[tex]\displaystyle\\Answer:\ y=\sqrt{\frac{x-1}{2} } \ \ \ \ (x\geq 1,\ \ \ \ y\geq 0)[/tex]
Step-by-step explanation:
[tex]y=2x^2+1\\[/tex]
We change the argument and the value:
[tex]\displaystyle\\x=2y^2+1\\\\x-1=2y^2+1-1\\\\x-1=2y^2\\[/tex]
Divide both parts of the equation by 2:
[tex]\displaystyle\\\frac{x-1}{2}=y^2\\\\ \sqrt{\frac{x-1}{2} }=y \ -\ the\ desired\ inverse\ function\\\\[/tex]
The restrictions are imposed on the inverse function by on x:
[tex]x-1\geq 0\\x\geq 1[/tex]
The restrictions are imposed on the inverse function by on y:
[tex]y\geq 0[/tex]
Then the original function is defined on the sets:
[tex]x\geq 1,\ \ \ \ y\geq 0[/tex]
The initial function, a parabola, is constrained because of the inverse function; only in this case the functions are reciprocal.
If you roll a standard 6 sided die and you get paid $1 for every spot it lands on (so if you roll a 5 that would mean $5), what's the average payout for one roll?
Answer:
20
Step-by-step explanation:
Solve the simultaneous equations
3y + 11 = 4x
10x + 2y + 1 = 0
In linear equation the solution set of the equations x = 1/2, y = -3.
What in mathematics is a linear equation?
A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. The variables in the preceding equation are y and x, and it is occasionally referred to as a "linear equation of two variables."Multiply both sides of the equation by a
coefficient - 2(4x - 3y ) = 11 × 2
3 ( 10x + 2y ) = ( - 1 ) × 3
apply multiplicative distribution law
8x - 6y = 11 × 2
3( 10x + 2y ) = (-1) × 3
calculate the first terms
8x - 6y = 22
3( 10x + 2y ) = ( -1) × 3
remove the parentheses
8x - 6y = 22
30x + 6y = -3
add up the two equation
8x - 6y + ( 30x + 6y ) = 22 + ( -3)
remove parentheses - 8x - 6y + 30x + 6y = 22 -3
cancel the unknown variables - 8x + 30x = 22 -3
combine like terms - 38x = 22 - 3
calculate the sum or difference - 38x = 19
reduce the greatest common factor on both
sides of equation - 2x = 1
divide both sides of the equation by the coefficient of variable - x = 1/2
substitute one unknown quantity into the elimination 8 * 1/2 - 6y = 22
reduce the expression to the lowest term 4-6y = 22
reduce the greatest common factor on both sides of the equation
2 - 3y = 11
Rearrange unknown terms to the left side of the equation - 2 - 3y = 11
calculate the sum or difference -3y = 9
reduce the greatest common factor on both sides of the equation -y = 3
divide both sides of the equation by the coefficient of variable y = -3
the solution set of the equations
x = 1/2
y = -3
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Please Help me ASAP 100 points for correct answer
Answer:
C
Step-by-step explanation:
Angie and Kenny play online video games. Angie buys 2 software package and 2 months of gameplay. Kenny buys 1 software package and 3 month of game play. Each software package cost $20. If their total cost is $160, what is the total cost of one month of gameplay?
What does it mean when a data set or distribution has more variability than another
Answer: Standard deviation
Step-by-step explanation: The standard deviation is the average amount of variability in your dataset. It tells you, on average, how far each score lies from the mean. The larger the standard deviation, the more variable the data set is.
49^((1)/(2))- 25^((3)/(2))
Answer: -118
Step-by-step explanation:
49^((1)/(2))- 25^((3)/(2))=
49^(1/2) -25^(3/2)=
7-25^((2+1)/2)=
7-25^((2/2)+(1/2))=
7-25^(1+1/2)=
7-25^(1) *25^(1/2)=
7-(25*5)=
7-125=-118
5/6 x 15 =
2/3 x 1/4=
4/9 x 3/8=
Answer:
1. 75/6 (improper fraction) = 12 3/6 (mixed number) = 12 1/2 (simplified)
2. 2/12 = 1/6 (simplified)
3. 12/72 = 1/6 (simplified)
Hope this helps :)
Answer:
[tex]\frac{5}{6} * 15 = 12\frac{1}{2}[/tex]
[tex]\frac{2}{3} * \frac{1}{4} = \frac{1}{6}[/tex]
[tex]\frac{4}{9} * \frac{3}{8} = \frac{1}{6}[/tex]
Step-by-step explanation:
[tex]\frac{5}{6} * 15 = \frac{5 * 15}{6} = \frac{75}{6}\\[/tex]
Reduce the fraction by diving both sides by the common factor.
[tex]\frac{75}{6} = \frac{75 / 3}{6/3} = \frac{25}{2}[/tex]
To convert the improper fraction to a mixed fraction, divide the numerator (25) by the denominator (2), put the whole part of the result in front and the remainder in place of the original numerator.
25 / 2 = 12 with remainder of 1
[tex]\frac{25}{2} = 12\frac{1}{2}[/tex]
[tex]\frac{2}{3} * \frac{1}{4} = \frac{2 * 1}{3 * 4} = \frac{2}{12} = \frac{2/2}{12/2} = \frac{1}{6}[/tex]
[tex]\frac{4}{9} * \frac{3}{8} = \frac{4 * 3}{9 * 8} = \frac{12}{72} = \frac{12 / 12}{72 / 12} = \frac{1}{6}[/tex]
f(9)=-4(9)^2-4(9)+18=
The first term of arithmetic sequence is 2 and 10th term is 39 find the 30th term
Which number rounds to 3,000 if you round it to the nearest thousand, AND to 2,500 if you round it to the nearest hundred?
Answer:
2,739 and 2,489
Step-by-step explanation:
There are many solutions to both problems:
(Rules)
If the number is 5 or higher round (up)
If the number is 4 or lower round (down)
2,739⇒3,000
↑↑↑
Higher than 500 so round up to get 3,000
2,489⇒2,500
↑↑
Higher than 50 so round up to get 2500
2,739 and 2500 are both possible solutions.
find the area of the shaded region.
round to the nearest tenth.
The area of the shaded region is 294.4 square meters
How to find the area of the shaded region?The given parameters are represented on the figure
By this;
The area of the shaded region is the sum of the area of the major sector and the area of the triangle
The area of the major sector is
A1= ∅/360 * πr²
The area of the triangle is
A2 = 0.5r²sin(x)
So, the total area is
Total = ∅/360 * πr² + 0.5r²sin(x)
This gives
Total = (360 - 130)/360 * 3.14 * 11.1^2 + 0.5 * 11.1^2 * sin(130 deg)
Evaluate
Total = 294.4
Hence, the area of the shaded region is 294.4 square meters
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What is the value of 5 x 3 + 4 y 3 when x=4 and y=3?
Answer:
96
Step-by-step explanation:
pls help with this question ASAP
What equations do u insert in between these numbers to get the answer
a.5 8 3 9 =50
b.12 6 2 10=14
c.4 5 6 10=24
d.7 4 6 9 7= 16
e.4 9 6 2 =52
f.45 5 9 3 7=102
hduodoydiyd9ydiydoyeykdoyx95eeykyei6djj
Step-by-step explanation:
a) 5
Which of the following is an equivalent expression of 15x2 +12x + 8?
Answer:
15 (x + 2\/5)^2 + 28\/5
Step-by-step explanation:
what is the perimeter of the vertices (1,4),(-1,-2),(2,0),(4,0) to the nearest hundredth
The Perimeter of the quadrilateral = 16.93 units
How to Find the Perimeter of a Quadrilateral?The perimeter of the quadrilateral with the given vertices is the sum of the distance between every vertices.
Calculate the distance between the vertices using the distance formula, d = [tex]\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}[/tex].
Name the vertices as shown below:
A(1,4)
B(-1,-2)
C(2,0)
D(4,0)
Distance between A and B:
AB = √[(−1−1)² + (−2−4)²]
AB = √(4 +36)
AB = 6.32 units
Distance between B and C:
BC = √[(−1−2)² + (−2−0)²]
BC = 3.61 units
Distance between C and D:
CD = √[(4−2)² + (0−0)²]
CD = 2 units
Distance between A and D:
AD = √[(4−1)² + (0−4)²]
AD = 5 units.
Perimeter of the quadrilateral = AB + BC + CD + AD = 6.32 + 3.61 + 2 + 5
Perimeter of the quadrilateral = 16.93 units
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can someone help me with these
Answer:
for the triangle question the ans is 2
for the equation question where u have to find the mistake the student made, its the last option
In a track meet, Team A won 3 more medals than two times the medals won by Team B. Team A won 9 more medals than Team B, Find the number of medals for each team. Show all set-up, work, and write a complete sentence for your answer.
The number of medals won by team A is 15 medals while the number of medals won by Team B is 9 medals.
How to solve Algebra Word Problems?
Team A won 3 more medals than two times the medals won by Team B.
If the number of medals won by team B is x, than;
Number of medals won by team A = 3 + 2x
Number of medals won by team B = x
Also, we are told that Team A won 9 more medals than Team B.
Thus;
(3 + 2x) = x + 9
2x - x = 9 - 3
x = 6
3 + 2x = 3 + 2(6) = 15 medals
Thus, we conclude that the number of medals won by team A is 15 medals while the number of medals won by Team B is 9 medals.
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Use the data and create a formula for the function that approximates the ground roll for a fully loaded cessna 172 at an elevation of:_____
The formula for the function that approximates the ground roll for a fully Cessna 172 at an elevation of x is y = 585(1.00009)x .
What is angle of elevation ?
The angle from the horizontal upward to an item is referred to as the angle of elevation. The line of sight of an observer would be above the horizontal. The angle from the horizontal downward to an item is referred to as the "angle of depression." The line of sight of an observer would be below the horizontal.Let the formula for the exponential function that approximates the ground roll for a fully loaded Cessna 172 at an elevation of x be
y =A(B)x ....(1)
Here,
A = ground roll at x =0,
B = growth factor.
Since at x =0, , Ground roll is = A = 585 ft ....(2)
On putting A = 585 in equation (1), we get
y = 585(B)x ....(3)
Now, at elivation of x = 1000 ft ,
Ground roll y = 640 ft.
So, putting these values in equation (3), to get
640 = 585(B)1000
Reversing the sides to get
585(B)1000 = 640
Or B1000 = 640/585
Or B1000 = 1.09017094
Or B = (1.09017094)1/1000
Or B = 1.00009 .....(4)
On putting the value of B in equation (3), we get
y = 585(1.00009)x
Hence, the formula for the function that approximates the ground roll for a fully Cessna 172 at an elevation of x is y = 585(1.00009)x .
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Given (2x + 3) (3x − 2) = 0
What are the values of x in 10th decimal places?
X=
X=
please answer fast
Natalie surveyed 800 of the students in her school about their favorite color. Students could choose between blue and red. 77% said their favorite color was red. How many students' favorite color was blue?
30 points
The total number of students whose favorite color was blue is 184 students.
Total number of students Natalie surveyed in her school = 800
Given the percentage of students who said their favorite color was red = 77%
Now to calculate 77% of the total students is
= 77% of 800
= 77/100 * 800
= 616
The number of students who said red was their favorite color was 616.
So, the number of students who stated that blue was their favorite color
= total students - red color favorite students
= 800 - 616
= 184
Therefore, There are a total of 184 students whose favorite color is blue.
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first person 2 answer will give u brainliest need to submit by 2 nite :)
Two angles are Complementary, if the measure of one of the angles is 66.7 degrees what is the measure of the other angle? Answer to the first decimal place, IE 79.5.
Answer:
probly 79.5
Step-by-step explanation:
i d k
What type of variable is the number of customers in line at the bank in a 24 hour period? qualitative continuous attribute discrete
The number of customers waiting in line at the bank over a 24-hour period is a discrete variable type.
By discrete variable, what do you mean?A variable whose value is determined by counting is referred to as a discrete variable. examples: the number of pupils in attendance. how many red marbles are in the container. when triple coins are turned, the count of heads. The number of pupils, kids, the shoe size, and so forth are some typical examples of discrete data. A statistical variable is referred to as a discrete variable if it presupposes a finite collection of data and a countable number of values. Contrarily, a continuous variable is a quantitative variable that accepts an endless quantity of data and an uncountable number of values.
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The maximum speed, in miles per
hour, of a cheetah is 18 more than 3 times
If the maximum speed of a cheetah is
the maximum speed of a hippopotamus.
75 miles per hour, which equation could be
used to find the maximum speed of a
hippopotamus h? (Lesson 1-2)
A. h= 3(75) + 18
B. 75=3h
C. 75 = 3h + 18
D. 18 + 75 = 3h
The equation could be used to find the maximum speed of a hippopotamus h is C. 75 = 3h + 18
The question has to do with linear equation
What is a linear equation?A linear equation is a mathematical expression in which the highest power of the unknown is 1.
How to find the equation for the maximum speed of the hippopotamusLet
x = speed of cheetah and h = speed of hippopotamusGiven that the maximum speed, in miles per hour, of a cheetah is 18 more than 3 times the maximum speed of the hippopotamus
Now, since the maximum speed of the hippopotamus is h, 3 times the maximum speed of the hippopotamus is 3h.
Since the cheetah is 18 more than 3 times the maximum speed of the hippopotamus, we have that
x = 3h + 18
Substituting x = 75 into the equation, we have
75 = 3h + 18
So, the equation could be used to find the maximum speed of a hippopotamus h is C. 75 = 3h + 18
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Which of the following options are examples of how you can name the angle? Select all that apply.
Answer:thr lerrkmaf
Step-by-step explanation:
and we are so cool DEA
Stella buys 5 pineapples for $4.50. How much would she pay if she bought 7 pineapples? (hint: find the unit rate first then multiply)
*
Answer:
Step-by-step explanation:
4.50 divides by 5 than times the answer by 7
Solve 2x+18=6y for x.
Answer:
x=3y−9Step-by-step explanation:
2x+18=6y
2x=6y−18
(2x)/2=(6y−18)/2
x=3y−9
Answer:
x = 3y−9Step-by-step explanation:
Add -18 to both sides:2x + 18+− 18=6y + −18
2x = 6y − 18
Divide both sides by 2:2x / 2= 6y −18 / 2
x = 3y −9
The sum of 4 consecutive odd integers is -24. What are they?
Step-by-step explanation:
4 consecutive odd integers means we start with x, then have x+2, x+4 and then x+6.
and then we have
-24 = x + x+2 + x+4 + x+6 = 4x + 12
4x = -36
x = -9
x+2 = -7
x+4 = -5
x+6 = -3
so, in sequence from small to large these 4 numbers are
-9, -7, -5, -3
The water level in Colorado river is 2.55 m below average. a large rainfall caused The water level to rise 0.8 m. what is the water level after the rainfall?
The water level after the rainfall is 3.05m
How to calculate the measurement of the water level after the rainfall ?
The water level in colorado river is 2.55m below average
A larger rainfall happened and the water level rose by 0.8m
Therefore the water level after the rainfall can be calculated by adding the previous water level which is 2.55 by the new increase which is 0.8
= 2.55 + 0.8
= 3.05
Hence the water level after the rainfall is 3.05 m
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Three angles are shown, ZHRM, ZHRD, and ZDRM.
D
M
H
If m/HRM = 54°, m/HRD =
m/DRM =
(²7*+11) ².
4
R
(1/22 +22), ar
x
and
what is the value of x?
Answer:
28
Step-by-step explanation:
By the angle addition postulate,
[tex]54=\frac{1}{2}x+22+\frac{1}{4}x+11 \\ \\ 54=\frac{3}{4}x+33 \\ \\ 21=\frac{3}{4}x \\ \\ x=28[/tex]
A 2-cup bottle of glass cleaner costs $6.56. What is the price per fluid ounce?
Answer:
82 cents per ounce
Step-by-step explanation:
There are 8 oz in a cup so two cups = 16 ounces
$6 .56 / 8 oz = $ .82 / oz
