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Answer:
a-b
Step-by-step explanation:
Add the two equations together:
(ax +by) +(bx +ay) = (a² -b²) +(0)
x(a +b) +y(a +b) = (a +b)(a -b)
x + y = a - b . . . . . divide by (a+b), assuming a+b ≠ 0
A car rental firm has 440 cars. Sixty-three of these cars have defective turn signals and 39 have defective tires. (Enter your probabilities as fractions.) (a) What is the probability that one of these cars selected at random does not have defective turn signals
Answer:
The probability is 0.857
Step-by-step explanation:
We know that:
There is a total of 440 cars
There are 63 cars with defective turn signals
There are 39 with defective tires.
Now we want to find the probability that a randomly selected car does not have defective turn signals.
If all the cars have the same probability of being selected, this probability will be equal to the quotient between the number of cars that do not have defective turn signals and the total number of cars.
We know that the total number of cars is 440
And 63 of these have defective turn signals, then the rest don't.
440 - 63 = 377 cars do not have defective turn signals.
Then the probability is:
P = 377/440 = 0.857
What are the zeros of f(x) = x^2 - x - 12?
A. x= -4 and x= 3
B. x=-3 and x = 4
C. x=-2 and x = 6
D. x=-6 and x = 2
Answer:
B. x = -3 and x = 4
General Formulas and Concepts:
Algebra I
Terms/CoefficientsFactoringSolving quadraticsStep-by-step explanation:
Step 1: Define
Identify
f(x) = x² - x - 12
Step 2: Solve for x
Factor: (x - 4)(x + 3) = 0Solve: x = 4, -31. (02.01)
Solve -4(x + 10) - 6 = -3(x - 2). (1 point)
-40
-46
-52
52
Answer:
-52
Step-by-step explanation:
-4(x + 10) - 6 = -3(x - 2)
Distribute the left side to get:
(-4x + -40) - 6
Now distribute the right side to get:
-3x + 6
Arrange the equation as the following:
-4x - 40 - 6 = -3x + 6
Add the like terms on each side:
-4x - 46 = -3x + 6
Do the inverse operation of each term:
-x = 52
Now we need to get x to become a positive, so we just divide -x by -1 to get x.
And 52/-1 to get our final answer of -52.
Answer: -52
Step-by-step explanation:
-4(x + 10) - 6 = -3(x - 2)
Distribute the left side to get:
(-4x + -40) - 6
Now distribute the right side to get:
-3x + 6
Arrange the equation as the following:
-4x - 40 - 6 = -3x + 6
Add the like terms on each side:
-4x - 46 = -3x + 6
Do the inverse operation of each term:
-x = 52
Now we need to get x to become a positive, so we just divide -x by -1 to get x.
And 52/-1 to get our final answer of -52.
Mila wants to buy a scooter for Rs 62,000 . She has only Rs 19,000 with her, so she decides to take a loan from a bank for the remaining amount. The bank offers Mini three loan schemes as shown below. Mini has to return the loan amount with interest in equal monthly instalments
1) How much money does mila take as loan from the bank?
a) Rs 62,000
b) Rs 44,000
c) Rs 45,000
d) Rs 43,000
Answer:
Scheme a 45000 is the answer
Consider the differential equation: 2y′′−13y′−7y = 0
a. Show that, for any constants A and B, the following is a solution to the above differential equation: y = Ae^(−9x)+Be^(x/3)
b. Find the values A and B that make the above general solution into a solution for the following initial value problem: 2y′′−13y′−7y = 0; y(0) = 3, y′(0) = −5
--------------------------------------------------
Just a correction, the characteristic roots of the equation are [tex]y = 7[/tex] and [tex]y = -\frac{1}{2}[/tex], thus, we should test for:
[tex]y = Ae^{7x} + Be^{-\frac{x}{2}}[/tex]
--------------------------------------------------
Question a:
First, we find the derivatives, thus:[tex]y = Ae^{7x} + Be^{-\frac{x}{2}}[/tex]
[tex]y^{\prime} = 7Ae^{-7x} - \frac{1}{2}Be^{-\frac{x}{2}}[/tex]
[tex]y^{\prime\prime} = 49Ae^{-7x} + \frac{1}{4}Be^{-\frac{x}{2}}[/tex]
Now, we replace into the equation:[tex]2y^{\prime\prime} - 13y^{\prime} - 7y = 0[/tex]
[tex]2(49Ae^{-7x} + \frac{1}{4}Be^{-\frac{x}{2}}) - 13(7Ae^{-7x} - \frac{1}{2}Be^{-\frac{x}{2}}) - 7(Ae^{7x} + Be^{-\frac{x}{2}}) = 0[/tex]
[tex]98Ae^{-7x} + \frac{1}{2}Be^{\frac{x}{2}} - 91Ae^{-7x} + \frac{13}{2}e^{-\frac{x}{2}} - 7Ae^{7x} - 7Be^{-\frac{x}{2}} = 0[/tex]
[tex]98Ae^{-7x} - 91Ae^{-7x} - 7Be^{-\frac{x}{2}} + \frac{1}{2}Be^{\frac{x}{2}} + \frac{13}{2}e^{-\frac{x}{2}} - 7Be^{-\frac{x}{2}} = 0[/tex]
[tex]0A + 0B = 0[/tex]
[tex]0 = 0[/tex], thus, we found the identity, and for each constant A and B, the following is a solution.
--------------------------------------------------
Question b:
[tex]y = Ae^{7x} + Be^{-\frac{x}{2}}[/tex]
Since [tex]y(0) = 3[/tex][tex]A + B = 3 \rightarrow B = 3 - A[/tex]
--------------------------------------------------
[tex]y^{\prime} = 7Ae^{-7x} - \frac{1}{2}Be^{-\frac{x}{2}}[/tex]
Since [tex]y^{\prime}(0) = -5[/tex][tex]7A - \frac{1}{2}B = -5[/tex]
Using [tex]B = 3 - A[/tex]
[tex]7A - \frac{3}{2} + \frac{A}{2} = -5[/tex]
[tex]\frac{14A}{2} + \frac{A}{2} = -\frac{10}{2} + \frac{3}{2}[/tex]
[tex]\frac{15A}{2} = -\frac{7}{2}[/tex]
[tex]15A = -7[/tex]
[tex]A = -\frac{7}{15}[/tex]
--------------------------------------------------
Then, B is given by:
[tex]B = 3 - A = 3 - (-\frac{7}{15}) = \frac{45}{15} + \frac{7}{15} = \frac{52}{15}[/tex]
Thus, the values are: [tex]A = -\frac{7}{15}, B = \frac{52}{15}[/tex]
A similar problem is given at https://brainly.com/question/2456414
Can anyone please help me out?
the image is located at the bottom of the screen.
Answer:
..... surface area = 16 km^2.
Which is the best way to write (8/x) as a verbal expression?
Answer:
None of these.
Step-by-step explanation:
8/x is the result when 8 is divided by x.
Question 5 of 10
Which of these groups of values plugged into the TVM Solver of a graphing
calculator will return the amount of a 20-year loan with an APR of 19.2%,
compounded monthly, that is paidoff with monthly payments of $510?
A. N=20; 1%=19.2; PV = ; PMT=-510; FV=0; P/Y=12; C/Y=12;
PMT:END
B. N=240; 1%=19.2; PV = ; PMT=-510; FV=0; P/Y=12; C/Y=12;
PMT:END
C. N=240; 1%=1.6; PV = ; PMT=-510; FV=0; P/Y=12; C/Y=12;
PMT:END
O D. N=20; 1%=1.6; PV = ; PMT=-510; FV=0; P/Y=12; C/Y=12; PMT:END
Answer:
N=240;I%=5.6=-205000;PMT=;Fv=0;P/Y=12;C/Y=12;PMT:END
Step-by-step explanation:
A P E X
The group of values to be plugged into TVM solver is
N=240 ; I % = 19.2% , P = -205000 , PMT= -$510, Fv =0 , P/Y =12.
We have 20 year loan then the number of periods will be
N = 20 x 12
N= 240
and, the Monthly payment is $510 then
PMT = - 510
and, Interest = 19.2%
and, PV = - 205, 000
Thus, N=240 ; I % = 19.2% , P = -205000 , PMT= -$510, Fv =0 , P/Y =12.
Learn more about TVM here:
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#SPJ7
Students at a virtual school are allowed to sign up for one math class each year. The numbers of students signing up for various math classes for the next school
year are given in the following table:
Grade Geometry Algebra II Pre-Calculus AP Statistics Total
10th
150
75
25
5
255
11th
50
100
75
20
245
12th
10
50
100
65
225
Total 210
225
200
90
725
Part A: What is the probability that a student will take AP Statistics? (2 points)
Part B: What is the probability that a 12th-grader will take either Pre-Calculus or AP Statistics? (2 points)
Part C: What is the probability that a student will take Algebra II given that he or she is in the 11th grade? (2 points)
Part D: Consider the events "A student takes Algebra II and "A student is a 10th-grader. Are these events independent? Justify your answer. (4 points)
A well formatted table of the distribution is attached below :
Answer:
0.124
0.733
0.408
Step-by-step explanation:
Using the table Given :
1.) P(AP Statistics) = 90 / 725 = 0.124
2.) P(12th grade ; Precalculus or AP Statistics) = (100 + 65) / 225 = 165 /225 = 0.733
3.) P(Algebra 11 | 11th grade) = P(Algebara11 n 11th grade) / P(11th grade) = 100 / 245 = 0.408
Stuck on this problem
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Answer:
-8,257,536·u^5·v^10
Step-by-step explanation:
The expansion of (a +b)^n is ...
(c0)a^nb^0 +(c1)a^(n-1)b^1 +(c2)a^(n-2)b^2 +... +(ck)a^(n-k)b^k +... +(cn)a^0b^n
Then the k-th term is (ck)a^(n-k)b^k, where k is counted from 0 to n.
The value of ck can be found using Pascal's triangle, or by the formula ...
ck = n!/(k!(n-k)!) . . . . where x! is the factorial of x, the product of all positive integers less than or equal to x.
This expansion has 11 terms, so the middle one is the one for k=5. That term will be ...
5th term = (10!/(5!(10-5)!)(2u)^(10-5)(-4v^2)^5
= (252)(32u^5)(-1024v^10) = -8,257,536·u^5·v^10
The fraction model below shows the steps that a student performed to find a quotient. Which statement best interprets the quotient? A: There are 5 1/5 five-sixths in 4 1/3. B: There 6 1/6 five sixths-in 4 1/3. C: There are 5 1/5 four and one-thirds in 5/6. D: There are 6 1/6 four and one-thirds in 5/6.
Answer:
The answer is D
Step-by-step explanation:
there are 8 1/6 five and one sixth in 2/3
Select the correct answer.
What is the value of this expression when x = -6 and ?
4(x2 + 3) − 2y
Answer:
D. 157
Step-by-step explanation:
4(x^2+3)-2y
4(6^2+3)-2(-1/2) add in given values
4(39)+1. start with parentheses
156+1. combine like terms
157. answer
Answer:
D. 157
Step-by-step explanation:
Hi there!
We want to find the value of the expression 4(x²+3)-2y is when x=-6 and y=-1/2
Let's first simplify the expression, as that will likely make it easier
Distribute 4 to both x² and 3
4x²+12-2y
That's the expression
Substitute -6 as x into the expression
4(-6)²+12-2y
Raise (-6) to the second power
4*36+12-2y
Multiply 36 by 4
144+12-2y
Add 12 and 144 together
156-2y
Now the expression is 156-2y
But remember that we know that y=-1/2, and we haven't substituted it into the expression yet
Substitute -1/2 as y into the expression
156-2(-1/2)
Multiply
156+2/2
Simplify
156+1
Add
157
Hope this helps!
I need help ASAP please please please
Answer:
n=39/5
Step-by-step explanation:
24=5(n-3)
24=5n-15
-5n= -15-24
-5n=39
n= 39/5
Find the exact area of this triangle: 10V3 30° 20 [?] [ square units
Answer:
50√3 square units.
Step-by-step explanation:
Let the two sides of the triangle given be 'a' and 'b'.
Let the angle between them be θ
From the question given above, the following data were obtained:
Side a = 20 units
Side b = 10√3
Angle (θ) = 30°
Area (A) =?
A = ½ × ab × Sineθ
A = ½ × 20 × 10√3 × Sine 30
A = ½ × 20 × 10√3 × ½
A = 10 × 5√3
A = 50√3 square units
Therefore, the area of the triangle is 50√3 square units
Suppose you choose a marble from a bag containing 4 red marbles, 2 white marbles, and 3 blue marbles. You return the first marble to the bag and then choose again. Find P(red then blue).
Answer:
4/27
Step-by-step explanation:
total number of marbles=9
probability of red=4/9
since you returned the first marble, the total number of marbles remains the same
prob(Blue)=(3/9)=1/3
P(red then blue)=(4/9)*(1/3)
=4/27
How to do this question?
Answer:
40
Step-by-step explanation:
2x² - 5y + 7 when x = 2 and y = -5
2(2)² - 5(-5) + 7
= 2(4) -5(-5) + 7
= 8 + 25 + 7
= 40
Suppose that 25% of people own dogs If you pick three people at random, what
is the probability that they all three own a dog? (Let me add that we don’t know the
populations size so calculate the probability as if the population is infinite.)
Answer:
1/64
Step-by-step explanation:
25% own a dog, so picking one person has a probability of 1/4 (0.25) for that person to own a dog.
picking 3 people means combining (multiplying) the probabilities of the non-overlapping and non-depending events.
picking the third person has 1/4 chance of owning a dog (as the population is "infinite") combined with the chance that also the second pick owned a dog, which has to be combined with the chance of the first pick owning a dog.
so,
1/4 × 1/4 × 1/4 = 1/4³ = 1/64 = 0.015625
Please help me with 9 I really need it
Answer:
605 boys.
Step-by-step explanation:
5:7 means 5 parts consists of boys and 7 parts consist of girls.
Since 7 parts = 847, 1 part = 121 and 5 parts = 605
Hence there are 605 boys.
Hope you have a nice day :)
To draw a graph for y = 3/4x + 7, a person can draw a point at x of 0 and y of ___, a second point by going over 3 and up ___, and then draw a line through the points
For drawing the graph for y = 3/4x + 7, a person can draw a point at x of 0 and y of __7_, a second point by going over 3 and up __8.25__, and then draw a line through the points.
How to know if a point lies in the graph of a function?All the points (and only those points) which lie on the graph of the function satisfy its equation.
Thus, if a point lies on the graph of a function, then it must also satisfy the function.
For this case, the equation given to us is:
[tex]y = \dfrac{3}{4}x + 7[/tex]
Any equation of the form [tex]y = mx + c[/tex] where m and c are constants and x and y are variables is the equation of a straight line.
For a straight line to be characterized, only two points are sufficient.
For x = 0, the y-coordinate would be such that it would satisfy the equation [tex]y = \dfrac{3}{4}x + 7[/tex]
Putting x = 0, we get:
[tex]y = \dfrac{3}{4} \times 0 + 7 = 7[/tex]
Thus, y-coordinate of the point on this line whose x-coordinate is 0 is 7. Thus, (0,7) is one of the point's coordinate on the considered line.
Putting x = 3, we get:
[tex]y = \dfrac{3}{4} \times 3 + 7 = 9.25[/tex]
Thus, y-coordinate of the point on this line whose x-coordinate is 0 is 9.25 . Thus, (0,9.25) is another of the point's coordinate on the considered line.
Thus, for drawing the graph for y = 3/4x + 7, a person can draw a point at x of 0 and y of __7_, a second point by going over 3 and up __8.25__, and then draw a line through the points.
Learn more about points lying on graph of a function here:
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Please help, if you can’t answer all just answer one
Answer:
Inverses
Step-by-step explanation:
One things I could tell about the earth from this graph is that the northern and southern hemispheres are inverses because when the temp of one goes up over the months, the other goes down.
PLSSS HELPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPP
Answer:
I believe its EG and NE but i might be wrong
Step-by-step explanation:
Agyappng is three times as old as Atsu .three years ago ,he was four times as old as Atsu ..how old is each boy now
9514 1404 393
Answer:
Atsu is 9Agyappng is 27Step-by-step explanation:
Let x represent Atsu's current age. Then Agyappng is 3x. Three years ago the relationship was ...
(3x -3) = 4(x -3)
9 = x . . . . . . . . . . . . add 12-3x
Atsu is 9; Agyappng is 27.
I am planning to attend a company-paid conference. My charges will include $412.00 for airfare, $378.00 for conference registration, and $210.00 for food.”
Supervisor: “Please submit an expense form for a total of __________ when you return.”
Answer:
$1000.00
Step-by-step explanation:
The supervisor is asking for an expense form of a total (?) when you return.
Given the charges given in the word problem, it is only logical to assume the supervisor wants a expense form of how much you spent (total) on the trip. Thus, you add!
solve for x please help (show ur work)
Answer:
x = -3
Step-by-step explanation:
12 -4x-5x = 39
Combine like terms
12 - 9x = 39
Subtract 12 from each side
12-9x-12 = 39-12
-9x = 27
Divide by -9
-9x/-9 = 27/-9
x = -3
Answer:
x = -3
Step-by-step explanation:
12 - 4x - 5x = 39
Combine like terms
12 - 9x = 39
Subtract 12 from both sides
12 - 12 - 9x = 39 - 12
-9x = 27
Divide both sides by -9
-9x/-9 = 27/-9
x = -3
Most brainiest for the right answer on this problem!
Answer:
82.8
Step-by-step explanation:
mean = sum of all points, over the total given number of points
84 * 26 = 2184
2184 + 69 + 66 = 2319
Now the total number of tests is 26 + 2 or 28
So divide 2319 by 28
2319/28 = 82.82142
rounded to the nearest tenth is 82.8
If my answer is incorrect, pls correct me!
If you like my answer and explanation, mark me as brainliest!
-Chetan K
Please help me!
14
33
46
60
200
Answer:
46
Step-by-step explanation:
200/2 = 100, and the x coordinate that line up with the y-coordinate of 100 is 46.
Find the smallest number from which 3 is to be subtracted so that the difference is exactly divisible 18,24,36
Answer:
72
Step-by-step explanation:
look at the prime factors of each number.
18 = 2*3^2
24 = 2^3*3
36 = 2^2*3^2
The most factors of 2 in any of these numbers is 3: 2^3
The most factors of 3 in any of these numbers is 2: 3^2
2^3*3^2 is 8*9 or 72.
72 is the lowest number exactly divisible by 18, 24, and 36.
find the equation of the line that is perpendicular to y=6x-2) and contains to the point (6-,2)
Answer:
y = -1/6x - 1.
Step-by-step explanation:
I am assuming that the point id (6, -2).
The slope of the required line = -1/6.
y - y1 = m(x - x1) where m = slope and x1,y1 is a point on the line so we have
y - (-2) = -1/6( x- 6)
y + 2 = -1/6x + 1
y = -1/6x - 1.
If the areas of the given pairs of shapes are equal, find the value of x.
Answer:
X= 8cm
Step-by-step explanation:
area of the square = s×s = 16×16 = 256cm
area of the rectangle = l×b = 32×x = 32x
Given , area of triangle = area of square
32x = 256
x= 256/32
x= 8cm
Answer:
[tex]x = 8cm[/tex]
Step-by-step explanation:
we are given a square and rectangle.we want to figure out x which is the width of the rectangle. we are also given a condition i.e
the area of the square equal to the area of the rectangletherefore,
[tex] \displaystyle \rm A _{square } = A _{rect}[/tex]
recall the formula of the area of square and rectangle so,
[tex] \displaystyle {s}^{2} = lw[/tex]
now assign variables
[tex]s \implies16cm[/tex][tex]l \implies32cm[/tex][tex]w \implies x[/tex]thus substitute:
[tex] \displaystyle 32cmx = {16cm}^{2} [/tex]
simplify square:
[tex] \displaystyle 32cmx = 256cm^2[/tex]
divide both sides by 32:
[tex] \displaystyle \boxed{x = 8cm}[/tex]
and we're done!
