Inverse function for the function f(x)= |x+5|, x>-5 is f⁻¹(x) = -5 ± x
What is inverse function?An inverse function or an anti function is defined as a function, which can reverse into another function. In simple words, if any function “f” takes x to y then, the inverse of “f” will take y to x. If the function is denoted by 'f' or 'F', then the inverse function is denoted by f-1 or F-1.
Given function,
f(x) = |x + 5| , x>-5
It can be written as
y = |x + 5|
Replacing x with y
x = |y + 5|
Solving for y
y + 5 = ± x
y = -5 ± x
Replacing y with f⁻¹(x)
f⁻¹(x) = -5 ± x
Hence, f⁻¹(x) = -5 ± x is the inverse function for function f(x)= |x+5|, x>-5
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PLEASE HELP QUICKLY
Answer: 10.7 or 10.8
Step-by-step explanation:
so, first [tex]a^{2} +b^{2} =c^{2}[/tex]
while [tex]a = 3.75[/tex] and [tex]b=10[/tex] and [tex]c=?[/tex]
so, it will be written as,
[tex]3.75^{2} +10^{2} =c^{2} \\[/tex]
[tex]14.0625+100=c^2[/tex]
[tex]114.0625=c^2[/tex] then square root both sides to have an answer of:
[tex]10.7=c[/tex]
That's if you are going to use the [tex]a=3.75[/tex]. as written in the question...
while if you're going to use [tex]a=4[/tex] (as shown in the figure) then only change the 3.75 with 4.
which will equal to...
[tex]4^2+10^2=c^2[/tex]
[tex]16+100=c^2[/tex]
[tex]116=c^2[/tex] then square root both sides to have an answer of:
[tex]10.77=c[/tex]
[tex]10.8[/tex] ≈ [tex]c[/tex]
hope you've understanded.!
Can someone please help me with this equation
The measure of the angles m∠BOX = 77.5° and m∠AOX = 77.5°.
What is the angle bisector of an angle?
The angle bisector of an angle is a line or line segment that divides the angle into two equal parts, creating two smaller angles that are congruent (i.e., have the same measure). The angle bisector starts from the vertex of the angle and extends to the opposite side or ray of the angle, dividing the angle into two smaller angles that have the same number of degrees.
By the definition of the angle bisector of an angle, the angle bisector divides the angle in two equal measures.
As m∠AOB = 155°
m∠BOX = 1/2 * m∠AOB
m∠BOX = 1/2 * 155
m∠BOX = 77.5°
also m∠AOX = 77.5°
Hence, the measure of the angles m∠BOX = 77.5° and m∠AOX = 77.5°.
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if an object is projected horizontally from a height of 5m with an initial velocity of 7 m/s what is the value of V0y?
The value of the final velocity before striking the ground will be 9.899 meters per second.
What is a vector?The quantity which has magnitude, and direction, and follows the law of vector addition is called a vector.
If an object is projected horizontally from a height of 5m with an initial velocity of 7 m/s.
We know that if the object is projected horizontally, so initially the object has a vertical speed is zero. Then it increases due to acceleration due to gravity.
The speed of the object before striking the ground is given as,
v² - u²= 2gh
v² - 0² = 2 × (9.8) × (5)
v² = 98
v = 9.899 meters per second
The value of the final velocity before striking the ground will be 9.899 meters per second.
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The lunch special at Rachel's Restaurant is a sandwich, a drink and a dessert. There are 2 sandwiches, 3 drinks, and 2 desserts to choose from. How many lunch specials are possible?
Answer:
3 lunch specials are possible.
20% discount on $365 purchase
Answer:
To find the amount of the discount, we need to multiply the purchase price by 20% or 0.20.
Discount = $365 × 0.20 = $73
So, the discount on a $365 purchase is $73.
The price after the discount would be $365 - $73 = $292.
To calculate the discount on a $365 purchase with a 20% discount, you can follow these steps:
1. Calculate the discount amount:
Discount = 20% x $365 = $73
2. Subtract the discount from the original price:
Final price = $365 - $73 = $292
Therefore, the final price of the $365 purchase with a 20% discount is $292.
Jan, Freda and Pieter share some money.
Freda gets 3 times as much as Jan.
Pieter gets half as much as Freda.
(a) Write down the ratio of the amounts of money that they each get.
Give your answer in its simplest form.
The ratio of the amounts of money that they each get:
1 : 3 : 3/2
What is the ratio?A ratio in mathematics is a comparison of two or more numbers that shows how big one is in comparison to the other. The dividend or number being divided is referred to as the antecedent, while the divisor or number that is dividing is referred to as the consequent.
Let's represent the amount of money that Jan gets as x.
Then, the amount of money that Freda gets is 3x,
and the amount of money that Pieter gets is:
= (1/2) x 3x
= 3/2 x (x)
The ratio of the amounts of money that they each get can be written as:
⇒ x : 3x : 3/2 x (x)
⇒ 1 : 3 : 3/2
So, Jan gets 1 unit of money, Freda gets 3 units of money, and Pieter gets 3/2 units of money.
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Graph the line with slope -1 passing through the point (1,-5)
Answer:
please review the attachment
Use calculator to find 61.6 to the nearest hundredth
Answer : 61.60
Step-by-step explanation:
Answer:61.60
Step-by-step explanation:
i just typed it in
riya wants to buy a mirror which one of these shapes has only one line of symmetry
Answer:
Of the shapes you mentioned (circle, square, triangle, rectangle), the only one that has only one line of symmetry is the triangle. All other shapes have multiple lines of symmetry.
Step-by-step explanation:
rj and is 2 brother are given php2000 weekly allowance they have allocoted 60% for food 8% for fare 15% for school needs and the remaining 17% for savings how much is allocoted for the following
Answer:
RJ and his 2 brothers are given a weekly allowance of PHP 2,000. They have allocated 60% for food, 8% for fare, 15% for school needs, and 17% for savings.
For food, the allocation would be: PHP 2,000 x 60% = PHP 1,200.
For fare, the allocation would be: PHP 2,000 x 8% = PHP 160.
For school needs, the allocation would be: PHP 2,000 x 15% = PHP 300.
For savings, the allocation would be: PHP 2,000 x 17% = PHP 340.
So, for food, the allocation is PHP 1,200, for fare, it's PHP 160, for school needs, it's PHP 300, and for savings, it's PHP 340
i need help with this question ASAP
In the image of the trapezoid the value of angle C is 82 degrees
What is a trapezoid?A trapezoid is a quadrilateral with one pair of parallel sides.
Opposite angles of a trapezoid are angles that are located across from each other, with a side of the trapezoid between them.
In a trapezoid, opposite angles are always congruent, meaning they have the same measure. This is a result of the fact that a trapezoid is a parallelogram, which means that its opposite sides are parallel and equal in length.
When opposite sides of a parallelogram are parallel, it follows that opposite angles are congruent.
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Which of the following is an example of a continuous random variable?a. A Bernoulli trial
b. Binomial random variable
c. Normal random variable
d. Discrete uniform random variable
An example of a continuous random variable is a Normal random variable.
What is a normal random variable?
A random variable is a variable with an unknown value or a function that gives values to each of the results of an experiment. A random variable can be either discrete (having definite values) or continuous (any value in a continuous range).
Here, we have
We have to determine the example of a continuous random variable.
We concluded that the example of a continuous random variable is a normal random variable.
Hence, an example of a continuous random variable is a Normal random variable.
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Choose all of the values that are solutions to inequality x < -2
Answer:
The solution to the inequality x < -2 is all real numbers that are less than -2. This means that any number that is less than -2 will satisfy the inequality, but any number that is greater than or equal to -2 will not.
So, the solution set for x < -2 is all real numbers that are less than -2. This solution set can be expressed as (-∞, -2).
Therefore, the values that are solutions to the inequality x < -2 are:
• all real numbers less than -2, such as -3, -4, -5, etc.
Note that -2 itself is not part of the solution set, since it is not less than -2.
statements about -27 that are true
The statements about the number -27 that are true are given as follows:
-27 is an integer number.-27 is a rational number.What are rational and irrational numbers?Rational numbers are numbers that can be represented by fractions, such as numbers that have no decimal parts, or numbers in which the decimal parts are terminating or repeating.
Irrational numbers are numbers that cannot be represented by fractions, being non-terminating and non-repeating decimals, such as non-exact square roots.
Integer numbers are numbers that have no decimal part, hence -27 is an example of an integer number, which are also rational numbers.
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Place the following set of scores in a frequency distribution table.
7, 5, 6, 4, 4, 3, 8, 9, 4, 7, 5, 5, 6
9, 4, 7, 5, 10, 6, 8, 5, 6, 3, 4, 8, 5
Are the scores clustered together, or are they spread out across the scale? a. Most of the scores are clustered within 1 or 2 points of X = 6. b. The scores are spread out fairly evenly across the scale. c. Most of the scores are clustered within 1 or 2 points of X = 8. d. The scores are clustered in two peaks near X = 3 and near X = 9.
GIven the set of scores, it is seen that a. Most of the scores are clustered within 1 or 2 points of X = 6.
What is a Frequency Table?
A frequency table is just a two-column "t-chart" or table that lists all of the potential outcomes and their corresponding frequencies as seen in a sample.
Here is a frequency distribution table for the given set of scores:
Score Frequency
3 2
4 5
5 5
6 5
7 2
8 3
9 2
10 1
You can see that the scores are clustered around X = 6, with the highest frequency (5) at score 6 and the next highest frequency (5) at score 5.
The scores are not evenly spread out across the scale.
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(c) 10:35 f the foll ing ratio
The ratio 10:35 can be simplified to 2:7.
What is a Ratio?
A ratio in mathematics demonstrates how many times one number is present in another.
For instance, if a dish of fruit contains eight oranges and six lemons, the ratio of oranges to lemons is eight to six.
Similarly, the ratio of oranges to the overall amount of fruit is 8:14, while the ratio of lemons to oranges is 6:8.
The ratio 10:35 can be simplified to 2:7.
To simplify a ratio, you can divide both values by the greatest common factor. In this case, the greatest common factor of 10 and 35 is 5, so 10 divided by 5 is 2, and 35 divided by 5 is 7.
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Simply the following ratio 10:35
The width of a table is 4 2/5
feet. The length of the table is 2 1/5
times as long as its width.
Which equation shows the length of the table?
Please answer ASAP
The equation that shows the length of the table is length = 11/5 × 22/5
What is a fraction?A fraction can be defined as the part of a whole number, variable or element.
The different types of fractions are;
Proper fractionsImproper fractionsMixed fractionsComplex fractionsSimple fractionsFrom the information given, we have that;
Length = 2 1/5 × Width
Width = 4 2/5 feet
Turn into improper fractions
Width = 22/5 feet
Then, length = 11/5 × 22/5
Hence, the equation is 11/5 × 22/5
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Supervisor: "Your average time to process a sale is 14 minutes. You have to decrease
that by 25% this month in order to meet your goals."
Employee: "Thank you for the feedback. I will work on lowering my processing time to
minutes by the end of the month."
3.5
7
10.5
12
17.5
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{\textit{\LARGE a}\% of \textit{\LARGE b}}\\ \cline{1-1} \\ \left( \cfrac{\textit{\LARGE a}}{100} \right)\cdot \textit{\LARGE b} \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{25\% of 14}}{\left( \cfrac{25}{100} \right)14}\implies \text{\LARGE 3.5}[/tex]
A young channel catfish weighs about 0. 1 pound. During the next 8 weeks, its weight increases by about 23% each week.
Weight is 0.229 pounds after 4 weeks.
As a young channel catfish only weights 0.1 pounds,
It gains weight over the following 8 weeks at a rate of roughly 23% every week.
In this case, the exponential growth function is as follows:
Exponential formulas are provided by.
[tex]y=a(1+r)^{x}[/tex]
where an is the starting amount, r is the growth rate, x is the duration, and y is the weight at the end of "x" weeks.
Our values are a = 0.1, r = 0.23 (or 23%), and t = 4.
As a result,
[tex]y=0.1(1+0.23)^{4} \\[/tex]
y = 0.1(2.289)
y = 0.229
Consequently, the weight at 4 weeks is 0.229 pound.
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Complete question:
A young channel catfish weighs about 0.1 pound. During the next 8 weeks, its weight increases by about 23% each week. About how much will the catfish weigh after 4 weeks? Round your answer to the nearest thousandth of a pound.
what is the least common denominator for 5/18, 11/12, and 6/13
Answer:
LCD → 468
Step-by-step explanation:
[tex]\frac{5}{18} = \frac{5}{18} * \frac{26}{26} = \frac{130}{468}[/tex]
[tex]\frac{11}{12} = \frac{11}{12} * \frac{39}{39} = \frac{429}{468}[/tex]
[tex]\frac{6}{13} = \frac{6}{13} * \frac{36}{36} = \frac{219}{468}[/tex]
Hence, the least common denominator for these three fractions would be 468.
Circles and please answers please just need help Thank you so much
The area of the shaded region is given as follows:
As = 324(2π - 1) in².
What is the area of the shaded region?The area of a circle of radius r is given by π multiplied by the radius squared, as follows:
A = πr².
For this problem, the circle has a radius of [tex]18\sqrt{2}[/tex], as the radius is the diagonal of the square, hence the area is given as follows:
A = π x [tex](18\sqrt{2})²[/tex]
A = 648π in².
The area of a square of side length s is given by the square of the side length, hence the area of the square is given as follows:
A = 18²
A = 324 in².
Hence the area of the shaded region is given as follows:
As = 648π - 324
As = 324(2π - 1) in².
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The circumferrence of the circle at the center of a basketball court is 37.68 feet. Find the area of the circle at center court. Use 3.14 for pi. Please answer.
113.097 is the area (i used 3.14) pls comment for explanation :)
Find the value of x that makes each sentence true.
If (5 1/5)^5=25x then x =
If (8 1/3)^2= 4x, then x =
The first equation is:
(5 1/5)^5 = 25x
To solve for x, we need to simplify the left side of the equation first.
(5 1/5)^5 = (5 + 1/5)^5 = 6^5 = 7776
So,
7776 = 25x
Therefore,
x = 7776/25 = 311.04
For the second equation:
If (8 1/3)^2 = 4x, then x =
We need to simplify the left side of the equation first.
(8 1/3)^2 = (8 + 1/3)^2 = 9^2 = 81
So,
81 = 4x
Therefore,
x = 81/4 = 20.25
So the values of x that make each sentence true are 311.04 and 20.25, respectively.
How can the statement be rewritten as a conditional statement in if-then form? the sum of the digits of a two-digit number is less than the value of the original two-digit number.
The statement "the sum of a two-digit number is less than the value of the original two-digit number" can be rewritten as conditional statement. If the sum of two digits of a two-digit number is less than the value of the original two-digit number, the number is valid.
A conditional statement, "if p, then q," with p representing the hypothesis and q representing the conclusion. We can identify the hypothesis and conclusion by rewriting the statement "the sum of the digits of a two-digit number is less than the value of the original two-digit number" as an if-then conditional statement.
The hypothesis is the condition that must be satisfied in order to valid the conclusion. In this case, the hypothesis is "the sum of the digits of a two-digit number is less than the value of the original two-digit number".
By combining these, we can rewrite the statement as follows:
If the sum of a two-digit number's digits is less than the value of the original two-digit number, the number is valid.
The hypothesis (the sum of the digits of a two-digit number is less than the value of the original two-digit number) is a sufficient condition for the conclusion, according to this conditional statement (the number is valid). In other words, if the hypothesis is correct, we can be certain that the conclusion is correct as well.
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Find the perimeter of the triangle as both a decimal and in simplest
radical form
Add the sides' lengths to find a triangle's perimeter. As an illustration, the perimeter of a triangle with sides a, b, and c is given by P = a + b + c.
What is meant by perimeter?The radius of a shape's edge is known as the perimeter. Discover how to calculate a shape's perimeter by multiplying its side lengths.It is measured from the object's edge to its perimeter. Like the yard that is fenced in at your home. The distance around anything is called its perimeter. The fence is 200 feet long for a yard that is 50 feet by 50 feet.The measurement of a shape's perimeter is its length. It takes adding the lengths of all four sides to determine a rectangle's or square's perimeter.The length of a two-dimensional shape's perimeter is referred to as its perimeter. The total length of all the sides of the thing is also a definition for it.To learn more about perimeter refer to:
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The value of a machine, V , at the end of t years
The value of machine after 2 years is $346.4.3
What is Rate of Depreciation?Subtract the asset's cost from its salvage value (what you anticipate it to be worth at the end of its useful life) to determine depreciation using the straight-line technique. The amount that can be depreciated, or the depreciable basis, is the outcome. Subtract this sum from the asset's useful life, which is measured in years.
Given:
C = $707 (the original cost),
r = 0.3 (the rate of depreciation),
and t = 2 (years that have gone by)
Using the Formula
V = C [tex](1-r)^t[/tex]
V = (707)(1 - 0.3)²
V = (707)(0.7)²
V = (707)(0.49)
V = 346.43
Thus, the value of machine is $346.43
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A distribution of all sample means or sample variances that could be obtained in samples of a given size from the same population is called
Answer:
sampling distribution
Step-by-step explanation:
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the ratio of the number of students playing basketball to soccer at a local middle school is 5:2. what percent of the students at the middle school play soccer?(round to the nearest percent)
Answer: Let's say there are a total of 100 students at the middle school. Then, 5 parts out of 7 are playing basketball and 2 parts out of 7 are playing soccer. The percent of students playing soccer can be calculated as follows:
(2/7) * 100 = 28.57% (rounded to the nearest percent)
So, approximately 28.57% of the students at the middle school play soccer.
Step-by-step explanation:
Suppose you invest $500 into an account earning simple interest. The APR is 2% and you invest it for 5 years. Choose two answers: How much would your investment be worth at the end? What equation should you use to calculate this?
1a. $2500.10
2a. $550
3a. $1000
4a. $2550
5a. $5500
1b. A = 500 ( 1 + 2(5))
2b. A = 500 (1 + 0.2(5))
3b. A = 500 (1 + 0.02(5))
Answer:
a=1000.10
Step-by-step explanation:
Her little sister's birthday is next week, so Brittany is planning a bubble-themed birthday party! She buys a big bottle of bubble solution and divides it equally among 6 small bottles. Each small bottle holds 1/8 of a gallon of bubble solution.
Use an equation to find the amount of bubble solution in the big bottle.
There is 3/4 of a gallon of bubble solution in the big bottle.
What is an equation?
In mathematics, an equation is a statement that asserts the equality of two expressions, typically separated by an equal sign (=). An equation contains one or more variables, which are symbols that represent unknown values, and may also contain constants, coefficients, and arithmetic operations such as addition, subtraction, multiplication, and division.
Let's use "x" to represent the amount of bubble solution in the big bottle, in gallons.
According to the problem, the big bottle was divided equally among 6 small bottles, and each small bottle holds 1/8 of a gallon of bubble solution. Therefore, the total amount of bubble solution in the big bottle is equal to the sum of the amounts in the 6 small bottles:
x = 6 * (1/8)
Simplifying the right-hand side of the equation, we get:
x = 3/4
Therefore, there is 3/4 of a gallon of bubble solution in the big bottle.
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