The roots of the quadratic equation [tex]3x^2 - 14x - 5 = 0[/tex], in exact square root form, are x = 5 and x = -1/3.
According to given information :Using the quadratic formula to solve the quadratic equation [tex]3x^2 - 14x - 5 = 0[/tex],we have
[tex]x = (-(-14) ± sqrt((-14)^2 - 4(3)(-5))) / (2(3))\\x = (14 ± sqrt(14^2 + 4(3)(5))) / (2(3))\\x = (14 ± sqrt(196 + 60)) / 6\\x = (14 ± sqrt(256)) / 6\\x = (14 ± 16) / 6\\[/tex]
Therefore, the two roots of the quadratic equation in exact square root form are:
[tex]x = (14 + 16) / 6 = 5\\x = (14 - 16) / 6 = -1/3\\[/tex]
Thus, the roots of the quadratic equation [tex]3x^2 - 14x - 5 = 0[/tex], in exact square root form, are x = 5 and x = -1/3.
What is quadratic equation ?A quadratic equation is a second-degree polynomial equation in one variable of the form:
[tex]ax^2 + bx + c = 0[/tex]
where x is the variable, and a, b, and c are constants. In this equation, the highest power of x is 2, and it is called the coefficient of x^2. The coefficient of x is b, and the constant term is c.
The quadratic equation is called "quadratic" because the highest power of x is a square (i.e., x^2), and the graph of the equation is a parabola.
The quadratic equation can have zero, one, or two real solutions, depending on the values of a, b, and c. The solutions can be found by using the quadratic formula:
[tex]x = (-b ± √(b^2 - 4ac)) / 2a[/tex]
where the symbol ± means "plus or minus" and the square root is of the discriminant (b^2 - 4ac).
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Sin (29) = 12/x step by step pls
The value of x is given as follows:
x = 24.75.
How to obtain the value of x?The value of x is obtained solving the proportion in the context of the problem.
The proportion is defined as follows:
sin(29º) = 12/x.
Applying cross multiplication, we can isolate the variable x as follows:
xsin(29º) = 12
x = 12/sin(29º).
Then a calculator is used to divide 12 by the sine of 29 degrees, and then the result is given as follows:
x = 24.75.
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find the value of a in the number 6a subtract 4 a+ 5a=210
The value of "a" will be 30 for the given Algebraic expression.
What is algebraic Expression?Any mathematical statement that includes numbers, variables, and an arithmetic operation between them is known as an expression or algebraic expression. In the phrase 4m + 5, for instance, the terms 4m and 5 are separated from the variable m by the arithmetic sign +.
Given, a algebraic expression 6a -4a +5a = 210
Simplifying the equation in terms of a
6a -4a +5a = 210
adding or subtracting the terms with the same variables
7a = 210
divide by 7 on both sides
a = 30
Therefore, the value of "a" will be 30 for the given Algebraic expression.
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Pls help solve this math
The constant of proportionality (k) for the graph is 11.7.
The proportional equation for the graph is y = 11.7x.
What is a proportional relationship?In Mathematics, a proportional relationship can be defined as a type of relationship that generates equivalent ratios and it can be modeled or represented by the following mathematical expression:
y = kx
Where:
x and y represents the variables or data points.k represents the constant of proportionality.Next, we would determine the constant of proportionality (k) for money earned per hour as follows:
Constant of proportionality, k = y/x
Constant of proportionality, k = 35.1/3 = 81.9/7
Constant of proportionality, k = 11.7.
Therefore, the required equation is given by:
y = kx
y = 11.7x
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If the equations x² - 5x+6=0 and X² + ax +6=0 common roots, find the Value a
Answer:
Step-by-step explanation:
Write the equation of the circle given center: (1,-3) and diameter:20
I put it as (x-1)^2+(y+3)^2=400
Answer:
(x - 1)^2 + (y + 3)^2 = 400.
Step-by-step explanation:
Your equation is correct.
The center of the circle is (1, -3), which is the midpoint of the diameter. The diameter is 20, so the radius is 10. The equation of a circle with center (h, k) and radius r is given by:
(x - h)^2 + (y - k)^2 = r^2
Substituting the values, we get:
(x - 1)^2 + (y + 3)^2 = 10^2
Simplifying the right side, we get:
(x - 1)^2 + (y + 3)^2 = 100
Therefore, the equation of the circle is (x - 1)^2 + (y + 3)^2 = 400.
Round to the closest whole number. 32% of the animals were males. If the herd had 112 animals how many were female?
Using arithmetic operations it is obtained that there were approximately 76 female animals in the herd.
What is arithmetic operation?
A subject of mathematics known as arithmetic operations deals with the study and use of numbers in all other branches of mathematics. Basic operations including addition, subtraction, multiplication, and division are included.
If 32% of the animals were males, then 100% - 32% = 68% of the animals were female.
To find the number of female animals in the herd of 112 animals, multiply the total number of animals by the percentage that were female -
68% = 68/100 = 0.68
Number of female animals = 0.68 x 112
Number of female animals = 76.16
Rounding this to the closest whole number gives -
Number of female animals ≈ 76
Therefore, the number of female animals is 76.
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Find the number of positive integers that satisfy both the following conditions:
Each digit is a 1 or a 2
The sum of the digits is 3
Answer:
12
Step-by-step explanation:
1+2=3 and 12 satisfied all the conditions
4. Compute the unadjusted cost of goods sold for the year. Do not include any underapplied or overapplied overhead in your answer.
5. Assume that the $70,000 ending balance in Work in Process includes $24,000 of direct materials. Given this assumption, supply the information missing below:
The unadjusted cost of goods sold for the year is calculated by subtracting the ending inventory from the sum of beginning inventory and purchases. The formula is as follows:
Unadjusted Cost of Goods Sold = Beginning Inventory + Purchases - Ending Inventory
Without knowing the values for beginning inventory, purchases, and ending inventory, we cannot compute the unadjusted cost of goods sold for the year.
5. Given that the $70,000 ending balance in Work in Process includes $24,000 of direct materials, we can calculate the missing information as follows:
Direct Labor = Total Work in Process - Direct Materials - Overhead
Direct Labor = $70,000 - $24,000 - Overhead
Without knowing the value for overhead, we cannot compute the direct labor cost. However, we can rearrange the formula to solve for overhead:
Overhead = Total Work in Process - Direct Materials - Direct Labor
Overhead = $70,000 - $24,000 - Direct Labor
Without knowing the value for direct labor, we cannot compute the overhead cost.
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(2x³-x + 1) / (x² + x + 1)
Answer:
Hopefully this is the answer you are looking for.
a triangular field has boundaries of lengths 170m,195m and 210m,find the size of the largest interior angle of the field
The size of the largest interior angle of the field is 69.86°
What is cosine law?The law of cosines relates the lengths of the sides of a triangle to the cosine of one of its angles.
Given that, a triangular field has boundaries of lengths 170m, 195m and 210m, we need to find the size of the largest interior angle of the field,
We know that, angle opposite to the largest side is largest,
Therefore,
The largest angle is opposite is 210 m side, (say c)
Using the cosine rule,
210² = 170²+195²-2(170)(195)cosC
CosC = 170²+195²-210² / 2(170)(195)
CosC = 22825 / 66300
CosC = 0.344268477
C = 69.86°
Hence, the size of the largest interior angle of the field is 69.86°
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Can you find the lengths and areas and type the correct code? Please remember to type in ALL CAPS with no spaces.
1)
Area of a = 25 m²
2)
Length b = 5 m
3)
Length c = 7.94 m
4)
Area of d = 35.75 m²
What is the Pythagorean theorem?Pythagorean theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
We have,
1)
Figure a is a square:
Side = b
Area = b²
From (1),
Side = 5 m
Area of a = 5² = 25 m²
2)
Length b is in a triangle:
Using the Pythagorean theorem.
b² = 3² + 4²
b² = 9 + 16
b² = 25
b = 5 m _____(1)
3)
Length b is in a square:
From (2),
c = 7.94 m
4)
Figure d is a triangle.
Using the Pythagorean theorem.
c² + 9² = 12²
c² = 144 - 81
c² = 63
c = 3√7 m
c = 7.94 m _____(2)
Area = 1/2 x 9 x 7.94
Area = 35.73 m²
Thus,
Area of a = 25 m²
Length of b = 5 m
Length of c = 7.94 m
Area of d = 35.75 m²
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A number cube is rolled three times. An outcome is represented by a string of the sort oee (meaning an odd number on the first roll, an even number on the second roll, and even number on the third roll). The 8 outcomes are listed in the table below. Note that each outcome has the same probability.
Answer:16/10
Step-by-step explanation:
add 4/5+4/5=16/10
so the answer is 16/10
The legislature in a state has 32 seats. Apportion these seats to the five counties below using Hamilton's method.
County Population Seats?
Adams 213,000.
Grant 225,000
Colton 351,000
Davis 158,000
Hayes 70,000
Using the Hamilton's method of apportioning of seats, the five countries will get the following number of seats:
Adams = 7
Grant =7
Colton= 11
Davis= 5
Hayes= 2
Total = 7+7+11+5+2 = 32 seats
How to calculate the number of seats using Hamilton's method?To calculate the number of seats, first find the Standard Divisor (SD). That is: SD = Total population / Number of seats available
Total population = 213,000+225,000+351,000+158,000+70,000 = 1,017,000
Then divide the total population by number of seats available (32).
That is: SD = 1,017,000/32
SD = 31,781.25
Find the Standard Quota (SQ) for each county by using the formula;
SQ = County population / SD
Adam's SQ = 213,000/31,781.25 = 6.70
Grant's SQ = 225,000/31,781.25 = 7.08
Colton's SQ = 351,000/31,781.25 = 11.04
Davis's SQ = 158,000/31,781.25 = 4.97
Hayes's SQ = 70,000/31,781.25 = 2.20
Find the Lower Quota for each county and find the total number of occupied seats:
Adams = 7
Grant =7
Colton= 11
Davis= 5
Hayes= 2
Total = 7+7+11+5+2 = 32 seats
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NO LINKS!!! URGENT HELP PLEASE!!! NOT MULTIPLE CHOICE!!!!
1. You and a friend take a hot air balloon ride for Valentine's Day. The path of the balloon can be modeled by the equation b(h) = 2h - 1/115h^2 in feet per minute. Use this scenario to answer questions a - c.
a. How is the balloon ride?
b. What is the maximum height the balloon reaches?
c. When you have been on the ride for 180 minutes, what is the height of the balloon? (round your answer to the nearest foot)
Answer:
1.
a.
b. 115 feet.
c. 78.26feet.
Step-by-step explanation:
a.
some mathematical observations we can make about the path of the balloon based on the given equation:
The balloon's vertical velocity decreases as the balloon rises. This is because the second term in the equation, 1/115h^2, becomes larger and larger as h decreases, which causes the velocity to decrease.The balloon's vertical velocity is zero at two points: h = 0 and h = 230. At h = 0, the balloon is on the ground and has not yet started to rise, so its velocity is zero. At h = 230, the balloon has reached its maximum height and has stopped rising, so its velocity is also zero.The balloon's vertical velocity is positive when h is less than 115, and negative when h is greater than 115. This means that the balloon is rising when its height is less than 115, and descending when its height is greater than 115.The maximum height the balloon can reach is 115 feet, which occurs at h = 115. At this height, the balloon's velocity is 1.74 feet per minute.The balloon cannot fly below a certain height, which is the vertical asymptote at h = 0. This means that the balloon cannot go below the ground level.b. The maximum height of the balloon occurs at the vertex of the parabola described by the function b(h). We can find the height of the vertex by using the formula h = -b/(2a), where b and a are the coefficients of the linear and quadratic terms in the equation, respectively.
In this case, a = -1/115 and b = 2, so the height of the vertex is:
h = -b/(2a) = -2/(2(-1/115)) = 115 feet
Therefore, the maximum height the balloon reaches is 115 feet.
c. To find the height of the balloon after 180 minutes, we can substitute h = 180 into the equation b(h) and simplify:
b(180) = 2(180) - 1/115(180)^2 = 360 - 281.73≈ 78.26
Therefore, when you have been on the ride for 180 minutes, the height of the balloon is approximately78.26feet.
Answer:
a) The balloon ride is 230 minutes long.
b) The maximum height the balloon reaches is 115 m.
c) The height of the balloon at 180 minutes is 78 feet.
Step-by-step explanation:
Given quadratic equation:
[tex]b(h)=2h-\dfrac{1}{115}h^2[/tex]
Part aThe height of the balloon at the start and end of the balloon ride is zero feet. Therefore, to determine how long the balloon ride is, set the given quadratic equation to zero and solve for h.
[tex]\begin{aligned}\implies2h-\dfrac{1}{115}h^2&=0\\\\h\left(2-\dfrac{1}{115}h\right)&=0\\\\2-\dfrac{1}{115}h&=0\\\\\dfrac{1}{115}h&=2\\\\h&=230\end{aligned}[/tex]
Therefore, the balloon ride is 230 minutes long.
Part bTo determine the maximum height the balloon reaches, find the y-value of the vertex of the given quadratic equation.
The formula for the x-value of the vertex is -b/2a for a quadratic equation in the form y=ax²+bx+c. Therefore, the x-value of the vertex of the given equation is:
[tex]\implies -\dfrac{2}{2\left(-\frac{1}{115}\right)}=115[/tex]
To find the y-value of the vertex, substitute h = 115 into the given equation:
[tex]\begin{aligned}\implies b(115)&=2(115)-\dfrac{1}{115}(115)^2\\&=230-115\\&=115\; \sf ft\end{aligned}[/tex]
Therefore, the maximum height the balloon reaches is 115 ft.
Part cTo determine the height of the balloon when you have been on the ride for 180 minutes, substitute h = 180 into the equation:
[tex]\begin{aligned}\implies b(180)&=2(180)-\dfrac{1}{115}(180)^2\\\\&=360-\dfrac{6480}{23}\\\\&=78.260869...\\\\&=78\; \sf ft\end{aligned}[/tex]
Therefore, the height of the balloon at 180 minutes into the ride is 78 feet (rounded to the nearest foot).
PLSSSS HELP ASAP!!! 50 POINTS BIG BALLER
Find the value of x.
2xdegree symbol
20degree symbol
A.10
B.45
C.35
D.80
Plss help and also if you put a random answer or a answer just for the points just remember that report button looks really nice today !
what is the solution to the equation
The requried solution of the two linear equations is given as x = (b - d)/a-c and y = a (d - c)/(a-c).
What are simultaneous linear equations?Simultaneous linear equations are two- or three-variable linear equations that can be solved together to arrive at a common solution.
Here,
The question seems to be incomplete so the solution is a standard solution by assuming a standard linear equation.
The given equation,
ax + y = b - - - - - (1)
cx + y = d - - - - -(2)
Subtract equation 2 from 1
ax - cx + y - y = b - d
x(a - c) = b - d
x = b - d / a - c
Now,
Put x in equation 1
a (b - d) / (a - c) + y = b
y = b - a(b - d)/(a - c)
y = ab - ac -ab + ad/(a - c)
y = a (d - c)/(a - c)
Thus, the requried solution of the two linear equation are given as x = (b - d)/a-c and y = a (d - c)/(a - c).
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The question seems to be incomplete,
The solution given is standard solution for the simultaneous equations.
Bob has a total of 60 adventure cards for a game. The table shows the number of cards, c, distributed to p players. Which equation describes the pattern in the table?
p 2 3 4 5
c 30 20 15 12
c = 60 ÷ p
c = 60 – p
c = 60p
c = 60 + p
For a game, Bob has a total of 60 adventure cards. The distribution of cards, c, to players, p, is shown in the table. c = 60 ÷ p
Describe probability. Describe using an example.Probability defines the possibility of occurrence of an event. Probability is the unit of measurement for an event's likelihood. It represents the proportion of positive results to all results. For instance: Receiving the numbers 3 and 5 while rolling the dice, as well as getting both an even and an odd number.
The equation would read: c = 60 / 2, which implies c = 30 if p=2. The equation would read 12 = 60 / p, p = 5, 20 = 60 / 3, etc. If c = 12, the equation would read... 12 = 60 / p, and p = 5, and so on, 20 = 60 / 3, and 15 = 60 / 4.
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if you have to go to school 3 days from tuesday what day will you go back to school
Answer:
Three days from Tuesday is Friday.
Solve this polynomial P(m)= -m+5m²-8m+4m⁵-8m⁰
Answer:
Step-by-step explanation:
To solve the polynomial P(m) = -m + 5m² - 8m + 4m⁵ - 8m⁰, we can simplify the expression by combining like terms:
P(m) = 4m⁵ + 5m² - 9m - 8
Therefore, the simplified form of the polynomial is P(m) = 4m⁵ + 5m² - 9m - 8.
Answer:p=\frac{4m^5+5m^2-9m-8}{m};\quad \:m\ne \:0
Step-by-step explanation:
Determine if the statement is true or false. Construct an argument that can be used to defend your solution.
An exterior angle of a triangle will always be obtuse.
The statement "an exterior angle of a triangle will always be obtuse" is actually false.
Why it is?
An exterior angle of a triangle is formed by extending one of the sides of the triangle, and it is the angle between that extended side and the adjacent side of the triangle.
The measure of an exterior angle is equal to the sum of the measures of the two interior angles that are not adjacent to it.
Now, consider a triangle with interior angles of 70, 60, and 50 degrees. If we extend the side opposite the 70-degree angle, we get an exterior angle of 110 degrees. However, 110 degrees is not obtuse, since an angle is obtuse if and only if it is greater than 90 degrees. Therefore, we have shown that an exterior angle of a triangle does not always have to be obtuse.
In summary, the statement "an exterior angle of a triangle will always be obtuse" is false, and we have provided a counterexample to show why this is the case.
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Suppose that, in 2006, Germany produced 13.239 million bikes. The total world production that year totaled 84 million bikes. What percent of the world's total production of bikes is contributed by Germany? Round your answer to the nearest tenth of a percent.
Answer:
15.8%
Step-by-step explanation:
You want the percentage of world bike production represented by 13.239 million bikes out of a world production of 84 million bikes.
PercentageA fraction is converted to a percentage by multiplying it by 100%.
13.239/84 × 100% ≈ 15.8%
Germany contributed about 15.8% of the world's bike production in 2006.
A right triangle has a base, b
, that is 6
inches. The area of the triangle, with h
representing the height, is given by the expression
Answer:
Below
Step-by-step explanation:
See the image below :
Area of the ENTIRE rectangle would be: Area = Base * Height
I think you can see that the triangle is 1/2 of the rectangle. so the
Area of the right triangle would be: Area = 1/2 * base * height
simple workingo ut :)
Answer: b = 82°
To solve for angle b, calculate using the given angles and the straight angle theorem.
Straight Angle TheoremThe straight angle theorem is a rule that says all straight lines are 180°.
Since the angle formed by XY is a straight line, it is also equal to 180°.
XY is divided into three separate angles, a, b and c.
If we add a, b, and c, it will equal to 180°.
Write an equationXY = a + b + c XY is the sum of a, b, and c.
180° = 46° + b + 52° Substitute what we know.
To solve for b using this equation, isolate.
180° - 46° = 46° + b + 52° - 46° Subtract 46° on both sides.
134° = b + 52°
134° - 52° = b + 52° - 52° Subtract 52 on both sides.
82° = b Keep the variable on the left.
b = 82° Final answer.
Therefore, angle b is 82°.
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Select ALL of the solutions of the following system of linear inequalities below.
The solutions of the given system of linear inequalities are (0, 3) and (6, 2)
What is a system of linear inequalities?A system of inequalities is a set of two or more inequalities in one or more variables. Systems of inequalities are used when a problem requires a range of solutions, and there is more than one constraint on those solutions.
Given is a graph of a system of linear inequalities, we need to select the solutions of the following,
The solution of the system of linear inequalities, are given by the combined shaded reason of the graph,
Here, only points (0, 3) and (6, 2) are lies in the common combined part of the graph,
Hence, the solutions of the given system of linear inequalities are (0, 3) and (6, 2)
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triangle RA, and is an isosceles with RA equal MA. find X in the side of of RA show work
The value of x is 2 or 10 and the value of length RA is 96
What is an isosceles triangle?An isosceles triangle is a triangle with (at least) two equal sides. In the figure above, the two equal sides have length and the remaining side has length. . This property is equivalent to two angles of the triangle being equal. An isosceles triangle therefore has both two equal sides and two equal angles.
If RA = MA
x²-4x = 8x -20
x²-4x-8x +20 = 0
x²-12x +20 = 0
x²-10x -2x +20 = 0
(x²-10x)(-2x+20) = 0
x( x -10) -2(x-10) = 0
(x-2)(x-10) = 0
x-2 = 0
or x-10 = 0
x = 2 or 10
therefore RA = x²-4
when x = 2
RA = 0
when x = 10
RA = 100-4
= 96
therefore the value of length of RA is 96
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Winston, a dog, loves to play fetch. He catches each ball mid-air independently with probability 0.4. What is the probability that in four tosses, Winston makes exactly three mid-air catches? Round your answer to three decimal places.
The probability that Winston makes exactly three mid-air catches in four tosses is 0.154, rounded to three decimal places.
What is probability?Probability is a number that indicates the likelihood of an event occurring. Probability is defined as the ratio of favorable outcomes to all outcomes.
This is a binomial distribution problem, where each toss is a Bernoulli trial with a probability of success of 0.4 (i.e., catching the ball mid-air) and a probability of failure of 0.6 (i.e., not catching the ball mid-air).
The number of successes (mid-air catches) in four tosses follows a binomial distribution with parameters n = 4 and p = 0.4.
The probability of getting exactly three mid-air catches in four tosses is:
P(X = 3) = (4 choose 3) * 0.4^3 * 0.6^1 = 4 * 0.064 * 0.6 = 0.154
where (4 choose 3) is the number of ways to choose 3 out of 4 tosses, and 0.4^3 and 0.6^1 are the probabilities of getting 3 mid-air catches and 1 miss, respectively, in any order.
Therefore, the probability that Winston makes exactly three mid-air catches in four tosses is 0.154, rounded to three decimal places.
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In the equation y=6x+1/4,which one is a “rate of change” and which is the initial value
Answer:
Step-by-step explanation:
6 is the rate of change and 1/4 is the initial value
The total cost of producing a type of tractor is given by C(x)=23000−20x+0.02x2
, where x is the number of tractors produced. How many tractors should be produced to incur minimum cost?
Therefore , the solution of the given problem of function comes out to be the number of tractors that should be produced to incur minimum cost is 500.
What is function?The study of numbers and their variables, as well as our surrounds, structures, and both real and imagined locations, are all included in the mathematics curriculum. A function is a visual representation of the relationship between the quantities of inputs and the corresponding outputs for each. Simply described, a function is a collection of inputs that, when integrated, produce unique outputs for each input. Each role is given a country, city, or scope (also known as a realm).
Here,
The total cost function is:
C(x) = 23000 - 20x + 0.02x²
To find the minimum cost, we need to find the value of x that minimizes the total cost.
One way to do this is to find the vertex of the parabola that represents the total cost function.
The vertex of the parabola y = ax² + bx + c has an x-coordinate of -b/2a and a y-coordinate of c - b²/4a.
In this case, a = 0.02, b = -20, and c = 23000.
So, the x-coordinate of the vertex is:
x = -b/2a = -(-20)/(2 × 0.02) = 500
The minimum cost occurs at this x-value, so the number of tractors that should be produced to incur minimum cost is 500.
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Sadie is younger than Guadalupe. Their ages are consecutive integers. Find Sadie's age if the sum of the square of Sadie's age and 5 times Guadalupe's age is 71.
The age of Sadie is 6 years.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
Let x be the age of Sadie
x+1 be the age of Guadalupe
The sum of the square of Sadie's age and 5 times Guadalupe's age is 71.
x² +5(x+1)=71
x² +5x+5=71
x² +5x-66=0
Factor out the expression.
x²+11x-6x-66=0
x(x+11)-6(x+11)=0
(x-6)(x+11)=0
x=6 and x=-11
Hence, the age of Sadie is 6 years.
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Supreme Auto Parts produces components for motorcycle engines. It has plants in Amarillo, Texas, and Charlotte, North Carolina, and supply factories in Detroit and Atlanta. Production and cost data for a major component are as follows. Freight Costs Plant Detroit Atlanta Capacity Unit CostAmarillo $15 $9 $1,500 $110Charlotte $7 $5 $3,300 $120Demand 2,100 1,000 Formulate a transportation model to determine the best distribution plan. If the constant is equal to one, enter "1".Let: X11 = number of components produced in Amarillo and supplied to DetroitX12 = number of components produced in Amarillo and supplied to AtlantaX21 = number of components produced in Charlotte and supplied to DetroitX22 = number of components produced in Charlotte and supplied to Atlanta Min X11 + X12 + X21 + X22 Subject to the constraints X11 + X12 -Select-≤≥=Item 7 X21 + X22 -Select-≤≥=Item 11 + X21 -Select-≤≥=Item 15 X12 + X22 -Select-≤≥=Item 19 X11, X12, X21, X22 ≥ 0
According to the given information the Minimize equation is
Z = 110X11 + 120X12 + 120X21 + 130X22.
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Minimize:
Z = 110X11 + 120X12 + 120X21 + 130X22
Subject to:
X11 + X12 ≤ 1500 (capacity constraint for Amarillo)
X21 + X22 ≤ 3300 (capacity constraint for Charlotte)
X11 + X21 ≥ 2100 (demand constraint for Detroit)
X12 + X22 ≥ 1000 (demand constraint for Atlanta)
where:
X11 = number of components produced in Amarillo and supplied to Detroit
X12 = number of components produced in Amarillo and supplied to Atlanta
X21 = number of components produced in Charlotte and supplied to Detroit
X22 = number of components produced in Charlotte and supplied to Atlanta
Therefore, according to the given information the Minimize equation is
Z = 110X11 + 120X12 + 120X21 + 130X22
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