Answer: A. 14,841
Step-by-step explanation:
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
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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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/ZFind the two smallest positive solutions for x in the equation 12cos(2pi/5 x)+10=16, when (2pi/5 x) is in radians.
The two smallest positive solutions for x in the equation 12cos(2π/5x) + 10 = 16 are x = 5/6 and x = 17/6. Therefore, the correct option is B) 5/6, 25/6.
To find the two smallest positive solutions for x in the equation 12cos(2π/5x) + 10 = 16, we need to solve the equation for x.
Let's start by isolating the cosine term:
12cos(2π/5x) = 16 - 10
12cos(2π/5x) = 6
Next, divide both sides of the equation by 12:
cos(2π/5x) = 6/12
cos(2π/5x) = 1/2
To find the values of x that satisfy this equation, we can take the inverse cosine (arccos) of both sides:
2π/5x = arccos(1/2)
To determine the two smallest positive solutions, we need to find the values of x that correspond to the acute angles whose cosine is 1/2.
The arccosine of 1/2 is π/3, so:2π/5x = π/3
Next, solve for x:
x = (π/3)(5/2π)
x = 5/6
Therefore, the first solution for x is 5/6.
To find the second solution, we can add 2π to the right-hand side of the equation:
x = (π/3)(5/2π) + 2π
x = 5/6 + 12π/6
x = 5/6 + 2
x = 5/6 + 12/6
x = 17/6
Therefore, the second solution for x is 17/6.
Option b
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PLEASE HELP ME WITH THESE 4 QUESTION thx :) WORTH 100 POINTS!!!
1. 4 2/9 =6 1/3∙d
2. c÷ 2/11 =8 1/4
3. 2 1/2 =1 2/3÷y
4. 6x=24 12/19
Answer:
d = 2/3c = 3/2y = 2/3x = 4 2/19Step-by-step explanation:
Solving for variables
1.......................................
4 2/9 =6 1/3∙d 38/9= 19/3dd = 38/9 ÷ 19/3d = 38/9*3/19d = 2/32.......................................
c÷ 2/11 =8 1/4 c ÷ 2/11 = 33/4c = 33/4*2/11c = 3/23.......................................
2 1/2 =1 2/3÷y 5/2 = 5/3 ÷ yy = 5/3 ÷ 5/2y = 5/3 * 2/5y = 2/34.......................................
6x=24 12/196x = 24 + 12/19x = 24/6 + 12/19 *1/6x = 4 + 2/19x = 4 2/19here are your answer
d = 2/3
c = 3/2
y = 2/3
x = 4 2/19
have a good day
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:
If y= -7(-2-2x), what is the value of x when y is equal to 70?
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
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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Help me out please an thank you
Answer:
A. a // b
Step-by-step explanation:
1:How much does it cost to produce 900 printed shirts?
2:Determine the profit you will make if you sell 900 printed shirts.
3:Find an expression for P(x).
show solution:
Answer:
P(x) = (-0.2x² + 480x - 24480)
Step-by-step explanation:
1). Expression representing the "Cost" to produce the shirts is,
C(x) = 160x + 24480
Where 'x' represents the number of shirts.
Cost to produce 900 printed shirts will be,
C(900) = 160×900 + 24480
= 144000 + 24480
= Php 168480
2). Revenue generated by selling 900 shirts is,
R(x) = 640x - 0.2x²
For x = 900,
R(x) = 640(900) - 0.2(900)²
= 576000 - 162000
= Php 414000
3). Expression for profit:
Since, Profit = Revenue generated - Cost for production
P(x) = R(x) - C(x)
= (640x - 0.2x²) - (160x + 24480)
= (640x - 160x) - 0.2x² - 24480
= 480x - 0.2x² - 24480
P(x) = (-0.2x² + 480x - 24480)
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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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
PLEASE HELP ME ANSWER Q4
Answer:
x = tan (3/4) therefore you cannot use (4/3)
Step-by-step explanation:
tan = opp over adj
What is the value of x in the equation 5(3x-4)= 2x + 7 + 4x
Answer:
X=3
Step-by-step explanation:
Solve for x. Enter the solutions from least to greatest.
6x^2 – 30x – 84 = 0
Answer:
x = -2, 7
Step-by-step explanation:
1.Single out 6x^2 to x^2 by dividing 6 on both sides
= x^2-5x-14=0
2.Write -5x as a difference in order to factor
= x^2+2x-7x-14=0
3. Factor.
= (x+2)(x-7)
4. Set equal to 0
x+2=0
x=-2
x-7=0
x=7
The solution of the equation 6x² – 30x – 84 = 0 from least to greatest will be –2 and 7.
What is a factorization?It is a method for dividing a polynomial into pieces that will be multiplied together. At this moment, the polynomial's value will be zero.
The equation is given below.
6x² – 30x – 84 = 0
Then the factor of the equation will be
x² – 5x – 14 = 0
x² – 7x + 2x – 14 = 0
x(x – 7) + 2(x – 7) = 0
(x + 2)(x – 7) = 0
Then the solution will be
x = –2, 7
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.12. Ten percent of all Dynamite Mints candies are orange and 45 percent of all Holiday Mints candies are orange. Two independent random samples, each of size 25, are selected - one from Dynamite Mints candies and the other from Holiday Mints candies. The total number of orange candies in the two samples is observed. What are the expected total number of orange candies and the standard deviation for the total number of orange candies, respectively, in the two samples? A. 7 and 2.905 B. 7 and 3.987 C. 13.75 and 2.233 D. 13.75 and 2.905 E. 13.75 and 3.987
the expected total number of orange candies and the standard deviation for the total number of orange candies in the two samples, respectively, are 13.75 and 3.033. Option E is correct.
We are given that Ten percent of all Dynamite Mints candies are orange and 45 percent of all Holiday Mints candies are orange.
Two independent random samples, each of size 25, are selected - one from Dynamite Mints candies and the other from Holiday Mints candies and we are asked to find the expected total number of orange candies and the standard deviation for the total number of orange candies, respectively, in the two samples.
To solve this problem, we will use the formula for mean and variance of a binomial distribution.
Mean or Expected Value E(X) = np
Variance V(X) = np(1-p)The formula for standard deviation is as follows;
Standard deviation of X, σ(X) = √np(1 - p)The number of orange candies in each sample of size 25 is expected to be:
For Dynamite Mints: np = 25 × 0.1 = 2.5For Holiday Mints: np = 25 × 0.45 = 11.25Therefore, the expected total number of orange candies in the two samples is: 2.5 + 11.25 = 13.75The variance for Dynamite Mints is:
V(X) = np(1 - p) = 25 × 0.1 × (1 - 0.1) = 2.25The variance for Holiday Mints is:
V(X) = np(1 - p) = 25 × 0.45 × (1 - 0.45) = 6.9375Therefore, the total variance for the two samples is:
V(X1 + X2) = V(X1) + V(X2) = 2.25 + 6.9375 = 9.1875The standard deviation for the two samples is:
σ(X1 + X2) = √V(X1 + X2) = √9.1875 = 3.033
So, the expected total number of orange candies and the standard deviation for the total number of orange candies in the two samples, respectively, are 13.75 and 3.033. Option E is correct.
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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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twice the sum of a number and 5
Answer:
2(x+5)
Step-by-step explanation:
Is y=−2+5x a linear function?
Answer:
y+2=5×
Step-by-step explanation:
because it is unlike term
For what values of x are the following expressions equal to each other
the trinomials 3x^2−4x+3 and x^2+x+1
the trinomials 3x2−4x+3 and x2+x+1
To find the values of x for which the two trinomials are equal, we need to set them equal to each other and solve for x.
For the trinomials 3x^2 - 4x + 3 and x^2 + x + 1:
3x^2 - 4x + 3 = x^2 + x + 1
By rearranging the equation and combining like terms, we get:
2x^2 - 5x + 2 = 0
Now, we can solve this quadratic equation by factoring, completing the square, or using the quadratic formula. In this case, the equation can be factored as:
(2x - 1)(x - 2) = 0
Setting each factor equal to zero, we have:
2x - 1 = 0 --> 2x = 1 --> x = 1/2
x - 2 = 0 --> x = 2
Therefore, the values of x for which the two trinomials are equal are x = 1/2 and x = 2.
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ayudenme por favor nesecito ayuda con estas respuestas
Answer:
ill help
Step-by-step explanation:
HElP ME !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
D the last one
Step-by-step explanation:
Answer:
∠VUR and ∠QRU
Step-by-step explanation:
In 2008, the population of Earth reached 6,690,000,000. How would you represent this number in Scientific Notation?
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]
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
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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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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