A total of 2,000 square feet is to be enclosed in two pens, separated by a chain link fence. The outside walls are to be constructed of brick. The brick wall costs $20 per linear foot and the chain link costs $4 per linear foot. Find the dimensions that minimize the construction cost

Answer:

k = -21

Step-by-step explanation:

Slope y-intercept form : y = mx +c

kx + 7y = 10

        7y = -kx + 10

          y = [tex]\frac{-k}{7}x+\frac{10}{7}[/tex]

[tex]\frac{-k}{7}=3\\\\ -k = 3*7\\\\ -k = 21\\\\ k = -21[/tex]

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Hint :

[tex]slope = The \: \: coefficient \: \: of \: \: x \: \: in \: \: the \: \: slope-intercept \: \: form \\ [/tex]

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Thus we need to find the slope-intercept form of the line which must be like this :

[tex]y = ax + b[/tex]

[tex]7y + kx = 10[/tex]

Subtract sides kx

[tex]7y + kx - kx = 10 - kx[/tex]

[tex]7y = 10 - kx[/tex]

[tex] 7y = - kx + 10[/tex]

Divide sides by 7

[tex] \frac{7y}{7} = \frac{ - kx + 10}{7} \\ [/tex]

[tex]y = \frac{ - kx}{7} + \frac{10}{7} \\ [/tex]

[tex]y = - \frac{k}{7} x + \frac{10}{7} \\ [/tex]

This is the slope-intercept form .

[tex]The \: \: coefficient \: \: of \: \: x = - \frac{k}{7} \\ [/tex]

The slope is 3 ,

Thus :

[tex] - \frac{k}{7} = 3 \\ [/tex]

Multiply sides by 7

[tex]7 \times ( - \frac{k}{7}) = 7 \times 3 \\ [/tex]

[tex] - k = 21[/tex]

Multiply sides by - 1

[tex] ( - 1) \times ( - k) = ( - 1) \times (21)[/tex]

[tex]k = - 21[/tex]

And we're done....

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Answer:

1. slope

2. slope

3. slope

4. y intercept

5. slope

6. it crosses the x axis

7. when the value of y is zero

8. when the form is y = something

9. when the form is x = something

10. Positive slope

11. Negative slope

12. y=x

13. Slope Intercept form

14. Standard form

Answer:

Perpendicular = 1

parallel = -1

Step-by-step explanation:

Parallel -  you must have the same slope, so it is -1

then, for a perpendicular line, the slope is the opposite, so 1

Answer:

Yes, and the unit rate is 1:48

Step-by-step explanation:

If you start by dividing 204 by 4.25, you will see you get an answer of 48. Now if you move on to the next row, and divide 252 by 5.25, you also get 48. If you do the same with the last two rows, you get 48 for both. This shows that the unit rate is 1:48.

Answer:

Step-by-step explanation:

a. p=2200+60n

b. p=2200+60(26)

p=2200 plus 1560

p=3760

The equation that should be related P to N should be considered as the 2200+60n.

And, the total pay when he sells 26 copies of Math is Fun should be 3760.

Since

His base salary is $2200, and he makes an additional $60 for every copy of Math is Fun he sells.

Here P means the total pay

So, here the equation be p=2200+60n

Now the total pay be

p=2200+60(26)

= 2,200 + 1,560

= 3,760

hence, The equation that should be related P to N should be considered as the 2200+60n.

And, the total pay when he sells 26 copies of Math is Fun should be 3760.

Learn more about an equation here: https://brainly.com/question/15844891

Answer:

x-35.75=40.00

Step-by-step explanation:

Let's use m as our variable.

So Marlen went to the mall and spent $35.75 on shoes. When she got home she had $40.00 in her purse.

An equation to represent this is : x-35.75=40.00

If you are interested in the value of x it is $75.75

Answer:

[tex]C(t)=125\cdot 0.9^t[/tex]

Step-by-step explanation:

Exponential Decay Function

The exponential function is often used to model natural growing or decaying processes, where the change is proportional to the actual quantity.

An exponential decaying function is expressed as:

[tex]C(t)=C_o\cdot(1-r)^t[/tex]

Where:

C(t) is the actual value of the function at time t

Co is the initial value of C at t=0

r is the decaying rate, expressed in decimal

The doctor prescribed 125 milligrams of a therapeutic drug. It decays by 10% each hour. The initial value is Co=125 and the decay rate is r=0.1 per hour. Substituting into the function:

[tex]C(t)=125\cdot(1-0.1)^t[/tex]

Operating:

[tex]\mathbf{C(t)=125\cdot 0.9^t}[/tex]

Where t is expressed in hours.

3²×3^-5

Multiply the terms with the same base by adding their exponents

3²-5

Calculate the differences

3^-³

Express with a positive exponent using  a ^-n =1/n

                                                                             a

1/3³

Write the exponentiation as a multiplication

3×3×3

Multiply the numbers

27

Answer is 1/27

Answer:

Your answer is: [tex]6x^2-12y+13x[/tex]

Simplify the expression.

Step-by-step explanation:

Hope this helped : )

Answer:

64 fl oz

Step-by-step explanation:

To find the best price you take the cost and divide it by the number of fluid ounces ($1.99/32). For the 32 oz it costs .062, for the 64 oz it costs .057, and for the 96 oz it costs .060 (these are all approximate number btw). Therefore, since 64 oz has the lowest number it has the lowest price per fluid oz.

Answer: 1000000

Step-by-step explanation:

Answer:

answer 1000000

have a nice day

1st Answer:

2 3/4 cups of dough divided by the amount used for each dumpling 3/16

would be

11/4/3/16=

=44/3

=14 2/3

which would be about 14 whole dumplings!

The maximum amount of bid for the toy will be equal to $80.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that you win an online auction for a toy. Your winning bid of $60 is 75% of your maximum bid.

The maximum bid will be calculated as,

Maximum bid = ( 100 x 60 ) / 75

Maximum bid = $80

Therefore, the maximum amount of bid for the toy will be equal to $80.

To know more about an expression follow

https://brainly.com/question/19559630

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Answer:

40

Step-by-step explanation:

plz mark B R A I N L I E S T

Answer:

the answer is 40.. the second one

Step-by-step explanation:

PEMDAS

Exponents first

2^3 = 2*2*2 = 8

Next up, Multiplication 4*8=32

Last but not least,  addition

Add 32+8

and your final answer is 40!

Answer:

Are you looking for coordinates or a equation?

Step-by-step explanation:

Answer:

y=-3/4x+3

Step-by-step explanation:

3x+4y=12

-3. -3

4y=-3x+12 (I put the 3x first just so that it is already in slope intercept form)

4y/4=-3x/4+12/4

y=-3/4x+3

Answer:

1. x is the amount of hours it took to repair the computer

2. 44+45x=$179

3. Around 3 hours

Step-by-step explanation:

44+45x=$179

Subtract 44 on both sides:

44-44+45x=179-42

45x=137

Divide 45 on both sides:

45x/45=137/45

x=3.044444444

Around 3 hours.

Answer: imma figure this out

Step-by-step explanation:

Answer:

Answer: imma figure this out

Step-by-step explanation:

Step-by-step explanation:

y²-y¹/x²-x¹

4-(-2)/5-(-3)

6/8

=3/4

y²-y¹/x²-x¹

(-3)-5/3-(-6)

-8/9

= -8/9

Answer:

f(6)=15

Step-by-step explanation:

Answer:

I've been working on with the area of the region in my calc II class, and now have to deal with the volume.

Find the volume V of the solid obtained by rotating the region bounded by the given curves about the specified line.

y=749√2,y=0,x=2,x=3

Step-by-step explanation:

Answer:

b. SSS

Step-by-step explanation:

The diagram provided shows that:

DE is congruent to DG,

EF is congruent to FG, and

DF is congruent to DF

Thus, all three sides of ∆DEF is congruent to all corresponding sides of ∆DFG. Therefore, by the Side-Side-Side Congruence Theorem, ΔDEF ≅ΔDFG.

Answer:

$300

Step-by-step explanation:

10% converted into a decimal is 0.10.

To find 10% of 3,000, you would multiply them.

3,000 times 0.10 is 300.

Therefore, Nora spends $300 a month on clothes.

Answer:

The average speed of the object is 18.67 ft/s.

Step-by-step explanation:

Given;

height function, f(t) = -16t² + 42t + 5

The average speed is given by ;

[tex]v = \frac{dx}{dt} \\\\h(t) = -16t^2+42t+5\\\\h(1.5)= -16(1.5)^2 + 42(1.5)+5 = 32 \ ft\\\\[/tex]

from 1.5 s to 2.25 s = 0.75 s,

[tex]h(0.75)= -16(0.75)^2 + 42(0.75)+5 = 27.5 \ ft[/tex]

[tex]h(2.25)= 27.5 +(-16(2.25)^2 + 42(2.25)+5) \\\\h(2.25) = 27.5 + 18.5 = 46 \ ft[/tex]

The average speed is given by ;

[tex]v = \frac{h(2.25) - h(1.5)}{2.25-1.5}\\\\v = \frac{46-32}{0.75}\\\\v = 18.67 \ ft/s[/tex]

Therefore, the average speed of the object is 18.67 ft/s.

Answer:

$120

Explanation:

Data provided as per the given question below:-

Investment = $4,000

Coupon rate in percentage = 3%

The computation of yearly return is shown below:-

Yearly return = Investment × Coupon rate in percentage

= $4,000 × 3%

= $120

Therefore for computing the yearly return we simply investment with coupon rate in percentage.

Answer:

The median is close to 90, but there is most likely one student and up to 25 % of the class who did poorly on an exam that otherwise looks pretty easy

Step-by-step explanation:

Hope this helps you!

~ Isimpfortnpu

[tex]\mathfrak{\huge{\pink{\underline{\underline{AnSwEr:-}}}}}[/tex]

Actually Welcome to the Concept of the ratio and proportion.

here, we clearly notice, that,

4 cups have 2 ounces each, that is

=> 4×2 = 8 ounces

also, 1 cup with 3 ounces,

=> 1×3 = 3 ounces,

adding both we get as,

8+3 = 11 ounces,

the total is 11 ounces.