes:

(1,1), (1,2), (1,3), (1,4), (1,5),(1,6)

(2,1), (2,2), (2,3), (2,4), (2,5),(2,6)

(3,1), (3,2), (3,3), (3,4), (3,5),(3,6)

(4,1), (4,2), (4,3), (4,4), (4,5),(4,6)

(5,1), (5,2), (5,3), (5,4), (5,5),(5,6)

(6,1), (6,2), (6,3), (6,4), (6,5),(6,6)

There are 36 possible outcomes

1) what is the probability of rolling 10+?

There are 6 possible outcomes in which 10+ is rolled:

(4,6), (5,5),(5,6), (6,4), (6,5),(6,6).

So there is a 6/36 = 0.167 = 16.7% probability of rolling 10+.

2) what is the probability of rolling an odd number?

There are 18 possible outcomes in which an odd number is rolled.

So there is a 18/36 = 0.5 = 50% probability an odd number is rolled.

3) what is the total that is most likely to result?

There are 6 outcomes in which 7 is rolled.

So 7 is the most likely total result.

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The value of the function g(f(2)) is 29 and 2.f(g(x)) is (x - 1)(2x - 2).

When the output of one function is given to the input of another function they are called composite functions.In (fog)x which is [f{g(x)}] here the out of the function g(x) is the input of the function f(x).

Given, f(x) = 4x² - 1. and g(x) = 2x - 1.

Now, g(f(2)) is the output of f(2) is the input of g(x).

∴ f(2) = 4(2)² - 1.

f(2) = 15.

Now, g(f(2)) = 2(15) - 1.

g(f(2)) = 29.

Also given,

f(x) = x² and g(x) = x - 1.

Now, 2.f(g(x)).

2.f(g(x)) = 2.f(x- 1).

2.f(g(x)) = 2(x - 1)².

2.f(g(x)) = 2(x² - 2x + 1).

2.f(g(x)) = 2x² - 4x + 2.

2.f(g(x)) = 2x² - 2x - 2x + 2.

2.f(g(x)) = 2x(x - 1) - 2(x - 1).

2.f(g(x)) = (x - 1)(2x - 2).

There is no restriction to the domain of this quadratic function.

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Answer:

Website A is cheaper by 29 cents

Step-by-step explanation:

A

49.95 + 4.39 = 54.34

B

47.68 + 6.95 = 54.63

54.63 - 54.34 = 0.29

Answer:

the difference is 0.29 cents

website A is cheaper

Step-by-step explanation:

(47.68 + 6.95) - (49.95 + 4.39)

54.63 - 54.34 = 0.29

The evaluation of the trendline in line graph of the trendline displaying the value of a 2000 Toyota Camry since the year 2000 are as follows;

a. Independent variable; Time

Dependent variable; Value

b. The equation is; V = 22,500 - 1,166.[tex]\overline 6[/tex]·t

c. The y-intercept is at the point (0, 22,500), which indicates that the value of the 2000 Toyota Camry in the year 2,000 is $22,500

d. The slope of the trendline is -1,166.[tex]\overline {6}[/tex], which indicates that the annual reduction in the price of the 2000 Toyota Camry is $1,166.[tex]\overline 6[/tex]

e. The value of the car in 2017 based on the trendline is $2,666.[tex]\overline{6}[/tex]

A trendline is a line drawn through a scatterplot, minimizing the distances between the points in the chart and the line itself, and shows the trend of the scatterplot.

a. The independent variable is the variable that is the input variable of the function, which the researcher can vary or the value that is controlled.

Therefor;

The dependent variable is the value under study, therefore;

b. The points on the line graph are; (0, 22,500), and (15, 5,000), the slope is therefore;

m = (5,000 - 22,500)/(15 - 0) = -3,500/3

The equation is therefore;

V - 22,500 = -3,500/3·t

V = -3,500/3·t + 22,500

c. The y-intercept of the trend line is (0, 22,500), which indicates that in the year 2,000, the price of the 2,000 Toyota Camry was $22,500

d. The slope of the trend line is -3,500/3 = -1,166.[tex]\overline 6[/tex], which indicates that the value of the Toyota Camry, 2000, reduces at a rate of $1,166.[tex]\overline 6[/tex], each year.

e. In the year 2017, t = 17, therefore;

V = 22,500 - (3,500/3) × 17 = 2,666.[tex]\overline {6}[/tex]

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The sample space S for the net amount you win (after deducting the cost of pay) is S = {-$2, $1, $4, $7}.

What is cost?

A cost is the worth of money that has been expended in the production or delivery of a good or service and is therefore no longer accessible for use in accounting, retail, research, or accounting. In business, the cost may be one of acquisition, in which case the cost is the sum of the money used to obtain it.

Let, a game consists of drawing three cards at random from a deck of playing cards.

You win $3 for each red card that is drawn.

It costs $2 to play.

After deducting the cost of pay the amount will start from -$2.

For first red card drawn you win $3.

So, the amount becomes, -$2 + $3 = $1.

For second red card drawn you again win $3.

So, the next amount becomes $1 + $3 = $4.

For third red card drawn the amount becomes,

$4 + $3 = $7.

Hence, the sample space S for the net amount you win is

S = {-$2, $1, $4, $7}.

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The number of stores in each level of the shopping mall are 56 stores.

An equation is an expression that can be used to show the relationship between variables and numbers. In this case, two or more components are taken into consideration to describe the scenario. It is vital to note that an equation is a mathematical statement which is made up of two expressions that are connected by an equal sign.

Let x represent the number of stores on each level.

A shopping mall has 226 stores on 4 levels. If there are same number of stores in each level:

(4 × x) = 226

4x = 226

Divide

x = 226 / 4

x = 56.5

There are about 56 stores per level.

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