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Gennadij [26K]
3 years ago
12

How do you know what number to multiply everything by using the elimination method on systems of equations??

Mathematics
1 answer:
Marrrta [24]3 years ago
8 0

Answer:

See below  

Step-by-step explanation:

You multiply the equations by numbers that will give you the least common multiple of the coefficients.

Suppose you have a system of two equations:

\begin{cases}(1)& 2x + y = 40\\(2) & x + 2.5y = 60\end{cases}\\

You can choose to eliminate either x or y.

1. Eliminating x

The coefficients of x are 2 and 1. The least common multiple is 2, so you multiply (1) by 1 and (2) by 2 to get

\begin{array}{lrcll}(3) & 2x + y & = & 40 &\ \\(4) & 2x + 5y & = & 120 & }\\\end{array}

Then you can subtract (3) from (4) and get

4y = 80. Solve for y.

2. Eliminating y

The coefficients of y are 1 and 2.5. The least common multiple is 2.5, so you multiply (1) by 2.5 and (2) by 1 to get

\begin{array}{lrcll}(5) & 5x + 2.5y & = & 100 &\ \\(6) & x + 2.5y & = & 60 & }\\\end{array}

Then you can subtract (6) from (5) and get

4x = 40. Solve for x.

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Answer:

a = 3

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Step-by-step explanation:

gradient function (y') = ax² + b

curve function (y) = 1/3 ax³ + bx + c  

pass (1,-11) : -11 = 1/3 a + b + c  ..... (1)

pass (2,-16) : -16 = 8/3 a + 2b + c  ..... (2)

slope at (2,-16) is 0 (its tangent parallel to x axis)

at (2 , -16) ax² + b = 0         4a + b = 0         b = -4a   .... (3)

(2) - (1) : -5 = 7/3 a + b = 7/3 a -4a = -5/3 a   ... (4)

3 x (4) : -15 = -5a            a = 3

b = -4a = -4 x 3 = -12

5 0
3 years ago
A semi circle will be rotated 360 about its straight edge. What three dimensional solid will be created as a result of the rotat
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Answer:

Step-by-step explanation:

a sphere

4 0
2 years ago
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Sally has $200 in her savings account last month. She added $35 this month and earned $0.75 interest. What is the percent of the
Phoenix [80]

Answer:

The percentage increase in the amount in her savings is 17.9%

Step-by-step explanation:

The formula for percentage increase is given as,  

Percentage\:Increase=\dfrac{New\:Value-Old\:Value}{Old\:Value}

In previous month, amount of saving in Sally’s account was $200.  

In the current month she added $35 and earned an interest of $0.75. So the total earning in current month will be,  

Total earning = Amount in previous month + Amount added + Interest earned  

Total earning = $ 200 + $ 35 + $ 0.75  

Total earning = $235.75

So, current month amount of saving in account is $ 235.75 which becomes new value and previous month balance that is $ 200 becomes old amount.  

Therefore, New value = $ 235.75 and Old value = $ 200  

Substituting the values in the formula,  

Percentage\:Increase=\dfrac{235.75-200}{200}

Percentage\:Increase=\dfrac{35.75}{200}

Percentage\:Increase=0.17875

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Rounding to nearest tenth means one digit after the decimal place. So, percentage increase is 17.9 %

7 0
2 years ago
A collection of dimes and nickels is worth $5.60. The ratio of dimes to nickels is 3:2. How many dimes and how many nickels are
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Answer:

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Step-by-step explanation:

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A carton of 24 bottles of sports drink costs $16. How many bottles of sports drink can you get
MrRa [10]

Answer:

8

Step-by-step explanation:

24 bottles = 16 dollars!

? bottles = 12 dollars

Note:

In these type of Questions, find out  any dollars you could get with 1 bottle

or in simple terms, (first find the unit Rate)

<em>24/16 = 1.5</em>

1 bottle = 1.5 dollars

? bottles = 12 Dollars?

12/1.5

= 8

<h2>I hope that helps! </h2><h3>Have a wonderful day! </h3>
8 0
3 years ago
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