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Given parameters:

Area of the rectangular garden  = 359ft²

Unknown:

length and width of the garden  = ?

To find the length and breadth of the garden, we need to define and know that the area of a rectangle is.

 Area of a rectangle  = Length x Breadth

From the problem statement;

 Let w = width of the rectangular garden

        L = length of the garden;

 Now,

          length of a rectangular garden is 5 feet less than 4 times its width

           L = 4w - 5

Now let us substitute this into the equation;

       Area  = L x w

    359 = (4w - 5)w

           4w² - 5w - 359

Using:

          w = -b ± √b² -  4ac  /  2a

 where b  = -5 , a  = 4  and c = -359

  w  =   -(-5)  ± √-5² - 4(4)(-359)  /  2(4)

 w = 5 ± √25 + 5744 / 8

 w =  5 ± 75.9 / 8

 w  = [tex]\frac{5 + 75.9}{8} or \frac{5 - 75.9}{8}[/tex]

  w  = 10.1ft

 The other solution is not possible it will be a negative value. Width value cannot be negative.

So L = 4w - 5  = 4(10.1) - 5 = 35.5ft

The length and breadth of the rectangular are 35.5ft and 10.1ft respectively.

Answer:

226

Step-by-step explanation:

Answer:

100 students selected randomly as their enter your middle school in the morning

Step-by-step explanation:

Answer:

C (100 students selected randomly from your middle school)

Step-by-step explanation:

The first one is wrong because its only 10 people from your homeroom.

The next one is also wrong sense its only 5 people who could also share the same interests as you.

The next one is wrong because its not from their middle school

That leaves us with the last one, its selected randomly with a lot of people involved from their middle school.

Answer:

10.7 grams

Step-by-step explanation:

hey there, again!

this is a similar process the mass is denisty*area HOWEVER keep in mind it's flat so the area is just x deltax while denisity is 3 + sin(x)

mass of rod = integral 0 to 3pi/4 of (3 + sin(x))*x deltax

= integral 0 to 3pi/4 of 3x + xsin(x) deltax

= 0 to 3pi/4 [3/2*x^2 + x(-cos(x)) + sin(x)]

= 10.7 grams

Answer:

24

Step-by-step explanation:

Answer:

24

Step-by-step explanation:

you can split it into two parts. One with 4 x 3 = 12 and the other with 2 x 6 = 12. then add them together and you get 24.

Answer:

x=48

Step-by-step explanation:

Since these angles are supplementary, they add up to 180. so, you can set the equation x+23+x+61=81. Simplify the equation and solve for x

Answer:

#1 is x+23°=23

#2 is x+61°=61

Step-by-step explanation:

Because when you are adding it will always be a positive number

But when you are subtracting it will always be a negative number

Answer:

no solution

Step-by-step explanation:

[1]    6x - 9y = 16

  [2]    2x - 3y = 7

// Solve equation [2] for the variable  x  

 [2]    2x = 3y + 7

 [2]    x = 3y/2 + 7/2

// Plug this in for variable  x  in equation [1]

  [1]    6•(3y/2+7/2) - 9y = 16

  [1]    0 = -5 =>  NO solution

No solution

Answer:

G. 6 months

Step-by-step explanation:

1. 495-165 to remove the one-time payment = 330

2. 330/55 to find the number of months = 6

Barbara receive 6 months of dance lessons from Dance Unlimited

A function can be defined as the outputs for a given set of inputs.

The inputs of a function are known as the independent variable and the outputs of a function are known as the dependent variable.

Given, Barbara signed up for dance lessons at Dance Unlimited. She was charged $55 per month for lessons and a one-time recital fee of $165.

Let m be the no of months and f(m) is the total cost.

∴ f(m) = 55m + 165.

The equation represents the $495 total cost,

∴ 495 =  55m + 165.

55m = 330.

m = 330/55.

m = 6.

Barbara receives 6 months of dance lessons from Dance Unlimited.

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Answer:

-3.7

Step-by-step explanation:

-3.2 + 1.5 -2 = -3.7

Answer:

-5/2

Step-by-step explanation:

-6+11/2+(-2)

-12+11+(-4)/2

-5/2

Answer:

Points G and J are correct.

Step-by-step explanation:

idek dwjejdjjriiwknansns

Step-by-step explanation:

nmjwjw

Answer:

120

Step-by-step explanation:

Use the permutation and combination formulas to evaluate.

Answer:

20

Step-by-step explanation:

just took the test

Answer: 1

Step-by-step explanation:

First you need to multiply 3 x 3 (9), because that's all 3 squared means.

Now the equation should be 9x-6x+3=0

Next we need to combine like terms. Do 9x - 6x which should give you 3x

Now your equations should be 3x+3=0

Now for the somewhat harder part...

Under the three (the one without the x) write -3 and under the zero write the same thing.  the +3-3 cancels out so just put a line or something across it.

0-3= -3

so now you should have...

3x=-3    ignore the 3x, at this point it's useless in getting the answer because it would cancel out.

-3 divided by -3  is 1 because a negative (-)  divided by a negative (-) equals a positive (+).

The answer should be  x = 1

Let a be the amount of 40% solution and b be the amount of pure alcohol that you will use.

You want to end up with a volume of 660 mL, so

a + b = 660

For each mL of solution used, the 40% solution would contribute 0.4 mL of alcohol, and the pure alcohol will contribute 1 mL of alcohol. In the desired solution, you want a concentration of 80% alcohol, so that it contains 0.8 • 660 mL = 528 mL of alcohol, and

0.4a + b = 528

Solve the system of equations above. Subtracting the second from the first eliminates b and lets us solve for a :

(a + b) - (0.4a + b) = 660 - 528

0.6a = 132

a = 220

Then

220 + b = 660

b = 440

So you will need 220 mL of the 40% solution and 440 mL of pure alcohol.

Answer:

c=-4

Step-by-step explanation:

14=-2c-6-3c

14=-5c-6

20=-5c

-4=c

Answer:

1

Step-by-step explanation:

The expected value for the given case is $-4.75.

Probability is the branch of Mathematics that deals with the measurement of the chance of occurrence of a random event.

The probability of any event always lies in the close interval of 0 and 1 [0,1].

Given that,

The probability of winning $76 is 1/20.

And, the probability of losing $9 is 19/20.

The expected value for the given probability can be given by taking the product of the probability and the wining or losing amount and then substracting them as,

Expected value = 1/20 × 76 - 19/20 × 9

                          = 3.8 - 8.55

                          = -4.75

Hence, the expected value of amount for losing and winning the game is $-4.75.

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Answer:

37, 3, 37

Step-by-step explanation:

Answer:

negitive 3

Step-by-step explanation:

i think of it like digging. Negitive going down and positive going up aka put dirt down in the whole. so i am down 7 so i add dirt because the 4 is positive. so then i am at 3. wait make that negitive 3. so the answer is negtive 3.

Answer:

-3

Step-by-step explanation:

Answer:

-0.86

Step-by-step explanation:

12x + 9 = 2x - 15 + 5x + 2

Combine

19x = -22

Answer:

someone please answer this equation

Step-by-step explanation:

i have this on my test and i really need help with it

Answer:

(3, 4)

Step-by-step explanation:

Answer:

55%

Step-by-step explanation:

Answer:

it would have won 1/3 or .333333

Step-by-step explanation:

8/24 simplifies to 1/3, which equals .33333

Answer:

I'm pretty sure it's 33%

Step-by-step explanation:

8 is 1/3 of 24 and 1/3 as a fraction is 33%

Answer:

12 multiplied by 8.24=98.88

Subtract 24 from 98.88=74.88

Answer:

distance is 5

midpoint is (1/2,-2)

Step-by-step explanation:

Answer:

60/100 and .6

Step-by-step explanation:

Answer: In algebra, like terms are terms that have the same variables and powers. The coefficients do not need to match. Unlike terms are two or more terms that are not like terms, i.e. they do not have the same variables or powers. The order of the variables does not matter unless there is a power. For example, 8xyz² and −5xyz² are like terms because they have the same variables and power while 3abc and 3ghi are unlike terms because they have different variables. Since the coefficient doesn't affect likeness, all constant terms are like terms.

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Answer:

by combining them like the ordinary like ordinary integers.

Step-by-step explanation:

For example we have

8x + 4y = 3x - 6

you will bring 3x to the left so it will become -3x

8x - 3x + 4y = -6

then combine like terms

there you have

5x + 4y = -6

The given:

8x + 4y = 3x - 6

8x - 3x + 4y = -6

5x + 4y = -6

answer for the example: 5x + 4y = -6

Answer:

Y=-2/3x+10

Step-by-step explanation:

We have the slope -2/3, so we can find the y intercept by plugging in the given coordinate (-3,8). if y=mx+b, 8=-2/3(-3)+b. If you simplify the equation, you would get 8=-2+b, and then you would get 10=b. 10 would then be the y intercept.