Mathematics College

Can you please help me identify the property that justifies the work between step 3 and step 4

Answers

Answer 1

Answer:

Division property of inequality

Step-by-step explanation:

24<4x

24/4<4x/4

6<x

(1/4)×24 < (1/4) ×4x

6 < x

Related Questions

Question 13 (5 points)
Find the greatest common factor of 48a²b7 and 48a6b5z.
a.) 12a²b5
b.) 12a8b¹2
c.) 18a6b7
d.) 48a²b5

Answers

The greatest common factor of 48a²b⁷ and 48a⁶b⁵z is the number 48a²b⁵

What is an equation?

An equation is an expression that shows the relationship between two or more variables and numbers.

The greatest common factor is the highest number that all the numbers share.

The greatest common factor of 48a²b⁷ and 48a⁶b⁵z is the number 48a²b⁵

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(2x + 1) (x - 1) solve for X

Answers

Put brackets equal 0

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

(2x + 1) = 0

-1, then ÷2

x = - 1/2 or - 0.5

(x - 1) = 0

x = 1

So, x = - 0.5 & x = 1

Hope this helps!

Answer:

x = -0.5

x = 1

Step-by-step explanation:

Hello!

We can set each factor to 0 and solve for x in both.

(2x + 1) = 0
2x = -1
x = -0.5
(x - 1) = 0
x = 1

There are 2 solutions for x, -0.5 and 1.

8.
Find the arc length of a central angle of 7pi/3 in a circle whose radius is
3inches

Answers

[tex]\textit{arc's length}\\\\ s = r\theta ~~ \begin{cases} r=radius\\ \theta =\stackrel{radians}{angle}\\[-0.5em] \hrulefill\\ \theta =\frac{7\pi }{3}\\ r=3 \end{cases}\implies s=(3)(\frac{7\pi }{3})\implies s=7\pi \implies s\approx 21.99~in[/tex]

The graph of the parent function f(x) = x3 is translated to form the graph of g(x) = (x − 4)3 − 7. The point (0, 0) on the graph of f(x) corresponds to which point on the graph of g(x)?

(4, −7)
(−4, −7)
(4, 7)
(−4, 7)

Answers

Using translation concepts, it is found that the point (0, 0) on the graph of f(x) corresponds to point (4,-7) on g(x).

What is a translation?

A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.

Considering the translations, the equivalent point is found as follows:

x - 4 = 0 -> x = 4.y = 0 - 7 -> y = -7.

Hence the point (0, 0) on the graph of f(x) corresponds to point (4,-7) on g(x).

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centered at the origin given its...
Give the equation of the circle centered at the origin and passing through the point (0, -5).

Answers

Step-by-step explanation:

the equation of a circle centered at the origin is

x² + y² = r²

r being the radius (the distance of the center to every point on the circle's arc).

so, we get a point on the arc : (0, -5).

what is its distance to the origin ?

the origin is (0, 0).

we see, both points have the same x coordinates. they are therefore on the same vertical line going through x=0.

that means there is no distance between them in x direction.

the only distance is in y direction : 0 to -5.

a distance is always positive (no matter in what direction).

so, the distance from 0 to -5 is : 5 units.

that means r = 5.

and our equation is

x² + y² = 5² = 25

2x+9=1x-5 what is x?

Answers

Answer:

2x+9=1x-5

2x-1x=-5-9

x=-14

2x+9=1x-5
2x-1x=-9-5
x=-14

Hooke's law for an elastic spring states that the distance a spring stretches varies directly as the force applied. If a force of 11 lb stretches a certain spring 9 in., how much will a force of 22 lb stretch the spring?

Answers

Using proportions, it is found that a force of 22 lb stretches the spring 18 inches.

What is a proportion?

A proportion is a fraction of a total amount, and the measures are related using a rule of three.

The measures are direct proportional, hence the rule of three is:

11 lb - 9 inches

22 lb - n inches

Applying cross multiplication:

11n = 9 x 22

n = 9 x 2

n = 18 inches.

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cual es el vaolor de t-19=1

Answers

Answer:

t=20

Step-by-step explanation:

t-19=1

t-19(+19)=1+19

t=20

find value of t:
t - 19 = 1

t = 20

A bacteria culture grows with constant relative growth rate. The bacteria count was 1,920 after 4 hours and 1,966,080 after 12 hours.

(a) What is the relative growth rate? Express your answer as a percentage. (Round your answer to two decimal places.)

(b) What was the initial size of the culture?

(c)Find an expression for the exact number of bacteria after t hours, y(t).

(d) Find the number of bacteria after 9.5 hours. (Round your answer to the nearest whole number.)

(e) Find the rate of growth (in bacteria per hour) after 9.5 hours. (Round your answer to the nearest whole number.)

(f) How many hours did it take for the population to reach 72,000? (Round your answer to two decimal places.)

Answers

From the calculation, the growth rate is 0.88.

What is the growth rate?

To find the relative growth rate

P1 = Poe^rt

P2 = Poe^rt

Thus;

1920 = Poe^4r ------ (1)

1966080 =Poe^12r -------(2)

P2/P1 gives;

1966080/1920 = Poe^12r/Poe^4r

1024 = e^12r/e^4r

1024 =e^8r

1024 = (e^r)^8

2^10 = (e^r)^8

e^r = 2^1.25

e^r = 2.38

r = ln(2.38)

r = 0.88

The initial size of the culture is;

1920 = Poe^(0.88 * 4)

Po = 1920/e^(0.88 * 4)

Po = 57

The expression for the exact number of bacteria after t hours is

P(t) = 57e^0.08t

The growth (in bacteria per hour) after 9.5 hours is

P(t) = 57e^(0.88 * 9.5)

P(t) = 243544

For the number to reach 72,000;

72,000 = 57e^0.88t

72,000/57 = e^0.88t

ln 126 = ln[e^0.88t]

4.8 = 0.88t

t = 4.8/0.88

t = 5.5 hours

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5. a. The area of an isosceles triangle is 60cm² and its base is 10cm. Find the length of its equal side.

Answers

Answer:

H = 12cm

I hope I was able to help

Solve for x.
A) 6
B) 4
C) 5
D) 7

Answers

Answer:

Step-by-step explanation:

Aight, let's hop to it:

So we got

[tex] \frac{5x}{45} = \frac{20}{36} = = > \\ \frac{x}{9} = \frac{5}{9} = = > \\ x = 5[/tex]

and boom

The average weight of the passengers of an airline has increased from 150 pounds in 2000 to 170 pounds in 2010. If an airline used to transport 270 passengers in a plane in 2000, and the total passenger weight is fixed, approximately how many passengers can travel with the same plane in 2010?

Answers

There are 238 passengers in the plane in 2010

How to determine the number of passengers?

The given parameters are:

Weight = 150 pounds and Passenger = 270 --- Year 2000

Weight = 170 pounds --- Year 2010

Represent the parameters using the following inverse proportion

Weight * Passenger= Fixed

So, we have:

150 * 270 = 170 * Passenger

Divide both sides by 170

150 * 270/170 = Passenger

Evaluate

238 = Passenger

Rewrite as

Passenger = 238

Hence, there are 238 passengers in the plane in 2010

Answers

Answer:

im not sure the answer tho- just trying

Use the graph of the polynomial function to find the factored form of the
related polynomial. Assume it has no constant factor.

Answers

The factored form of the related polynomial is (x - 1)(x - 9)

How to determine the factored form of the related polynomial?

In this question, the given parameter is the attached graph

From the graph, we can see that the curve crosses the x-axis at two different points

These points are the zeros of the polynomial function.

From the graph, the points are

x = 1 and x = 9

Set these points to 0

x - 1 = 0 and x - 9 = 0

Multiply the above equations

(x - 1)(x - 9) = 0

Remove the equation

(x - 1)(x - 9)

Hence, the factored form of the related polynomial is (x - 1)(x - 9)

Answers

The answer choice which explains that the three segments cannot be used to construct a triangle is; AC + CB < AB.

Which inequality explains why the three segments cannot be used to construct a triangle?

Since, It follows from the triangle inequalities theorem that sum of the side lengths of any two sides of a triangle is greater than the length of the third side.

Hence, since the sum of sides AC + CB is less than AB, it follows that the required inequality is; AC + CB < AB.

Answers

The expression that we need to get is:

[tex]N = \frac{(23)*(10.4) + (10.5)*(7.2)}{200}[/tex]

So the correct option is the second one.

Which expression gives the number of gallons of stain Bradley will need?

We know that 1 gallon is enough to cover 200 ft².

We have two rectangular areas, one of:

23 feet by 10.4 feet, and other of 10.5 feet by 7.2 feet.

Then the total area is:

A = (23 ft)*(10.4 ft) + (10.5ft)*(7.2 ft)

The number of gallons needed is given by the quotient between the area that we want to cover, and the area that covers one gallon, so the expression is:

[tex]N = \frac{(23ft)*(10.4ft) + (10.5ft)*(7.2ft)}{200ft^2} \\\\N = \frac{(23)*(10.4) + (10.5)*(7.2)}{200}[/tex]

So the corerect option is the second one.

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Tom's Sports Wear is a retailer of sports hats located in Atlanta, Georgia. Although Tom's carries numerous styles of sports hats, each hat has approximately the same price and invoice purchase cost, as shown below. Sales personnel receive large commissions to encourage them to be more aggressive in their sales efforts. Currently the economy of Atlanta is really humming, and sales growth at Tom's has been great. However, the business is very competitive, and Tom has relied on its knowledgeable and courteous staff to attract and retain customers, who otherwise might go to other sports wear stores. Also, because of the rapid growth in sales, Tom is finding it more difficult to manage certain aspects of the business, such as restocking of inventory and hiring and training new salespeople.

Sales price $ 31.00
Per-unit variable costs:
Invoice cost 17.05
Sales commissions 4.05
Total per-unit variable costs $ 21.10
Total annual fixed costs:
Advertising $ 23,100
Rent 28,200
Salaries 124,200
Total fixed costs $ 175,500

The annual breakeven point in unit sales is calculated to be:

Answers

The annual breakeven point is $550157

Given that the Sales price is $ 31.00, Per-unit variable costs: Invoice cost is 17.05, Sales commissions is 4.05, Total per-unit variable costs is $ 21.10, Total annual fixed costs: Advertising is $ 23,100, Rent is 28,200, Salaries is 124,200 and Total fixed costs is $ 175,500.

The break-even point is your total fixed cost divided by the difference between the unit price and the variable cost per unit.

The sales price is $31 and the total variable cost is $21.10.

Now, we will find the Contribution margin by subtracting the Total variable cost from the sales price, we get

Contribution margin= Sales price-Total sales price

Contribution margin=31-21.10

Contribution margin=9.9

Further, we will find the contribution margin ratio by dividing the contribution margin by Sales price, we get

contribution margin ratio=contribution margin/Sales price

contribution margin ratio=9.9/31

contribution margin ratio=0.319

contribution margin ratio=31.9%

Furthermore, we will find the break-even point, we get

Break-even point=Fixed cost/contribution margin

Break-even point=175500/9.9

Break-even point=17727.27

Now, we will find the break-even sales in dollars, we get

Break-even sales=Fixed cost/contribution margin ratio

Break-even sales=(175500/31.9)×100

Break-even sales=550157

Hence, the annual breakeven point in unit sales is calculated to be $550157.

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When
a number is
Substracted from 2, the
result equal 4 less
than one-fifth
the
of
number. Find the number

Answers

Answer: 5

Explanation:

Equation from problem
2-x = 1/5x - 4

Add 4 to both sides
6-x = 1/5x

Add x to both sides
6 = 6/5x

Divide both sides by 6/5
6/6/5 = 6*5/6 = 30/6 = 5
5=x

Complete the square to write y = 3x2 + 12x + 7 in vertex form, y = a(x - h)2 + k.

Answers

The vertex form of the equation is y = 3(x + 2)^2 - 5

How to complete the square?

The equation is given as:

y = 3x^2 + 12x + 7

Set to 0

3x^2 + 12x + 7 = 0

Subtract 7 from both sides

3x^2 + 12x = -7

Divide through by 3

x^2 + 4x = -7/3

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

Take the coefficient of x

k = 4

Divide by 2

k/2 = 2

Square both sides

(k/2)^2 = 4

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

So, we add 4 to both sides of x^2 + 4x = -7/3

x^2 + 4x + 4 = -7/3 + 4

Express as perfect square

(x + 2)^2 = -7/3 + 4

Multiply through by 3

3(x + 2)^2 = -7 + 12

Evaluate

3(x + 2)^2 = 5

Subtract 5 from both sides

3(x + 2)^2 - 5 = 0

Rewrite as

y = 3(x + 2)^2 - 5

Hence, the vertex form of the equation is y = 3(x + 2)^2 - 5

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Determine the equation (picture).

Answers

The line perpendicular to the equation and has the same y-intercept with another is y = - 4 / 3 x + 4.

How to find equation of a line?

The equation of a line can be describe as follows:

y = mx + b

where

m = slopeb = y-intercept

Therefore, lines that a perpendicular follows the rule below:

m₁m₂ = -1

Hence,

y + 6 = 3 / 4 (x - 2)

y + 6 = 3 / 4 x - 6 / 4

y = 3 / 4 x - 6 / 4 - 6

y = 3 / 4 x - 30 / 4

y = 3 / 4 x - 15 / 2

Hence,

3 / 4 m₂ = -1

m₂ = - 4 / 3

Therefore,

slope of the line is - 4 / 3

Let's find the y-intercept of the second line

4x + 5y -20 = 0

5y = -4x + 20

y = -4 / 5 x + 4

y-intercept = 4

Therefore, the line perpendicular to the equation and has the same y-intercept with another is y = - 4 / 3 x + 4.

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Which point do the graphs of f and g have in common?

Answers

The point that the graphs of f and g have in common are (1,0)

How to get the points?

The given functions are:

f(x) = log₂x

and

g(x) = log₁₀x

We know that logarithm of 1 is always zero.

This means that irrespective of the base, the y-values of both functions will be equal to 0 at x=1

Therefore the point the graphs of f and g have in common is (1,0).

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Answer:

Its (1,0)

and the second one is A. F

Step-by-step explanation:

Please help me with this math quickly

Answers

The area of the shaded part is 52 sq. inches. The correct option is b. 52 sq. inches

Calculating Area

From the question, we are to determine the area of the shaded part

In the given diagram, the shaded part is a rectangle

Area of a rectangle = Length × Width

Length of the shaded part = 18 inches - 4 inches - 1 inch = 13 inches

Width of the shaded part = 6 inches - 2inches = 4 inches

Then,

Area of the shaded part = 13 inches × 4 inches

Area of the shaded part = 52 sq. inches

Hence, the area of the shaded part is 52 sq. inches. The correct option is b. 52 sq. inches

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The eccentricity of the conic section shown is

Answers

Answer:

Step-by-step explanation:

This is a U shaped graph, so the shape is a parabola

Eccentricity of any parabola is 1.

Answer:

Step-by-step explanation:

Just for some extra confrontation indeed the correct answer is 1.

Need help with this question

Answers

The domain f the function is (-∞, 1/3) U (1/3, ∞)

Composite functions

The composite functions are also known as function of a function

Given the following functions

f(x) = √2-6x

g(x) = -1/x

In order to determine the composite function g(f(x))

g(f(x)) = g(√2-6x)

Replace x with √2-6x in g(x)

g(f(x)) = -1/√2-6x

The expression does not exist when √2-6x = 0

2-6x = 0

x = 1/3

The values shows that the domain of the function exists on all real numbers except 1/3.

Hence the domain f the function is (-∞, 1/3) U (1/3, ∞)

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The function y=f(x)is graphed below. What is the average rate of change of the function f(x) on the interval 7≤x≤8?

Answers

Answer:

Step-by-step explanation:

the average rate of change of f(x) in the closed interval [ a, b ] is

[tex]\frac{f(b)-f(a)}{b-a}[/tex]

here [ a, b ] = [ 7, 8 ] , then

f(b) = f(8) = 20 ← point (8, 20 ) on graph

f(a) = f(7) = - 20 ← point (7, - 20 ) on graph

average rate of change = [tex]\frac{20-(-20)}{8-7}[/tex] = [tex]\frac{20+20}{1}[/tex] = 40

I know question on central limit theorem has been asked numerous times
and I have searched around the website but still couldn't get what I wanted
to find out(probably most people who asked the question is stuck at
different parts of the theory).
Attached in my question is a lecture slide for the search for a
transformation of x that has a limiting distribution.I do not understand
why x and u is multiply by vn instead of n.Also,why when the statistic /n(x
-μ）is used，μbecomes zero?
Thank you in advance!

Answers

So basically take the N in add it to the 0 or that o and then times it by 7

A person mixed 80l milk with 2% fat and 40l milk together. If the fat amount in the whole mixture is 3%, what is the fat percentage in the second type of milk?

Answers

The fat percentage in the second type(40 liters) of milk is 1%

Percentage

fats in 80 liters milk = 2% fat40 liters = x % fatTotal fat = 3%

Fats in 40 liters of milk = Total fat - fats in 80 litrrs milk

= 3% - 2%

= 1%

Therefore, the fat percentage in the second type of milk is 1%

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how can i got 24.8 show your work

Answers

I hope this helpssssss:)

in the diagram , what is the value of x

Answers

The value of x from the given diagram is 100 degrees

Sum of interior angle

From the given diagram, we will use the theorem "angle at the vertex is half that at the centre.

<50 = 1/2 x

Cross multiply

50 * 2 = x

x = 50 * 2

x = 100 degrees

Hence the value of x from the given diagram is 100 degrees

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cual es el coeficiente de variacion de los resultados de 30,60,90,45?

Answers

based on the given results, the coefficient of variation can be found to be 45.54.

what is the coefficient of variation?

first, find the mean:
= (30 + 60 + 90 + 45) / 4

= 56.25

find the standard deviation using a spreadsheet:

= 25.61737691

the coefficient of variation is therefore:

= standard deviation / mean x 100

= 25.61737691 / 56.25 x 100

= 45.54

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