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When a function is compose by its inverse, the result is its original input. Therefore,
[tex]f(f^{-1}(x))=x[/tex]Related Questions
Rosalie is training for a marathon. She jogs for 30 minutes at a rate of 5 miles per hour then she decreases her speed over a period of time and walks for 60 minutes at a rate of 3 miles per hourWhat is the range of this relation
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Answer:
A. 3 ≤ y ≤ 5
Explanation:
The range is the set of values that the variable y can take. In this case, the variable y is the speed, so the range is the set of values of Rosalie's speed in her training.
Since the speed takes values from 3 miles per hour to 5 miles per hour, the range is
3 ≤ y ≤ 5
Please help will mark Brainly
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Answer:x=7
Step-by-step explanation:
I answered a problem for my prep guide, I just need to know if I’m correct or not. And I would like it to be answered as well just to make sure that I did everything correctly
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Notice that,
[tex]f(x)=3^{x-1}-6=3^x\cdot3^{-1}-6=\frac{3^x}{3}-6[/tex]And there are no restrictions for the values that x can take. The domain is the whole set of real numbers.
Now, we need to check for the limits when x->+/- infinite, as follows:
[tex]\begin{gathered} \lim _{x\to\infty}3^x=\infty \\ \lim _{x\to-\infty}3^x=\lim _{x\to\infty}\frac{1}{3^x}=0 \end{gathered}[/tex]Then, the range of 3^x is (0, infinite).
Finally, we can get the range of function f(x):
[tex]\lim _{x\to\infty}f(x)=\frac{1}{3}(\lim _{x\to\infty}3^x)-6=\frac{1}{3}\infty-6=\infty[/tex][tex]\lim _{x\to-\infty}f(x)=\frac{1}{3}(\lim _{x\to-\infty}3^x)-6=\frac{1}{3}\cdot0-6=-6[/tex]Then,
[tex]\begin{gathered} The\text{ range of }f(x)\text{ is} \\ Range=(-6,\infty) \end{gathered}[/tex]which expression are equivalent to[tex]( \frac{750}{512})^{ \frac{1}{3} } [/tex]
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Fractional exponents refer to the radicals
Option A (Correct)
[tex]\frac{\sqrt[3]{750}}{\sqrt[3]{512}}[/tex]Option B (Incorrect)
750 is not a perfect cube
Option C (Correct)
[tex]\sqrt[3]{\frac{750}{512}}[/tex]Option D (Incorrect)
The denominator does not have the root
Option E (Incorrect)
The numerator does not have the root
Option F (Correct)
[tex]\frac{5}{8}\sqrt[3]{6}[/tex]May I please get help with Solve for x: −3<−10(x+15)≤7
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Given the compound inequality;
[tex]-3<-10(x+15)\le7[/tex]We would begin by simplifying the parenthesis as follows;
[tex]\begin{gathered} -3<-10(x+15) \\ \text{AND} \\ -10(x+15)\le7 \end{gathered}[/tex]We shall now solve each part one after the other;
[tex]\begin{gathered} -3<-10(x+15) \\ -3<-10x-150 \\ \text{Collect all like terms and we'll have;} \\ -3+150<-10x \\ 147<-10x \\ \text{Divide both sides by -10} \\ \frac{-147}{10}>x \end{gathered}[/tex]We can switch sides, and in that case the inequality sign would also "flip" over, as shown below;
[tex]\begin{gathered} \frac{-147}{10}>x \\ \text{Now becomes;} \\ x<\frac{-147}{10} \end{gathered}[/tex]For the other part of the compound inequality;
[tex]\begin{gathered} -10(x+15)\le7 \\ -10x-150\le7 \\ \text{Collect all like terms and we'll have;} \\ -10x\le7+150 \\ -10x\le157 \\ \text{Divide both sides by -10} \\ \frac{-10x}{-10}\le\frac{157}{-10} \\ x\ge-\frac{157}{10} \end{gathered}[/tex]Therefore, the values are;
[tex]\begin{gathered} x<-\frac{147}{10} \\ \text{And } \\ x\ge-\frac{157}{10} \\ \text{Hence;} \\ -\frac{157}{10}\le x<-\frac{147}{10} \end{gathered}[/tex]Written in interval notation, this now becomes;
[tex]\lbrack-\frac{157}{10},-\frac{147}{10})[/tex]In rectangle ABCD, the diagonals intersect at E. If m angle∠AEB= 3x and m angle∠DEC= x+80, find m angle∠AEB and m angle∠EBA.
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Since the angles∠ AEB and ∠DEC are vertically opposite angles, they are congruent, so we have:
[tex]\begin{gathered} 3x=x+80 \\ 2x=80 \\ x=40 \end{gathered}[/tex]So the measure of angle ∠AEB is:
[tex]\begin{gathered} \angle\text{AEB}=3x \\ \angle\text{AEB}=3\cdot40=120\degree \end{gathered}[/tex]The diagonals of a rectangle are congruent and intersect in their middle point, so the segment AE is congruent to the segment EB, therefore the triangle AEB is isosceles, so the angle ∠BAE is congruent to ∠EBA.
The sum of the internal angles of a triangle is 180°, so in triangle AEB we have:
[tex]\begin{gathered} \angle\text{BAE}+\angle\text{EBA}+\angle\text{AEB}=180\degree \\ \angle\text{EBA}+\angle\text{EBA}+120=180 \\ 2\angle\text{EBA}=60 \\ \angle\text{EBA}=30\degree \end{gathered}[/tex]Find x if g(x + 2) = 6
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timothy and freda were asked to solve 675÷5 who is correct and why I can send you a picture would you like that ??
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Since both came to the same answer using a different method, I would say that both are correct.
Kiera is decorating for a party. She wants balloons in 6 different locations. In each location, she will have 3 bunches of 4 balloons. How many balloons will Kiera need in all?
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6 x 12 = 70 balloons needed in total
Suppose ABC is a right triangle of lengths a, b and c and right angle at c. Find the unknown side length using the Pythagorean theorem and then find the value of the indicated trigonometric function of the given angle. Rationalize the denominator if applicable.Find tan B when a=96 and c=100
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To begin with, we will have to sketch the image of the question
To find the value of tan B
we will make use of the trigonometric identity
[tex]\tan \theta=\frac{opposite}{adjacent}[/tex]From the diagram given
[tex]\tan B=\frac{\text{opposite}}{\text{adjacent}}=\frac{b}{96}[/tex]Since the value of b is unknown, we will have to get the value of b
To do so, we will use the Pythagorean theorem
[tex]\begin{gathered} \text{hypoteuse}^2=\text{opposite}^2+\text{adjacent}^2 \\ b^2=100^2-96^2 \\ b=\sqrt[]{784} \\ b=28 \end{gathered}[/tex]Since we now know the value of b, we will then substitute this value into the tan B function
so that we will have
[tex]\tan \text{ B=}\frac{opposite}{adjecent}=\frac{b}{a}=\frac{28}{96}=\frac{7}{24}[/tex]Therefore
[tex]\tan \text{ B=}\frac{7}{24}[/tex]The diameter of a circle is 20 kilometers. What is the angle measure of an arc bounding a sector with area 10pi square kilometers?Give the exact answer in simplest form. ____°. (pi, fraction,)
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The area of a circular sector is given by:
[tex]A=\frac{1}{4}\cdot\pi\cdot d^2\cdot\frac{\theta}{360}[/tex]Where:
π ≈ 3.14159
d = diameter of the circle
θ = angle of the circular sector
In our problem we have that:
[tex]\begin{gathered} A=10\cdot\pi\cdot km^2 \\ d=20\operatorname{km} \end{gathered}[/tex]And we need to find the value of the angle θ. So in order to solve the problem, we replace the given data in the formula of above:
[tex]\begin{gathered} A=\frac{1}{4}\cdot\pi\cdot d^2\cdot\frac{\theta}{360^{\circ}} \\ 10\cdot\pi\cdot km^2=\frac{1}{4}\cdot\pi\cdot(20\operatorname{km})^2\cdot\frac{\theta}{360^{\circ}} \end{gathered}[/tex]And now we solve for θ:
[tex]\begin{gathered} 10\cdot\pi\cdot km^2=\frac{1}{4}\cdot\pi\cdot400\cdot km^2\cdot\frac{\theta}{360^{\circ}} \\ 10=100\cdot\frac{\theta}{360^{\circ}} \\ 360^{\circ}\cdot\frac{10}{100}=\theta \\ \theta=36^{\circ} \end{gathered}[/tex]So the answer is that the angle of the circular sector is: 36°
Determine if the expression -4c5 + c3 is a polynomial or not. If it is a polynomial, state the type and degree of the polynomial. .
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It is a polynomial. 5th degree (incomplete) polynomial. Binomial.
1) Considering the expression:
[tex]-4c^5+c^3[/tex]2) And the Polynomial definition as:
[tex]P(x)=a_nx^n+a^{}_{n-1}x^{n-1}+.\ldots+a_0[/tex]We can state that this is an incomplete polynomial.
About the degree, it is a 5th-degree polynomial given by its highest exponent.
Binomial since it has two terms.
3) Hence the answer is an incomplete polynomial, 5th degree.
Write the fraction as equivalent fraction with the given denominator
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Okay, here we have this:
Considering the provided fraction, we are going to rewrite it as equivalent fraction with the given denominator, so we obtain the following:
Then we will solve the following proportion to find the missing value:
[tex]\frac{3}{4}=\frac{x}{12}[/tex]Solving for x:
[tex]\begin{gathered} x=\frac{3}{4}\cdot12 \\ x=\frac{36}{4} \\ x=9 \end{gathered}[/tex]Finally we obtain the following fractions:
[tex]\frac{3}{4}=\frac{9}{12}[/tex]Answer: 9/12
Step-by-step explanation:
Use point-slope form to write the equation of a line that passes through the point (-8,-16)(−8,−16) with slope 11.
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The general point-slope equation of a line is:
[tex]y=m\cdot(x-x_0)+y_0\text{.}[/tex]Where:
• m is the slope of the line,
,• and (x0,y0) are the coordinates of one of the points of the line.
In this problem we have:
• m = 11,
,• (x0,y0) = (-8,-16).
Replacing these values in the general equation, we have:
[tex]y=11\cdot(x+8)-16[/tex]Answer
The point-slope equation of the line is:
[tex]y=11\cdot(x+8)-16[/tex]A private college advertise that last year their freshman students on average how do you score of 1140 on the college entrance exam. Assuming that the average refers to the mean, Which of the following claims must be true based on this information? Last year some of their freshman students had a score of exactly 1140 on the exam last year more than half of their freshman students had a score of at least 1140 on the exam last year all their freshman students have a score of at least 1140 on the exam next year at least one of their freshman students will have a score of at least 1140 on theexam last year at least one of their freshman students had a score of more than 900 on the exam or none of the above statements are true
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We know that the mean score obtained by the freshman students last year was 1140.
It means that the sum of all the freshman students' scores from last year, divided by the number of freshmen students resulted in the number 1140.
It doesn't mean necessarily that one or more students had a score of exactly 1140.
Step 1
Find an example showing that some of the statements must not be true.
A way of obtaining this score is if half the N students had a score of 0, and the other half had a score of 2280:
[tex]mean=\frac{\frac{N}{2}\cdot0+\frac{N}{2}\cdot2280}{N}=\frac{N\cdot1140}{N}=1140[/tex]From this example, none of the students had a score of exactly 1140, and half of them had a score less than 1140. So, we can conclude that the first three statements must not be true.
Step 2
Analyze the other statements.
The fourth statement must not be true because we can't conclude anything for sure for next year's scores based on the last year's scores.
Let's analyze the fifth statement. Suppose it must not be true, i.e., all the freshman students had scores equal to or less than 900. Then, since the mean score can't be greater than the maximum score, the mean score would be no more than 900. Wich is false because it was 1140 > 900.
Therefore, the fifth statement must be true.
Answer
The only claim that must be true is:
Last year, at least one of their freshman students had a score of more than 900 on the exam.
???. Can you help me .???I have to find the simple interest earned to the nearest cent for each principle, interest rate, and time
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Given:
Principal amount, P = $640
Time, T = 2 years
Interest rate, R = 3%
Let's find the simple interest.
To find the simple interest, apply the Simple Interest formula:
[tex]I=\frac{P\ast R\ast T}{100}[/tex]Substitute values into the formula:
[tex]\begin{gathered} I=\frac{640\ast3\ast2}{100} \\ \\ I=\frac{3840}{100} \\ \\ I=38.40 \end{gathered}[/tex]Therefore, the simple interest to the nearest cent is $38.40
ANSWER:
$38.40
in the triangle abc a =65 b =58 identity the longest side of the triangle
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We know two angles of a triangle, ∠A = 65° and ∠B = 58°, and we have to identify the longest side.
The longest side will be the one that is opposite to the widest angle. In our case, we don't know the measure of C, but we know that the sum of the three measures has to be 180°, so we can calculate it as:
[tex]\begin{gathered} m\angle A+m\angle B+m\angle C=180\degree \\ 65+58+m\angle C=180 \\ m\angle C=180-65-58 \\ m\angle C=57\degree \end{gathered}[/tex]As the widest angle is at vertex A, the longest side will be its opposite, which correspond to the side formed by the other two vertices: B and C.
The longest side is BC.
Which equation can Pablo use to find p the regular price of the shirt
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The final price of the shirt is given by the regular price minus the discount value. Since the final price is $28, the regular price is p, and the discount is $16, the equation is
[tex]p-16=28[/tex]If we add 16 to both sides of the equation, we have
[tex]\begin{gathered} p-16+16=28+16 \\ p=28+16 \end{gathered}[/tex]If we invert the order of the equality, we get the last option as the answer
[tex]16+28=p[/tex]if 5 plus 5 is 10 and 44 plus 87 plus 98 plus 1415 is what???
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Answer:
5+5=10
44+87= 131
98+131=229
1415+229=1644
Step-by-step explanation:
the answer is 1644 so all you need to kno w is to follow the procedure you use for the 5 plus 5 method
If a ^20 = (a^n)^m, which of the following could be values for m and n?obA) m = -5, n = -4B) m = 10, n = 10C) m = 22, n = -2D) m = 15, n = 5d
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a ^20 = (a^n)^m
When we have a number raised to a power two time, we can multiply the powers;
(a^n)^m = a ^ (n x m)
So, since both sides have the same base:
a^20 = a^ (nxm)
20 = n x m
So, the product of n and m must be 20
A) -5 x -4 = 20
B) 10 x 10 =100
c) 22 x -2 =-44
d)15 x 5 = 75
The correct answer is A.
I’m trying to find out where the second point can be marked
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ANSWER
First point = (0, 3)
Second point = (1, -1)
Third point = (2, -5)
Graph:
EXPLANATION
To plot a graph using the slope and the y-intercept, simply apply the following rules:
1. Evaluate the function at x = 0, to determine the y-intercept which was (0,3) from the question
2. Determine the slope by finding the change in y divided by change in x. This was -4 according to the question. Which could also be written as -4/1; that is, rise divided by run
3. Now, from the value (0, 3) we got in step 1, we move down by 4 units and then to the right by 1 unit. This will lead us to the Second point of (1, -1). Also from this point, we move down by 4 units and then to the right by 1 unit to get to the Third point of (2, -5). You may decide to continue this pattern if you want more points.
4. Draw a straight line joining the 3 points together.
U is defined as the set of all integers. Consider the following sets:A = {1, 2, 3, 4, 5}B = {x| 0 < x < 5}C = {p|P is an even prime number}D = {4. 5. 6. 7}E = {x| x is a square number less than 50}Find BDGroup of answer choices40, 1, 2, 3, 4, and 54 and 50, 1, 2, 3, 4, 5, 6, and 7
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We will have te following
BUD:
[tex]B\cup D\colon1,2,3,4,5,6,7[/tex]So BUD is 1,2,3,4,5,6 & 7.
(Please reference attached photo for problem.)Show your work please. Also, What is the perimeter?
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Solution:
Given the shape below:
The above shape is a combination of a semicircle and a rectangle labeled as A and B respectively.
To find the perimeter of the shape:
step 1: Evaluate the perimeter of the circle.
The perimeter of the semicircle is expressed as
[tex]\begin{gathered} perimeter\text{ of semicircle=2}\pi r \\ where\text{ r is the radius} \\ \pi\Rightarrow3.14 \end{gathered}[/tex]Thus, we have
[tex]\begin{gathered} perimeter=2\times3.14\times(\frac{10}{2}) \\ =31.4\text{ cm} \end{gathered}[/tex]step 2: Evaluate the perimeter of the rectangle.
The perimeter of the rectangle is expressed as
[tex]\begin{gathered} perimeter=2(l+w) \\ where \\ l\Rightarrow length \\ w\Rightarrow width \end{gathered}[/tex]In this case, we have
[tex]\begin{gathered} l=10\text{ cm} \\ w=4\text{ cm} \\ thus, \\ Perimeter\text{ = 2\lparen10+4\rparen} \\ =2(14) \\ =28\text{ cm} \end{gathered}[/tex]step 3: Sum up the perimeters.
Thus, we have
[tex]\begin{gathered} perimeter\text{ of shape = perimeter of circle + perimeter of rectangle} \\ =31.4+28 \\ \Rightarrow perimeter\text{ of shape = 59.4 cm} \end{gathered}[/tex]Hence, the perimeter of the shape is evaluated to be
[tex]59.4\text{ cm}[/tex]Since f is parallel to line g, use the diagram to the right right to answer the following question
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Step 1
[tex]\begin{gathered} m\angle2=m\angle6=117^o(\text{ corresponding angles are equal)} \\ m\angle6=m\angle7=117^o(vertically\text{ opposite angles are equal)} \\ \end{gathered}[/tex]Step 2
[tex]undefined[/tex]Notation scientific ad and subtract2.4 *10^5 + 0.5*10^5 =
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We will operate as follows:
[tex]2.4\cdot10^5+0.5\cdot10^5=2.9\cdot10^5[/tex]Dana rode her bike for 5 miles on Wednesday. On Thursday, she biked 4 1/3 times as far ason Wednesday. How many miles did Dana bike on Thursday?fraction or as a whole or mixed number.
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First, let's express the mixed number as a fraction:
[tex]4\text{ }\frac{1}{3}=\frac{4\cdot3+1}{3}=\frac{13}{3}[/tex]She rode her bike for 5 miles on wednesday and on thursday she biked 13/3 times as far as on wednesday, so:
5 miles * (13/3) =
[tex]5\times\frac{13}{3}=\frac{65}{3}\approx21.667miles[/tex]Circumference and the area of a circle with radius 5 ft you
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The circunference formula is given by
[tex]C=2\pi r[/tex]where r is the radius. Since r measures 5 ft, we have
[tex]\begin{gathered} C=2\pi\cdot5 \\ C=10\pi \end{gathered}[/tex]By taking into account that Pi is 3.14, the circuference is equal to 31.4 ft.
On the other hand, the area formula is given by
[tex]A=\pi r^2[/tex]Then, by substituting r=5 into this formula, we get
[tex]\begin{gathered} A=(3.14)(5^2) \\ A=3.14\times25 \\ A=78.5ft^2 \end{gathered}[/tex]then, the area is equal to 78.5 square feet
Mrs. Everett is shopping for school supplies with her children. Rose selected 3 one-inch binders and 1 two-inch binder, which cost a total of $23. Judy selected 5 one-inch binders and 3 two-inch binders, which cost a total of $49. How much does each size of binder cost?
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We define the following variables:
• x = cost of one-inch blinders,
,• y = cost of two-inch blinders.
From the statement of the problem, we know that:
• Rose selected 3 one-inch blinders and 1 two-inch blinder, which cost a total of $23, so we have that:
[tex]3x+y=23,[/tex]• Judy selected 5 one-inch blinders and 3 two-inch blinders, which cost a total of $49, so we have that:
[tex]5x+3y=49.[/tex]We have the following system of equations:
[tex]\begin{gathered} 3x+y=23, \\ 5x+3y=49. \end{gathered}[/tex]We must solve the system of equations using the elimination method, where you either add or subtract the equations to get an equation in one variable.
1) We multiply the first equation by 3, and we have:
[tex]\begin{gathered} 9x+3y=69, \\ 5x+3y=49. \end{gathered}[/tex]2) Now, we subtract the second equation to the first equation:
[tex]\begin{gathered} (9x+3y)-(5x+3y)=69-49. \\ 4x=20, \\ x=\frac{20}{4}=5. \end{gathered}[/tex]3) Replacing the value x = 5 in the second equation, and solving for y we get:
[tex]\begin{gathered} 5\cdot5+3y=49, \\ 25+3y=49, \\ 3y=49-25, \\ 3y=24, \\ y=\frac{24}{3}=8. \end{gathered}[/tex]We have found that:
[tex]\begin{gathered} x=5, \\ y=8. \end{gathered}[/tex]Answer
A one-inch binder costs $5, and a two-inch binder costs $8.
5. Math home work thanks type the answer out domain and range
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Answer:
Explanation:
Given the below quadratic function in vertex form;
[tex]g(x)=-0.25(x-1)^2+19[/tex]A quadratic equation in vertex form is generally given as;
[tex]y=a(x-h)^2+k[/tex]where (h, k) is the coordinate of the vertex.
When a
1) 3 = x + 13I need help
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We have the following:
[tex]3=x+13[/tex]solving:
[tex]\begin{gathered} x=3-13 \\ x=-10 \end{gathered}[/tex]The answer is -10