Answer:
[tex]4(x-5)[/tex]
Step-by-step explanation:
The expression 4x - 20 has the greatest common factor (GCF) of 4.
[tex]4x-20\\4(x-5)[/tex]
Therefore, the factored expression is 4(x - 5).
The coefficient of the variable for the expression 4x - 20 is found as 4.
What is defined as the coefficient of the variable?A coefficient is just an integer that is either written alongside or multiplied by a variable. A coefficient, in other words, is the numerical factor of the a term containing constants and variables. For example, the coefficient in the term 12x is 12.For the given question,
The expression is given as;
4x - 20
where,
4 is the coefficient of the variable of the expression.
-20 is the constant in the expression.
Thus, the coefficient of the variable is found as 4.
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A small city gets its water supply from three sources: two wells and a small upland reservoir. The well supplies require pumping, and so are more expensive. Reservoir water flows directly to the town by gravity. The town needs a total of 20 mgd (million gallons per day) of water. The cost of water is zero if obtained from the reservoir, $60/million gallons if from Well-field 1, and $30/million gallons if from Well-field 2. The reservoir can deliver 9 mgd; Well-field 1 has a capacity of 25 mgd, and Well-field 2 has a capacity of 3 mgd. (Hint: use the Lagrange multipliers for the last three questions. You can check your answers using Excel solver)
a) Formulate this problem in terms of an objective function and constraint(s).
b) Solve the problem by hand using the Lagrange Multipliers, and find the minimum total cost combination of flows from each source, and minimum total cost.
c) How much, annually, should the city be willing to pay to expand the capacity of the reservoir, Well-field 1, and Well-field 2
d) If the city decided to conserve water and the demand decreased from 20 to 19.5 mgd, how much would the city benefit from this conservation?
e) If you had a chance to expand the capacity of reservoir, Well-field 1, or Well-field 2 reservoir, Well-field 1, and Well-field 2 What would be the new cost? which one(y) would you prefer to increase, why?
Answer: A small city gets its water supply from three sources: two wells and a small upland reservoir. The well supplies require pumping, and so are more expensive. Reservoir water flows directly to the town by gravity. The town needs a total of 20 mgd (million gallons per day) of water. The cost of water is zero if obtained from the reservoir, $60/million gallons if from Well-field 1, and $30/million gallons if from Well-field 2. The reservoir can deliver 9 mgd; Well-field 1 has a capacity of 25 mgd, and Well-field 2 has a capacity of 3 mgd. (Hint: use the Lagrange multipliers for the last three questions. You can check your answers using Excel solver)
a) Formulate this problem in terms of an objective function and constraint(s).
b) Solve the problem by hand using the Lagrange Multipliers, and find the minimum total cost combination of flows from each source, and minimum total cost.
c) How much, annually, should the city be willing to pay to expand the capacity of the reservoir, Well-field 1, and Well-field 2
d) If the city decided to conserve water and the demand decreased from 20 to 19.5 mgd, how much would the city benefit from this conservation?
e) If you had a chance to expand the capacity of reservoir, Well-field 1, or Well-field 2 reservoir, Well-field 1, and Well-field 2 What would be the new cost? which one(y) would you prefer to increase, why?
Step-by-step explanation: A small city gets its water supply from three sources: two wells and a small upland reservoir. The well supplies require pumping, and so are more expensive. Reservoir water flows directly to the town by gravity. The town needs a total of 20 mgd (million gallons per day) of water. The cost of water is zero if obtained from the reservoir, $60/million gallons if from Well-field 1, and $30/million gallons if from Well-field 2. The reservoir can deliver 9 mgd; Well-field 1 has a capacity of 25 mgd, and Well-field 2 has a capacity of 3 mgd. (Hint: use the Lagrange multipliers for the last three questions. You can check your answers using Excel solver)
a) Formulate this problem in terms of an objective function and constraint(s).
b) Solve the problem by hand using the Lagrange Multipliers, and find the minimum total cost combination of flows from each source, and minimum total cost.
c) How much, annually, should the city be willing to pay to expand the capacity of the reservoir, Well-field 1, and Well-field 2
d) If the city decided to conserve water and the demand decreased from 20 to 19.5 mgd, how much would the city benefit from this conservation?
e) If you had a chance to expand the capacity of reservoir, Well-field 1, or Well-field 2 reservoir, Well-field 1, and Well-field 2 What would be the new cost? which one(y) would you prefer to increase, why?
Someone pls help- am struggling.
500 = 400 + 50s. Therefore, Bart can buy 2 pairs of shoes.
=============================================================
Explanation:
s = number of pairs of shoes
50s = amount spent on shoes ($50 per pair)
50s+400 = total amount spent on shoes and uniforms
That expression is the same as 400+50s because we can add numbers in any order we want. Set this equal to the $500 he started with to get the equation 500 = 400 + 50s
We have enough info to determine the answer must be choice B
We can stop here if you wanted.
----------
Let's solve that equation for s
500 = 400 + 50s
400 + 50s = 500
50s = 500-400 .... subtract 400 from both sides
50s = 100
s = 100/50 .... divide both sides by 50
s = 2
This means he can buy 2 pairs of shoes.
Buying the shoes only will cost 50s = 50*2 = 100 dollars, which on top of the $400 for the uniforms, leads to a grand total of 400+50s = 400+100 = 500 dollars. This helps confirm we have the correct value for s.
The graph of a proportional relationship passes through the point (5, 2) .
What is the constant of proportionality of the relationship?
5
2
25
I don't know.
Well, 5 is like the point where it is, and 2 is the constant of proportionality.
Answer:
0.4
Step-by-step explanation:
2= slope *5 ,slope = 0.4
Change 3/2 3.14 to degree measure
A. 180 degrees
B. 90 degrees
C. 270 degrees
D. 360 degrees
Answer:
option b
hope ut is help full
Facts about a linear relationship
Answer:
A linear relationship (or linear association) is a statistical term used to describe a straight-line relationship between two variables. Linear relationships can be expressed either in a graphical format or as a mathematical equation of the form y = mx + b
Step-by-step explanation:
Does any one the the answer
Answer:
18 Square Feet
Step-by-step explanation:
ABC is 3 times larger then DEF so you multiply 6 by 3 which gives you 18. Let me know if I'm wrong.
Answer:
18 square feet
Step-by-step explanation:
Because the area of ADEF =6 sq ft
And you have 12ft in A and B
help on this please
Answer:
Opening: Opens upwards
Axis of Symmetry: -7/2
Vertex: (-7/2, -81/4)
X - intercepts: (1, 0) and (-8, 0)
Y - intercept: (0, -8)
Step-by-step explanation:
Opening: 'a' is greater than zero
Axis of Symmetry:
[tex]\frac{-7}{2(1)} =\frac{-7}{2}[/tex]
Vertex:
[tex]y= (\frac{-7}{2})^{2} +7(\frac{-7}{2}) -8\\y= (\frac{49}{4}) +(\frac{-49}{2}) -8\\y= \frac{49}{4} +\frac{-98}{4} -8\\y=\frac{-49}{4}-8\\y = \frac{-81}{4}[/tex]
X - intercepts:
(x-1)(x+8)
x = 1 and x = -8
Y - intercept: (0, -8)
[tex]y= 0^{2} +7(0) -8\\\\y= -8\\[/tex]
Express your answer in scientific notation. 0.00045 – 2.5-10-5
Answer:
17.49955
Step-by-step explanation:
Hope this helps
Which kind of triangle is showing
Answer:
it's an scalene triangle
having all the sides and angels different from each other
Step-by-step explanation:
brainliest plz
Diane took a loan out for $3000 for 11 months and was charged a simple interest. The total interest she paid was $253. What’s her interest rate
Answer:
$300
Step-by-step explanation:
Diane's interest rate on the loan is approximately 8.43%.
Let's determine Diane's interest rate step by step.
1. First, we need to understand the formula for simple interest:
Simple Interest (SI) = Principal (P) × Rate (R) × Time (T)
where:
P = Principal amount (initial loan amount)
R = Interest rate (unknown, what we want to find)
T = Time period in years
2. We have the following information from the problem:
P = $3000 (Principal amount)
SI = $253 (Total interest paid)
T = 11 months
3. However, to use the formula, we need to convert the time from months to years. Since 1 year has 12 months, we can write:
T = 11 months ÷ 12 months/year
≈ 0.917 years
4. Now, let's rearrange the formula to solve for the interest rate (R):
R = SI / (P × T)
Substituting the given values:
R = $253 / ($3000 × 0.917) ≈ 0.0925
5. Finally, we need to convert the interest rate from a decimal to a percentage:
R = 0.0925 × 100 ≈ 8.43%
So, Diane's interest rate on the loan is approximately 8.43%.
In summary, to find the interest rate, we used the simple interest formula and rearranged it to solve for the rate. We converted the time from months to years before calculating the interest rate. The result is approximately 8.43% interest rate, indicating the percentage of the principal that Diane had to pay as interest over 11 months.
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A tune-up automotive facility marks up its
parts by 45%. Suppose that the facility
charges its customers $2.03 for each spark
plug it sells. What is the facility's cost for each
spark plug?
Answer: $1.40
Work Shown:
x = cost before markup
1.45x = cost after the 45% markup
1.45x = 2.03
x = (2.03)/(1.45)
x = 1.40
Heyyyyy help mee please
need help with this plz
Answer:
[tex]x = \frac{ - 24 \pm \sqrt{ - 288} }{4} \\ = \frac{ - 24 \pm \sqrt{ ( - 1) {(12)}^{2} (2)} }{4} \\ = \frac{ - 24 \pm \sqrt{ - 1} \sqrt{ {12}^{2} } \sqrt{2} }{4} \\ = \frac{ - 24 \pm i 12\sqrt{2} }{4} \\ =-\frac{24}{4}\pm \frac{i12\sqrt{2}}{4}\\= - 6 \pm \: i3 \sqrt{2} [/tex]
Please Help! I will give you a lot of points and the brainiest!
A married man filing separably with a taxable income of $130,000. Compute the tax owned (look at chart)
--PLEASE show work
First, find the tax rate for a person whose taxable income is $130,000. By looking at the table, you can see the tax rate is 33%. To find the total tax, multiply 33% by $130,000.
[tex]0.33 \times 130000 = 42900[/tex]
Thus, the tax this person has to pay is $42,900.
what is the answer to 28.2 divided by 2
Answer:
14.1
Step-by-step explanation:
Need help with a math question
First: Find out their decimal form.
- 2 1/6 as a decimal is 2.16
7/3 as a decimal
To get 7/3 converted to decimal, you simply divide 7 by 3. Don't worry. You don't need to get the calculator out, because we did this for you.
7/3 as a decimal is:
2.333333333
Alani has a summer job as a lifeguard. She makes $8/h for up to 40 h each week. If she works more than 40 h, she makes 1.5 times her hourly pay, or $12/h, for each hour over 40 h. 1. How much will Alani earn if she works: a. 37 hours?
Please i need this now
Answer:
356
Step-by-step explanation:
She will earn a total of $296.
We have - Alani who has a summer job as a lifeguard. She makes $8/h for up to 40 h each week. If she works more than 40 h, she makes 1.5 times her hourly pay, or $12/h for each hour over 40 h. How much will Alani earn if she works: a. 37 hours.
We have to determine - How much will Alani earn if she works for 37 hours.
If you earn $x per hour and you work for 30 hours, them calculate the amount of money you will earn.The amount of money you will earn will be = $30[tex]x[/tex].
According to question, we have -
Pay per hour = $8
Number of hours she work in a week = 40 hours
For working 37 hours, which is less than 40, she will receive an hourly wage of $8 only. Therefore -
$8 x 37 = $296
Hence, she will earn a total of $296.
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solve pls brainliest
Answer:
7.5 < 7.5061 < 7.56 < 9.213
Step-by-step explanation:
Determine whether the equation is a linear equation in two variables. 5y = x - 5
Answer:
Yes
Step-by-step explanation:
start with 5y=x-5
divide both sides by 5 to get:
y= x/5 - 1
since a linear equation is represented by y=mx+b, and this can be represented in that form, this is a linear equation.
The sum of the lengths of KLM is 16.14 cm. The length of KL is 6 cm and the length of KM is 4.9 cm. What is the length of KM? A. 27.04 cm B. 5.34 cm C. 5.24 cm D. 5.14 cm
Answer:
im pretty sure its 1/44 plz make me branliest
Step-by-step explanation:
Help with Algebra 2, forgot how to do it
Answer:
[tex]f(x) = 3 \: \: \: \: for \: \: \: \: - 6 < x < 1 \\ f(x) = - x \: \: \: \: for \: \: \: \: 1 < x < 6[/tex]
write the rational expressions as equivalent rational expressions with the lowest common denominator
1. The equivalent rational expression with the lowest common denominator of [tex]\frac{2}{3d^{2} + 14d^{2} - 5 }[/tex] is [tex]\frac{2}{(d+5)(3d-1)}[/tex]
2. The equivalent rational expression with the lowest common denominator of [tex]\frac{3d}{3d^{2} - 22d + 7}[/tex] is [tex]\frac{3d}{(d-7)(3d-1)}[/tex]
1.
[tex]\frac{2}{3d^{2} + 14d^{2} - 5 }[/tex]
Let factorise the denominator below
3d² + 14d - 5
-15 and 14
Two numbers we can multiply to get -15 and add to get 14 are 15 and -1.
Therefore,
3d²- d + 15d - 5
d(3d - 1) + 5(3d - 1)
(d+5)(3d-1)
Therefore, the equivalent rational expression with the lowest common denominator will be
[tex]\frac{2}{(d+5)(3d-1)}[/tex]
2.
[tex]\frac{3d}{3d^{2} - 22d + 7}[/tex]
Factorise the denominator
3d²- 22d+7
3d²- d - 21d + 7
d(3d - 1) - 7(3d - 1)
(d - 7)(3d - 1)
Therefore, the equivalent rational expression with the lowest common denominator will be
[tex]\frac{3d}{(d-7)(3d-1)}[/tex]
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ERIOD
DATE
NAME
4. Priya bought these items at the grocery store. Find each unit price.
a. 12 eggs for $3. How much is the cost per egg?
b. 3 pounds of peanuts for $7.50. How much is the cost per pound?
c. 4 rolls of toilet paper for $2. How much is the cost per roll?
d. 10 apples for $3.50. How much is the cost per apple?
Answer:
A 3.00/12=.25 ea
B 7.50/3=2.50/1lb
C 2.00/4=.50ea
S 3.50/10=.35/ea
Here you go! Hope it helps.
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Thank you -= Miss Hawaii
Footlocker and Footaction are each having a sell on all of the latest name brand shoes. At Footlocker, you can get 2 pairs of Nikes for $69.98. At Footaction you can get 3 pair of shoes for $99.99
Answer:
I'm not sure what this is asking but footaction is cheaper
Step-by-step explanation:
footlocker the shoes (single pair) is 69.98/2 or 34.99
footaction is 99.99/3 or 33.33
a
In the year 2005, a company made $6 million in profit. For each consecutive year
after that, their profit increased by 13%. How much would the company's prohl be in
the year 2007, to the nearest tenth of a million dollars?
Answer:
The profit will be 7.7 million in 2007
Step-by-step explanation:
6x(1+ 0.13)^2
6x1.13^2
6x1.2769
in order to start a small business a student takes out a simple interest loan for $8,000 for 6 months at a rate of 6.25%, how much interest must the student pay and find the future value of the loan round to the nearest cent as needed
Answer:
The student must pay 4247.5 - 4000 = 247.50 dollars in interest
Step-by-step explanation:
Consider the following, what is the summation of all solutions?
(2x+4)^2+1=5
Answer:
- 4
Step-by-step explanation:
(2x + 4)² + 1 = 5 ← expand left side using FOIL and simplify
4x² + 16x + 16 + 1 = 5
4x² + 16x + 17 = 5 ( subtract 5 from both sides )
4x² + 16x + 12 = 0 ( divide terms by common factor 4 )
x² + 4x + 3 = 0 ← in standard form
(x + 3)(x + 1) = 0 ← in factored form
Equate each factor to zero and solve for x
x + 3 = 0 ⇒ x = - 3
x + 1 = 0 ⇒ x = - 1
Summation of solutions = - 3 + (- 1) = - 3 - 1 = - 4
help me answrr the 4th question please
Step-by-step explanation:
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Carlos has earned more than $260 selling magazines subscriptions. Each subscription
was sold for $12. How many did Carlos sell?
Answer:
21.6 magazines
Step-by-step explanation:
260/12=21.6
Which choice is the correct graph of [x1 < 5?
A 4
B
C
D
E
-
F
5
A. Graph A
O B. Graph B
C. Graph
ОО ОООО
O D. Graph D
O E. Graph E
OF. Graph F
Answer:
B
Step-by-step explanation:
Da"B"a"B"y
2 B so
"B" graph "B"
↑that explains it