100 points, please help
In 8-11, write a justification for each conclusion.

Answer:

(a) 75 minutes

(b) 50 minutes

A component of the interval is x (π/4, 5π/4) when 5 sin(x) > 5 cos(x).

A relation in mathematics that compares two numbers or even other mathematical expressions in an unequal way is known as an inequality. When comparing two numbers on a number line, it is most frequently used to compare their sizes.

5 sin(x) > 5 cos(x)

To removing constant we divide both the side by 5:

5sin(x) > 5 cos(x)

sin(x) >  cos(x)

sin x > cos x;

sin x = cos x; tan x = 1; x = π/4 or x = 5π/4

sin x > cos x for x ∈ (π/4, 5π/4)

A component of the interval is x (π/4, 5π/4) when 5 sin(x) > 5 cos(x).

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I understand that the question you are looking for is:

Find all values of x in the interval [0, 2] that satisfy the inequality. (Enter your answer using interval notation.) 5 sin(x) > 5 cos(x)

El grafico de la ecuación lineal se puede ver en la imagen al final.

En este caso queremos graficar la ecuación lineal:

5y - 15 = -4x

Para ello debemos encontrar dos puntos en la linea, y para hacer eso podemos evaluar en dos valores de x.

Sí x = 0 obtenemos:

5y - 15 = -4*0

5y = 15

y = 15/5 = 3

Sí x= 5 obtenemos:

5y - 15 = -4*5

5y = -20 + 15

5y = -5

y = -5/-5 = -1

Entonces solo tenemos los dos puntos (0, 3) y (5, 1), ahora debemos graficar estos en un eje de coordenadas y trazar una linea que pase por ambos, como en el ejemplo de abajo.

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The graph of function f(x) = [tex]2^{x}[/tex] + 3 will be increases without bound As x increases without bound and As x decreases without bound, f(x) approaches the line y = 3 therefore option (C) and (D) will be correct.

A graph is a diametrical representation of any function between the dependent and independent variables.

The graph is easy to understand behavior of the graph.

Given the function,

f(x) = [tex]2^{x}[/tex] + 3

At x = 0 → f(0) = 2⁰ + 3 = 3

This is an exponential function as shown below which will be increasing as x increase while it will gain the value y = 3 as x decrease.

Hence "The graph of function f(x) = [tex]2^{x}[/tex] + 3 will be increases without bound As x increases without bound and As x decreases without bound, f(x) approaches the line y = 3".

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The number of people who would prefer Choco chocolate chip  is 120.

Ratio expresses the relationship between two or more numbers. It shows the frequency of the number of times that one value is contained within other value(s).

In order to determine the number of people who would prefer Choco chocolate chip , multiply the given ratio of people who prefer Choco chocolate chip by the total number of people in the group.

The number of people who would prefer Choco chocolate chip = (ratio of people who prefer choco / sum of ratios) x number of people

(3/5) x 200 = 120

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The total cost for going to the concert = $90.

The loss of value or benefit that'd result from engaging in a particular activity option in comparison to engaging in such an alternative activity which offers a higher come back on value or benefit is referred to as opportunity cost. The value of the best alternative picked during the decision-making process is provided.

We can select the best option out of all the options available with the aid of the idea of opportunity cost. It helps us use all of our resources as skillfully and productively as possible in order to maximize our financial gains.

For her part-time job, Karen receives a $10 hourly wage. The cost of the concert ticket after the discount is $50, so she decided to go.

It will cost money to take four hours off work. $10 x 4

                                                                           =$40

Opportunity costs of going to the concert = $50 + $40

                                                                      = $90

It is evident that the opportunity cost will be $90.

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I understand that the question you are looking for is:

Karen earn $10 per hour. she wants to go to a concert on Saturday and the price of the ticket is $75, but her friend sold her a ticket for $50. if Karen had to take 4 hours off of work to attend the concert ,What was her opportunity cost of attending the concert?

a.$40

b.$50

c.$75

d.$90

If 1/2 cup of soup equals 120 milliliters, then there are 780 milliliters in

3 1/4 cups of soup.

A milliliter is a metric unit that is abbreviated as ml and is used to measure volumes for liquid and gas states. It is usually used to measure smaller volumes of liquids as it is equal to 1/1000 of a liter.

We can find the milliliters in 3 1/4 cups of soup as follows:

1/2 cup of soup = 120 milliliters

As 1/2 = 0.5

We can rewrite it as:

0.5 cup of soup = 120 milliliters

3 1/4 cups = 3.25 cups

Consider milliliters in 3 1/4 cups = x

Therefore,

0.5 cup = 120 ml

3.25 cups= x

Cross multiply to find x,

0.5 x = 120x3.25

0.5 x = 390

x= 390/0.5 = 780 milliliters

Hence it is found that 3 1/4 cups of soup is equal to 780 milliliters.

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Answer:

-8/3 < -2 1/2 < 9/2 < 4 3/4

Step-by-step explanation:

-2.667 < -2.5 < 4.5 < 4.75

Blue whale is 15 times longer than otter.

To find how many times the blue whale is  longer than the otter, we will perform division. We will divide the length of blue whale by length of otter, which we will give us the desired result.

Now, performing calculation as per the above statements -

Number of times longer length = [tex]\frac{3*10^{4} }{2*10^{3} }[/tex]

Performing division of numbers. Also, as we know, on division the exponents are subtracted. Hence, subtracting the exponents to get the desired result.

Number of times longer length = 1.5*[tex]10^{4-3}[/tex]

The result will be -

Number of times longer length = 1.5*10

Performing multiplication -

Number of times longer length = 15

Hence, we get that blue whale is 15 times longer than otter.

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The expressions that simplifies to 41 are:

a) 10 + 2³ * 4 - 1

d) 10 + (2³ * 4) - 1

Information about the problem:

a) 10 + 2³ * 4 - 1

b) 10 + 2³ * (4 - 1)

c) (10 + 2³) * 4 - 1

d) 10 + (2³ * 4) - 1

We solve the equations respecting the level of hierarchy:

a) 10 + 2³ * 4 - 1

10 + 8*4 - 1

10 + 32 - 1

42 - 1

41 (it applies)

b) 10 + 2³ * (4 - 1)

10 + 8 * (3)

10 + 24

34 (it doesn't applies)

c) (10 + 2³) * 4 - 1

(10 + 8) * 4 - 1

18*4 - 1

72 - 1

71 (it doesn't applies)

d) 10 + (2³ * 4) - 1

10 + (8*4) - 1

10 + 32 -1

42 - 1

41 (it applies)

We can say that they are the set of numbers and symbols that are related by the different mathematical operation signs such as addition, subtraction, multiplication, division among others.

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Answer: 1.42 x 10^1

Step-by-step explanation:

Answer: 1.42x10

Step-by-step explanation:

Answer:

1.5797 x 10^-4

Step-by-step explanation:

Answer:-41/4 try that

Final answer obtained is 2/3

A geometric progression, sometimes referred to as a geometric sequence in mathematics, is a series of non-zero numbers where each term following the first is obtained by multiplying the preceding one by a constant, non-zero value known as the common ratio. For instance, the geometric progression 2, 6, 18, 54, etc. has a common ratio of 3. Similar to that, the geometric series 10, 5, 2.5, 1.25,... has a common ratio of 1/2.

Powers [tex]r^{k}[/tex] of a given non-zero number r, like [tex]2^{k}[/tex] and [tex]3^{k}[/tex], are examples of a geometric sequence. A geometric sequence's basic structure is

[tex]ar,ar^{2},ar^{3}.ar^{4},-----[/tex]

where a is not equal to 0 is a scale factor that is equal to the initial value of the series and r is not equal to 0 is the common ratio.

A series is a sum, whereas a progression is a sequence. This is the difference between the two.

∑[tex]_{i=0}^{n}[/tex] [tex]ar^{i}=\frac{a(1+r^{n+1})}{1-r}[/tex]

We see that n= 99, r= -1/2, a=1

∑[tex]_{i=0}^{99}[/tex] [tex](\frac{-1}{2}) i=[/tex] [tex]\frac{1-(\frac{-1}{2})^{99+1} }{1-\frac{1}{2} }=\frac{1-(\frac{-1}{2})^{100} }{1+\frac{1}{2} }=\frac{1-\frac{1}{2}^{100} }{\frac{3}{2} }[/tex]

[tex]=\frac{\frac{2^{100}}{2^{100}} -\frac{1}{2^{100}} }{\frac{3}{2} } =\frac{2*(2^{100}-1)}{3*2^{100}}[/tex]

[tex]\frac{2*(2^{100}-1)}{3*2^{100}}[/tex]

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Answer:

The first rectangle is 3x² - 6x + 13 more square feet then the second rectangle

Step-by-step explanation:

A rule for subtracting polynomials

Steps

At the end of the expression is (7x²- 4x + 12) + -4x² - 2x + 1

At this point you combine like terms like you do with adding polynomials so ( 7x² + (-4x²) is 3x², (-4x) + (-2x) is (-6x), and 12 + 1 is 13) so the final answer would be 3x²-6x+13

Answer:

B

it is the right equation

Answer:

2, 20, 200, 2,000, 20,000, 200,000

Answer: 0.2, 0.02 0.002

The area of the parallelogram ABCD with the vertices is 40 square units

The vertices are given as

(2, 3), B (7, 3), C (8, -5), and D (3, -5)

From the graph, we have the following dimensions

Base = 5 units i.e. distance AB

Height = 8 units i.e. the distance between the parallel sides

The area of the parallelogram is then calculated as

Area = Base * Height

So, we have

Area = 5 * 8

Evaluate

Area = 40

Hence, the area of the parallelogram ABCD with the vertices is 40 square units

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Step-by-step explanation:

In the equation y = mx + b for a straight line, the number m is called the slope of the line. In the equation y = mx + b for a straight line, the. number b is called the y-intercept of the line.

1.2 because you take 2 congruent sides of each shape and divide the larger one by the small one. in this example you could do

8.4÷7

36.6÷30.5

19.2÷16

they all give you 1.2

Answer:

Hello,

Step-by-step explanation:

1. We must decompose the conic into 2 lines.

[tex]f(x,y)=x^2-5xy+y^2+5x-2y+1=0\\\\We\ are\ going\ to\ find\ the\ center\\\\\left\{\begin{array}{ccc}\dfrac{ \partial{f} }{\partial{x} }&=&12x-5y+5=0\\\\\dfrac{ \partial{f} }{\partial{y} }&=&-5x+2y-2=0\\\end {array} \right.\\\\\\\left\{\begin{array}{ccc}x=0\\y=1\\\end {array} \right.\\\\We\ must\ find\ an\ other\ point\ of\ f(x,y).\\\\if\ y=0\ then\ x=\dfrac{-1}{2} \ or\ x=\dfrac{-1}{3}[/tex]

The 2 lines are: 2x-y+1=0 and 3x-y+1=0

Paralleles are y=2x and y=3x

Perpendiculars are x+2y=0 and x+3x=0

Step-by-step explanation:

could it be that the equation is rather

-5 = (-8 + v)/3

?

that is a huge difference ...

to solve such an equation we keep transforming it (every change we make we have to do on both sides of the equation to keep the equality), until we have only the variable on one side, and everything else (which is then the solution) on the other side.

1st step : we get rid of the "/3" by multiplying both sides by 3.

that gives us

-5×3 = ((-8 + v)/3)×3 via the multiplication property.

2nd step : we simplify

-15 = -8 + v

3rd step : we get rid of the -8 on the side of the variable by adding 8 to both sides.

that gives us

-15 + 8 = -8 + 8 + v via the addition property.

4th step : we combine like terms (or simplify, if we can use it a second time) :

-7 = 0 + v

-7 = v

that's it.

Answer:

y = [tex]\frac{1}{4}[/tex] x + 6

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

given

4x + y = 7 ( subtract 4x from both sides )

y = - 4x + 7 ← in slope- intercept form

with slope m = - 4

given a line with slope m then the slope of a line perpendicular to it is

[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{-4}[/tex] = [tex]\frac{1}{4}[/tex] , then

y = [tex]\frac{1}{4}[/tex] x + c ← is the partial equation of the perpendicular line

to find c substitute )- 4, 5 ) into the partial equation

5 = - 1 + c ⇒ c = 5 + 1 = 6

y = [tex]\frac{1}{4}[/tex] x + 6 ← equation of perpendicular line

Answer:

156, because the mean is 13, and the mean in equal to all of the numbers added up and divided by how many numbers there are.

Answer: (2, -3)

Step-by-step explanation:

To get these points, you just need to multiply the coordinates by 1/4, or divide by 4

Yes,  the moving boxes will fit in this volume.

The current volume of box :

Volume = height * width * depth

Volume = 12 * 9 * 2

Volume = 216 in³

New dimension :

Height and volume are the same

Width = 9 - 1 = 8

Depth = x

Volume = height * width * depth

216 = 12 * 8 * x

216 = 96x

x = 216 / 96

x = 2.25 inch

Volume is a measurement of three-dimensional space that is occupied. It is frequently expressed mathematically using imperial or SI-derived units. Volume and the notion of length are connected.

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Answer:

multiples of 14

Step-by-step explanation:

we multiply 7×2

If n =12 then there are 50 person who can sit .

Hexagonal - In geometry, a hexagon is a closed two-dimensional six-sided polygon. It is made up of six line segments and six vertices that form six internal angles. The sum of all the internal angles of a hexagon is 720°.

Each table seats 4 people, which can be represented with n,plus two more people at either end of the set of tables. The table is hexagonal and so can seat 6 people. So, the given equation defines this situation.

The number of people who can sit at the tables increases by 4 each time a table is added

P=4n+2

the given equation to find the number of tables n.

P=4n+2

Where P = person

and n= no of tables .

given that

n=12

put value of n in equation to find the no. of person .

P = 4(12) +2

P = 48 +2

P = 50.

Hence,in this given seating arrangement 50 person can sit on 12 tables. .

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