The inverse of the function x^7 is x^-7 and it is also a function.
An inverse function or an anti function is defined as a function, which can reverse into another function.
A standard method to find inverse of a function is to set y=f(x)
let y= f(x)=x^7
thus
[tex]\sqrt[7]{y}[/tex]=x
thus [tex]f^{-1}[/tex](y)=[tex]\sqrt[7]{y}[/tex]
thus [tex]f^{-1} (x)=\sqrt[7]{x}[/tex]
(To verify this if a function is inverse or not we are required to check for the identity)
f([tex]f^{-1}[/tex](x))=[tex]f^{-1}[/tex](f(x))=x
Therefore, The inverse of the function x^7 is x^-7 and it is also a function.
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Find the value of y if M is the midpoint of LN. LM=9y-4 MN=6y+5 LN?
The value of y for which M is the mid-point of LN is equal to 3 and the numerical length of LN is 46 units.
What is Mid - point of a line?The mid - point of a line is the point which divides it into two equal parts of same length.
Given in the question is a line segment LN such that M is its mid - point. From the question, we can write -
LM = 9y - 4
MN = 6y + 5
According to the question, M is the midpoint of LN, therefore -
LM = MN
9y - 4 = 6y + 5
9y - 6y = 9
3y = 9
y = 3
So, the length of LN will be -
LN = LN + MN = 9 x 3 - 4 + 6 x 3 + 5 = 23 + 23 = 46 units
Therefore, the value of y is equal to 3 and the numerical length of LN is 46 units.
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1. Find the sum of the measures of all the angles in all of the triangles shown in
this diagram.
The sum of the measures of all the angles in all of the triangles shown in the given diagram is 3,600°.
We need to find the sum of the measures of all the angles in all of the triangles shown in this diagram.
What is the triangle?A triangle is a closed shape with 3 angles, 3 sides, and 3 vertices.
The sum of all the angles of the triangle is equal to 180°.
From the figure, by counting, we get there are 20 triangles.
As we know, the sum of all the interior angles of a triangle is 180°.
So, the sum of the measures of all the angles in all of the triangles = The number of triangles × 180°
= 20 × 180°
= 3,600°
Therefore, the sum of the measures of all the angles in all of the triangles shown in the given diagram is 3,600°.
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if the test scores of a class of 35 students have a mean of 73.1 and the test scores of another class of 26 students have a mean of 65.6, then the mean of the combined group is
The mean of the combined group of classes is 69.35
Mean is given by by dividing the sum of the given numbers by the entire number of numbers, the mean—the average of the given numbers—is determined. Mean is equal to (Sum of All Observations/Total Observations).
It is given that,
The mean of test scores of a class having 35 students = 73.1
And,
The mean of test scores of a class having 26 students = 65.6
We need to find,
The mean of the combined group of classes = mean of both classes
Mean of both classes = [tex]\frac{73.1 + 65.6}{2}[/tex]
= [tex]\frac{138.7}{2}[/tex]
= 69.35
Hence, 69.35 is the mean of the combined group of classes
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PLEASE HELP ME! Find the percent of change when 40 is increased to 83. If necessary, round your answer to the nearest tenth.
51.8% increase
51.8% decrease
107.5% increase
107.5% decrease
The percent of change when 40 is increased to 83 to the nearest tenth is: C. 107.5% increase.
The types of percentage.In Mathematics, there are two main types of percentage and these include the following:
Percentage decreasePercentage increaseMathematically, percentage increase can be calculated by using this formula:
Percentage increase = [Final value - Initial value]/Initial value × 100
Substituting the given parameters into the formula, we have;
Percentage increase = [83 - 40]/40 × 100
Percentage increase = 43/40 × 100
Percentage increase = 1.075 × 100
Percentage increase = 107.5%.
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The product of two positive integers is always
Answer: positive
Step-by-step explanation: That's just how it works. It's an algerbra rule. Hope that helped. Have a nice day.
Rule 1: The product of a negative integer and a positive integer is a negative integer. Rule 2: The product of two positive integers or two negative integers is a positive integer. That means if you multiply two OF the same sign numbers, the product is always positive.
ction T...
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Question 4 (25 points)
Charley wants to start taking golf lessons. There is a one-time fee of $45 to sign up, then it costs $80 per month. a) Write an equation to model
this problem. b) What will be the total cost after 7 months?
a
d
C = 45m +80; The total cost will be $395 after 7 months.
C = 80m + 45; The total cost will be $605 after 7 months.
C = 45m +80; The total cost will be $125 after 7 months.
C = 80m + 45; The total cost will be $125 after 7 months.
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Question 4 of 20 | Page 4 of 20
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Solve the equation
sec x=√2 in the interval 0≤x≤2π
[tex]\displaystyle\\Answer:\ x=\frac{\pi }{4} \ \ \ \ \ x=\frac{7\pi }{4}[/tex]
Step-by-step explanation:
[tex]\displaystyle\\secx=\sqrt{2} \ \ \ \ 0\leq x\leq 2\pi \\\\\frac{1}{cosx} =\sqrt{2} \\\\cosx=\frac{1}{\sqrt{2} } \\\\cosx=\frac{(1)(\sqrt{2)} }{(\sqrt{2})(\sqrt{2)} } \\\\cosx=\frac{\sqrt{2} }{2} \\\\x=\frac{\pi }{4} \\\\x=\frac{7\pi }{4}[/tex]
a sporting event coordinator has 200 mini foam fingers. She gives 2 foam fingers to each student in attendance. there are 26 left. how many students are in attendance
⚡️PLEASE HELP-URGENT⚡️
I only need help with 34.. but I. So confused and I need to go to bed
-12
----- = -4 that's the key to the operation so -4x 3
3
Solve each equation. If necessary, round to the nearest ten-thousandth. log₇3 x=3
The solution of the given equation by rounding off it to the nearest ten-thousandth is 7.8295.
What is a round-off of the digit?
In mathematics, a round-off is defined as an approximation of the given number to a fewer number of significant digits by taking into consideration some rules.
For eg: 13.58 ~ 13.6
Solving the given equation: log₇3x = 3
We are given a logarithmic expression: log₇3x = 3 —- 1
We know that log₇3 = log 3 / log 7 and log (ab) = log a + log b
Using in equation 1, we have,
log₇3x = 3
log 3x / log 7 = 3
(log 3 + log x) / log 7 = 3
log 3 + log x = 3 × log 7
log 3 + log x = 2.535
log x = 2.535 - 0.4771
log x = 2.0579
x = 7.8295
Hence, the solution of the given equation rounded off to the nearest ten-thousandth is 7.8295.
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Students in Mr. Kendrick's class are divided into two groups for an activity. Students in group A must always tell the truth. Students in group B must always lie. Jonah and Janeka are in Mr. Kendrick's class. When asked if he and Janeka are in group A or B, Jonah says, "We are both in Group B. " To which group does each student belong? Explain your reasoning
In the class of Mr. Kendrick's, Jonah is in Group B and Janeka is in Group A using the concept of Logical Reasoning.
As per the question statement, we are given that in Mr. Kendrick's class, students are divided into two groups for an activity. Students in group A must always tell the truth and correct info. Students in group B must always lie. Jonah and Janeka are in Mr. Kendrick's class. When asked if Jonah and Janeka are in group A or B, Jonah says, "We are both in Group B. "
By their statement and using the concept of Logical Reasoning, we can conclude that Jonah is in Group B and Janeka is in Group A.
As Jonah said, "We are both in Group B. " and as both the students can't be in same group so Jonah lied and hence he is in group B and Janeka is in group A.
This is a classic example of Logical Reasoning.
Logical Reasoning: Working through a set of rules that govern a scenario is a method of problem-solving known as logical reasoning.
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35 x dash x 37 = 10,360 what can be said about the number in the box
Answer:
The missing number is 8
Step-by-step explanation:
[tex]10,360 \div 37 \div 35 = 8[/tex]
3. ASSESS REASONABLENESS Two moving truck companies offer the same
vehicle at different rates. At Haul-n-Save, the truck can be rented for $30,
plus $0.79 per mile. At Rent It Trucks, the truck can be rented for $75,
plus $0.55 per mile.
a. Write equations for the total cost of renting a truck from each company.
b. Graph the equations on the same coordinate plane. Examine the graph
to estimate after how many miles of driving the total rental cost will be
the same from each company.
c. Check your estimate. How reasonable is your estimation?
Justify your reasoning.
Using linear functions, it is found that:
a. The equations are given by: H(x) = 30 + 0.79x, R(x) = 75 + 0.55x.
b. The costs will be the same after 187.5 miles.
c. The estimate from the graph is reasonable, as it is the value of x for which both equations are equal.
What is the definition of a linear function?A linear function is defined according to the following rule:
y = mx + b
In which:
m is the slope of the function, also called the rate of change of the function, given by the change in y divided by the change in x.b is the y-intercept of the function, which is the the value of y when the function crosses the x-axis(x = 0).For each function in the context of this problem, we have that:
The slope is the cost per mile.The intercept is the rent cost.Hence the equations for each company are given as follows:
H(x) = 30 + 0.79x.R(x) = 75 + 0.55x.The graph is given at the end of the answer, and from the intersection point, we have that the costs will be the same after 187.5 miles.
Numerically, this value is given as follows:
H(x) = R(x)
30 + 0.79x = 75 + 0.55x
0.24x = 45
x = 45/0.24
x = 187.5.
Hence the estimate from the graph is reasonable.
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Bill and Ted plan to buy a ps4 for $299.00. Games for the system cost $60 each. They plan to buy one console to share. If bill and Ted buy 1 console and 3 games, how much will they spend total?
Answer:
$459
Step-by-step explanation:
60x3=180
$299+180=$459
On a map 2cm represents 30 mi. The actual distance between two towns is 75mi. What is the distance between the towns on the map
On the map, the separation between the two towns would be 5 cm.
Detailed explanation:
First, consider 2 cm and 30 miles as a ratio, which means that wherever you measure 2 cm with a ruler on a map, 30 miles will be scaled to that location.
Then, using some logic, we can state that if 2 cm = 30 mi, then 4 cm = 60 mi (double the 2 cm will result in doubling the 30 cm), and 1 cm = 15 mi (if you divide the 2cm by 2, 30mi will also be divided by 2). Because of this, 5cm (4cm + 4cm + 1cm) on the map equals 75mi (which is 30mi + 30mi + 15mi).
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10. The mass of planet Earth is about
5.98 x 1024 kilograms. How many significant
digits does this number contain?
The scientific notation has 3 significant digits.
What is a scenic notation?A significant number is the the numbers that are in in the coefficient of an expression in scientific notation, 5, 9 and 8 are the significant numbers.
Scientific notation is used in expressing large numbers in smaller numbers. In order to write a number in scientific notation, the number is written as a decimal number, between 1 and 10 and multiplied by a power of 10.
For example, the number : 1 x 10² is equivalent to 100
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İfadesinin en sade şekli aşağıdakilerden hangisidir?
Answer:
A
Step-by-step explanation:
HELP..........................
Answer: D
Step-by-step explanation:
Find the 96th term of the arithmetic sequence 1, -12, -25, ...1,−12,−25
96th term of the arithmetic sequence 1, -12, -25, ...1,−12,−25 is -1234
arithmetic sequence 1, -12, -25, .. .1,−12,−25
an arithmetic sequence can be written as
a , a + d , a + 2d , a + 3d , . . . . . a + (n-1)d
nth tern of an arithmetic sequence is
aₙ= a+ (n-1)d
a= first term of an arithmetic sequence
d = common difference of an arithmetic sequence
n = number of terms in an arithmetic sequence
So in the above arithmetic sequence
a= 1
d= -13
n= 96
a₉₆= 1+ (96-1)(-13)
= 1- (95)13
= 1- 1235
= -1234
96th term of the arithmetic sequence 1, -12, -25, ...1,−12,−25 is -1234
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Which of the following equations have an infinite solution set?
The equation has infinite solutions is the last option:
6(x - 1) = 2*(3x - 3)
Which equation has an infinite solution set?Any equation in which we can remove the variable has infinite solutions (because it does not depend on the value of x) only if the equation is true.
Let's look at the fourth equation:
6(x - 1) = 2*(3x - 3)
If we expand both sides, we will get:
6x - 6 = 2*3x - 2*3
6x - 6 = 6x - 6
So we have the exact same thing in both sides, if we remove 6x - 6 in both sides we will get:
0 = 0
Then this equation has infinite solutions.
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Simplify the expression.
-1- 2/3(6/7-3/7n)
[Mathematical Situation]
Simplify the expression.
[tex]-1-\frac{2}{3} (\frac{6}{7}-\frac{3}{7}n)[/tex]
Solution:
[tex]-\frac{11}{7}+\frac{2n}{7}[/tex]
Hope this helps!
The simplified expression is -1 - 4/7 + (2/7)n.
What is an expression?An expression contains one or more terms with addition, subtraction, multiplication, and division.
We always combine the like terms in an expression when we simplify.
We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.
Example:
1 + 3x + 4y = 7 is an expression.
3 + 4 is an expression.
2 x 4 + 6 x 7 – 9 is an expression.
33 + 77 – 88 is an expression.
We have,
-1 - 2/3 (6/7 - (3/7)n)
Distributive operation.
= -1 - 2/3 x 6/7 + 2/3 x (3/7)n
= -1 - 4/7 + (2/7)n
Thus,
The simplified expression is -1 - 4/7 + (2/7)n.
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PLEASE HELP!!!!
Translation using the rule
(x. y)-(x-5. y).
Answer:
P= (-12,0)
Q= (0,-8)
R= (-2,-16)
P'= (-17,0)
Q'= (-5,-8)
R'= (-7,-16)
Step-by-step explanation:
Assuming that each square is equal to one point, the shape is in quadrant 3, where all coordinates are negative.
Determine where each coordinate is for P, Q, and R; then move over each x coordinate by -5 (a.k.a. subtract 5).
This will give you your translation to P', Q', and R'.
Please let me know if I made any mistakes, and hope this helped!
Ryan wants to buy two video games. One costs $35.89 and the other costs $43.65. He estimates the total cost of the two games to be about $80. Is his estimate higher or lower than the actual cost? Explain.
Answer:
Actual cost = 35.89 + 43.65 = 79.54 so it is some what lower than estimated cost.
Step-by-step explanation:
Write each expression in simplest form. (-27x⁻⁹)¹/₃
The given expression can be written in its simplest form by using the rule of exponents.
There are three components to the given expression, there is a negative base term -27, there is a base term with negative exponent x^-9, and both base terms have a fractional exponent 1/3.
Solving the term with negative exponent, the rule dictates that a term with a negative exponent can be written as its reciprocal. As x^-n=1/x^n,
x^-9=1/x^9
Hence, the expression becomes (-27/x^9)^1/3
The fractional exponent is applied to both the base terms. As (x^n)^m=x^nm,
(-27/x^9)^¹/₃=(-27)^1/3/(x^9*1/3)
Solving the negative term, the rule dictates that when there is a negative term with an odd number power, the negative sign can be extracted from the expression.
Hence,
(-27)^1/3=-(27^1/3)
Further simplifying the term, we know that 3^3=27,
-(27^1/3)=-(3^3*1/3)
Multiplying the powers for the entire expression,
-(3^3*1/3)/(x^9*1/3)=-3^1/x^3=-3/x^3
The simplest form of the expression (-27x^-9)^¹/₃ is -3/x^3
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Yuson must complete a certain number of hours of community service. she does 2 hours of service each day. after 8 days, yuson has completed half of her required community service.
Answer:
i don't know what the question is but the total amount of comunity service she must do is 32 hours
Step-by-step explanation:
2 x 8 = 16 16 x 2 or 16 + 16 = 32 thus she must complete 32 hours of comunity service and she has already completed 16 hours of comunity service so she has 16 hours left to complete.
hope this helped = )
6 in.
4 in.
6 in. Math
It is an isosceles triangle.
A triangle with two equal sides is said to be isosceles. Also equal are the two angles that face the two equal sides. In other terms, an isosceles triangle is a triangle with two sides that are the same length.
There are mainly three types of triangles:
Equilateral triangle
A triangle with three equal-length sides is said to be equilateral, matching what might also be referred as as a "regular" triangle. Because all three sides of an isosceles triangle are equal, an equilateral triangle is a particular case of an isosceles triangle. There are three equal sides to an equilateral triangle.
Isosceles triangle
A triangle with two equal sides is said to be isosceles.
Scalene triangle
A scalene triangle is a triangle wherein all 3 facets have distinct lengths. Also the angles of a scalene triangle have distinct measures. Some proper triangles may be a scalene triangle while the alternative angles or the legs aren't congruent.
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Deepa needed to get her computer fixed. She took it to the repair store. The
technician at the store worked on the computer for 4.25 hours and charged her $167
for parts. The total was $655.75. Write and solve an equation which can be used to
determine 2, the cost of the labor per hour.
Answer:115
Step-by-step explanation:
(4.25x) + 167= 117.35
Anybody know the answer to this question?
Answer:
slope 1/3
y = -2
x=1/3-2
Step-by-step explanation:
slope 1/3
y = -2
x=1/3-2
do these ratios form a proportion? 5:10 11:14
Answer: no
Step-by-step explanation:
A = 7, B = 13 and C = 6 then D = 11.1428571429. 3. A = 28, B = 34 and D =15 then C= 12.3529411765. 4. A = 13, B = 15, C = 2 and D = 33 then 13: 15
Look at the image.
Please help
Answer:
well, best i can do for you : F
Step-by-step explanation:
Calculator soup
I forgot how to do this stuff, sorry