What is the value of f(−3)?

Which number has the least value?<br><br> 1. 2 3/4<br> 2. 5/2<br> 3. 2.62<br> 4. 245%

Leni [432]

The number with the least value is 2.62

8 0

2 years ago

The sum of twice a first number and five times a second number is 78. If the second number is subtracted from five times the fir

ss7ja [257]

The numbers are: "9" and "12" .
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Explanation:
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Let: "x" be the "first number" ; AND:

Let: "y" be the "second number" .
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From the question/problem, we are given:
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2x + 5y = 78 ; → "the first equation" ; AND:

5x − y = 33 ; → "the second equation" .
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From "the second equation" ; which is:

" 5x − y = 33" ;

→ Add "y" to EACH side of the equation;

   5x − y + y = 33 + y ;

to get: 5x = 33 + y ;

Now, subtract: "33" from each side of the equation; to isolate "y" on one side of the equation ; and to solve for "y" (in term of "x");

5x − 33 = 33 + y − 33 ;

to get: " 5x − 33 = y " ; ↔ " y = 5x − 33 " .
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Note: We choose "the second equation"; because "the second equation"; that is; "5x − y = 33" ; already has a "y" value with no "coefficient" ; & it is easier to solve for one of our numbers (variables); that is, "x" or "y"; in terms of the other one; & then substitute that value into "the first equation".
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Now, let us take "the first equation" ; which is:
"  2x + 5y = 78 " ;
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We have our obtained value; " y = 5x − 33 " .
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We shall take our obtained value for "y" ; which is: "(5x− 33") ; and plug this value into the "y" value in the "first equation"; and solve for "x" ;
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Take the "first equation":
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→ " 2x + 5y = 78 " ; and write as:
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→ " 2x + 5(5x − 33) = 78 " ;
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Note the "distributive property of multiplication" :
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a(b + c) = ab + ac ; AND:

a(b − c) = ab − ac .
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So; using the "distributive property of multiplication:

→ +5(5x − 33) = (5*5x) − (5*33) = +25x − 165 .
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So we can rewrite our equation:

→ " 2x + 5(5x − 33) = 78 " ;

by substituting the: "+ 5(5x − 33) " ; with: "+25x − 165" ; as follows:
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  → " 2x + 25x − 165 = 78 " ;
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→ Now, combine the "like terms" on the "left-hand side" of the equation:

+2x + 25x = +27x ;

Note: There are no "like terms" on the "right-hand side" of the equation.
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→ Rewrite the equation as:
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→ " 27x − 165 = 78 " ;

Now, add "165" to EACH SIDE of the equation; as follows:

→ 27x − 165 + 165 = 78 + 165 ;

→ to get: 27x = 243 ;
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Now, divide EACH SIDE of the equation by "27" ; to isolate "x" on one side of the equation ; and to solve for "x" ;
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27x / 27 = 243 / 27 ;

→ to get: x = 9 ; which is "the first number" .
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Now; Let's go back to our "first equation" and "second equation" to solve for "y" (our "second number"):

2x + 5y = 78 ; (first equation);

5x − y = 33 ; (second equation);
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Start with our "second equation"; to solve for "y"; plug in "9" for "x" ;

→ 5(9) − y = 33 ;

45 − y = 33;

Add "y" to each side of the equation:

45 − y + y = 33 + y ; to get:

45 = 33 + y ;

↔ y + 33 = 45 ; Subtract "33" from each side of the equation; to isolate "y" on one side of the equation ; & to solve for "y" ;

→ y + 33 − 33 = 45 − 33 ;

to get: y = 12 ;

So; x = 9 ; and y = 12 . The numbers are: "9" and "12" .
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To check our work:
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1) Let us plug these values into the original "second equation" ; to see if the equation holds true (with "x = 9" ; and "y = 12") ;

→ 5x − y = 33 ; → 5(9) − 12 =? 33 ?? ; → 45 − 12 =? 33 ?? ; Yes!
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2) Let us plug these values into the original "second equation" ; to see if the equation holds true (with "x = 9" ; and "y = 12") ;

→ 2x + 5y = 78 ; → 2(9) + 5(12) =? 78?? ; → 18 + 60 =? 78?? ; Yes!
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So, these answers do make sense!
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3 0

3 years ago

Make the subject of the formular<br> A=arh <br>C=2Ar<br>

prohojiy [21]

Answer:

Step-by-step explanation:

I think this is it but you question want super clear

A = C/2r

3 0

2 years ago

PLEASE HELPPPPPPPPPP!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

OLga [1]

The set of numbers in the Collatz Conjecture are 1, 4, 2, 1, 4, 2, 1, 4, 2....

<h3>How to generate the numbers in the Collatz Conjecture</h3>

To start with, we make use of the following starting point:

Starting point = 1

The rule is given as:

If the last number is odd, multiply it by 3 and add 1.
If the last number is even, divide the number by 2.

1 is an odd number.

So, we use the first rule

So, we have:

1 * 3 + 1 = 4

4 is an even number.

So, we use the second rule

So, we have:

4/2 = 2

So, the first three numbers in the Collatz Conjecture are:

1, 4, 2

Using the given rules, we have:

1, 4, 2, 1, 4, 2, 1, 4, 2....

The above means that there is only one set of repeating numbers in the Collatz Conjecture.

Hence, the set of numbers in the Collatz Conjecture are 1, 4, 2, 1, 4, 2, 1, 4, 2....