Answers
Answer:
1,2,3,4,6,8,12,24 sub set
Related Questions
Resuelva:
1) |3 x-1|-|2 x+5-(5-x)|=0
2) |2(x+1)-4|=|2-2(2-x)|
3) |x-2/4|-1/3=x
4) 1/2|x-3|-1=|x-3|+2
Answers
The absolute functions |3x - 1| - |2x + 5 - (5 - x)| = 0, |2(x + 1) - 4| - 4| = |2 - 2(2 - x)|, |(x - 2) / 4| - 1/3 = x and 1/2|x - 3| - 1 = |x - 3| + 2 have solutions of 1/6, 1, 2/15 and no solutions respectively
Absolute FunctionAn absolute value function is a function in algebra where the variable is inside the absolute value bars. This function is also known as the modulus function and the most commonly used form of the absolute value function is f(x) = |x|, where x is a real number. Generally, we can represent the absolute value function as, f(x) = a |x - h| + k, where a represents how far the graph stretches vertically, h represents the horizontal shift and k represents the vertical shift from the graph of f(x) = |x|. If the value of 'a' is negative, the graph opens downwards and if it is positive, the graph opens upwards.
In the questions given;
1) |3x - 1| - |2x + 5 - (5 - x)| = 0
x = 1/6
2) |2(x + 1) - 4| - 4| = |2 - 2(2 - x)|
x = 1
3) |(x - 2) / 4| - 1/3 = x
x = 2 / 15
4) 1/2|x - 3| - 1 = |x - 3| + 2
The equation has no solution
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On a recent trip to the convenience store, you picked up 3 gallons of milk, 4 bottles of water, and 7 snack-size bags of
chips. Your total bill (before tax) was $23.40. If a bottle of water costs twice as much as a bag of chips, and a gallon of
milk costs $2.20 more than a bottle of water, how much does each item cost?
Answers
Answer:
Chips are $0.80 a bag
A bottle of water is $1.60
A gallon of milk costs $3.80
Step-by-step explanation:
Answer:
$3.80 = cost of one gallon of milk.
$1.60 = cost of one bottle of water.
$0.80 = cost of one snack-size bag of chips.
Step-by-step explanation:
Define the variables:
Let x = one gallon of milk.Let y = one bottle of water.Let z = one snack-size bag of chips.Total items purchased:
3 gallons of milk.4 bottles of water.7 snack-size bags of chips.Given information:
Total bill (before tax) = $23.40.A bottle of water costs twice as much as a bag of chips.A gallon of milk costs $2.20 more than a bottle of water.Create a system of equations with the given information:
[tex]\begin{cases}3x+4y+7z=23.40\\y=2z\\x=y+2.20\end{cases}[/tex]
Rearrange the second equation to make z the subject:
[tex]\implies z=0.5y[/tex]
Substitute the found expression for z and the third equation into the first equation and solve for y:
[tex]\implies 3(y+2.20)+4y+7\left(0.5y\right)=23.40[/tex]
[tex]\implies 3y+6.6+4y+3.5y=23.4[/tex]
[tex]\implies 10.5y+6.6=23.4[/tex]
[tex]\implies 10.5y=16.8[/tex]
[tex]\implies y=1.60[/tex]
Substitute the found value of y into the third equation and solve for x:
[tex]\implies x=1.60+2.20[/tex]
[tex]\implies x=3.80[/tex]
Substitute the found value of y into the second equation and solve for z:
[tex]\implies 1.60=2(z)[/tex]
[tex]\implies z=0.80[/tex]
Conclusion:
$3.80 = cost of one gallon of milk.$1.60 = cost of one bottle of water.$0.80 = cost of one snack-size bag of chips.Write the point-slope form of the equation of the line that passes through the points (6, -9) and (7, 1). a. Using variables, write out the formula for the point-slope form of the equation. b. Determine the slope of the line. c. Write the point-slope form of the line. Show all work on how you found the slope. Use the box provided to submit all of your calculations and final answers. Simplify the answer as needed.
Answers
The point slope form of the equation of the line that passes through the points (6, -9) and (7, 1) is y - 1 = 10(x - 7)
How to represent equation in point slope form?Linear equation can be represented in different form such as point slope form, slope intercept from, standard form and general form.
The line passes through the points (6, -9) and (7, 1). The point slope form can be represented as follows:
y - y₁ = m(x - x₁)
where
m = slopex₁ and y₁ are variablesTherefore, let's find the equation of the line that passes through the points (6, -9) and (7, 1).
Let's find the slope.
slope = m = 1 + 9 / 7 - 6
slope = 10 / 1
slope = 10
Therefore,
y - 1 = 10(x - 7)
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a group of friends were working on a student flim. they spent $504 on props, which was 42% of their total budget. What was the total budget for the student film.
Answers
Answer:
1200 dollars
Step-by-step explanation:
1.) Create an equation. If we use x as a variable for the total money, we get [tex]\frac{504}{x}=\frac{42}{100}[/tex] .
2.) By solving this equation, we get 42x = 50400, and x = 1200.
Therefore, their total budget was 1200 dollars.
Write the equation of the linear relationship in slope-intercept form.
The equation that represents this relationship is y =
(select)
Answers
The equation of the linear relationship in slope-intercept form is: y = 2/3x + 50/3.
How to Write the Equation of a Linear Relationship in Slope-intercept Form?The equation in slope-intercept form for a linear relationship can be expressed as y = mx + b, where the slope is m and the y-intercept is b.
Using two points on the graph, (20, 30) and (50, 50), find the slope:
Slope (m) = change in y / change in x = (50 - 30) / (50 - 20)
Slope (m) = 20/30
Slope (m) = 2/3.
Find the y-intercept (b) by substituting m = 2/3 and (x, y) = (20, 30) into y = mx + b:
30 = 2/3(20) + b
30 = 40/3 + b
30 - 40/3 = b
50/3 = b
b = 50/3
Write the equation of the linear equation in slope-intercept form by substituting b = 50/3 and m = 2/3 into y = mx + b:
y = 2/3x + 50/3
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Does the equation describe a function?
y=8
yes or no?
Answers
Yes, the equation:
y = 8
describes a function.
Does the equation describe a function?A function is a relation that maps elements x into elements y, such that each element x is mapped into a single value of y.
In this case, we have the equation:
y = 8
So all our points are of the form (x, 8).
Notice that all the inputs x are mapped into a single output y = 8, then this relation is a function.
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A drink has the ratio 3 parts orange juice to 6 parts mango juice. If you have 4 litres of orange juice to use, how much mango juice do you need?
Answers
The amount of mango juice you need is 8 litres
How to determine the amount of mango juice needed?From the question, we have the following parameters that can be used in our computation:
Orange juice = 3 parts
Mango juice = 6 parts
When these parameters are represented as ratio, we have the following expression
Ratio = Orange : Mango
This is then represented as
Orange : Mango = 3 : 6
When the litres of orange juice is 4, we have
4: Mango = 3 : 6
Express as fraction
Mango/4 = 6/3
Multiply through by 4
Mango = 4 * 6/3
Evaluate
Mango = 8
Hence, the mango juice is 8 litres
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3. What is the proper ordering
(from greatest to least) of the
following numbers?
I.58/67
II. 0.58%
III. 58%
IV. 5.8%
O I, III, II, IV
III, IV, II, I
I, III, IV, II
IV. I. III. II
Answers
The proper order from greatest to least is option (C) I, III, IV and II
Convert each term to the decimal form
The first terms is 58/ 67
58 / 67 = 0.87
The second term is 0.58%
Convert the percentage to simple fraction
0.58% = 0.58 / 100
= 0.0058
The third term is 58%
Convert the percentage to simple fraction
58% = 58/100
= 0.58
The fourth term is 5.8%
Convert the percentage to simple fraction
5.8% = 5.8/100
= 0.058
The order from greatest to least is
0.87 > 0.58 > 0.058 > 0.0058
Hence, the proper order from greatest to least is option (C) I, III, IV and II
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The values of l, ll, lll, lV respectively,
→ 58/67, 0.58%, 58%, 5.8%
→ 0.87, 0.0058, 0.58, 0.058
Arranging them in descending order,
→ 0.87 > 0.58 > 0.058 > 0.0058
→ 0.87, 0.58, 0.058, 0.0058
→ l, lll, lV, ll
Therefore, the option (c) is correct.
Find the area and the circumference of a circle with radius 7 m.
Use the value 3.14 for π, and do not round your answers.
Area=?
Circumference=?
Answers
Answer:
[tex]Area = 153.938040026m^2[/tex]
[tex]Circumference= 43.9822971503m[/tex]
Step-by-step explanation:
Area
[tex]Area = \pi r^2\\Area = \pi *7^2\\Area = 49\pi\\Area = 153.938040026[/tex]
Circumference
[tex]C = 2\pi r\\C = 2\pi*7\\C= 14\pi\\C=43.9822971503[/tex]
Please solve and send good quality picture xx
Answers
Answer:
See attached file
Step-by-step explanation:
See attached file for the answer!
If you need help with more like these, I would suggest checking out Khan Academy.
They provide great free videos on every topic you could imagine!
Hope this helped!
4. Four years ago, Melody was one fourth as old as her sister was then. In six years, Melody will be half as old as her sister will be then. Find their ages now.
5. The sum of the digits of a fwo-digit number is 12. The value of the number is 6 less than 5 times the units digit. Find the number.
6. Hannah likes to spend her free time hanging out at the airport. She likes to run on the walkways. While running with the walkway, she can cover 48 feet in 3 seconds. While running against the walkway, she can cover 24 feet in 2 seconds. Find Hannah's rate (in feet per second) if the walkway stopped moving.
Answers
The present age of Melody is 9 and her sister is 24 .
the two digit number is 39
How to find the ages of a person ?
Consider the difference between the individual's birthdate and the present day: days = current day - birth date. Age = (years 365) + (months 31) + days should be replaced with these variations. The individual's age is expressed in days. To get the age in years, divide the outcome by 365.
Let present age of melody be y and her sister age be x
Four years ago age of Melody be (y - 4) and her sister age be (x - 4)
After six years age of Melody be (y + 6) and her sister age be (x + 6)
∴ [tex]\frac{(x-4)}{4} = (y - 4)[/tex]
[tex]\frac{(x+6)}{2} = (y + 6)[/tex]
The equation becomes
x + 6 = 2y + 12
x = 2y +6 ⇒ (1)
x - 4 = 4y -16
x = 4y - 12 ⇒(2)
Solving (1) and (2)
x - 2y = 6
x - 4y = -12
2y = 18
y = 9
Substituting the value of y in eq(1)
x = 2*9 + 6
x = 18 +6
x = 24
Let xy be the two digit number.
10x + y
The value of this number is 6 less (-6) than five times the unit digit (5y). So:
10x + y = 5y - 6
The sum of the digits of the 2-digit number is 12:
x + y = 12
So y = 12 - x
Substitute 12-x for y:
10x + y = 5y - 6
10x + 12 - x = 5(12-x) - 6 [Substituted 12-x in place of y]
9x + 12 = 60 - 5x - 6
14x = 42
x = 3
y = 12 - x
= 12 - 3
= 9
The two digit number is 39
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Please HELP MEE ms. Williams wrote a test. part a had true/false questions, each worth 6 points. part b had multiple choice questions, each worth 8 points. she made the number of points for part an equal to the number of points for part b. it was the least number of points for which this was possible.
Answers
The amount of points of each question in each part are given as follows:
Part A: 6 points.Part B: 8 points.It is stated in the problem that:
Both parts have the same number of points.The amount of points of each part is the least amount of points for which this was possible.Hence the amount of points of each part is the least common multiple of 6 and 8, obtained by factoring by prime factors as follows:
6 - 8|2
3 - 4|2
3 - 2|2
3 - 1|3
1
Hence:
lcm(6,8) = 2³ x 3 = 24.
Meaning that each part was worth 24 points, and the number of questions is given as follows:
Part A: 24/6 = 4 questions.Part B: 24/8 = 3 questions.More can be learned about the least common factor at brainly.com/question/10749076
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Linday scored a 10-ring hit in 80% of her 30 attempts during archery match. In order to find the number of rooms they rented, what do you need to find?
A. The part
B. The whole
C. The percent
D. Benchmark percent
Answers
A. The. part
B. The. whole
C. The. People
D. Benchmark. percent
Is this right? I need help! I need the correct answers Ill give you 58 pts and brainliest to the first correct!
Answers
Answer:
its right
Step-by-step explanation:
Answer: Its right i just got the same question
Step-by-step explanation:
a triangle ABC angle ABC =90 has length of the side AB= 72 cm and the length of BC = 54cm what is the length of the perpendicular line from side AC to point B?
Answers
The length of the perpendicular line from side AC to point B is approximately 43cm to the nearest whole number using the trigonometric ratio of sine rule.
What is trigonometric ratios?The trigonometric ratios is concerned with the relationship of an angle of a right-angled triangle to ratios of two side lengths.
The basic trigonometric ratio of sine to be used states that for any triangle say ABC, then (a/sinA) = (b/sinB) = (c/sinC) where a,b, and c are the sides.
Considering right-angled triangle ABC, by Pythagoras rule
AC = √(54² + 72²)
AC = √1800
AC = 90°
so using sine rule;
AC/sinB = AB/sinC
90/sin90 = 72°/sinC
C = sin^-1[(72°×sin90°)/90°] {cross multiplication}
C = 53.13°
The new triangle formed has hypotenuse 54cm with the opposite side as the length of the perpendicular line from side AC to point B(which we can call x)
hence;
sinC = x/54
sin53.13° = x/54
x = 54 × sin53.13° {cross multiplication}
x = 43.2cm
Therefore, the length of the perpendicular line from side AC to point B is approximately 43cm to the nearest whole number, by application the trigonometric ratio of sine and it's rule for triangle.
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What is the hardest part of AP stats?
Answers
AP Statistics students generally scored very well on questions about Units 1, 2, and 3, with 18% of students answering all such questions correctly.” “The most challenging units were 4 (Probability, Random Variables, and Probability Distributions) and 5 (Sampling Distributions).
Hope it helps you.
The hardest part of AP stats is Physics 1, AP U.S. History and AP Chemistry.
What AP course is the most difficult?The course and exam for AP Statistics frequently prove to be difficult, especially for students who have not previously taken algebra II or calculus.
Newtonian mechanics, electrical charge and force, and other subjects are covered in AP Physics 1, which is regarded as one of the hardest AP courses. Students also complete college-level lab experiments and write reports for around 25% of the class period.
In general, AP Statistics students do find it hard or difficult in "Probability, Random Variables, and Probability Distributions Unit 4 and Unit 5.
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Girard buys 9 tons of rocks to build a long rock wall. Each section
of the wall weighs 500 pounds, or ¼
ton. How many sections can
Girard build?
Answers
Answer: 36
Step-by-step explanation:
4 sections are 2,000 lbs or 1 ton
To find the pounds Girard has to build, we know we have 9 tons, therefore if each ton is 2,000 lbs, multiply 2,000 by 9 to get 18,000 lbs to use
2,000 lbs per ton x 9 tons= 18,000 lbs to use
now take the 18,000lbs and divide by 500 to find the number of sections we can build
18,000lbs / 500 pounds per section = 36
36 sections is the answer
You are baking chocolate chip cookies. One batch makes 5 dozen big cookies. The recipe calls for 3/4 cup brown sugar. How many cups of brown sugar would you need it you wanted to make 13 dozen cookies?
Answers
Answer:
1 [tex]\frac{19}{20}[/tex] cups
Step-by-step explanation:
[tex]\frac{cookies}{sugar}[/tex] = [tex]\frac{cookies}{sugar}[/tex]
[tex]\frac{5}{\frac{3}{4} }[/tex] = [tex]\frac{13}{x}[/tex] Cross multiply and solve for x
5x = (13)([tex]\frac{3}{4}[/tex])
5x = [tex]\frac{39}{4}[/tex] Divide both sides by 5
x = [tex]\frac{39}{4}[/tex]÷5
x = [tex]\frac{39}{4}[/tex] x [tex]\frac{1}{5}[/tex]
x = [tex]\frac{39}{20}[/tex]= 1 [tex]\frac{19}{20}[/tex]
Does the equation describe a function? y=8
Answers
The equation y = 8 does not describe a function
How to determine if an equation describes a function?
A function is an equation that has only one output or answer (y) for every input (x) e.g y = 2x
If we plot y =8 on a coordinate plane, you would see that at the point of (0, 8) is a horizontal line.
Also, no matter the value of the input (x), the value of when of the output (y) will always remain 8. This does not fit the description of a function
Therefore, the equation y =8 does not describe a function
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100 POINTS + BRAINLIEST IF CORRECT
See attached screenshot
Answers
Answer:
[tex] p(x)= -2x^3-4x^2+6x[/tex]
Step-by-step explanation:
We need to write a polynomial with zeroes -3 , 0 and 1 , with a leading coefficient of 2 . We know that if a polynomial has 3 zeroes say [tex]\alpha[/tex] , [tex]\beta[/tex] and [tex]\gamma[/tex] , then the polynomial can we written as ,
[tex]\longrightarrow p(x) = k[ ( x -\alpha)(x-\beta)(x-\gamma)] [/tex]
where k is a constant , and here k = -2 .So , similarly we can write it as;
[tex]\longrightarrow p(x) = -2[ (x -(-3)) (x-0) (x-1)\\[/tex]
Simplify,
[tex]\longrightarrow p(x) = - 2[ (x+3)(x)(x-1) ]\\[/tex]
[tex]\longrightarrow p(x) = -2[ (x^2+3x)(x-1)]\\[/tex]
[tex]\longrightarrow p(x) = -2[ x(x^2+3x)-1(x^2+3x)\\ [/tex]
[tex]\longrightarrow p(x) = -2[ x^3 +3x^2 -x^2-3x ]\\[/tex]
[tex]\longrightarrow p(x)= -2[ x^3 +2x^2 -3x]\\[/tex]
[tex]\longrightarrow\underline{\underline{ p(x)= -2x^3-4x^2+6x }} [/tex]
And we are done!
solve ((-3) x (10 + (-7))) to the power of 2 divided by 3 - (-9) to the power of 2)
Answers
The solution of the given expression will be 9/16.
What is an expression?Expressions in maths are mathematical statements that have a minimum of two terms containing numbers or variables, or both, connected by an operator in between.
Given an expression, [-3*(10+(-7))]²÷[(3-(-9)]²
= [-3*(10+(-7))]²÷[(3-(-9)]² = (-9)²/12²
= 9/16
Hence, The solution of the given expression will be 9/16.
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1) A bus stops every 400m. How many stops does it make in travelling a distance of 20kmaround a city?
2: A kitchen garden is made up of a rectangle and a square as shown in Fig. 4.2. What is the perimeter of the garden in
(a) metres?
(b) centimetres?
Answers
Answer: 1. 50 stops.
Step-by-step explanation:
There is 1,000 meters in a Kilometer. So 20,000/400=50
Answer:
1) 50 stops
2) a: 60 meters
b: 6,000 centimeters
Step-by-step explanation:
A) we have to convert 20k into meters to solve it
To do that we multiply by 1000
20x1000
20,000 meters now we divide by 400 to see how many stops
20,000/400
50 stops
2)
to find perimeter is meters we add all of the sides together
20+10+5+5+15+5
30+10+20
30+30
60 m is the perimeter
Now in centimeters we multiply by 100
60x100
6,000 centimeters
Hopes this helps please mark brainliest
When a tree is planted in an orchard, it is 78 cm tall. Every year, the tree's height increases by 8%
. Which of the following formulas could be used to calculate the height of the tree n
years after planting?
Note that when n=0, the height of the tree is 78 cm.
Answers
Answer:
78(0.08n)+78
The answer options might not look exactly like this, it may be in different orders but if all these numbers are there like this it should be right
Step-by-step explanation:
When you are increasing by a percent you always turn the percent to a decimal is a formula
8%=0.08
This can be multiplied by n to show how many years
0.08n
And we multiply this by 78 since it’s 8 percent of this
78(0.08n)
And now we add 78 since the tree starts off as 78
78(0.08n)+78
Also to check when n=0 the height will be 78
78(0.08(0)+78
78(0)+78
78
Hopes this helps please mark brainliest
Find x to make an equation that equals the slope on the right of each formula. Plug in the other numbers and find how to solve with the value of x that you have found. What does x equal for each equation and how do I set up the formula with my given coordinates?
Answers
The value of x for which (-1, 4) and (x, -2) make a slope of m = 5/4 is - [tex]\frac{29}{5}[/tex]
What is slope?The slope of a line is the ratio of the amount that y increases as x increases some amount. Slope tells you how steep a line is, or how much y increases as x increases. The slope is constant (the same) anywhere on the line.
equation of straight line is y = mx + c
when x = -1, y = 4, m = 5/4
so that
4 = -1(5/4) + c
c = 4 + 5/4
4 can be written as fraction as 16/4
c = 16/4 + 5/4
Adding the numerator
c = 12/4
at x = x, y = -2
substituting
-2 = x( 5/4) + 21/4
-2 = 5x/4 + 21/4
-2 = [tex]\frac{5x + 21}{4}[/tex]
cross multiplying
5x + 21 = -8
collect like terms
5x = -8 - 21
5x = -29
x = -29/5
In conclusion, the value of x is -29/5
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Joe’s distance from the start of the path can also be modeled by D = 4s^2/5s+ 10
where D is measured in yards and s is the total number of steps Joe has taken. If Joe jogs at a constant rate of 100 steps per minute, find the rate that Joe’s distance from the start of the path is changing with respect to time, in yards per minute, when s= 200.
Answers
The rate that Joe’s distance from the start of the path is changing with respect to time, in yards per minute is; 1.91 yards per minute
How to solve constant rate problems?
We are given the equation that represents Joe’s distance from the start of the path as;
D = 4s²/(5s + 10)
where;
D is distance measured in yards.
s is the total number of steps Joe has taken.
When s = 200, we have;
D = 4(200²)/(5(200) + 10)
D = 158.4158 yards
We are old that the constant rate is;
s/t = 100 steps per minute
From conversion rates, we know that , we know that;
1 step = 0.83 yards
Thus; 100 steps per minute = 83 yards per minute
Thus;
83 yards = 1 minute
Time for D = 158.4158 yards is;
158.4158 yards/83 yards per minute = 1.91 minutes
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A triangular prism is 17 meters long and has a triangular face with a base of 16 meters and a height of 15 meters. The other two sides of the triangle are each 17 meters. What is the surface area of the triangular prism?
Answers
The surface area of the triangular prism is 1090 metres squared.
How to find the surface area of a triangular prism?A triangular prism is a polyhedron made up of two triangular bases and three rectangular sides.
Therefore, let's find the surface area of the triangular prism.
Surface area of the triangular prism = bh + l(a + b + c)
where
b = base of the triangular faceh = height of the trianglesa, b and c are the sides of the trianglel = height of the prismTherefore,
Surface area of the triangular prism = 16 × 15 + 17(17 + 17 + 16)
Surface area of the triangular prism = 240 + 17(50)
Surface area of the triangular prism =240 + 850
Surface area of the triangular prism = 1090 metres squared
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I NEED HELP ASAP WITH THIS QUESTION
Answers
Answer: B. The Total profit made when a person buys a car for $10,000 and sells it for $10,000.
Step-by-step explanation:
Answer A would be wrong since when there is a temperature change from 15 degrees to -15 degrees would lead to an overall change of 30 degrees.
Answer C would be wrong as well since it is decreasing 500 feet in altitude, meaning that there is a negative change in altitude.
Answer D would also be wrong since the train is traveling 35 miles north, then south. That means that even though the train is in the same place that is was before, it traveled a total of 70 miles to return to where it was previously at.
Hope this helps!
A quality control expert at LIFE batteries wants to test their new batteries. The design engineer claims they have a variance of 3844 with a mean life of 997 minutes.
If the claim is true, in a sample of 73 batteries, what is the probability that the mean battery life would differ from the population mean by greater than 8.3 minutes? Round your answer to four decimal places.
Answers
Answer: 3.2
Step-by-step explanation:
i did this
If f(x)=x^(2 )+4 then verify (fof^(-1))(x)=(f^(-1) of)(x)=x. (Consider the positive values only)
Answers
Answer:
Step-by-step explanation:
If f(x)=x²+4 then (fof⁻¹)(x)=(f⁻¹of)(x)=x is proved
What is a function?A relation is a function if it has only One y-value for each x-value.
Composite functions are when the output of one function is used as the input of another.
If f(x)=x²+4
Then we have to prove f⁻¹of(x)=f⁻¹(f(x)
Let us consider fof⁻¹(x)
f(f⁻¹(x))
x
So (fof⁻¹(x))=x
Now f⁻¹of(x)=f⁻¹(f(x)
=x
Hence, If f(x)=x²+4 then (fof⁻¹)(x)=(f⁻¹of)(x)=x is proved
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How to solve with the process
Resuelva:
1) |3 x-1|-|2 x+5-(5-x)|=0
2) |2(x+1)-4|=|2-2(2-x)|
3) {x-2}/{4}-{1}/{3}=x
4) {1}/{2}|x-3|-1=|x-3|+2
Answers
The solutions of the absolute value equations are:
1) |3x - 1| - |2x + 5 - 5 + x| = 0
x = 1/6
2) |2*(x + 1) - 4| = |2 - 2*(2 - x)|
x can be any real number.
3) | (x - 2)/4 | - 1/3 = x
This absolute value equation has two solutions, these are:
x = 2/15
x = -10/9
How to solve the absolute value equations?Here we need to solve some absolute value equations, the first one is:
|3x - 1| - |2x + 5 - (5 - x)| = 0
First, we need to simplify the arguments of both absolute values, then we get:
|3x - 1| - |2x + 5 - 5 + x| = 0
|3x - 1| - |3x| = 0
|3x - 1| = |3x|
Now we can remove the absolute value parts, obviusly this is ony true if the right part is negative:
3x - 1 = -3x
-1 = -3x - 3x
-1 = -6x
-1/-6 = x
1/6 = x
That is the solution of the first equation.
2) The second part is:
|2*(x + 1) - 4| = |2 - 2*(2 - x)|
Simplify this:
|2x + 2 - 4| = |2 - 4 + 2x|
|2x - 2| = |2x - 2|
this is true for all values of x, we have the same thing in both sides.
3)
| (x - 2)/4 | - 1/3 = x
|(x - 2)/4| = x + 1/3
We can separate the absolute value part in two equations:
(x - 2)/4 = x + 1/3
(x - 2)/4 = -(x + 1/3)
The first equation gives:
(x - 2) = 4*x + 4/3
x - 4x = 4/3 + 2
-3x = 4/3 + 6/3
x = (10/3)*(-1/3) = -10/9
The second equation gives:
(x - 2)/4 = -(x + 1/3)
(x - 2) = -4*(x + 1/3)
x - 2 = -4x - 4/3
x + 4x = 2 - 4/3
5x = 2/3
x = 2/3/5 = 2/15
This equation has two solutions, x = 2/15 and x = -10/9
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