9514 1404 393
Answer:
(x, y) = (0, 0), (1/3, 0), (1/4, 5/24)
Step-by-step explanation:
It is often helpful to write equations in general form. That way, factoring and use of the zero product rule can find solutions.
x = 1.5x(1 -x) -0.6xy . . . . given
1.5x -1.5x² -0.6xy -x = 0 . . . . . subtract x
0.5x -1.5x² -0.6xy = 0 . . . . . . . collect terms
0.1x(5 -15x -6y) = 0 . . . . . . . . factor; [eq1]
__
y = y +2xy -0.5y . . . . . . given
y +2xy -0.5y -y = 0 . . . . . subtract y
-0.5y +2xy = 0 . . . . . . . . . . collect terms
-0.5y(1 -4x) = 0 . . . . . . . factor; [eq2]
__
Solutions to [eq1] will be ...
x = 0
15x +6y = 5 . . . . . . a set of possible solutions
Solutions to [eq2] will be ...
y = 0
1 -4x = 0 ⇒ x = 1/4
Then (x, y) pairs that will satisfy both equations simultaneously are ...
(x, y) = (0, 0), (1/3, 0), (1/4, 5/24)
__
In the attached graph, solutions to [eq1] are the red lines; solutions to [eq2] are the green lines. Then simultaneous solutions to both equations are found at the intersection points of red and green lines.
Write the complex number in polar form:
9514 1404 393
Answer:
2√30 ∠-120°
Step-by-step explanation:
The modulus is ...
√((-√30)² +(-3√10)²) = √(30 +90) = √120 = 2√30
The argument is ...
arctan(-3√10/-√30) = arctan(√3) = -120° . . . . a 3rd-quadrant angle
The polar form of the number can be written as ...
(2√30)∠-120°
_____
Additional comments
Any of a number of other formats can be used, including ...
(2√30)cis(-120°)
(2√30; -120°)
(2√30; -2π/3)
2√30·e^(i4π/3)
Of course, the angle -120° (-2π/3 radians) is the same as 240° (4π/3 radians).
__
At least one app I use differentiates between (x, y) and (r; θ) by the use of a semicolon to separate the modulus and argument of polar form coordinates. I find that useful, as a pair of numbers (10.95, 4.19) by itself does not convey the fact that it represents polar coordinates. As you may have guessed, my personal preference is for the notation 10.95∠4.19. (The lack of a ° symbol indicates the angle is in radians.)
Chris is reading a book that has nine-hundred seventy-eight pages in it. Every night
Chris reads a number of pages that can be rounded to the nearest hundred. The rst
night Chris reads one-hundred two pages. The second night Chris reads ninety-eight
pages. The third night Chris read one-hundred fty-four pages. The fourth night Chris
reads fty-six pages. The fth night Chris reads two-hundred thirty-four pages. The
sixth night Chris reads forty-eight pages. The seventh night Chris reads one-hundred
seventy pages. On what nights does Chris read a number of pages that can be rounded
to the nearest hundred? Show all your mathematical thinking.
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Answer:
Every night
Step-by-step explanation:
The problem statement tells you ...
"Every night Chris reads a number of pages that can be rounded to the nearest hundred."
Then it asks you ...
"On what nights does Chris read a number of pages that can be rounded to the nearest hundred?"
If we take the problem statement at face value, the answer must be ...
"Every night."
How many paths are there from C to E?
Оeri
В
12
8
О 10
O 14
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Answer:
(b) 8
Step-by-step explanation:
We assume that a path must not repeat any node. (So, loops at G are forbidden.)
There are 2 paths through B to A.
There are 2 paths through D to A, so a total of 4 ways to get from C to A.
There is one path from A to H.
There are two paths from H to F, and one path from F to E.
The total number of possible paths is (4)(1)(2)(1) = 8.
Here is a list.
CBAHFE, CDBAHFE, CBAHGFE, CDBAHGFE,
CDAHFE, CBDAHFE, CDAHGFE, CBDAHGFE
El largo de un terreno es el doble de la medida de su ancho, como se muestra en la imagen. Si el perímetro es de 96 hectómetros, ¿cuáles son las dimensiones del terreno?
Answer:
Step-by-step explanation:
The following configured particulars are states, in accordance by the interrogate:
Perimeter = 96 hectometers.
Assuming the figure is a square, we can assume that,
S = A side length where,
4s = 96, where all side lengths are equivalent.
If so, then s = 24
Thus, that means that w, denoted as width, must be less than or equal to 24.
In addition, likewise, l, denoted as length, must be less than or equal to 24.
Furthermore, the length is acknowledged or stated to be twice that of the width:
Length = 2w
The listed above may be equated to the following:
2w + 2L = 96
2(24) + 2L = 96
2L + 48 = 96
2L = 48
L = 24
Thus, the width of the figure is equivalent to 24. (Length divided by two).
Thus, the length of the figure is equivalent to 24 (twice the width).
*I hope this helps.
Initial value question help
Answer:
Initial amount of fish: 530
Population increase or decrease: decrease
Decrease rate: 92%
Step-by-step explanation:
P(t) = Size/population of fish after t years
t = numbers of years
Good luck! :D
If a student (represented by initials) was chosen at random, find P(HHU C).
Answer:
[tex]P(HH\ u\ C) = \frac{13}{16}[/tex]
Step-by-step explanation:
Given
The Venn diagram
Required
[tex]P(HH\ u\ C)[/tex]
This is calculated as:
[tex]P(HH\ u\ C) = \frac{n(HH\ u\ C)}{n(U)}[/tex]
Where:
[tex]n(U) = 16[/tex] --- count of students
[tex]n(HH\ u\ C) =13[/tex]
So, we have:
[tex]P(HH\ u\ C) = \frac{n(HH\ u\ C)}{n(U)}[/tex]
[tex]P(HH\ u\ C) = \frac{13}{16}[/tex]
Round 61,565 to the
nearest hundred.
Answer:
61600
Step-by-step explanation:
the 3rd digit is the hundreds. because the digit in the 10s is greater 5, we round it up
Answer:
61,600 is your answer please
please solve pre calculus i am cruing
Answer:
neither
[tex]a_{n} = \frac{n+1}{n+4}[/tex]
Step-by-step explanation:
Answer: an=n+1/n+4
~~~~~
True or false : There exists a function f such that f(x) <0, f'(x) > 0, and F"(x) < 0 for all x.
Answer:
false
Step-by-step explanation:
f can never have x next to it
Please proved explanation for answer.
Answer:
inverse it and do fx and gx inverse its value
What are the coordinates of A’ after a 90° counterclockwise rotation about the origin.
Answer:
A' (- 1, - 5 )
Step-by-step explanation:
Under a counterclockwise rotation about the origin of 90°
a point (x, y ) → (- y, x ), then
A (- 5, 1 ) → A' (- 1, - 5 )
lee has a collection of dvds he had 8 dramas 15 comedies and 2 westerns if he selects at random a dvd to watch what is the probability that he will select a western
Explanation:
There are A = 2 westerns out of B = 8+15+2 = 25 movies total
The probability of selecting a western is A/B = 2/25
In decimal form, this is 2/25 = 0.08 which converts to 8%
Answer:
2/25
Step-by-step explanation:
so first u have to add them all up to get 25 because 8 +15+2=25. then, since there are 2 westerns, the probability that he will select a western is 2 out of 25
Help me please, Domain & Range problem
Answer:
Domain: all reals
Range: 4 ≤y <∞
Step-by-step explanation:
The domain is the possible input values(x)
From the arrows at the left and right ends on the graph, the inputs can be all reals
The range is the possible output values (y)
Y goes from 4 to infinity
4 ≤y <∞
An account manager for a local software firm believes there is a relationship between the number of contacts and the amount of the sales. To verify this belief, the following data was collected: Salesperson Number of Contacts Sales (in millions) 1 14 24 2 12 14 3 20 28 What is the dependent variable
Answer:
Amount of sales
Step-by-step explanation:
The dependent variable also called the measured or predicted variable is simply the variable obtained due to inputs in of the independent variable. It is the variable which is being measured in an experiment. Here, the test is that the number of sales depends on the number of contact. Here, the number of contacts will has an influence or determines the amount of sales, hence, the number of contacts is the independent variable while the amount of sales is the dependent variable.
Use the substitution method to solve the system of equations. Choose the
correct ordered pair.
y = 12x-8
y = 8x
A. (4, 12)
B. (5, 11)
C. (2,16)
O D. (3, 15)
Answer:
C. (2,16)
Step-by-step explanation:
[tex]y=12x-8\\y=8x\\\\\\8x=12x-8\\-4x=-8\\x=2\\\\y=8(2)=16[/tex]
Answer:
It might be B
Step-by-step explanation:
12(5)-8
8(11)
52
88
Every year, a town surveys the size of its wetland ecosystems. This equation estimates the total wetland area, in acres, over time, t, in years.
F(t)= 740(0.95)^t
Which statements are supported by the function?
When t=10, the town is predicted to have around 443 acres of wetlands.
At one time, the town had 740 acres of wetlands.
The wetland area in the town decreases by 5% per year.
When t=10, the town is predicted to have around 492 acres of wetlands.
The wetland area in the town increases by 95% per year.
Answer:
When t=10, the town is predicted to have around 443 acres of wetlands.
At one time, the town had 740 acres of wetlands.
The wetland area in the town decreases by 5% per year.
Step-by-step explanation:
Given
[tex]f(t) = 740 * (0.95)^t[/tex]
Required
The true statements
[tex](a)\ f(10) = 443[/tex]
We have:
[tex]f(t) = 740 * (0.95)^t[/tex]
Substitute 10 for t
[tex]f(10) = 740 * (0.95)^{10[/tex]
[tex]f(10) = 443[/tex]
Hence, (a) is true
[tex](b)\ f(t) = 740[/tex]
We have:
[tex]f(t) = 740 * (0.95)^t[/tex]
Substitute 740 for f(t)
[tex]740 = 740 * (0.95)^t[/tex]
Divide through by 740
[tex]1 = 0.95^t[/tex]
Express 1 as 0.95^0
[tex]0.95^0 = 0.95^t[/tex]
Cancel out the bases
[tex]0 = t[/tex]
[tex]t = 0[/tex]
Hence, the area had 740 acres initially;
(b) is true
[tex](c)\ r = 5\%[/tex]
We have:
[tex]f(t) = 740 * (0.95)^t[/tex]
Using the general formula
[tex]f(t) = a * b^t[/tex]
By comparison:
[tex]b = 0.95[/tex]
0.95 < 1 means that:
[tex]b = 1 - r[/tex] --- where r = rates
[tex]0.95 = 1 - r[/tex]
Collect like terms
[tex]r = 1 - 0.95[/tex]
[tex]r = 0.05[/tex]
Express as percentage
[tex]r = 5\%[/tex]
Hence, (c) is true
[tex](d)\ f(10) = 492[/tex]
In (a)
[tex]f(10) = 443[/tex]
Hence, (d) is false
[tex](e)\ r = 95\%[/tex]
In (c)
[tex]r = 5\%[/tex] ---- decrement
Hence, (e) is incorrect
Answer: When the town is predicted to have around 443 acres of wetlands.
At one time, the town had 740 acres of wetlands.
The wetland area in the town decreases by 5% per year.
Step-by-step explanation:
Your friend offers to place a bet with you. He will pay you $1 if your favorite sports team wins the game on Tuesday night. But you will pay him $3 if his team wins. Your team has an 80% chance of winning, whereas his only has a 20% chance. This bet is in your favor. True or False.
False because $1 =$1 not $3
True. The expected value of the bet is positive ($0.2),
What is probability?Probability is defined as the possibility of an event being equal to the ratio of the number of favorable outcomes and the total number of outcomes.
Let's calculate the expected value of the bet for both outcomes:
If your team wins: You get paid $1, so the expected value is 0.8 × $1 = $0.8
If your friend's team wins: You pay $3, so the expected value is 0.2 × -$3 = -$0.6
The overall expected value of the bet is the sum of these two outcomes: $0.8 + (-$0.6) = $0.2
Since the expected value of the bet is positive ($0.2), this means that on average, you can expect to win money if you take this bet. Therefore, the bet is in your favor.
Learn more about probability here:
brainly.com/question/11234923
#SPJ2
The length of the base of a triangle is twice it’s height. If the area of the triangle is 441 square kilometers, find the height
Answer:
21 kilometers
Step-by-step explanation:
Let the height be [tex]x[/tex]. Then, the length of the base is [tex]2x[/tex]. The formula for the area is of the triangle is given by base*height/2. Therefore, the area of the triangle is equal to [tex]\frac{x \cdot 2x}{2} = x^2[/tex], which is in turn equal to 441. Since [tex]x[/tex] must be positive, then [tex]21^2=441[/tex], meaning that the height is [tex]21[/tex] kilometers.
What is the area of the shaded part of the figure?
Answer:
14cm²
Step-by-step explanation:
3x2=6,
3x2=6,
2x1=2,
6+6+2=14 cm^2
Question 13 plz show ALL STEPS so I can learn thnx
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Answer:
a) (x³ -x² +x +2) +2/(x+1)
b) (x² +2x -5) +6/(x+3)
Step-by-step explanation:
Polynomial long division is virtually identical to numerical long division, except that the quotient term does not require any guessing. It is simply the ratio of the leading terms of the dividend and divisor. As with numerical long division, the product of the quotient term and the divisor is subtracted from the dividend to form the new dividend for the next step.
The process stops when the dividend is of lower degree than the divisor.
In part (a), you need to make sure the dividend expression has all of the powers of x present. This means terms 0x³ and 0x² must be added as placeholders in the given dividend. They will become important as the work progresses.
During the construction of a road a mountain of 250 metres in height, through it will be the construction of a tunnel. The top of the mountain is seen at an angle of 48°30' from a point P at one end of the mountain, and at an angle of 38° from the other end. How long will this tunnel be?
Answer:
542.74 m
Step-by-step explanation:
Tan(48.3) = 250/a Multiply by a
a*tan(48.3) = 250 Divide by tan(48.3)
a = 250/Tan(48.3)
a =222.74
By a similar method b = 250/tan(38)
b = 319.99'
The total length =542.73 meters
Internet providers: In a survey of 780 homeowners with high-speed Internet, the average monthly cost of a high-speed Internet plan was $64.22 with standard deviation S10.75. Assume the plan costs to be approximately bell-shaped. Estimate the number of plans that cost between $42.72 and $85.72. pprosimately bell-shaped. The number of plans that cost between $42.72 and $85.72 is:_________
Answer:
Hence the number of plans that cost between $42.72 and $ 85.72 is
95.44 %.
Step-by-step explanation:
Now the given are
μ = $64.22.
σ = $10.75.
Here,
[tex]P\left ( 42.72 < x< 85.72 \right )=P\left ( \frac{42..72-64.22}{10.75}< \frac{x-\mu }{\sigma } < \frac{85.72-64.22}{10.75}\right )\\P\left ( 42.72 < x< 85.72 \right )= P\left ( -2.00< Z <2.00 \right )\\P\left ( 42.72 < x< 85.72 \right )= P\left (Z<2.00\right )-P\left ( Z<-2.00 \right )\\P\left ( 42.72 < x< 85.72 \right )= P\left (0.9772\right )-P\left (0.0228\right )\\Probability = 0.9544[/tex]
Probability = 95.44%.
25[tex]25^x=125^x^+^3[/tex] = 125x + 3
Answer:
x = -9
Step-by-step explanation:
25^x = 125 ^(x+3)
Rewriting
5^2^x = 5^3^(x+3)
We know a^b^c = a^(b*c)
5^(2x) = 5^(3(x+3))
5^(2x) = 5^(3x+9)
The bases are the same so the exponents are the same
2x = 3x+9
Subtract 3x from each side
2x-3x = 3x+9-3x
-x =9
x = -9
Answer:
x is -9
Step-by-step explanation:
Write an expression 9 multiplied by t
Answer:
9t
Step-by-step explanation:
That's 9 multiplied by t
The sum of two integers is -360. One of them is 60, then the other integer is
X^2 + bx + 49 is a perfect squad trinomial what is one possible value of b? & I need help with the others also due soon!
20. (2) 14
A perfect square trinomial will factor into two expressions that are the same, for example: x^2 + 6x + 9 = (x + 3)(x + 3). Since this problem has a C value of 49, it will factor into (x + 7)(x + 7). 7 doubled is 14, therefore one possible value of B is 7.
21. (4) 2, -12
x^2 + 10x + 25 = 24 + 25
(x + 5)^2 = 49
x + 5 = +/- 7
x = 2, -12
22. (3) 3 + sqrt(17)
x^2 - 6x = 8
Complete the Square
x^2 - 6x + 9 = 8 + 9
(x - 3)^2 = 17
x - 3 = +/- sqrt(17)
x = 3 + sqrt(17), 3 - sqrt(17)
23. (1) 1, -5
x^2 + 4x - 5 = 0
x^2 + 4x = 5
x^2 + 4x + 4 = 5 + 4
(x + 2)^2 = 9
x + 2 = +/- 3
x = 1, -5
Hope this helps!
find the solution to this system of equations x+y=1
2x-y+z=1
x+2y+z=8/3
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Answer:
(x, y, z) = (1/3, 2/3, 1)
Step-by-step explanation:
We can use the first equation to write an expression for x that can be substituted into the other equations.
x = 1 -y
2(1 -y) -y +z = 1 ⇒ -3y +z = -1
(1 -y) +2y +z = 8/3 ⇒ y +z = 5/3
Subtracting the first of these equations from the second gives ...
(y +z) -(-3y +z) = (5/3) -(-1)
4y = 8/3
y = 2/3
z = 5/3 -y = 1
x = 1 -y = 1/3
The solution is (x, y, z) = (1/3, 2/3, 1).
Which of the following choices shows the complete factorization of 50?
52 • 5
2 • 25
52 • 2
None of these choices are correct.
Hello can anyone answer this question please I need help
9514 1404 393
Answer:
maximum: 40(8/3, 8/3)Step-by-step explanation:
The graph shows the relevant vertex of the feasible region is ...
(x, y) = (8/3, 8/3).
The value of z there is ...
z = 11(8/3) +4(8/3) = (88 +32)/3
z = 40
An investor puts $800 into an account that pays 7.5% interest compounded annually. The total amount A in the account after t years is given by which function below?
A = 800(1.75) ^t
A = 800(1.075) t
A = 800(1.075)^ t
A = 800 + (1.075)^ t
Answer:
A = 800( 1.075)^(t)
Step-by-step explanation:
The equation for interest is
A = p (1+r/n) ^ nt where p is the principle, r is the interest rate, n is the number of times per year and t is the years
A = 800( 1+ .075/1)^(1*t)
A = 800( 1.075)^(t)
Let's see
[tex]\\ \tt\leadsto A=P(1+r/n)^{nt}[/tex]
n is 1[tex]\\ \tt\leadsto A=P(1+r)^t[/tex]
[tex]\\ \tt\leadsto A=800(1+0.075)^t[/tex]
[tex]\\ \tt\leadsto A=800(1.075)^t[/tex]
Option C
