x - coordinate of the solution of given system of linear equations is :
-3now, let's plug the value of x as -3 in the first equation, we get :
\( - x + y = 6\)\( - ( - 3) + y = 6\)\(3 + y = 6\)\(y = 6 - 3\)\(y = 3\)therefore, value of y = 3
correct choice - b
Answer:
\( y = 3 \)
Step-by-step explanation:
Given system of equations ,
\(\begin{cases} -x +y = 6\dots (i) \\ 2x -5y = -21 \dots (ii)\end{cases}\)
2(i) + (ii) :-
\(\implies -2x +2y +2x -5y = -21+12 \)
Simplify RHS and LHS ,
\(\implies -3y = -9 \)
Divide both sides by -3 ,
\(\implies \boxed{ y = 3}\)
−|9| = −9 True or False
Answer:
True
Step-by-step explanation:
|9| means the absolute value, how far it is away from zero, so that's 9. Then it's just -9=-9. If it were |-9| then the absolute value would be 9 making the equation false.
The expression −|9| is the negation of the absolute value of 9, which is 9. This is not equal to -9.
Hence, The answer is False.
The absolute value of a number is its distance from zero. It is always non-negative. Therefore, the absolute value of 9 is 9, not -9.
The negation of a number is its opposite. The opposite of 9 is -9.
Therefore, the expression −|9| is the negation of the absolute value of 9, which is 9. This is not equal to -9.
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Where did my dad go? He went to get milk but never came back
The phrase "He went to get milk but never came back" is often used as a humorous way to explain someone's absence or to imply that someone is unreliable or untrustworthy.
The phrase likely originates from a common experience where a child's parent, often their father, promises to go out to get something, like milk, but never returns. This can be a source of disappointment and confusion for the child, and the phrase has since been used in a joking manner to explain someone's failure to show up or fulfill a promise.
However, it is important to recognize that this experience can also be a source of trauma and should not be used to make light of someone's pain or loss.
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what’s 2+5,,,,!!!!!’mmmmmmmmmwwwww
The cost for a pack of 18 pens is $3.24 Find the unit price in dollars per pen. If necessary, round your answer to the nearest cent.
Answer:
Each pen cost 0.18 cents
Step-by-step explanation:
3.24/18=0.18
respectively Q 1
=160−10P 1
OR r 1
=16−0.1Q 1
aWD 1/P 6
=16 6
−2T −
Q 2
=200−20P 2
ORP 2
=10−0,050,…H1AP 2
=15−0:0% Saga's Total Cost function is: TC =120+4Q With third degree price discrimination, the condition for peofit marimizater is MR 1
=MR 2
=MR=MC Find P 1
,Q 1
,P 2
,Q 1
Total Revenue, Total Cost, and Total proft wit sree discrimination. Find P,Q,TR,TC&π In the absence of price discrimination. Marks: 7
In the absence of price discrimination, the profit-maximizing conditions would be different, and the resulting prices, quantities, total revenue, total cost, and profit would also be different.
To find the profit-maximizing conditions with third-degree price discrimination, we need to equate the marginal revenue (MR) to the marginal cost (MC) for each market segment.
Given the demand equations and the total cost function:
Market 1: Q1 = 160 - 10P1 or P1 = 16 - 0.1Q1
Market 2: Q2 = 200 - 20P2 or P2 = 10 - 0.05Q2
Total Cost: TC = 120 + 4Q
To find the profit-maximizing prices and quantities, we equate MR to MC for each market segment:
MR1 = MC:
16 - 0.2Q1 = 4
0.2Q1 = 12
Q1 = 60
MR2 = MC:
10 - 0.1Q2 = 4
0.1Q2 = 6
Q2 = 60
Substituting the quantities back into the demand equations, we find:
P1 = 16 - 0.1(60) = 10
P2 = 10 - 0.05(60) = 7
The total revenue (TR) can be calculated by multiplying the price by the quantity for each market segment:
TR = P1 * Q1 + P2 * Q2
TR = (10 * 60) + (7 * 60)
TR = 600 + 420
TR = 1020
The total cost (TC) is given by the total cost function:
TC = 120 + 4Q
TC = 120 + 4(60 + 60)
TC = 120 + 480
TC = 600
Finally, the profit (π) can be calculated by subtracting total cost from total revenue:
π = TR - TC
π = 1020 - 600
π = 420
In the absence of price discrimination, the profit-maximizing conditions would be different, and the resulting prices, quantities, total revenue, total cost, and profit would also be different.
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The Steelers beat the Seahawks by 10 points. The total points scored between both teams was 44. How many points did the Seahawks have?
Answer:
17
steelers had 27
Step-by-step explanation:
The vertex of this angle is:
R
T
S
The vertex of this angle is point S.
A sales associate in a jewelry store earns $450 each week, plus a commission equal to 2% of her sales. this week her goal is to earn at least $800. how much must the associate sell in order to reach her goal
In order for the associate to meet her objective of making at least $800, she must sell at least $17,500 worth of jewelry.
To solve this problemWe must figure out how many sales are necessary to get that income.
Let's write "S" to represent the sales amount.
The associate's base pay is $450 per week, and she receives a commission of 2% of her sales. Her commission is therefore equal to 0.02S (2% of sales), which can be computed.
The total income must be at least $800 in order for her to fulfill her goal. As a result, we may construct the equation shown below:
Base Salary + Commission ≥ Goal
$450 + 0.02S ≥ $800
Now, we can solve the inequality to find the minimum sales amount:
0.02S ≥ $800 - $450
0.02S ≥ $350
Divide both sides by 0.02 to isolate 'S':
S ≥ $350 / 0.02
S ≥ $17,500
Therefore, In order for the associate to meet her objective of making at least $800, she must sell at least $17,500 worth of jewelry.
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The temperature was -5°F and then fell 8°F.
Answer:
The temperature is now -13 degrees Fahrenheit
Hope that helps!
Step-by-step explanation:
Answer:
It increased??
Step-by-step explanation:
AB is parallel to CD. CD is rotated 180° Which statement describes the relationship between ('D' and the transformed AB? How can
you prove it?
Answer:
Answer :- Statement (B) ,C'D' ll AB
Given AB is parallel to CD. CD rotated.
Consider a transversal line l intersecting AB and CD at angle x.
therefore By slope formula,
slope of AB and CD = m =tanx
Now after rotation of 180 CD become C'D'
therefore, slope of C'D' = =tanx=m
Hence C'D' ll AB.
Will Give Brainliest and 5 star..... Please Help
Q. ε = {x: 2 ≤ x ≤30, x is an integer}, M = {even numbers}, P = {prime numbers}, T = {odd numbers} Find: (i) MUP (ii) M - T (iii) P∪(M∩T) (iv) P’U(M∩T’)
Answer:
(i)\(M \cup P=\{2,3,4,5,6,7,8,10,11,12,13,14,16,17,18,19,20,22,23,24,26,28,29,30\}\)
(ii)M-T={2,4,6,8,10,12,14,16,18,20,22,24,26,28,30}
(iii)P∪(M∩T) = {2, 3, 5, 7, 11, 13, 17, 19, 23, 29}
(iv)P’U(M∩T’)={2,4,6,8,9,10,12,14,15,16,18,20,21,22,24,25,26,27,28,30}
Step-by-step explanation:
Given the sets:
ε = {x: 2 ≤ x ≤30, x is an integer}
M = {even numbers}={2,4,6,8,10,12,14,16,18,20,22,24,26,28,30}
P = {prime numbers}={2, 3, 5, 7, 11, 13, 17, 19, 23, 29}
T = {odd numbers} ={3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29}
(i)This is the union of sets M and P. (Do not repeat same elemnts)
\(M \cup P=\{2,3,4,5,6,7,8,10,11,12,13,14,16,17,18,19,20,22,23,24,26,28,29,30\}\)
(ii)M-T: This is the set M less elements in set T.
Since \(M \cap T =\{\}\), the set M-T=M.
M-T={2,4,6,8,10,12,14,16,18,20,22,24,26,28,30}
(iii) P∪(M∩T)
\(M \cap T =\{\}\)
Therefore:
P∪(M∩T) = P
P∪(M∩T) = {2, 3, 5, 7, 11, 13, 17, 19, 23, 29}
(iv) P’U(M∩T’)
Since T is the set of odd numbers, its complement will be the set of even numbers.
T'=M={2,4,6,8,10,12,14,16,18,20,22,24,26,28,30}
M∩T’=M={2,4,6,8,10,12,14,16,18,20,22,24,26,28,30}
\(P' =\{4,6,8,9,10,12,14,15,16,18,20,21,22,24,25,26,27,28,30\}\)
Therefore:
P’U(M∩T’) = {4,6,8,9,10,12,14,15,16,18,20,21,22,24,25,26,27,28,30} U {2,4,6,8,10,12,14,16,18,20,22,24,26,28,30}
={2,4,6,8,9,10,12,14,15,16,18,20,21,22,24,25,26,27,28,30}
A homogeneous equation is given by y'' - 11y = 0, determine the general solution of this equation
A homogeneous equation is given by y" + 7y' + 12y = 0, determine the solution of this equation where y(0) = -4,y'(0) = -1
To find the general solution of the homogeneous equation y'' - 11y = 0, we can assume a solution of the form\(y = e^{rt}\), where r is a constant. Substituting this into the equation, we get:
\((r^2 - 11)e^{rt} = 0\)
For this equation to hold for all t, we must have r² - 11 = 0, which gives us the characteristic equation:
r² = 11
The roots of this equation are ±√11. Therefore, the general solution is:
\(y(t) = C_1 e^{\sqrt{11}t} + C_2 e^{-\sqrt{11}t}\)
where C₁ and C₂ are arbitrary constants.
For the second equation, y'' + 7y' + 12y = 0, we can also assume a solution of the form y = e^(rt). Substituting this into the equation, we get:
\(r^2 e^{rt} + 7r e^{rt} + 12 e^{rt} = 0\)
Dividing through by e^(rt), we obtain the characteristic equation:
r² + 7r + 12 = 0
This equation can be factored as (r + 3)(r + 4) = 0. So the roots are r = -3 and r = -4. Therefore, the general solution is:
\(y(t) = C_1 e^{-3t} + C_2 e^{-4t}\)
To find the specific solution given the initial conditions y(0) = -4 and y'(0) = -1, we substitute these values into the general solution:
\(y(0) = C_1 e^{-3(0)} + C_2 e^{-4(0)} = C_1 + C_2 = -4\)
\(y'(0) = -3C_1 e^{-3(0)} - 4C_2 e^{-4(0)}\)
= -3C₁ - 4C₂ = -1
Solving this system of equations, we find C₁ = -1 and C₂ = -3. Thus, the specific solution for the given initial conditions is:
\(y(t) = -e^{-3t} - 3e^{-4t}\)
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How does changing the sign of the constant a from positive to negative affect the domain and range of f(x) = a|x|?
When changing the sign of the constant a from positive to negative, the domain remains the same. But the range changes.
A function's range is the set of all values it can accept, whereas its domain is the set of all values for which it is defined.
Consider the given function f(x)=a|x|. Let us consider "a" takes positive values that is \(a\geq0\). Then, the given function is defined as follows,
\(f(x)=\begin{cases}a(x)=ax}\; &x\geq0\\{a(-x)=-ax\;&x < 0\end{cases}\)
Then, the domain will be \(\text{domain}=\mathbb{R}\{(-\infty, \infty)\) and the range will be given as \(\text{Range} = \text{only non-negative real numbers} = \mathbb{R}^++\{0\}\).
Now let us consider "a" takes negative values that is a<0. Then, the given function is defined the same and the domain will remain the same. But the range will be given as \(\text{Range} = \text{only negative real numbers} = \mathbb{R}^-+\{0\}\).
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Factor the perfect square trinomial x2 − 12x + 36.
A. (x − 6)2
B. (x − 6)(x + 6)
C. (x + 6)2
D. (x − 12)2
The difference between the largest six digit number made from 2,9,1,7,5and 8 the smallest six digit number made from 7,4,2,5,3 and if each digit is only used once is...
The difference between the largest six-digit number made from 2, 9, 1, 7, 5, and 8 and the smallest six-digit number made from 7, 4, 2, 5, 3 (each used only once) is 752,954.
The largest six-digit number that can be formed using the digits 2, 9, 1, 7, 5, and 8 is 987,521. The smallest six-digit number that can be formed using the digits 7, 4, 2, 5, 3 (each used only once) is 234,567.
To calculate the difference between these two numbers, we subtract the smallest number from the largest number: 987,521 - 234,567 = 752,954.
Therefore, the difference between the largest six-digit number made from 2, 9, 1, 7, 5, and 8 and the smallest six-digit number made from 7, 4, 2, 5, 3 (each used only once) is 752,954.
To find the largest six-digit number, we arrange the given digits in descending order: 9, 8, 7, 5, 2, 1. The resulting number is 987,521. Similarly, to find the smallest six-digit number with distinct digits,
we arrange the given digits in ascending order: 2, 3, 4, 5, 6, 7. The resulting number is 234,567. Finally, we subtract the smaller number from the larger number to obtain the difference of 752,954.
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Question 14 of 21
If you apply the changes below to the quadratic parent function, f(x) = x²,
which of these is the equation of the new function?
• Shift 1 unit right.
• Vertically stretch by a factor of 3.
• Reflect over the x-axis.
A. g(x)=-3x²-1
OB. g(x) = -3(x + 1)²
C. g(x) = (-3x + 1)²
D. g(x) = -3(x-1)²
Solve for S. 3.25 + 5.50s is less than or equal to 30
Answer:
less than
Step-by-step explanation:
During a basketball game, chiyann made 15 baskets. She made three more baskets then twice number of baskets made by whitney. How many baskets did whitney make
Answer:
Whitney made 6 baskets
Step-by-step explanation:
Let the number of baskets made by Whitney be x.
The 15 baskets made by
Chiyann is equal to 2 times plus 3 what Whitney made
Mathematically what she made would be 2x + 3
To get x, we equate this equation to 15
2x + 3 = 15
2x = 12
x = 12/2
x = 6 baskets
Evaluate the following expression when x is π/6. Use exact values.
2 cos(2x + π/3)
The exact value of the expression 2 cos(2x + π/3) when x = π/6 is -1.
Given that the expression is:2 cos(2x + π/3) and we need to evaluate this expression when x = π/6. We need to substitute x = π/6 in the given expression and simplify as shown below: 2 cos(2x + π/3) = 2 cos(2(π/6) + π/3)
Now, cos(2(π/6) + π/3) can be simplified as: cos(2(π/6) + π/3) = cos(π/3 + π/3) = cos(2π/3)
To find the value of cos(2π/3), we know that cos(π/3) = 1/2 and that cos(2θ) = cos2(θ) - sin2(θ).
Therefore, cos(2π/3) = cos2(π/3) - sin2(π/3) = (1/2)2 - (√3/2)2= 1/4 - 3/4 = -2/4 = -1/2
Therefore, 2 cos(2x + π/3) = 2 cos(2(π/6) + π/3) = 2 cos(2π/3) = 2 (-1/2) = -1. Therefore, the value of the expression 2 cos(2x + π/3) when x = π/6 is -1.
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Help, I need to answer this question
Answer:
Step-by-step explanation:
factors of 8
Answer:
F- of a 8* i think
Step-by-step explanation:
How long will it take for an object to fall from 15m?
The object is on Mercury and starts falling from rest. As it is on Mercury there is no air resistance to account for. Make sure your answer is rounded to the nearest hundredth (x.xx) decimal. Gravity on Mercury is 3.7 m/s²
The time taken by the object to fall from 15 m on the Mercury which has a gravity of 3.7 m/s² is 10.54 seconds.
What is kinematics?It is the study of the motion of a body without considering mass. And the reason behind them is neglected.
The object is on Mercury and starts falling from rest.
As it is on Mercury there is no air resistance to account for.
Gravity on Mercury is 3.7 m/s².
Then the time taken by the object to fall from 15 m will be given as
\(\rm t = \sqrt{2gh}\\\\t = \sqrt{2\times 3.7\times 15}\\\\t = 10.5356 \approx 10.54 \ seconds\)
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(2b-4c) divided by 2 equals?
Answer:
The answer is b - 2c
Step-by-step explanation:
Factor the numerator and denominator and cancel the common factors.
Hoped this helped!
Answer:
The answer to this question is b - 2c
Have a function f defined by
\(f(x)=(\sin{x}+1)^x\)
determine the value of
\(f'\left(\dfrac{3\pi}{2}\right)\)
Answer:
\(f'(\frac{3\pi}{2})\) is undefined
Step-by-step explanation:
\(f(x)=(sinx+1)^x\)
\(\frac{d}{dx}(sinx+1)^x\)
\(\frac{d}{dx}e^{ln((sinx+1)^x)}\)
\(\frac{d}{dx}e^{xln(sinx+1)}\)
\((\frac{d}{dx}(x)*ln(sinx+1)+x*\frac{d}{dx}ln(sinx+1))e^{xln(sinx+1)}\)
\((ln(sinx+1)+x*cosx(\frac{1}{sinx+1}))(sinx+1)^x\)
\([ln(sinx+1)+\frac{xcosx}{sinx+1}](sinx+1)^x\)
\(f'(\frac{3\pi}{2})=[ln(sin\frac{3\pi}{2} +1)+\frac{\frac{3\pi}{2} cos\frac{3\pi}{2} }{sin\frac{3\pi}{2} +1}](sin\frac{3\pi}{2} +1)^{\frac{3\pi}{2}}\)
\(f'(\frac{3\pi}{2})=[ln(-1+1)+\frac{\frac{3\pi}{2} (0) }{-1+1}](-1+1)^{-1}\)
\(f'(\frac{3\pi}{2})=[ln(0)+\frac{0}{0}](0)^{-1}\)
Because the derivative is undefined, then the function isn't differentiable at the point \((\frac{3\pi}{2},0)\), making it a critical point since the slope of the function is 0.
in the adjoining figure, pq//mr and nmr=150 and qnm=40 calculate the value of X
The missing angle of the given diagram is: x = 70°
How to find the value of the missing angle?We are given that:
∠NMR = 150°
∠QNM = 40°
PQ ║ MR
If we imagine that the line RM is extended to meet QM at a point O.
Now, since PQ is parallel to MR, we can also say that PQ is parallel to OR.
Thus, by virtue of alternate angles theorem, we can say that:
∠PQN = ∠QOR = x
Sum of angles in a triangle sums up to 180 degrees. Thus:
∠OMN + ∠NMR = 180
∠QOR = ∠OMN + ∠ONM = 70
Thus:
x = 70°
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Let an = 5n/4n + 1 Determine whether {an) is convergent. convergent divergent
To determine whether the sequence {an} = 5n/4n + 1 is convergent or divergent, we can analyze its behavior as n approaches infinity.
First, let's rewrite the expression for the nth term of the sequence:
an = 5n / (4n + 1)
As n approaches infinity, the denominator 4n + 1 becomes dominant compared to the numerator 5n. Therefore, we can simplify the expression by neglecting the term 5n:
an ≈ n / (4n + 1)
Now, we can consider the limit of the sequence as n approaches infinity:
lim(n→∞) n / (4n + 1)
To evaluate this limit, we can divide both the numerator and denominator by n:
lim(n→∞) (1 / 4 + 1/n)
As n approaches infinity, the term 1/n approaches zero, leaving us with:
lim(n→∞) 1 / 4 = 1/4
Since the limit of the sequence is a finite value (1/4), we can conclude that the sequence {an} = 5n/4n + 1 is convergent.
In other words, as n gets larger and larger, the terms of the sequence {an} get closer and closer to the limit of 1/4. This indicates that the sequence approaches a fixed value and does not exhibit wild oscillations or diverge to infinity. Therefore, we can say that the sequence is convergent.
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From 2006 to 2010, the population of a town declined to 22,000. The population is expected to continue to decline at a rate of 2. 8% each year.
What will the population be in 2040?
Round to the nearest whole number
Enter your answer in the box
The population of the town in 2040 will be 9384.
According to the question,
We have the following information:
From 2006 to 2010, the population of a town declined to 22,000. The population is expected to continue to decline at a rate of 2.8% each year.
Rate of decline = 2.8/100
Rate of decline = 0.028
Number of years = 30 years (time between 2010 and 2040)
We know that the following formula is used to find the future population:
Future population = present population\((1-I)^{n}\) where I is the rate of decline and n is the number of years
Future population = 22000\((1-0.028)^{30}\)
Future population = 9384.49
Future population = 9384
Hence, the population of the town in 2040 will be 9384.
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Compare the performance of the largest-coefficient and the smallest-index pivoting rules on the following linear program:maximize subject to 2x1+x23x1+x2≤3x1,x2≥0.
Comparing the performance, both pivoting rules will give the same result in this specific linear program since the variable chosen to enter the basis in the first iteration is x1 for both methods.
Consequently, the number of iterations and the final optimal solution will be the same for both the largest-coefficient and smallest-index pivoting rules. Linear Program: Maximize: z = 2x1 + x2
Subject to:
3x1 + x2 ≤ 3
x1, x2 ≥ 0
Let's analyze the performance of the largest-coefficient and smallest-index pivoting rules.
Largest-Coefficient Pivoting Rule:
1. Identify the largest coefficient in the objective function (z = 2x1 + x2). In this case, it's the coefficient of x1 (2).
2. Choose x1 as the entering variable and perform the necessary calculations to update the tableau.
3. Continue iterations until an optimal solution is reached.
Smallest-Index Pivoting Rule:
1. Choose the smallest index among the variables with a positive coefficient in the objective function. In this case, it's x1.
2. Choose x1 as the entering variable and perform the necessary calculations to update the tableau.
3. Continue iterations until an optimal solution is reached.
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Mike is traveling to the beach 30 miles away from his house. On Mike's
map, his house and the beach are 5 inches apart. What is the scale
used for Mike's map?
Answer:
A. 1 inch = 6 miles
Step-by-step explanation: We need to divide 30 by 5 to see how much 1 inch equals. 30÷5=6. We now known 1 inch = 6 miles.
Answer:
5 inch- 30 miles
Step-by-step explanation:
PLEASE HELP. I NEED THE ANSWER
Answer:
the answer is × = -1, -4 is the answer
A new projector for the classroom costs $358.25. The tax rate is 12%. How much will
the tax cost for the projector?
$4299
$42.99
$346.25
DELL
$29.85
$401.24
Sign out
USD 1:33