Step-by-step explanation:
from (2)
x-y=2
y=x-2 (3)
subs (3) into (1)
x²-2x+(x-2)=8
x²-2x+X-10=0
x²+x-10=0
quadratic formula
x= (-1±√1²-4×1×(-10))/2(1)
X=( -1±√41)/2
X=(-1+√41)/2
=
x=(-1-√41)/2
=
Is y=−2+5x a linear function?
Answer:
y+2=5×
Step-by-step explanation:
because it is unlike term
Help me out please! 15 points!
Answer:
Ok I will help because i'm the nicest person you'll ever meet lol Ok anyway
there will be no step by step explanation
Direction variation: and Not direction variation:
y= 3x
X= -1
and
Y= 4
now for the other one the non-direction---------------------> Y = (2/7)x
------------------------------------------------------------------------------> -0.5x = Y
------------------------------------------------------------------------------> Y= 2.2x + 7
TADA I'm finished and your welcome!!! :D
Help me out please an thank you
Answer:
A. a // b
Step-by-step explanation:
What is the equation in standard form of the line that passes through the point (-3,
-2) and has a slope of 4?
Answer:
[tex]-3x+y=10[/tex]
Step-by-step explanation:
To write this equation we first need to know what the standard form is. Standard form of a line is written as [tex]Ax + By = C[/tex]. To get this, we first need to put the equation into point slope form or [tex]y-y1 = m(x-x1)[/tex] where [tex]m[/tex] is slope and [tex](x1,y1)[/tex] is a point on the graph. Using the information we know we can make the equation [tex]y+2=4(x+3)[/tex].
Now that we have point slope form we need to convert it. To do this we need to first get rid of the parenthesis by distribution. This will give us [tex]y+2=3x+12[/tex]
Next, we know we need to get [tex]x[/tex] and [tex]y[/tex] on the same side of the equal sign. We do this by subtracting 3x on both sides to get [tex]-3x+y+2=12[/tex]
Finally, we can subtract 2 on both sides to put the equation into standard form. This will give us [tex]-3x+y=10[/tex]
What is the value of x in the equation 5(3x-4)= 2x + 7 + 4x
Answer:
X=3
Step-by-step explanation:
Evaluate the expression for each value of x. √3x + 7 - X (a) x = -2 (b) x = 3
We need to evaluate the given expression, √3x + 7 - x, for two different values of x: (a) x = -2 and (b) x = 3.
For x = -2:
Plugging in the value of x, we have √3(-2) + 7 - (-2).
Simplifying this expression, we get √(-6) + 7 + 2.
Since the square root of a negative number is not defined in the real number system, the expression is undefined for x = -2.
For x = 3:
Plugging in the value of x, we have √3(3) + 7 - 3.
Simplifying this expression, we get √9 + 7 - 3.
The square root of 9 is 3, so we have 3 + 7 - 3.
Further simplification yields 7.
Therefore, for x = -2, the expression is undefined, and for x = 3, the expression evaluates to 7.
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ayudenme por favor nesecito ayuda con estas respuestas
Answer:
ill help
Step-by-step explanation:
PLEASE HELP ME ANSWER Q4
Answer:
x = tan (3/4) therefore you cannot use (4/3)
Step-by-step explanation:
tan = opp over adj
Hurry please, help please
The solution of each of the quadratic equations are:
5) x = +3, -3
6) x = +3/2, -3/2
7) x = -4, 1/3
8) x = +9, -9
How to find the roots of quadratic equations?The general form of a quadratic equation is:
ax² + bx + c = 0
The quadratic formula to find the roots is:
x = [-b ± √(b² - 4ac)]/2a
5) The quadratic equation is given as 4x² - 36.
Thus:
x = [-0 ± √(0² - 4(4 * -36))]/2(4)
x = ±√4(4 * 36))/8
x = ±24/8
x = +3, -3
6) The quadratic equation is given as 64x² - 144
Thus:
x = [-0 ± √(0² - 4(64 * -144))]/2(64)
x = ±(√36864)/8
x = ±192/128
x = ±3/2
x = +3/2, -3/2
7) The quadratic equation is given as 3x² + 11x - 4
Thus:
x = [-11 ± √(11² - 4(3 * -4))]/2(3)
x = [-11 ± (√169)]/6
x = (-11 ± 13)/6
x = -4, 1/3
8) The quadratic equation is given as x² - 81
Thus:
x = [-0 ± √(0² - 4(1 * -81))]/2(1)
x = ±(√324)/2
x = ±18/2
x = ±9
x = +9, -9
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IS 3x+4=8x-9 one solution, no solution or infinitely Many
Answer:
One solution
Step-by-step explanation:
Seperate the like terms.
3x-8x=-9-4
-5x=-9-4
-5x=-13
x=13/5
The expression 3x + 4 = 8x - 9 has one solution.
Option A is the correct answer.
What is a solution?Solutions are the values of an equation where the values are substituted in the variables of the equation and make the equality in the equation true.
We have,
3x + 4 = 8x - 9
4 + 9 = 8x - 3x
13 = 5x
x = 13/5
This means,
It has one solution.
Thus,
The expression has one solution x = 13/5.
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C. 2 Use Simplex tableau method to solve the following linear programming problem:
maximize = 2x1 + 5x2 + 4x3
subject to x1 +x2 + 2x3≤ 20
2x1 + x2 + x3 ≤ 10
x2 − x3 ≤ 5
3x1 +3x3 ≤ 12
x1,x2,x3 ≥0
New Simplex Tableau:
| Basis | x1 | x2
To use the simplex tableau method to solve the given linear programming problem, we need to convert it into standard form. The standard form includes non-negativity constraints and all inequalities as less than or equal to constraints. Let's rewrite the problem in standard form:
Maximize: Z = 2x1 + 5x2 + 4x3
Subject to:
x1 + x2 + 2x3 + x4 = 20
2x1 + x2 + x3 + x5 = 10
0x1 + x2 - x3 + x6 = 5
3x1 + 0x2 + 3x3 + x7 = 12
x1, x2, x3, x4, x5, x6, x7 ≥ 0
Now, let's construct the initial simplex tableau:
Basis x1 x2 x3 x4 x5 x6 x7 RHS
x4 1 1 2 1 0 0 0 20
x5 2 1 1 0 1 0 0 10
x6 0 1 -1 0 0 1 0 5
x7 3 0 3 0 0 0 1 12
Z -2 -5 -4 0 0 0 0 0
Next, we will perform iterations to find the optimal solution. The goal is to make the coefficients in the Z row non-negative. We will select the most negative coefficient as the pivot column and the smallest ratio of the RHS to the pivot column value as the pivot row.
Iteration 1:
Pivot Column: x2 (most negative coefficient)
Pivot Row: x6 (smallest ratio of RHS / pivot column value)
Perform row operations to make x6 a basic variable:
Row 3 = Row 3 / 1
Perform column operations to clear the pivot column:
Row 1 = Row 1 - 1 * Row 3
Row 2 = Row 2 - 1 * Row 3
Row 4 = Row 4 - 0 * Row 3
Row 5 = Row 5 + 5 * Row 3
New Simplex Tableau:
Basis x1 x2 x3 x4 x5 x6 x7 RHS
x4 1 0 3 1 0 0 0 15
x5 2 0 2 0 1 0 0 35
x2 0 1 -1 0 0 1 0 5
x7 3 0 3 0 0 0 1 12
Z -2 0 -3 0 0 5 0 20
Iteration 2:
Pivot Column: x3 (most negative coefficient)
Pivot Row: x4 (smallest ratio of RHS / pivot column value)
Perform row operations to make x4 a basic variable:
Row 1 = Row 1 - 3 * Row 4
Row 2 = Row 2 - 2 * Row 4
Row 3 = Row 3 - (-1) * Row 4
Row 5 = Row 5 - 3 * Row 4
Perform column operations to clear the pivot column:
Row 2 = Row 2 - 2 * Row 5
Row 1 = Row 1 - 3 * Row 5
Row 3 = Row 3 - (-1) * Row 5
Row 7 = Row 7 - 0 * Row 5
New Simplex Tableau:
| Basis | x1 | x2
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10 , 12 , 13 , 16 , 17 , 23 , 25 , 39
From the list above , write down :
• a prime number that is one more than a square number
Answer:
prime number is 17 and the square number is 16 if you subtract them you get 1 .
RBT/Z + H/K = M, Solve for H
Answer:
H = MK - RBTK/ZStep-by-step explanation:
Given
RBT/Z + H/K = MSolving for H
RBT/Z + H/K = MK×RBT/Z + K×H/K = K×M ⇒ multiplying all terms by K to clear fractionRBTK/Z + H = MKRBTK/Z + H - RBTK/Z= MK - RBTK/Z ⇒ subtracting RBTK/Z from both sidesH = MK - RBTK/ZHow do you rewrite and then solve -5 - (-7)
Answer:
-5-(-7)
=-5+7
=7-5
=+2
Angle A and angle B are supplementary. If
m2A = (16x – 7º and m2B = (21x + 2)", what
is the measure of angle A in degrees?
a 107
b. 37°
c. 5°
d. 73
Answer:
d
Step-by-step explanation:
Supplementary angles sum to 180°
Sum the angles A and B and equate to 180m that is
16x - 7 + 21x + 2 = 180
37x - 5 = 180 ( add 5 to both sides )
37x = 185 ( divide both sides by 37 )
x = 5
Thus
∠ A = 16x - 7 = 16(5) - 7 = 80 - 7 = 73° → d
Simplify -3 + 2x + (-1) - 4x
Answer:
-2x-4
Step-by-step explanation:
We have to combine like terms in this expression. So, only -3 and -1 can be combined, and the same thing applies to 2x and -4x. If we add -3 and -1 as it says in the expression, that is -4. If we add 2x and -4x which is also in the expression, it is -2x. We can combine these two resulting terms to simplify the expression. The answer is -2x-4.
how many monthly payments must be made for a 2 ½ -year loan?
The number of monthly payments that need to be made for a 2 ½ -year loan is 30. This is because there are 12 months in a year and 2 ½ years are equal to 30 months.
It's important to know the number of payments needed to be made when taking out a loan to ensure that the loan can be repaid in a timely manner. The number of monthly payments that need to be made for a 2 ½ -year loan is 30. This is because there are 12 months in a year and 2 ½ years are equal to 30 months. This information is important to know because it will allow you to budget your finances and ensure that you can make the necessary payments on time. It is important to note that some lenders may offer more flexible repayment schedules, so it's important to research the terms and conditions of the loan before signing the agreement. If you are unsure about the terms of a loan, it's always a good idea to seek the advice of a financial advisor. With the right information and planning, taking out a loan can be a responsible financial decision.
In conclusion, for a 2 ½ -year loan, 30 monthly payments need to be made. It is important to know this information to budget finances and make payments on time. It's important to research loan terms and seek the advice of a financial advisor to make informed financial decisions.
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Q2) For total cost: TC(q)=10−6q+q2 determine: a. the production level (q∗) that minimizes total cost. b. The amount of Total cost for the q∗, in other words TC(q∗) ? (10 pints)
The amount of total cost at q* is 1.
To determine the production level that minimizes total cost, we need to find the value of q (production level) at which the derivative of the total cost function TC(q) is equal to zero. Let's begin by finding the derivative of TC(q):
TC(q) = 10 - 6q + q^2
To find the minimum point, we differentiate TC(q) with respect to q:
d(TC(q))/dq = -6 + 2q
Setting the derivative equal to zero and solving for q:
-6 + 2q = 0
2q = 6
q = 3
So the production level q* that minimizes the total cost is 3.
To find the amount of total cost at q*, we substitute q = 3 into the total cost function TC(q):
TC(q*) = 10 - 6(3) + (3)^2
TC(q*) = 10 - 18 + 9
TC(q*) = 1
Therefore, the amount of total cost at q* is 1.
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Complete the following statement.
(?) x (-7) = 42
In 2008, the population of Earth reached 6,690,000,000. How would you represent this number in Scientific Notation?
Find the value of x
(2x + 5)
(6x + 5)
Answer:
x=5/2 or 2.5
Step-by-step explanation:
1 Divide both sides by 22.
x=5/2
decimail form 2.5
Which expression is a prime polynomial? A.x+9y^2 B. 3m+9n C. 8x^7-9x+12x^2 D. x^9-y^6
Answer:
C
Step-by-step explanation:
A prime polynomial is simply an irreducible polynomial.
[tex]\mathbf{x + 9y^2}[/tex] is a prime polynomial
First, we test the options.
[tex]\mathbf{x + 9y^2}[/tex]
The above function cannot be reduced further.
Hence, [tex]\mathbf{x + 9y^2}[/tex] is a prime polynomial
[tex]\mathbf{3m + 9n}[/tex]
Factor out 3
[tex]\mathbf{3(m + 3n)}[/tex]
[tex]\mathbf{3m + 9n}[/tex] is not a prime because it can be factored as [tex]\mathbf{3(m + 3n)}[/tex]
[tex]\mathbf{8x^7 - 9x + 12x^2}[/tex]
Factor out x
[tex]\mathbf{x(8x^6 - 9 + 12x)}[/tex]
[tex]\mathbf{8x^7 - 9x + 12x^2}[/tex] is not a prime because it can be factored as [tex]\mathbf{x(8x^6 - 9 + 12x)}[/tex]
Hence, [tex]\mathbf{x + 9y^2}[/tex] is a prime polynomial
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PLZZZZ HELP WILL GIVE BRAINLEST
Your monthly expenses are represented below. The expenses with an asterisk beside them represent an essential expense. Only $100 of the gasoline and $30 of the credit card payment are essential. How much should you have in emergency savings as a minimum?
The minimum amount of emergency savings you should have is $130.
To determine the minimum amount of emergency savings you should have, we need to consider the essential expenses.
In this case, the gasoline expense and the credit card payment are marked as essential expenses.
Let's calculate the minimum amount of emergency savings required to cover these essential expenses.
Essential expenses:
Gasoline (essential) = $100
Credit card payment (essential) = $30
To calculate the minimum emergency savings required, we add up the essential expenses:
Minimum emergency savings = Gasoline (essential) + Credit card payment (essential)
Minimum emergency savings = $100 + $30
Minimum emergency savings = $130
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Start with the original matching pennies game, where player 1 wins by matchups and player 2 wins by mismatches; and the winning versus losing payoffs are +1 and – 1 respectively. Then decrease the payoff from a mismatch loss for player 1 (when players 1 and 2 choose tails and heads respectively) from –1 down to – 6, and decrease the losing payoff from a double tails loss for player 2 from –1 down to – 10; but keep all other winning or losing payoffs the same as before (at either +1 or – 1). (A) Draw the payoff matrix with the modified losing payoffs. (B) Also draw two diagrams showing each player’s pair of expected payoff lines, and showing the other player’s equilibrium decision probability. (C) Finally, calculate the numerical values of these Nash equilibrium probabilities (p1*, p2*) for this case.
There is no Nash equilibrium in pure strategies because neither player has a strategy that maximizes their expected payoff.
(A) The modified payoff matrix for the matching pennies game with the updated losing payoffs is as follows:
Player 2
Heads (H) Tails (T)
Player 1 +1, -1 -6, +6
Heads (H)
Tails (T) -10, +10 +1, -1
(B) The diagrams showing each player's pair of expected payoff lines and the other player's equilibrium decision probability are as follows:
Player 1's Expected Payoff Line:
H T
Probability: p1 1-p1
Expected Payoff: p1(-6) + (1-p1)(+1)
Player 2's Expected Payoff Line:
H T
Probability: p2 1-p2
Expected Payoff: p2(-10) + (1-p2)(+1)
The equilibrium decision probability for each player will be the value that maximizes their expected payoff. In this case, player 1 will choose heads (H) with probability p1* and player 2 will choose tails (T) with probability p2*.
(C) To calculate the numerical values of the Nash equilibrium probabilities (p1*, p2*), we need to find the values that maximize each player's expected payoff.
For player 1:
Expected Payoff = p1(-6) + (1-p1)(+1)
= -6p1 + 1 - p1 + p1
= -5p1 + 1
To maximize this expected payoff, we set the derivative equal to zero:
d/dp1 (-5p1 + 1) = -5 = 0
-5 = 0 (No solution)
For player 2:
Expected Payoff = p2(-10) + (1-p2)(+1)
= -10p2 + 1 + p2 - p2
= -9p2 + 1
To maximize this expected payoff, we set the derivative equal to zero:
d/dp2 (-9p2 + 1) = -9 = 0
-9 = 0 (No solution)
There is no Nash equilibrium in pure strategies because neither player has a strategy that maximizes their expected payoff.
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A company has a multi-tier investment. They have $40 million in operating expenses each year and a cost of capital of 12%. They can invest $12 million in new technology for their plant. There is a 40% chance that the new equipment reduces expenses by 15%, a 30% chance it reduces expenses by 10%, and a 30% chance it reduces expenses by 5%. Shareholders will view the results after 3 years and vote on continuing or abandoning the project. Abandoning costs the company $5 million. If expenses drop 15%, there is a 95% chance the vote is yes, to continue for another 3 years, If they drop 10%, the vote has a 75% chance to be yes. If expenses only drop 5%, there is a 40% change the shareholders vote to continue the project. Draw out the timeline, decision tree, and calculate the probabilities for all six possible scenarios.
The probabilities for all six possible scenarios based on the given information. The likelihood of each scenario and its respective outcome have been determined by multiplying the probabilities of the relevant events.
To analyze the given scenario and calculate the probabilities for all six possible scenarios, let's create a decision tree and timeline to visualize the information provided.
Timeline:
Year 1: Initial investment of $12 million in new technology.
Year 2: Results evaluated by shareholders.
Year 3: Final decision made by shareholders.
Decision Tree:
``` ┌─── Continue (95%)
│
15% ─────┼─── Continue (75%)
│
$12 million ─────┼─── Continue (40%)
investment │
│
10% ─────┼─── Abandon ($5 million cost)
│
│
5% ─────┼─── Abandon ($5 million cost)
│
└─── Abandon ($5 million cost)
```
Now, let's calculate the probabilities for each scenario:
1. New equipment reduces expenses by 15% (40% probability):
Probability = 40% * 95% = 0.4 * 0.95 = 0.38 (38%)
Outcome: The shareholders vote to continue for another 3 years.
2. New equipment reduces expenses by 10% (30% probability):
Probability = 30% * 75% = 0.3 * 0.75 = 0.225 (22.5%)
Outcome: The shareholders vote to continue for another 3 years.
3. New equipment reduces expenses by 5% (30% probability):
Probability = 30% * 40% = 0.3 * 0.4 = 0.12 (12%)
Outcome: The shareholders vote to continue for another 3 years.
4. New equipment does not reduce expenses (10% probability):
Probability = 10%
Outcome: The shareholders vote to abandon the project, incurring a $5 million cost.
5. New equipment reduces expenses by 15%, but shareholders vote to abandon (5% probability):
Probability = 15% * (1 - 95%) = 0.15 * 0.05 = 0.0075 (0.75%)
Outcome: The shareholders vote to abandon the project, incurring a $5 million cost.
6. New equipment reduces expenses by 10%, but shareholders vote to abandon (5% probability):
Probability = 10% * (1 - 75%) = 0.1 * 0.25 = 0.025 (2.5%)
Outcome: The shareholders vote to abandon the project, incurring a $5 million cost.
To summarize, we have calculated the probabilities for all six possible scenarios based on the given information. The likelihood of each scenario and its respective outcome have been determined by multiplying the probabilities of the relevant events.
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HElP ME !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
D the last one
Step-by-step explanation:
Answer:
∠VUR and ∠QRU
Step-by-step explanation:
twice the sum of a number and 5
Answer:
2(x+5)
Step-by-step explanation:
Andrew bought a new computer for $2,100. The value of the computer decreases by 30% annually. Let y represent the value of the computer after x years.
Which type of sequence does the situation represent?
The situation represents an arithmetic sequence because the successive y-values have a common difference of 0.3.
The situation represents an arithmetic sequence because the successive y-values have a common difference of 30.
The situation represents a geometric sequence because the successive y-values have a common ratio of 0.3.
The situation represents a geometric sequence because the successive y-values have a common ratio of 0.7.
Answer:
Hi there! I just answered this question and the situation represents a geometric sequence because the successive y-values have a common ratio of 0.7.
Step-by-step explanation:
Every year, the value of the computer decreases by 30%.
The value of the computer is originally $2,100. Determine the value of the computer after one year by subtracting 30% of the original value.
2,100 - 0.30(2,100) = 2,100 - 360 = 1,470
The cost of the computer after one year will be $1,470 and the original cost was $2,100. Find the ratio of these two values.
1,470/2,100 = 0.7!
Therefore, after one year, the value of the computer is 0.7 times the value of the computer the previous year. Since the value is decreasing 30% annually, this trend will continue each year.
So, the situation represents a geometric sequence because the successive y-values have a common ratio of 0.7.!
Hope this helps I was confused too!
Answer:
0.7
got it right.
If triangle ABC is rotated 90 counterclockwise and then reflected across the x- axis, what will be the coordinate of A?
NEED THIS ASAP!!!!!
Answer:
34
Step-by-step explanation: