Answer:
[15-√226, 1] ∪ [29, 15+√226]
Step-by-step explanation:
You want all solutions to |x^2 - 30x - 1| + |x^2 - 30x + 29| = 30.
DomainsThe equation resolves to a piecewise equation whose domains are delimited by the points where the absolute value arguments are zero.
Left argumentThe argument of the left absolute value function will be zero where ...
x^2 - 30x - 1 = 0
x = (-(-30) ±√((-30)² -4(1)(-1)))/(2(1) = 15 ± √226 ≈ {-0.0332964, 30.0332964}
Right argumentThe argument of the right absolute value function will be zero where ...
x^2 -30x +29 = 0
(x -29)(x -1) = 0
x = {1, 29}
Piece-wise equations-∞ < x < 15-√226In this domain, both absolute value arguments are positive, so the equation is ...
x^2 -30x -1 +x^2 -30x +29 = 30
2x^2 -60x +28 = 30 . . . . . collect terms
x^2 -30x -1 = 0 . . . . . . . . . write in standard form
x = {15 -√226, 15 +√226} . . . . solutions to the equation
These solutions are not in the domain we have defined for this equation.
15-√226 ≤ x ≤ 1In this domain, the left absolute value argument is negative, and the right argument is positive, so the equation is ...
-(x^2 -30x -1) +(x^2 -30x +29) = 30
30 = 30
All values of x in this domain (15-√226 ≤ x ≤ 1) are in the solution set.
1 < x < 29In this domain, both absolute value arguments are negative, so the equation is ...
-(x^2 -30x -1) -(x^2 -30x +29) = 30
-2x^2 +60x -58 = 0 . . . . . . write in standard form
x^2 -30x +29 = 0 . . . . . . . divide by -2
The solutions to this are x={1, 29}, neither of which is in the domain we have defined for this equation.
29 ≤ x ≤ 15+√226In this domain, the left absolute value argument is negative and the right argument is positive. The equation resolves to the same one as for the domain 15-√226 ≤ x ≤ 1: 30 = 30. Hence, all x-values in this domain (29 ≤ x ≤ 15+√226) are part of the solution set.
15+√226 < xIn this domain, both absolute value arguments are positive, so the equation is ...
x^2 -30x -1 = 0 . . . . . . . . . write in standard form
x = {15 -√226, 15 +√226} . . . . solutions to the equation
These solutions are not in the domain we have defined for this equation.
SolutionsIn interval notation, the solution set for the equation is ...
[15-√226, 1] ∪ [29, 15+√226]
You are driving on a freeway to a town that Is 300 kilometers from your home. After 30 minutes, you pass a freeway exit that you know is: 50 Kilometers from your home. Assuming that you continue at the same constant speed, how long (in hr) does the entire trip take?
It'll take you 3 hours to reach your destination.
Determine by direct integration the product of inertia of the given area with respect to the x and y axes.
To evaluate the integral, you will need to define the limits of integration and use appropriate coordinate systems for the given area.
And the area is given as [tex]I_{xy} =\int \limits \int \limits {(y^2 - x^2)} \,dm[/tex]
What is direct integration?
Direct integration is a method of finding the moment of inertia of a body or a region about a given axis by directly integrating the product of the mass of each infinitesimal element of the body or region and the square of its distance from the axis.
To determine the product of inertia of a given area with respect to the x and y axes, you will need to first define the area and its mass distribution. Then, you can use the following formula for the product of inertia:
[tex]I_{xy} =\int \limits \int \limits {(y^2 - x^2)} \,dm[/tex]
Where Ixy is the product of inertia, y is the distance from the y-axis, x is the distance from the x-axis, and dm is the mass of an infinitesimal element of the area.
Hence, To evaluate this integral, you will need to define the limits of integration and use appropriate coordinate systems for the given area.
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The area of a rectangle is 45cmsquare if its length is 9 cm find its breadth
Answer: width is 13.5 cm
Step-by-step explanation:
9 x 2 +2x =45
45-18
2x=27
2x/2=27/2
x=13.5
width is 13.5 cm
Can someone pls help me with this last question pls hurry I got 10 mins hurry I’ll do brainliest
Answer:
(12,1)
Step-by-step explanation:
Before the transformation, Point B is at (-8,1).
When it will be reflected, it will be at (8,1)
Then, it shifts 4 points to the right, and so it will be at (12,1)
Find the slope of the line that contains the following points: (17, -12)(17,−12) and (17,(17, 8)
Answer:
Slope is undefined. { Infinity }
Step-by-step explanation:
Formula we use,
→ Slope(m) = (y2 - y1)/(x2 - x1)
Now required slope will be,
→ m = (y2 - y1)/(x2 - x1)
→ m = (8 + 12)/(17 - 17)
→ m = 20/0
→ [ m = 0 ]
Hence, the slope is undefined.
The slope of the line passing through the points ( 17 , -12 ) and ( 17 , 8 ) is undefined
What is an Equation of a line?The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept
And y - y₁ = m ( x - x₁ )
y = y-coordinate of second point
y₁ = y-coordinate of point one
m = slope
x = x-coordinate of second point
x₁ = x-coordinate of point one
The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )
Given data ,
Let the equation of line be represented as A
Now , the value of A is
Let the first point be P ( 17 , -12 )
Let the second point be Q ( 17 , 8 )
Now , the slope of the line is m = ( y₂ - y₁ ) / ( x₂ - x₁ )
Substituting the values in the equation , we get
Slope m = ( 8 - ( -12 ) ) / ( 17 - 17 )
On simplifying the equation , we get
Slope m = ( 8 + 12 ) / 0
Slope m = 20 / 0
So , the slope is undefined
Hence , the slope of the line is m = undefined
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A bag contains 4 red marbles and 6 blue marbles. A marble is drawn and then replaced. This is done 50 times. Round all answers to the nearest hundredth (two decimal places). What is the probability that a red marble is drawn:
a. exactly 15 times:
b. at least 15 times:
c. at most 15 times:
d. less than 15 times:
e. between 17 and 25 times, inclusive:
Answer: e
Step-by-step explanation:
4+6= 10 and then divide by 50 and add 25 so 0.2+25+25.02 so then subtract 4 so about 21 or 21.02
Write an equation in standard form (1,1) (2,5) Ax+By=-3
The Equation of the Line in Standard form is 4x - y = 3
What is Slope of a Line?
The slope formula is used to compute the inclination or steepness of a line. The slope of the lines is calculated using the x and y coordinates of the lines. It is the ratio of the y-axis change to the x-axis change.
Solution:
Slope of the Line passing through the points (1, 1), (2, 5)
is
m = 5-1/2-1 = 4
Equation of the line = (y - y1) = m(x - x1)
y - 1 = 4(x - 1)
y - 1 = 4x - 4
4x - y = 3
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your shift runs 8 hours. from the 8 hours, 30 minutes is allowed for lunch and 30 minutes for breaks. you must produce 78.0 units per shift. give the takt time in minutes.
The stated statement indicates that the takt time is 5.38 minutes for each section.
What is an example of takt time?Takt time is calculated as the amount of manufacturing time that is available divided by the volume of orders. Takt time, for instance, is two minutes if a factory makes widgets for 480 minutes a day and clients need 240 widgets per day. Similar to this, the takt time is one week if clients desire two new goods per month.
How does takt time change?Takt time depends on client demand and the amount of time that is available, and for many items, it is always changing as the demand from the market shifts. Takt time is unaffected by system changes, although cycle time is affected.
Briefing:Available hours are 7 * 60 minutes, which is 420 minutes.
No. of parts = 78 units
Available time for work / No of parts = Takt time
= 420/ 78
= 5.38 minutes per part
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Find the values of x and y in parallelogram PQRS. PT=y, TR=5x+1, QT=2y, TS=6x+10 x= ? and y= ?
The required values of x and y are x = 2 and y = 11.
We have been given that parallelogram PQRS which has:
PT = y, TR = 5x+1, QT = 2y, TS = 6x+10
We know that the diagonals of a parallelogram bisect each other.
So, PT = TR and QT = TS
Substitute the values and we have a system of equations:
y = 5x + 1 ....(i)
2y = 6x + 10 ....(ii)
Substitute the value of the equation y = 5x + 1 in equation (ii), and solve for x
2(5x + 1) = 6x + 10
10x + 2 = 6x + 10
10x - 6x = 10 - 2
4x = 8
x = 8/4
x = 2
Substitute the value of x = 2 in equation (i), and solve for y
y = 5(2) + 1
y = 10 + 1
y = 11
Therefore, the required values of x and y are x = 2 and y = 11.
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Help please, what is the slope and y intercept
Answer:
Hope the picture will help you
Which ordered pairs are solutions to the inequality y−3x<−8 ? Select EACH correct answer.
(1, −5)
(5, 4)
(−3, −2)
(0, −9)
(2, −1)
Answer:
Step-by-step explanation:
(0,-9)
What is the probability of drawing a 4 then another 4 from a
deck of cards?
On a test that has a normal distribution, a score of 33 falls two standard deviations above the mean, and a score of 24 falls one standard deviation below the mean. Determine the mean of this test.
So our goal is to determine the mean test score, which we don't know, we know to raw scores, we know one raw score is 38 that's one standard deviation below the mean, which by definition of a Z score that Z equals negative one. one
What is meant by mean?Mean is the simple mathematical average of a set of two or more numbers. The mean for a given set of numbers can be computed in more than one way, including the arithmetic mean method, which uses the sum of the numbers in the series, and the geometric mean method, which is the average of a set of products. However, all the primary methods of computing a simple average produce the same approximate result most of the time.The formula for calculating the geometric mean is to multiply all the values in a data set, then take the root of the sum equal to the quantity of values within that data set.To learn more about arithmetic mean refer to:
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Which values make the inequality 0.3m ≥ 0.55-0.2m true?
(choose three)
A 2.11
B 1.004
C 1.1
D 1.63
E 1.06
The values that make the inequality true are (a) 2.11 (c) 1.1 and (d) 1.63
How to determine the values that make the inequality true?From the question, we have the following parameters that can be used in our computation:
0.3m ≥ 0.55-0.2m
Evaluate the like terms
0.5m ≥ 0.55
Divide both sides by 0.5
So, we have the following representation
m ≥ 1.1
This means that the true values are at least 1.1
In this case, they are 1.1, 1.63 and 2.1
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?? Help me pls??? Thank you
it would be inconsistent. Meaning it won't have a solution
Mike took clothes to the cleaners three times last month. First, he brought 3 shirts and 1 pair of slacks and paid
$13.46. Then he brought 7 shirts, 3 pairs of slacks, and 1 sports coat and paid $43.39. Finally, he brought 5 shirts
and 2 sports coats and paid $28.43. How much was he charged for each shirt, each pair of slacks, and each
sports coat?
***
Mike charged for each shirt is $2.49, each pair of slacks is $5.99 and each sports coat is $7.99.
What is system of equations?
A finite set of equations for which common solutions are sought is referred to in mathematics as a set of simultaneous equations, also known as a system of equations or an equation system.
Let
Price of shirts = x
Price of slacks = y
Price of sports = z
From the given information,
3x + y = $13.46 ..(1)
7x + 3y + z = $43.39 ..(2)
5x + 2z = $28.43 ..(3)
From equation (1), y = 13.46 - 3x
From equation (3), z = (28.43 - 5x) / 2
Plug the value of x and z in equation (2)
7x + 3(13.46 - 3x) +(28.43 - 5x)/2 = 43.39
7x + 40.38 - 9x + 14.22 - 2.5x = 43.39
-4.5x +54.6 = 43.39
4.5x = 54.6 - 43.39
4.5x = 11.21
x = 2.49
Plug x = 2.49 in equation (1)
3(2.49) + y = 13.46
2.47 + y = 13.46
y = 5.99
Plug x = 2.49 in equation (3),
5(2.49) + 2z = 28.43
12.45 + 2z = 28.43
2z = 15.98
z = 7.99
Hence, Mike charged for each shirt is $2.49, each pair of slacks is $5.99 and each sports coat is $7.99.
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There are 15 circles and 3 squares What is the simplest ratio of squares to circles?
Answer:
1:5
Step-by-step explanation:
What is the answer to this please help asap
Answer:
19°
Step-by-step explanation:
m<A + m<B + m<C = 180°
a + 17° + 49° + 5a = 180°
6a + 66° = 180°
6a = 114°
a = 19°
Find the values of x and y in the diagram.
The value of x is 9.
The value of y is 5.
What is a triangle?It is a two-dimensional figure which has three sides and the sum of the three angles is equal to 180 degrees.
We have,
Two triangles in a composite triangle.
We see that,
m∠UST = m∠STR
This means,
x + 4 = 13
x = 13 - 4
x = 9
The sum of the angles in a triangle is 180 degrees.
One triangle is an equilateral triangle.
All three angles are equal.
This means,
The angle has to be 60°.
m∠UTR + m∠URT + m∠TUR = 180
3m = 180
m = 60
Now,
m∠URS = 180
m∠URT + m∠SRT = 180
60 + m∠SRT = 180
m∠SRT = 120
The isosceles triangle has two equal angles.
m∠RTS = m∠RST
m∠SRT + m∠RTS + m∠RST = 180
120 + 6y + 6y = 180
12y = 180 - 120
12y = 60
y = 5
Thus,
The value of x and y are 9 and 5.
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If the determinant of a 5 X 5 matrix A is det(A)=-8, and the matrix C is obtained from A by swapping the second and third rows, then det(C)=If the determinant of a x 5 matrix A is \det\,(A)=9 , and the matrix D is obtained from A by adding 2 times the fourth row to the first, then \det\,(D)=
By using determinant, it can be calculated that-
det(C) = 8
det(D) = 9
What is a determinant?
Determinant of a square matrix is equal to the product of the elements of a square matrix and their cofactors.
Here,
det(A) = -8
The matrix C is obtained from A by swapping the second and third rows
We know if the rows and columns of a matrix are swapped then the value of the determinant of the new matrix changes in sign only
So det(C) = 8
Now,
det(A) = 9
We know that the value of determinant remain unchanged on adding any combination row or column
Matrix D is obtained from A by adding 2 times the fourth row to the first
det(D) = 9
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solve the inequality -2 / 5 x <-2 show your work in complete sentences describe how solution set a graph on a number line ed
The solution of the inequality will be;
⇒ x > 5
And, The solution is shown on number line.
What is Inequality?A relation by which we can compare two or more mathematical expression is called an inequality.
Given that;
The inequality is,
⇒ - 2/5x < - 2
Now,
Solve the inequality as;
⇒ - 2/5x < - 2
⇒ - 2x < - 2 × 5
⇒ - 2x < - 10
Multiply by - 1,
⇒ 2x > 10
⇒ x > 5
Thus, The solution of the inequality = x > 5
And, The solution is shown on number line in figure.
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Question 1 of 21
Which of the following are solutions to the quadratic equation? Check all that
apply.
x² + 3x-10 = 0
☐ A. 1
B. 2
C. -2
D. -4
OE. -5
OF. 28
Answer:
2 and -5 (B & E)
Step-by-step explanation:
Factor the equation into
(x-2) (x+5)
Thus the zeros are 2 and -5
x=2 and x=-5 are the solutions of the quadratic equation x² + 3x-10 = 0
What is quadratic equation?A quadratic equation is a second-order polynomial equation in a single variable x , ax²+bx+c=0. with a ≠ 0 .
The given quadratic equation is x² + 3x-10 = 0
We have to find the solutions of the quadratic equation
x² + 3x-10 = 0
Let us factorize the given equation
x² +5x-2x-10=0
x(x+5)-2(x+5)=0
(x-2)(x+5)=0
Now equate both the terms with zero to find the solutions
x=2 and x=-5
Hence, x=2 and x=-5 are the solutions of the quadratic equation x² + 3x-10 = 0
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The expression 10ax+14ay+15bx+21by can be factored into two binomials such that all the coefficients are integers. Which is one of the factors
The expression 10ax + 14ay + 15bx + 21by has a coefficient of (2a + 3b)
as a factor.
What is a numerical expression?A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.
Given, An expression 10ax + 14ay + 15bx + 21by.
The given expression is in 4 variables namely a, b, x and y we'll combine the x and y terms in the expression.
Now, 10ax + 15bx + 14ay + 21by.
= 5x(2a + 3b) + 7y(2a + 3b).
= (2a + 3b)(5x + 7y)
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A city has a population of 330,000 people. suppose that each year the population grows by 3.25. what will the population be after 8 yesrs
The population of the city after eight years is 35,125,731,743
What is population growth rate?Population growth is the increase in the number of people in a population or dispersed group. The expression P(t) = P(o)(1+r)^t can be used to determine the growth rate of a population.
Where P(t) is the population at a particular time
P(o) is the initial population , t is the time and r is the growth rate.
Here the growth rate has been given, but we are to find p(t).
P(t) = 330,000(1+3.25)⁸
P(t) = 330,000(4.25)⁸
P(t) = 330,000× 106441.61
P(t) = 35,125,731,743( nearest billion)
Therefore the population of the city after 8years is 35,125,731,743
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callie is on vaction and wants to rent a bicycle to explore the town. She pays $10 flat fee and then $12 per hour for the rental.
After solving the equation, we can conclude that Callie should rent the bicycle for a maximum of 3 hours.
What are equations?The equals sign is indeed a symbol used in mathematical formulas to denote the equality of two reactions.
Algebraically speaking, an equation is a statement that shows the equality of two mathematical expressions.
For example, the two equations 3x + 5 and 14, which are separated by the 'equal' sign, make up the equation 3x + 5 = 14.
So, according to the given information, form the equation as follows:
12x + 10 = 45
Where x is the number of hours Callie rents the cycle.
Now, calculate for x as follows:
12x + 10 = 45
12x = 45 - 10
12x = 35
x = 35/12
x = 2.91
Rounding off: 3
Therefore, after solving the equation, we can conclude that Callie should rent the bicycle for a maximum of 3 hours.
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Complete question:
Callie is on vacation and wants to rent a bicycle to explore the town. She pays a $10 flat fee and then $12 per hour for the rental.
If Callie has $45 to spend, what is the greatest number of full hours she can rent the bicycle?
Sine, Cosine, and Tangent
Possible answers
0.42
0.92
1.08
0.38
Answer:
0.38
Step-by-step explanation:
imagine a circle, with C being the center, and 13 being the radius.
the triangle is then representing the trigonometric functions. remember, they are all multiplied by the radius as the circle is much higher than the norm circle (radius 1).
so,
5 = sin(C) × 13
sin(C) = 5/13 = 0.384615385... ≈ 0.38
Inverse function question!???
Answer:
D) [tex]f^{-1}(x)=(x-3)^2+2[/tex]
Step-by-step explanation:
[tex]f(x)=\sqrt{x-2}+3 \implies x=\sqrt{f^{-1}(x)-2}+3 \\ \\ x-3=\sqrt{f^{-1}(x)-2} \\ \\ (x-3)^2=f^{-1}(x)-2 \\ \\ f^{-1}(x)=(x-3)^2+2[/tex]
Note we take the positive case because the domain of the original function is the same as the range of the inverse, and the domain of [tex]f(x)[/tex] is [tex][2, \infty)[/tex].
i don’t really know what this means lol so please help i’ll give you brainlist!!!
Answer:
Step-by-step explanation:
A vending machine
The user puts in money, punches a specific button, and a specific item drops into the output slot. (The function rule is the product price. The input is the money combined with the selected button. The output is the product, sometimes delivered along with coins in change, if the user has entered more money than required by the function rule.)
Answer: it is mean to state a real world relationship that consisted a state of a input and output
Step-by-step #hopethishelps
Find the measure of the three missing angles in the parallelogram below
128⁰
Answer: x = 52, y = 128, z = 52
Step-by-step explanation:
If $1743 is invested at 5.45% for 2 years, find the future value if the interest is compounded semi-annually. Round to the nearest
cent.
Do not put the $ in your answer or any units. Only put the number value for your answer.
Add your answer
Answer:
The future value of an investment is calculated by using the formula:
$FV = PV(1 + r/n)^{nt}$
where $FV$ is the future value, $PV$ is the present value (the initial investment), $r$ is the interest rate, $n$ is the number of times the interest is compounded per year, and $t$ is the number of years the investment is held.
In this case, we have $PV = 1743$, $r = 5.45% = 0.0545$, $n = 2$, and $t = 2$. Plugging these values into the formula, we get:
$FV = 1743(1 + 0.0545/2)^{2 \cdot 2} = 1743(1 + 0.0273)^{4}$
Now we can calculate the future value by raising $1 + 0.0273$ to the power of 4:
$FV = 1743(1.0273)^{4} \approx \boxed{1956}$
Note that we rounded the result to the nearest cent.
Step-by-step explanation: