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Answer:

[tex]f(x) = 3 \: \: \: \: for \: \: \: \: - 6 < x < 1 \\ f(x) = - x \: \: \: \: for \: \: \: \: 1 < x < 6[/tex]

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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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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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?

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

Answer:

option b

hope ut is help full

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

Answer:

17.49955

Step-by-step explanation:

Hope this helps

Answer:

B

Step-by-step explanation:

Da"B"a"B"y

2 B so

"B" graph "B"

↑that explains it

Step-by-step explanation:

gcvnjgcnhkk xdhvchjjudvhtuk xecn9

Answer:

14.1

Step-by-step explanation:

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

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.

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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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

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:

Answer:

7.5 < 7.5061 < 7.56 < 9.213

Step-by-step explanation:

Answer:

it's an scalene triangle

having all the sides and angels different from each other

Step-by-step explanation:

brainliest plz

Answer:

not sure about it this one is tuff

Answer:

The student must pay 4247.5 - 4000 = 247.50 dollars in interest

Step-by-step explanation:

Answer:

im pretty sure its 1/44 plz make me branliest

Step-by-step explanation:

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.

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.

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

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

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]

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

Answer:

The profit will be 7.7 million in 2007

Step-by-step explanation:

6x(1+ 0.13)^2

6x1.13^2

6x1.2769

Answer:

21.6 magazines

Step-by-step explanation:

260/12=21.6

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.