The inverse of the given function is f^-1(x)= (x - 63) /14
What is an inverse?A function's reverse function F is a function that reverses the action of f (sometimes known as the inverse of f). If the inverse of f exists, it is designated by f -1 and exists only if f is bijective. The graph of the inverse of a function shows the function and the inverse of the function, which are both plotted over the line y = x. This graph's line traverses the origin and has a slope value of 1.
The first step is to open the brackets
So now we get, f(x)= 14x - 63
Let f(x) be y so this becomes y= 14x+ 63
Now interchange the variables and we will get
x= 14y+ 63
(x- 63)/14= y
Replace y by f^-1(x).
f^-1(x)= (x - 63) /14
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Help with explaining please thank you
For given triangle, the value of x is 22.
In this question, we have been given three angles of triangle.
We need to find the value of x.
We can observe that (6x - 7)° is an exterior angle.
So, the third angle of the triangle is 180° - (6x - 7)°
We know that the sum of the all angles of the triangle is 180°
2x° + (103 - x)° + [180° - (6x - 7)°] = 180°
2x + 103 - x + 180 - 6x + 7 = 180
2x - x - 6x + 103 + 180 + 7 = 180
-5x + 290 = 180
-5x = 180 - 290
-5x = -110
x = 22
Therefore, for given triangle, the value of x is 22.
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Hello! Can you, please, explain how to solve this kind of equation "Find m+n, if P(x) = (2m-4)x^2+(5-n)x+13 is constant polynomial".
The value of m + n from getting the values of m and n from the constant polynomial P(x) = (2m - 4)x² + (5 - n)x + 13 is; 7
What is a constant polynomial?
A constant Polynomial is defined as a polynomial is a function of the form f(x) = a
where a is a real number, whose highest degree is zero.
Thus, examples of constant Polynomials are f(x) = 5, g(x) = -11 , h(y) = 7/4
Now, we are given the polynomial expression;
P(x) = (2m - 4)x² + (5 - n)x + 13
From the definition of constant Polynomials, we can say that;
2m - 4 = 0 and 5 - n = 0
Thus;
m = 2 and n = 5
Then, m + n = 2 + 5 = 7
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20% of Señora Clara's students are going to Spain for a semester. If 60 students are going to Spain, how many students does Señora Clara have in all?
The number of students in Señora Clara is 300 students
How to calculate the number of students in Señora Clara ?20% of Señora Clara's students are going to Spain for a semester
60 students are going to spain
The number of students in Señora Clara can by first calculating the percent of 20
20/100
= 0.2
Next is to divide 0.2 by 60
60/0.2
= 300
Hence there are 300 students in Señora Clara
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What transformations take f(x)=3x+1 to g(x)=-3x-5?
The transformation is:
g(x) = -f(x) - 4
So is a reflection across the x-axis followed by a translation of 4 units downwards.
What transformations take f(x) to g(x)?Here we have the two functions:
f(x) = 3x + 1
g(x) = -3x - 5
So we start at f(x), first we apply a reflection across the x-axis so we change the sign to get:
g(x) = -f(x) = -3x - 1
Now we can apply a translation of 4 units downwards so we get:
g(x) = -f(x) - 4 = -3x - 1 - 4 = -3x - 5
And in this way we transformed f(x) into g(x).
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find the value of $a 2 a 4 a 6 \dots a {98}$ if $a 1, a 2, a 3, \dots$ is an arithmetic progression with common difference 1, and $a 1 a 2 a 3 \dots a {98}
value of a2+a4+a6+……+a98 IS EQUAL TO 93.
Given, the common difference (d) =1
Let a1=a Given, a1+a2+……+a98=137
⇒(98/2)(2a+97)=137 [Sn=n/2[2a+(n−1)d]
⇒2a+97=137/49…eq.(1)
a2+a4+…+a98 (n=49 terms)
a2+a4+…+a98=49/2(a2+a98)
a2+a4+…+a98=49/2[(a+1)+a+97]
a2+a4+…+a98=49/2[2a+97+1]
a2+a4+…+a98=49/2[(137/49)+1] [using eq. 1]
a2+a4+…+a98=137/2+49/2
a2+a4+…+a98=186/2 =93
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a cellular phone company offers several different service options. one option, for people who plan on using the phone only in emergencies, costs the user $4.90 per month plus $0.52 per minute for each minute the phone is used. (a) write a linear function for the monthly cost y of the phone in terms of the number of minutes x the phone is used.
52x - 100y + 490 = 0 , is the required linear function.
What does the term "linear function" mean?
A mathematical function where the variables only occur in the first degree, where the constants are multiplied, and where the only possible combinations are addition and subtraction.
Given, the monthaly cost = y
the number of minute used = x
Hence,
the monthly cost of the phone = (4.90 + 0.52 × the number of minute used)
Given the monthly cost = y
the number of minute used = x
Hence y = 4.90 + 0.52 * x
or y = [tex]\frac{490}{100} + \frac{52}{100 } * x[/tex]
or 100y = 455 + 52x
or 52x - 100y + 490 = 0 , is the required linear function.
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A student calculated that a toy cart would roll 15.6 centimeters before stopping. After conducting an experiment, she found that her calculation had a 30% error. What are two possible values for the actual distance that the toy cart rolled before stopping?
Possible values for the actual distance that the toy cart rolled before stopping with 30% error in the calculation conducted earlier is equal to 10.92centimeters.
As given in the question,
Distance covered by toy cart before stopping =15.6
Percentage of error found in calculation= 30%
30% of 15.6
= (30/100) × 15.6
= 4.68cm
Possible value for the actual distance that toy cart rolled before stopping
= Calculated distance - error distance
= 15.6 -4.68
=10.92centimeters
Therefore, possible values for the actual distance that the toy cart rolled before stopping with 30% error in the calculation conducted earlier is equal to 10.92centimeters.
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1-5 Pairs of Angles W.S
The value of x is 26° and y is 9°.
What is linear pair angles ?A pair of neighboring angles created by the intersection of two lines is known as a linear pair of angles. When two angles share a vertex and an arm but do not overlap, they are said to be adjacent angles. Due to their formation on a straight line, the linear pair of angles are always complementary. So, the total of two angles in a pair of lines is always 180 degrees.
The value of x and y are : x= 26° and y= 9°.
As a linear pair, (5x - 17)° + (3x - 11)° = 180°.
or, 8x - 28°= 180°
8x = 180° + 28°
Therefore, the value of x is 26°.
Now,
3x - 11°= 3×26°-11° = 67°
Again,
67°+90°+(2y+5)° = 180° { being linear pair}.
157°+2y+5° = 180°
or, 2y + 162° = 180°
or, 2y = 180° - 162°
y =
Therefore, the value of y is 9°.
The value of x is 26° and y is 9°.
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Only two more questions to go
Could somebody help me please how did they get this answer
Brainliest to the best answer!!
pls answer asap
and read the description properly
Answer:
see below
Step-by-step explanation:
i need help on this pls
Answer:
a) No equation/Contradiction
b) One Solution/Conditional
c) Infinite Solutions/Neither
Step-by-step explanation:
a) you combine like terms: 7x+9=7x-8
then subtract 7x from both sides, since 9 isn't equal to -8 there is no solution that would make it a contradiction
b) Combine likes: 13x-7=12x+21
subtract 12 x: x-7=21
add 7: x=14
c) Combine like terms: -3x+24=-3x+24
24=24
please help with question fast and provide explanation so I can understand
Answer:
A
Step-by-step explanation:
C means the number of miles into the city, while H means the miles on the highway. If (c,h) becomes (138,200), this means that c=138 and h=200. So, 138 miles can be traveled into the city while 200 can be traveled on the highway. hope this helps!
Helpp explain how you got that answer
Answer:
1
Step-by-step explanation:
Flip 10/25 to become 25/10 and times it by 2/5
What is the percentile rank of a value with a z-score of 1.33?
The percentile rank of a value with a z-score of 1.33 as given in the task content is; 9.18% (10th percentile).
What is the percentile rank of a value whose z-score is as given in the task content?It follows from the task content that the percentage rank of.the value whose z-score is; 1.33 as in the task content is to be determined.
As evident in the image attached (z-score table) , it can be inferred that a z-score of 1.33 corresponds to 40.82% on the table.
Also, since the z-score is positive, the percentage of data values which are above the z score 1.33 is 50% - 40.82%.
And ultimately, the percentile rank of a value which has a z-score of 1.33 as given in the task content is therefore; 9.18%.
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Find (g∘w)(x)and (w∘g)(x)for g(x)=7x−4 and w(x)=x2−7x+3(g∘w)(x)=(w∘g)(x)=
In order to calculate the composite function (gow)(x), that is, g(w(x)), we need to use w(x) as the input (value of x) in the function g(x).
So we have:
[tex]\begin{gathered} g(x)=7x-4 \\ g(w(x))=7w(x)-4 \\ g(w(x))=7(x^2-7x+3)-4 \\ g(w(x))=7x^2-49x+21-4 \\ g(w(x))=7x^2-49x+17 \end{gathered}[/tex]Now, calculating (wog)(x), we have:
[tex]\begin{gathered} w(x)=x^2-7x+3 \\ w(g(x))=g(x)^2-7g(x)+3 \\ w(g(x))=(7x-4)^2-7\cdot(7x-4)+3 \\ w(g(x))=49x^2-56x+16-49x+28+3 \\ w(g(x))=49x^2-105x+47 \end{gathered}[/tex]All real number that are less than -3 or greater then or equal to 5
Answer:
If I assume that I can use x to mean "all real numbers that are less than -3 or greater than or equal to 5",
Then I can write this as follows: x<-3 and x>=5
This includes all whole numbers (or integers), all fractions (or rational numbers), and all numbers that cannot be expressed as fractions such as pi, or the square root of 29 (or irrational numbers).
PLS HELP ASAP!!! WILL GIVE BRAINLIEST
Answer:
[tex]a_5 = \frac{17}{20}[/tex]
Step-by-step explanation:
Use the general progression formula where
[tex]d=\frac{3}{20}\\a_n=\frac{1}{4}+\frac{3n-3}{20}[/tex]
Solving this for the 5th term returns the answer
[tex]a_5=\frac{17}{20}[/tex]
If p(x) = ax²-3x+10, for what value(s) of a is p(-2) = f(g(-2))? May you explain how you did this.
Answer:
If p(x) = ax²
-3x+10
p(-2) =
f(g(-2))
A circle has a radius of 23 centimetres.
Work out an estimate for the area of the circle.
Answer: 1.662E-7 square kilometers
Step-by-step explanation:
A circle of radius = 23 or diameter = 46 or circumference = 144.5 cm has an area of: 1.662E-7 square kilometers (km²) 0.1662 square meters (m²)
Factor out the coefficient of the variable term. -6y - 18
Answer:
-6(y+3)
Step-by-step explanation:
The Sweet Slice pie shop sells organic pies with locally-sourced ingredients. One night after work, Lester brings home part of a bumbleberry pie to share between his mom, dad, sister, and himself. Lester cuts the leftover pie into 4 equal parts, and each family member gets 1 6 of a whole pie.
Based on the number of equal parts that Lester divided the cake into such that each family member got 1/6 of the whole pie, the proportion of the part of the leftover pie that Lester brought home was 2 / 3
How to find the amount of cake brought back?Lester brought back part of some pie from the Sweet Slice pie shop, and then divided it into 4 equal parts for his family. This led to the family getting 1/6 of the pie each.
To find out how much of the total pie that Lester brought back from Sweet Slice pie shop, you need to add the proportions received by his family:
= 1 / 6 + 1 / 6 + 1/ 6 + 1/6
= 4 / 6
At the simplest form this is:
= 4 / 6
= 2 / 3
Rest of the question is:
How much of the pie had Lester brought back from the pie shop?
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I need help with this please :D
Answer:
75deg
Step-by-step explanation:
the angle for the entire thing is 131 degrees. Since you are given angle 1 you can subtract that value from the whole to find the remaining degrees. So 131-56=75
Please help me ill give brainly to best answer
Assuming they work until their cost become the same, obviously.
The difference between the first charge of painter A and painter B = 376 - 280 = 96.
The hourly cost difference between painter B and painter A = 15 - 12 = 3.
So, painter A in the first hour has 96 more dollars than painter B, and as every hour pass, the difference goes down by 3 (as painter B gets 3 more dollars every hour)
Therefore, it would take 96 : 3 = 32 hours for the cost to be the same
Recheck : After 32 hours, painter A has 376 + 32 x 12 = 760 (dollars)
painter B has : 280 + 15 x 32 = 760 (dollars)
Does anyone know the answer to (2n -9) - (2.4n +4)? It's for homework!!
The difference between the expressions (2n -9) - (2.4n +4) is -0.4n-13
What is an algebraic expression?An algebraic expression can be defined as an arithmetic expression made up of variables, coefficients, terms, factors and constants.
They are also known to be composed of mathematical operations which may include;
MultiplicationSubtractionDivisionBracketAdditionParentheses, including other operations.Given the expressions;
(2n -9)(2.4n +4)Let's determine their difference
(2n -9) - (2.4n +4)
expand the bracket
2n - 9 - 2.4n - 4
collect like term
2n - 2.4n -4 -9
Subtract like terms
-0.4n - 13
Hence, the difference is -0.4n - 13
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His recipe makes 12 hamburger sliders, but he wants to make 78 sliders. The recipe calls for 1 ¾ pound of ground beef to make 12 hamburger sliders. Michael has 7 pounds of ground beef. Does he have enough to make 78 sliders?
Answer:
No, he can only make 48 sliders with 7 pounds of ground beef.
He would need about 12 pounds to make 78 sliders
Step-by-step explanation:
Nora loves to play the bridge builders video game, where players gain and lose points by building safe and unsafe bridges. in level 1, nora earned 16 points because her bridge passed inspection. then, she lost 25 points because part of her bridge collapsed! what was nora's score at the end of level 1?
Answer:
-9
Step-by-step explanation:
16-25=-9
Answer: -9
Step-by-step explanation:
1. In △NBA, BO is a median. If NO=x+3 and OA=2x-9, what is the value of x?
2.In △MTV, TPis an angle bisector. If m∠MTP=12 and m∠MTV=3x-3, find the value of x.
Answer:
Step-by-step explanation:
1 . In the given triangle ΔNBA BO is a median.
By applying the property of median it divides the opposite side into two equal parts.
Therefore,
NO = OA ...(a)
We have,
NO = x+3 and OA = 2x-9
from (a)
NO = OA
x+3 = 2x-9
∴ 3+9 = 2x-x
∴ x = 12
∴ The Value of x is 12.
Que 2 - In ΔMTV
Given - TP is an angle bisector
m∠MTP = 12 , m∠MTV = 3x - 3.
Ans - TP is an angle bisector which means it divides the angle into two equal parts. (By angle bisector theorem)
∴ m∠MTP = m∠VTP ..... (a)
m∠MTV = m∠MTP + m∠VTP
∴m∠MTV = 2(m∠MTP)
∴3x-3 = 2(12)
∴3x-3 = 24
∴3x = 24 + 3
∴3x = 27
∴ x = 27/3
∴ x = 9
∴ The Value of x is 9.
10) There are 5 times as many fiction books in the class library as there are nonfiction books. The number of information books is 7 more than the sum of the number of fiction and nonfiction books. There are 19 information books in the library. How many nonfiction books are there? How many fiction books are there?
The number of fiction and non fiction books are 10 and 2 respectively.
How to find the number of fiction and non fiction books?There are 5 times as many fiction books in the class library as there are nonfiction books.
Therefore,
let
x = number of non fiction book.
number of fiction book = 5x
The number of information books is 7 more than the sum of the number of fiction and nonfiction books.
Therefore,
number of information book = 7 + x + 5x
number of information book = 7 + 6x
There are 19 information books in the library.
Hence,
19 = 7 + 6x
19 - 7 = 6x
6x = 12
x = 12 / 6
x = 2
Therefore,
The number of non fiction book = 2
The number of non fiction book = 5(2) = 10
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Find "x"
(ignore the writing around it lol)
PLEASE HELP ITS ANNOYING ME
The Value of X = 7.16 ( approximate value)
what is right triangle?A triangle with a right angle (i.e., a 90-degree angle), two perpendicular sides, or both is referred to as a right triangle (American English), a right-angled triangle (British), or more formally as an orthogonal triangle. The foundation of trigonometry is the relationship between the sides and various angles of the right triangle.The hypotenuse is the side that is opposite the right angle. Legs are the sides that are close to the correct angle (or catheti, singular: cathetus).A right triangle is considered to be a Pythagorean triangle and its three sides are referred to as a Pythagorean triple if the lengths of all three of its sides are integers.To learn more about : Right-angled triangle
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