The function y = (e⁻⁽ˣ⁺²⁾) / x + 2 increases along intervals of (-∞, 3) and decreases along (-3, -2), (-2, ∞) and the function y = 2x - 1 / (x - 1)² has no inflection points but concave downwards along (-∞, 1) ∪ (1 ,∞)
Extrema and Intervals of a FunctionAn extremum (or extreme value) of a function is a point at which a maximum or minimum value of the function is obtained in some interval. A local extremum (or relative extremum) of a function is the point at which a maximum or minimum value of the function in some open interval containing the point is obtained.
The function given;
y = (e⁻⁽ˣ⁺²⁾) / x + 2
The extrema and intervals of increase or decrease of this function are
(-1, 1.63) and it increases along (-∞, 3) and decreases along (-3, -2), (-2, ∞)
2. The inflection points and intervals of concavity and convexity of the function
y = 2x - 1 / (x - 1)² are
The function has no inflection pointsIt's concave downwards along (-∞, 1) ∪ (1 ,∞)Learn more on intervals of a function here;
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The measures of the legs of a right triangle both measure 7 yards. What is the length of the hypotenuse? Round your answer to the nearest tenth. A. 7 yards B. 9.8 yards C. 9.9 yards D. 10 yards
The length of the hypotenuse is (c) 9.9 yards
How to determine the length of the hypotenuse?From the question, we have the following parameters that can be used in our computation:
Legs = 7 yards
This means that
Opposite = 7
Adjacent = 7
The hypotenuse is then calculated using the following Pythagoras theorem
Hypotenuse = √(Opposite² + Adjacent²)
Substitute the known values in the above equation, so, we have the following representation
Hypotenuse = √(7² + 7²)
Evaluate
Hypotenuse = 9.9
Hence, the hypotenuse is 9.9 yards
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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
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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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.
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:
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Convert .805 liters to millimeter s
The binary operation * on the set of real numbers is defined as a * b = 2a + 3b - 5. Find the inverse element in *.
The inverse element of the binary operation is given by (20-7a)/9 .
The binary operation is defined by a * b = 2a + 3b - 5
Now let us first find the identity element of the operation.
let e be the identity element.
Hence we know that a * e = a
Therefore a * e = 2a + 3e - 5
or, a = 2a + 3e - 5
or, a - 2a = 3e - 5
or, -a = 3e - 5
or, e = (5-a) / 3
Now we know that the inverse of the operation will be such that
a * a⁻¹ = e
or, a⁻¹ = (20-7a) / 9
Therefore the inverse of the operation is given by (20-7a) / 9 .
A binary operation or dyadic operation is a rule that combines two elements (referred to as operands) to produce a third element. Formally, a binary operation is a two-arity operation.
An internally binary operation on a set is a binary action with the same set as its two domains or codomain. Examples include addition, multiplication, and other basic mathematical operations.
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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?
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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Can someone help me I don’t understand this question it’s geometry
All the missing lengths and missing angles of the given right angle triangle are as calculated below
How to use trigonometric ratios?We are given a right angle triangle and as such we can use the trigonometric ratios as;
sin θ = opposite/hypotenuse
cos θ = adjacent/hypotenuse
tan θ = opposite/adjacent
a) A = 30°, Thus;
B = 180 - (90 + 30)
B = 60°
Using sine rule;
a/sin A = b/sin B
a/sin 30 = 6/sin 60
a = 3.464
c/sin 90 = 6/sin 60
c = 6.928
b) a = 13 and b = 13
Using Pythagoras theorem;
c = √(13² + 13²)
c = 18.385
Since a = b, it means it is an isosceles triangle and so;
A = B = 45°
c) B = 30°, c = 10
A = 180 - (30 + 90)
A = 60°
10/sin 90 = b/sin 30
b = 5
10/sin 90 = a/sin 60
a = 8.66
d) A = 45°, c = 12
B = 45°
c/sin 90 = b/sin 45 = a/sin 45
b = a = 12 * sin 45 = 8.485
e) c = 1, b = 1/√2
c/sin 90 = b/sin B
1/sin 90 = (1/√2)/ sin B
B = 45° = A
a = √(1² - (1/√2)²)
a = 0.7071
f) c = 4 and b = 4;
a = √(4² - (4)²)
a = 0
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helpppppppppppppppppp
when y equals zero, x equals -2
or, at y = 0, the function touches the x-axis at -2
Equations/Rules 2
What is the zero of the function f(x)=3 x-9 ? Explain how you know.
?
What is the zero of the function f(x)=-x+4 ? Explain how you know.
?
The zero of the function f(x) = 3x - 9 is x = 3.
The zero of the function f(x) = -x + 4 is x = 4.
How to find zero of a function?The zero of a function is any replacement for the variable that will produce an answer of zero.
Therefore, let's find the zero of the function f(x) = 3x - 9.
0 = 3x - 9
add 9 to both sides of the equation
0 + 9 = 3x - 9 + 9
9 = 3x
divide both sides by 3
x = 9 / 3
x = 3
The zero of the function is x = 3.
Therefore, let's find the zero of the function f(x) = -x + 4.
0 = - x + 4
subtract 4 from both sides of the equation
0 - 4 = -x + 4 - 4
-4 = - x
x = 4
The zero of the function is x = 4.
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Write 33×√3 as a single power of 3.
Answer:
[tex]3^{7/2}[/tex]
Step-by-step explanation:
[tex]3^3 \sqrt{3} \\ \\ =3^3 \cdot 3^{1/2} \\ \\ =3^{3+\frac{1}{2}} \\ \\ =3^{7/2}[/tex]
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.
Answer: 3.2
Step-by-step explanation:
i did this
Please help!! I need all three answered.
Compute the standard error for sample means from a population with mean
μ = 90 and standard deviation o = 25 for sample sizes of n = 440, n = = 230,
and n =1200
The standard errors for the sample sizes of 440, 230, and 1200 are 1.2, 1.65, and 0.72, respectively.
The mean of the population is μ = 90. The standard deviation of the population is σ = 25. We are given three sample sizes. We need to compute the standard error for each sample size.
The standard error is computed by dividing the standard deviation by the square root of the sample size. It calculates the accuracy of a sample mean by factoring in sample-to-sample variability.
Let S1, S2, and S3 represent the standard errors for the sample sizes of 440, 230, and 1200, respectively.
S1 = σ/√n
S1 = 25/√440
S1 = 1.2
S2 = σ/√n
S2 = 25/√230
S2 = 1.65
S3 = σ/√n
S3 = 25/√1200
S3 = 0.72
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Please help will mark Brainly
Answer:
[tex]-2x+4[/tex]
Step-by-step explanation:
[tex]g(x)=f(x)+3=-2x+1+3=-2x+4[/tex]
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?
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.Please help Image below
Function g can be thought of as a translated (shifted) version of f(x)=x².
Write the equarion for g(x).
Answer:
[tex]g(x)=(x+4)^2-5[/tex]
Step-by-step explanation:
The graph of [tex]f[/tex] was shifted 4 units left and 5 units down,
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?
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.
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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Is this right? I need help! I need the correct answers Ill give you 58 pts and brainliest to the first correct!
Answer:
its right
Step-by-step explanation:
Answer: Its right i just got the same question
Step-by-step explanation:
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
A. The. part
B. The. whole
C. The. People
D. Benchmark. percent
ents
K-12
X Y
7 21
8 24
9 27
Function B
10
1
6
4
2
0
Function B
10
Which statement best compares the rate of change of the two functions? (1 point)
The rate of change of both functions is 2.
The rate of change of both functions is 3.
O The rate of change of function A is greater than the rate of change of function B.
O The rate of change of function B is greater than the rate of change of function A
Answer:
C
Step-by-step explanation:
FUNCTION A
21 : 7 = 3
FUNCTION B
8: 4 = 2
3 is greater than 2
Find two numbers that multiply to give 100 and have a difference of 21
The values can be 4, 25 and -4, -25.
What is a Linear Equation in Two Variable?
A linear equation in two variables is one that is stated in the form ax + by + c = 0, where a, b, and c are real integers and the coefficients of x and y, i.e. a and b, are not equal to zero.
Solution:
Let,
The first number be x and second number be y
Equation 1: x*y = 100
Equation 2: x - y = 21
From equation 2 we can write x = 21 + y
Substituting the value of x in equation 1
(21 + y)*y = 100
21y + y^2 - 100 = 0
y = 4, -25
this implies that x = 25, -4
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What is the hardest part of AP stats?
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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help me fast rapidly is of khan academy:
Answer:
0 hundreds
0 tens
7 ones
.
4 tenths
0 hundredths
8 thousandths
Standard form=7.408
Step-by-step explanation:
Lets first solve (7x1)+(4x1/10)+(8x1/1000)
7+0.4+0.008
Simplify:
7.408
PLEASE MARK AS BRAINLIESTPlease solve and send good quality picture xx
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!
Differentiate the function with respect to x. Shot steps
The value after differentiate will be;
⇒ [tex]\frac{dy}{dx} = 3x^2 3^{x^{3} } log_{e} 3[/tex]
What is an expression?
Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
The function is,
⇒ [tex]y = 3^{x^{3} }[/tex]
Now,
Differentiate the function with respect to x as;
The function is,
⇒ [tex]y = 3^{x^{3} }[/tex]
⇒ [tex]\frac{dy}{dx} = 3^{x^{3} } log_{e} 3 \frac{d}{dx} (x^3)[/tex]
⇒ [tex]\frac{dy}{dx} = 3^{x^{3} } log_{e} 3 * 3x^2[/tex]
⇒ [tex]\frac{dy}{dx} = 3x^2 3^{x^{3} } log_{e} 3[/tex]
Thus, The value after differentiate will be;
⇒ [tex]\frac{dy}{dx} = 3x^2 3^{x^{3} } log_{e} 3[/tex]
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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?
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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A certain shampoo is available in two sizes. A 14.2 - ounce bottle costs $3.98. A 33.9 -ounce bottle costs $9.98.
Find the unit price for each size. Then state which size is the better buy based on the unit price.
Round your answers to the nearest cent.
The unit price for A is 3.57 ounce per dollar and the unit price for B is 3.4 ounce per dollar and A is better than B.
According to the question,
We have the following information:
A certain shampoo is available in two sizes. A 14.2 - ounce bottle costs $3.98. A 33.9 -ounce bottle costs $9.98.
Unit price of A:
14.2 ounce = $3.98
1 dollar = 14.2/3.98 ounce
Unit price for A = 3.57 ounce per dollar
Unit price for B:
33.9 ounce = $9.98
1 dollar = 33.9/9.98
Unit price for B = 3.4 ounce per dollar
Now, the unit price for A is greater than the unit price for B. So, size A is better.
Hence, the unit price for A is 3.57 ounce per dollar and the unit price for B is 3.4 ounce per dollar and A is better than B.
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Suppose the mean income of firms in the industry for a year is 20 million dollars with a standard deviation of 1 1 million dollars. If incomes for the industry are distributed normally, what is the probability that a randomly selected firm will earn less than 22 million dollars? Round your answer to four decimal places.
The probability that a randomly selected firm will earn less than 22 million dollars is 0.8557
How to get the required probabilityThe probability is calculated using z score, this is used to determine the amount of standard deviations a sample, X is from the mean
The z score is given by the formula
z = (X - μ) / σ
Definition of variables
mean, μ = 20 million dollars = 20 m
standard deviation, σ = 11 million dollars = 11 m
The probability
differ from the population proportion by less than 22 m
X < 22 m
z score
z = (22 - 20) / 11
= 0.181818
p value for z < 0.181818 = 0.85573
The probability required = 0.8557
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Find all values of m for which the equation has two real solutions.
3x² + 7x- (m + 1) = 0
