Subtracting 4 from both sides of the equation ¹/₂x = -¹/₂ gives us; ¹/₂x - 4 = -¹/₂ - 4
How to use subtraction property of equality?We want to simply the expression which is;
¹/₂x = -¹/₂
Now, when we subtract 4 from both sides, it means we are using subtraction property of equality which states that subtracting the same value from both sides of an equation makes the equation still to be equal. Thus, we have;
¹/₂x - 4 = -¹/₂ - 4
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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)
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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Match each number on the left with the correct description of the number on the right.
Answer:
im not sure the answer tho- just trying
cual es el vaolor de t-19=1
Answer:
t=20
Step-by-step explanation:
t-19=1
t-19(+19)=1+19
t=20
Solve for x.
A) 6
B) 4
C) 5
D) 7
Answer:
c
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
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.)
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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Please help me with this math quickly
The area of the shaded part is 52 sq. inches. The correct option is b. 52 sq. inches
Calculating AreaFrom 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 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?
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
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2x+9=1x-5 what is x?
Answer:
2x+9=1x-5
2x-1x=-5-9
x=-14
cual es el coeficiente de variacion de los resultados de 30,60,90,45?
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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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!
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?
Answer:
40
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
A gallon of stain is enough to cover 200 square feet of decking. Bradley has two areas of decking he would like to cover with stain. One rectangular area is 23 feet by 10.4 feet, and the other is 10.5 feet by 7.2 feet. Which expression gives the number of gallons of stain Bradley will need?
Left-bracket (23) (10.5) + (10.4) (7.2) right-bracket divided by 200
Left-bracket (23) (10.4) + (10.5) (7.2) right-bracket divided by 200
Left-bracket (23) (10.5) + (10.4) (7.2) right-bracket times 200
Left-bracket (23) (10.4) + (10.5) (7.2) right-bracket times 200
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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8.
Find the arc length of a central angle of 7pi/3 in a circle whose radius is
3inches
[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 eccentricity of the conic section shown is
Answer:
1
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.
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?
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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Determine the equation (picture).
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-interceptTherefore, 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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5. a. The area of an isosceles triangle is 60cm² and its base is 10cm. Find the length of its equal side.
Answer:
H = 12cm
b
I hope I was able to help
When
a number is
Substracted from 2, the
result equal 4 less
than one-fifth
the
of
number. Find the number
how can i got 24.8 show your work
(2x + 1) (x - 1) solve for X
Put brackets equal 0
(2x + 1) (x - 1) = 0
(2x + 1) = 0
-1, then ÷2
x = - 1/2 or - 0.5
(x - 1) = 0
+1
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) = 0There are 2 solutions for x, -0.5 and 1.
Question 13 (5 points)
Find the greatest common factor of 48a²b7 and 48a6b5z.
a.) 12a²b5
b.) 12a8b¹2
c.) 18a6b7
d.) 48a²b5
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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Need help with this question
The domain f the function is (-∞, 1/3) U (1/3, ∞)
Composite functionsThe 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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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:
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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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?
The fat percentage in the second type(40 liters) of milk is 1%
Percentagefats 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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Use the graph of the polynomial function to find the factored form of the
related polynomial. Assume it has no constant factor.
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)
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Which inequality can be used to explain why these three segments cannot be used to construct a triangle?
AC + AB > CB
AC + CB < AB
AC + CB > AB
AC + AB < CB
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.
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Answer: Option 2 or B. AC + CB < AB
Step-by-step explanation: Trust Me! It is correct on Edge!
Q: Which inequality can be used to explain why these three segments cannot be used to construct a triangle?
A: AC + CB < AB
Which point do the graphs of f and g have in common?
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:
There are three one day cricket matches between India and Australia in a week 6359 people watch with the first match 8531 people watch the second match and 10027 watch the 3rd match how many people in all watch the three matches
please help me, im struggling
Part 1
[tex]f(a)=4-7a+16a^2[/tex]
Part 2
[tex]f(a+h)=4-7(a+h)+16(a+h)^2\\\\=4-7(a+h)+16(a^2 +2ah+h^2)\\\\=4-7a-7h+16a^2 +32ah+16h^2[/tex]
Part 3
[tex]\frac{f(a+h)-f(a)}{h}=\frac{(4-7a-7h+16a^2 +32ah+16h^2-(4-7a+16a^2)}{h}\\\\=\frac{-7h+32ah+16h^2}{h}\\\\=32a+16h-7[/tex]
Complete the square to write y = 3x2 + 12x + 7 in vertex form, y = a(x - h)2 + k.
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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