A function that "undoes" another function is referred to as an inverse in mathematics. To put it another way, if f(x) yields y, then y introduced into the inverse of f yields x. A function that can be inverted has an inverse, which is denoted by the symbol f1. The solution is: x>4;r-1(x)=4-(root of (11/x)
Explain about the inverse function?Something that is opposite or reversal in nature or quality. The inverse of "if A then B" is "if not-A then not-B" — compare contrapositive. 2: a proposition or theorem constructed by opposing both the subject and predicate or both the hypothesis and conclusion of a given proposition or theorem.
reciprocal, inverse multiplicative. (Mathematics) One of two numbers whose product is 1: the multiplicative inverse of 7 is 1/7, while the reciprocal of 2/3 is 3/2. type: antagonism, oppositeness. the connection between seemingly opposing parties.
If there is just one value of x in the domain where f(x)=y, then a function f does not have an inverse function. The term "f inverse" is widely used to refer to this particular inverse function, which is singular.
The solution is: x>4;r-1(x)=4-(root of (11/x)
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y ≥-x+1
y ≥ 2x - 2
how do i solve this algebraiclly??
evaluate. express each result in scientific and standard rotation. please help!
The simple forms of expressions are 11.5×10¹⁰,16.385×10⁻⁸,4.8672×10⁶,0.2×10⁻²
What is Expression?An expression is a combination of variable, numbers and operators.
The given expression is
(5×10⁻²)(2.3×10¹²)
Use the distributive property
(5×2.3)(10⁻²×10¹²)
The powers with same base will be added
11.5×10⁻²⁺¹²
11.5×10¹⁰
23) (3.9×10³)(4.2×10⁻¹¹)
(3.9×4.2)(10³×10⁻¹¹)
The powers with same base will be added
16.385×10⁻⁸
25) 3.12×10³/1.56×10⁻³
The sign of power of denominator changes to opposite sign when it shifted to numerator.
4.8672×10³⁺³
4.8672×10⁶
(28) 1.82×10⁵/9.1×10⁷
0.2×10⁵⁻⁷
The sign of power of denominator changes to opposite sign when it shifted to numerator.
0.2×10⁻²
Hence the simple forms of expressions are 11.5×10¹⁰,16.385×10⁻⁸,4.8672×10⁶,0.2×10⁻²
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find the equation of the line graphed
If a dog needs medicine at 0.5 mL / kg, and the dog weighs 5 kg, how many mL would you give the dog?
If a dog need medicine 0.5ml/kg then the amount of medicine given to the dog is 2.5mL.
word problem :
A word problem is a situation in which you must determine if two provided phrases are comparable in light of a group of rewriting identities.
we use three common types of word problems
part-part wholeseparate and join multiply and divideWeight of the dog = 5kg
dog needs medicine for each kg = 0.5ml
1kg = 0.5ml
the dog weighs 5 kg then
5kg = 5 x 0.5 ml
= 2.5 ml
If a dog need medicine 0.5ml/kg then the amount of medicine given to the dog is 2.5mL.
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The sum of two numbers is the same as four times the smaller number. If twice the larger is decreased by the smaller, the result is 20. Find the numbers.
Answer:
4 and 12
Step-by-step explanation:
let x be the smaller number and y the larger number , the
x + y = 4x ( subtract x from both sides )
y = 3x → (1)
2y - x = 20 → (2)
substitute y = 3x into (2)
2(3x) - x = 20
6x - x = 20
5x = 20 ( divide both sides by 5 )
x = 4
substitute x = 4 into (1)
y = 3x = 3 × 4 = 12
smaller number is 4 and larger number is 12
Most exhibition shows open in the morning and close in the late evening. A study of Saturday arrival times showed that the average arrival time was 3 hours and 48 minutes after the doors opened, and the standard deviation was estimated at about 53 minutes. Assume that the arrival times follow a normal distribution.
(a) At what time after the doors open will 94% of the people who are coming to the Saturday show have arrived? (Round your answer to the nearest number of minutes.)
minutes after doors open
(b) At what time after the doors open will only 14% of the people who are coming to the Saturday show have arrived? (Round your answer to the nearest number of minutes.)
minutes after doors open
Using the normal distribution:
(a) 309 minutes after the doors open
(b) 172 minutes after the doors open.
In a normal distribution with mean μ and standard deviation σ, the z-score of a measure X is given by:
Z = ( X - μ ) / σ
It counts the number of standard deviations the value deviates from the mean.
We look at the z-score table after determining the z-score to determine the p-value, which is the percentile of X.
Now, we have
Mean of 3 hours and 48 minutes, therefore:
μ = 3(60) + 48 = 228 minutes
The standard deviation, σ = 52 minutes
(a) The doors open with 94% of the people who come to the Saturday show.
We look 94%, or 0.94, up in the cells of a z table. The closest we can get to this value is 0.9406, which corresponds to a z score of 1.56:
Z = ( X - μ ) / σ
1.56 = ( X - 228 ) / 52
1.56 × 52 = X - 228
81.12 = X - 228
X = 309.12
X = 309 minutes
(b) We look 14%, or 0.14, up in the cells of a z table. The closest we can get to this value is 0.1401, which corresponds to a z score of - 1.08:
- 1.08 = ( X - 228 )/ 52
- 1.08 × 52 = X - 228
- 56.16 = X - 228
X = 228 - 56.16
X = 171.84
X = 172 minutes
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What’s the number of Organes
let the first orange x
second orange 3x
x+3x+14+9=143
4x+23=143
4x=143_23
4x/4=120/4
x=30
check
30+90+14+9=143
The sum of three numbers is 16. The third is 4 more than 5 times the second. 4 times the first is 9 more than 8 times the second. Find the numbers
The numbers in which is "the sum of three numbers is 16 are 4.6875, 1.21875 and 10.09375 respectively.
How to find unknown number using algebra?Let
The first number = aThe second number = bThe third number = cTotal sum = 16c = 5b + 4
4a = 8b + 9
From the second equation
a = (8b + 9) / 4
16 = a + b + c
16 = (8b + 9) / 4 + b + (5b + 4)
16 = (8b + 9) / 4 + b + 5b + 4
16 = (8b + 9)/4 + 6b + 4
16 - 4 = (8b + 9)/4 + 6b
12 = (8b + 9 + 24b) / 4
cross product12 × 4 = 8b + 9 + 24b
48 = 32b + 9
48 - 9 = 32b
39 = 32b
b = 39/32
b = 1.21875
Recall,
c = 5b + 4
c = 5(1.21875) + 4
c = 6.09375 + 4
c = 10.09375
Also,
16 = a + b + c
16 = a + 1.21875+ 10.09375
16 = a + 11.3125
16 - 11.3125 = a
a = 4.6875
So therefore, the three numbers represented by the expression are 4.6875, 1.21875 and 10.09375 respectively.
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The revenue for selling x units of a product is R = 40x. The cost of producing x units is C = 20x + 6600. In order to obtain a profit, the revenue must be greater than the cost, so we wantto know, for what values of a will this product return a profit.To obtain a profit, the number of units must be greater than ___
The revenue is given as:
R = 40x
The cost of producing x units is given as:
C = 20x + 6600
The profit P is given as:
P = R - C
P = 40x - (20x + 6600)
P = 40x - 20x - 660011111111111112222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222
What is the equation of the line that runs between the points (2, 15) and (-4, -21)
The equation of the line that runs between the points (2, 15) and (-4, -21) is y = 6x + 3.
We are given the coordinates for two points.The points are (2, 15) and (-4, -21).The line passes through both of these points.We have to find the equation of the line.We will use the two-point form of a line.(y - y1) = [(y2 - y1)/(x2 - x1)](x - x1)(y - 15) = [(-21 - 15)/(-4 - 2)](x - 2)(y - 15) = [(-36)/(-6)](x - 2)(y - 15) = 6(x - 2)y - 15 = 6x - 12y = 6x + 3Thus, the equation of the straight line that passes through the two given points is y = 6x + 3.To learn more about lines, visit :
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A 6 ft tall tent standing next to a cardboard
box casts a 9 ft shadow. If the cardboard
box casts a shadow that is 6 ft long then how
tall is it?
Answer: 4
Step-by-step explanation:
9/6=3/2(1.5)
6/1.5= 4
heyyaaa can anyone help me with this?
Answer:
b = 118
c = 62
Step-by-step explanation:
Find the missing angles
Angle b and 118 are vertical angles and vertical angles are equal
b = 118
Angle c and 118 form a straight line which add to 180
c+118 = 180
c = 180-118
c = 62
c and 118 degrees should add up to 180 degrees:
180 - 118 = 62 degrees for c
b and the unknown angle should also add up to 180 and from the line intersections are the same as c and 118.
b = 118
c = 62
A music store sold for 10³ CDs and 10² CD players. If each CD costs $12
and each CD player costs $35, what was the store's total earnings?
The total earning of the store from the formed equation is: 15,500 dollars.
What is equation?
In mathematics, the statement based problems can be solved by forming the equation. And it consists of dependent variable as well as independent variable.
According to the question, the given parameter states that the music store sold 1000 CDs and 100 CD players. And the cost of each CD is $12 and each CD player is $35.
Now, to calculate the total earning by forming the equation for the given statement and it is as follows:
(1000)(12) + (100)(35) = 12,000 + 3500 = 15,500 dollars
Hence, the total earning of the store from the formed equation is: 15,500 dollars.
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Identify any solutions to the system shown here
2x+3y>=6
3x=2y<=6
(1.5, 1)
(0.5, 2)
(–1, 2.5)
(–2, 4)
For the given equation 2x+3y≥6 and 3x=2y≤6, the solution is (1.5, 1). Option A is correct.
What is the equation?An equation is a statement that two expressions, which include variables and/or numbers, are equal. In essence, equations are questions, and efforts to systematically find solutions to these questions have been the driving forces behind the creation of mathematics.
It is given that,
3x=2y<=6
3x =2y
y=1.5x
3x≤6
x≤2
2y≤6
y≤3
As a result, we found that y is 1.5 times x, the value of x should be less than 2, and y should be less than 3.
We analyze each option one by one we obtained the correct values is,
(y,x) = (1.5, 1)
The values follow all the obtained condition
Thus, for the given equation 2x+3y≥6 and 3x=2y≤6 the solution is (1.5, 1). Option A is correct.
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Answer:
(0.5, 2) and (-2, 4)
Step-by-step explanation:
I did the assignment it is the correct answer.
WRITE AND SOLVE: Shannon has
spend $850 on gasoline and repairs
for her car in the last 6 months. Of
this total, she spent $300 on repairs.
The gasoline she purchased cost
$1.29 per gallon. Which of the
following can be used to determine
how many gallons of gas, g, Shannon
has bought within the last 6 months?
Researchers once surveyed students on which superpower they would most like to have. The following two-way table displays data for the sample of students who responded to the survey. What fraction of students chose a superpower that was other than flight and invisibility? (simplify if possible).
Superpower Male Female Total
Flight 26 11 37
Invisibility 14 31 45
Other 10 8 18
Total 50 50 100
Group of answer choices
The fraction of students who chose power other than flight and invisibility are 18/100.
Researchers surveyed the students and obtained different kind of data, the data found is,
The number of male students wanting superpower of fight are 26.
The number of female students wanting superpower of fight are 11.
The number of male students wanting superpower of invisibility are 14.
The number of female students wanting superpower of invisibility are 31.
The number of male students wanting other superpower are 10.
The number of female students wanting other superpower are 8.
Total number of students wanting the power other than flight and invisibility are 18.
So,
The fraction of student wanting power other than invisibility and flight = student wanting other power/total number of students.
= 18/100
The fraction of student wanting power other than invisibility and flight is 18/100
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The triangle below is equilateral. Find the length of side a in simplest radical form
with a rational denominator.
X
√6
Check the picture below.
since the triangle is equilateral, is also equiangular.
[tex]a\sqrt{3}=\sqrt{6}\implies a=\cfrac{\sqrt{6}}{\sqrt{3}}\implies a=\cfrac{\sqrt{2\cdot 3}}{\sqrt{3}}\implies a=\cfrac{\sqrt{2}\sqrt{3}}{\sqrt{3}}\implies a=\sqrt{3} \\\\[-0.35em] ~\dotfill\\\\ 2a=x\implies {\Large \begin{array}{llll} 2\sqrt{3}=x \end{array}}[/tex]
9th grade math easy pls help
Solve the following problems using the order of operations: PEMDAS.
1) 7(2+5). 2) 10- (2*3) +9.
3) 2^2+3 (5-2)
=−m equals , 5 fourths , n minus 7 to find m when =n equals 40.
It is to be noted that an equation is formed of two equal terms. As per the literal equation m=5/4n-7, the value of m when the value of n is 7 is 42.
What is a math expression?An expression or mathematical expression is a finite collection of symbols that is well-formed according to context-dependent norms.
The value of m from the given equation can be found by substituting the value of n as 7 in the given equation as shown below.
m = (5/4)n - 7
Substitute the value of n as 40,
m = (5/4)40 - 7
m = (5/1)10 - 7
m = 50 - 7
m = 42
Therefore, as per the literal equation m=5/4n-7, the value of m when the value of n is 7 is 42.
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Full Question:
Use the literal equation m=5/4n-7 to find m when n =40
Please help, there’s more than one answer!!!!
Answer:
A and d
Step-by-step explanation:
Find the equation of the linear function represented by the table below in slope-intercept form.
X y
0 1
1 8
2 15
3 22
4 29
Answer:
y=7x+
Step-by-step explanation:
y=mx + b
b is the number y is at when x is at
0
m us the slope or the number y goes up for each 1 number x does
in this set you can see when x is at 0 y is at 1 then for the next one you see when x is 1 y is 8 which is a 7 increase for
suppose cattle in a large herd have a mean weight of 1428lbs and a standard deviation of 119lbs. what is the probability that the mean weight of the sample of cows would differ from the population mean by less than 11lbs if 49 cows are sampled at random from the herd? round your answer to four decimal places.
The probability that the population mean is less than 11lbs is 0
How to determine the probability?From the question, the given parameters about the distribution are
Mean value = 1428Standard deviation = 119The raw data value, x = Less than 11Sample size, n = 49The z-score of the data value is calculated using the following formula
z = (x - mean value)/standard deviation
Substitute the given parameters in the above equation
z = (11 - 1428)/119
Evaluate the quotient
z = -11.91
The required probability of population mean is represented as
P(x < 11) = P(z < -11.91)
From the z table of probabilities, we have;
P(x < 11) = 0
Hence, the probability value is 0
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Subtract the Polynomials:
(5y^2+6y-1) - (-9y^2-5y+6)
The result of subtracting the polynomials is (5y² + 6y - 1) - (-9y² -5y + 6) = 14y² + 11y - 7
How to subtract the polynomials?The polynomial expression is given as
(5y^2 + 6y - 1) - (-9y^2 -5y + 6)
Rewrite the expression properly as follows
(5y² + 6y - 1) - (-9y² -5y + 6)
Open the brackets in the above polynomial expression
So, we have
(5y² + 6y - 1) - (-9y² -5y + 6) = 5y² + 6y - 1 + 9y² + 5y - 6
Collect the like terms in the above polynomial expression
So, we have
(5y² + 6y - 1) - (-9y² -5y + 6) = 5y² + 9y² + 6y + 5y - 1 - 6
Evaluate the like terms in the above polynomial expression
So, we have
(5y² + 6y - 1) - (-9y² -5y + 6) = 14y² + 11y - 7
Hence, the solution is 14y² + 11y - 7
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Mark ran 15 miles in 135 minutes. assume mark maintains a contants speed
Mark ran 15 miles in 135 minutes.
Maintaining a constant speed he can run:
60 minutes = 6.66 miles
30 minutes = 3.33 miles
10 minutes = 1.11 miles
What is a unit rate?It is the quantity of an amount of something at a rate of one of another quantity.
In 2 hours, a man can walk for 6 miles
In 1 hour, a man will walk for 3 miles.
We have,
15 miles = 135 minutes.
This can be considered speed.
Now,
Maintaining this speed we can find the miles covered in 10 minutes, 30 minutes, 60 minutes, and more.
135 minutes = 15 miles _____(1)
From (1),
Multiply 60/135 on both sides.
60/135 x 135 minutes = 60/135 x 15 miles
60 minutes = 6.66 miles
From (1)
Multiply 10/135 on both sides.
10/135 x 135 minutes = 10/135 x 15 miles
10 minutes = 1.11 miles
From (1)
Multiply 30/135 on both sides.
30/135 x 135 minutes = 30/135 x 15 miles
30 minutes = 3.33 miles
Thus,
Mark ran 15 miles in 135 minutes.
Maintaining a constant speed he can run:
60 minutes = 6.66 miles
30 minutes = 3.33 miles
10 minutes = 1.11 miles
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I need help what is 3.012 + 4.624 .
3012 +
4624
-------
7636
Answer:
Step-by-step explanation:
3.012+4.624=7.636
how to solve this is to line them up with the decimal point.
decimal point to decimal point. look at the example below.
3.012 plus
4.624 equals
7.636
NEED HELP
he proportional relationship between cost and pints of blueberries is shown in the table.
Blueberries (in pints) 2 5
Cost (in dollars) 6.80 17
Describe what a graph of the proportional relationship would look like.
A coordinate plane with the x-axis labeled Cost (in dollars) and the y-axis labeled Blueberries (in pints) shows a line going through (0, 0) and (5, 17).
A coordinate plane with the x-axis labeled Cost (in dollars) and the y-axis labeled Blueberries (in pints) shows a line going through (0, 0) and (2, 6.80).
A coordinate plane with the x-axis labeled Blueberries (in pints) and the y-axis labeled Cost (in dollars) shows a line going through (0, 0) and (5, 17).
A coordinate plane with the x-axis labeled Blueberries (in pints) and the y-axis labeled Cost (in dollars) shows a line going through (0, 0) and (6.80, 2).
A coordinate plane with the x-axis labeled Blueberries (in pints) and the y-axis labeled Cost (in dollars) shows a line going through (0, 0) and (5, 17).
What is directly proportional?It is defined as the relationship between two quantities as one quantity increases the other quantity also increases and vice versa.
It is given that there is a proportional relationship between cost and pints of blueberries as,
Blueberries (in pints) 2 5
Cost (in dollars) 6.80 17
17/6.80 = 5/2
As we draw the graph and analyze each option one by one we get the graph shown by the statement C following the given proportional relationship.
Thus, a coordinate plane with the x-axis labeled Blueberries (in pints) and the y-axis labeled Cost (in dollars) shows a line going through (0, 0) and (5, 17).
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1.1 Study: Rational and Irrational Numbers
entify each number as rational or irrational.
Number
4 1/3
8
√13
Type
Irration number
Rational number
ocitet..
Irrational numbers are real numbers that can't be expressed as a fraction, p/q, where p and q are integers.
The numerator q does not equal zero (q≠ 0). Furthermore, an irrational number's decimal expansion is neither terminating nor repeating.Irrational numbers are all square roots that are not a perfect square. {√2, √3, √5, √8}Some well-known irrational numbers include Euler's number, the Golden ratio, and Pi. {e, ∅, ㄫ}Any prime number's square root is an irrational number.Thus, √13 is irrational number.
Rational numbers are written in the form p/q, where p and q can be any integer as well as q≠ 0 respectively. Natural numbers, whole numbers, integers, fractions of integers, and decimals are all examples of rational numbers.Integers such as -2, 0, 3, and so on are rational numbers.Rational numbers are fractions with integer numerators and denominators, such as 3/7, -6/5, and so on.Thus, 4 1/3 and 8 are rational number.
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The 8th term of a GP is -7^32.
Find it’s common ratio if it’s first term is 28.
The common ratio of the geometric sequence with 8th term of -7^32 and first term is of 28 is of:
q = -4535.
What is a geometric sequence?In a geometric sequence the result of the division of consecutive terms is always the same, called common ratio q.
Hence, the nth term of a geometric sequence is obtained according to the rule presented as follows:
[tex]a_n = a_1q^{n-1}[/tex]
In which [tex]a_1[/tex] is the first term.
In this problem, the first term and the 8th term are given as follows:
[tex]a_1 = 28, a_8 = -7^{32}[/tex]
Hence the common ratio can be obtained as follows:
[tex]a_8 = a_1q^{7}[/tex]
[tex]-7^{32} = 28q^{7}[/tex]
[tex]q^7 = -\frac{7^{32}}{28}[/tex]
[tex]q = -\sqrt[7]{\frac{7^{32}}{28}}[/tex] (the 7th root is calculated with a calculator, elevating the number to 1/7).
q = -4535.
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Line AB formed by (2,3) and (-1,4)Line CD formed by (-5,3) and (-4,6)Parallel perpendicular or neither
To check whether the lines are perpendicular or parallel, we will use the following rules:
1) For parallel lines, the slopes are equal.
2) For perpendicular lines, the product of the slopes is equal to -1.
Slope of line AB:
Using
[tex]\begin{gathered} (x_1,y_1)=(2,3) \\ (x_2,y_2)=(-1,4) \end{gathered}[/tex]The slope is given as
[tex]\begin{gathered} m_A=\frac{y_2-y_1}{x_2-x_1} \\ m_A=\frac{4-3}{-1-2} \\ m_A=-\frac{1}{3} \end{gathered}[/tex]Slope of line CD:
Using
[tex]\begin{gathered} (x_1,y_1)=(-5,3) \\ (x_2,y_2)=(-4,6) \end{gathered}[/tex]The slope is given as
[tex]\begin{gathered} m_B=\frac{y_2-y_1}{x_2-x_1} \\ m_B=\frac{6-3}{-4-(-5)} \\ m_B=\frac{3}{-4+5} \\ m_B=3 \end{gathered}[/tex]Comparing both slopes, we can observe that
[tex]\begin{gathered} m_A\times m_B=-1 \\ \text{Given that} \\ -\frac{1}{3}\times3=-1 \end{gathered}[/tex]Therefore, both lines are PERPENDICULAR.
A graph is proportional if it has a straight line that goes through the origin.
true
false
It is false that a graph is proportional if it has a straight line that goes through the origin.
Given a statement that a graph is proportional if it has a straight line that goes through the origin.
We are required to find whether the statement is true or false.
A proportional relationship graph between two variables is basically a relationship where the ratio between the two variables is always the same.
The statement that a graph is proportional if it has a straight line that goes through the origin because there can be many graphs which can pass through origin. For proportionality along with passing through origin, a constant rate should also be there.
Hence it is false that a graph is proportional if it has a straight line that goes through the origin.
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