Please solve these questions. (Geometry)

A+b=180 A=-2x+115 B=-6x+169 What is the value of B?

natulia [17]

The answer is: " 91 " .
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→ " B = 91 " .
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Explanation:
__________________________________________________
Given:
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" A + B = 180 " ;

"A = -2x + 115 " ; ↔ A = 115 − 2x ;

"B = - 6x + 169 " ; ↔ B = 169 − 6x ;
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METHOD 1)
_____________________________________________________
Solve for "x" ; and then plug the solved value for "x" into the expression given for "B" ; to solve for "B"
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(115 − 2x) + (169 − 6x) =

115 − 2x + 169 − 6x = ?

→ Combine the "like terms" ; as follows:

+ 115 + 169 = + 284 ;

− 2x − 6x = − 8x ;
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And rewrite as:

" − 8x + 284 " ;
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→ " - 8x + 284 = 180 " ;

Subtract: "284" from each side of the equation:

 → " - 8x + 284 − 284 = 180 − 284 " ;

to get:

→ " -8x = -104 ;

Divide EACH SIDE of the equation by "-8 " ;
to isolate "x" on one side of the equation; & to solve for "x" ;

→ -8x / -8 = -104/-8 ;

→ x = 13
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Now, to find the value of "B" :
__________________________________________________________
 "B = - 6x + 169 " ; ↔ B = 169 − 6x ;

↔ B = 169 − 6x ;

= 169 − 6(13) ; ===========> Plug in our "solved value, "13", for "x" ;

= 169 − (78) ;

= 91 ;

 B = " 91 " .
__________________________________________________
The answer is: " 91 " .
____________________________________________________
→ " B = 91 " .
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Now; let us check our answer:
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→ A + B = 180 ;
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Plug in our "solved answer" ; which is "91", for "B" ; as follows:
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→ A + 91 = ? 180? ;

↔ A = ? 180 − 91 ? ;

→ A = ? -89 ? Yes!
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→ " A = -2x + 115 " ; ↔ A = 115 − 2x ;

Plug in our solved value for "x"; which is: "13" ;

" A = 115 − 2x " ;

→ A = ? 115 − 2(13) ? ;

→ A = ? 115 − (26) ? ;

→ A = ? 29 ? Yes!
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METHOD 2)
_________________________________________________
Given:
__________________________________________________
" A + B = 180 " ;

"A = -2x + 115 " ; ↔ A = 115 − 2x ;

"B = - 6x + 169 " ; ↔ B = 169 − 6x ;

→ Solve for the value of "B" :
_______________________________________________________
A + B = 180 ;

→ B = 180 − A ;

→ B = 180 − (115 − 2x) ;

→ B = 180 − 1(115 − 2x) ; ==========> {Note the "implied value of "1" } ;
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Note the "distributive property" of multiplication:__________________________________________________ a(b + c) = ab + ac ; AND:
a(b − c) = ab − ac .________________________________________________________
Let us examine the following part of the problem:
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→ " − 1(115 − 2x) " ;
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→ " − 1(115 − 2x) " = (-1 * 115) − (-1 * 2x) ;

= -115 − (-2x) ;

= -115 + 2x ;
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So we can bring down the: " {"B = 180 " ...}" portion ;

→and rewrite:
_____________________________________________________

→ B = 180 − 115 + 2x ;

→ B = 65 + 2x ;
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Now; given: "B = - 6x + 169 " ; ↔ B = 169 − 6x ;

→ " B = 169 − 6x = 65 + 2x " ;
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→ " 169 − 6x = 65 + 2x "

Subtract "65" from each side of the equation; & Subtract "2x" from each side of the equation:

→ 169 − 6x − 65 − 2x = 65 + 2x − 65 − 2x ;

to get:

→ " - 8x + 104 = 0 " ;

Subtract "104" from each side of the equation:

→ " - 8x + 104 − 104 = 0 − 104 " ;

to get:

→ " - 8x = - 104 ;

Divide each side of the equation by "-8" ;
to isolate "x" on one side of the equation; & to solve for "x" ;

→ -8x / -8 = -104 / -8 ;

to get:

→ x = 13 ;
______________________________________________________

Now, let us solve for: " B " ; → {for which this very question/problem asks!} ;

→ B = 65 + 2x ;

Plug in our solved value, " 13 ", for "x" ;

→ B = 65 + 2(13) ;

= 65 + (26) ;

→ B = " 91 " .
_______________________________________________________
Also, check our answer:
_______________________________________________________
Given: "B = - 6x + 169 " ; ↔ B = 169 − 6x = 91 ;

When "x = 13 " ; does: " B = 91 " ?

→ Plug in our "solved value" of " 13 " for "x" ;

→ to see if: "B = 91" ; (when "x = 13") ;

→ B = 169 − 6x ;

= 169 − 6(13) ;

= 169 − (78)______________________________________________________
→ B = " 91 " .
______________________________________________________

6 0

3 years ago

The table represents a linear function.

Alona [7]

Answer: -6

See attached picture

6 0

3 years ago

A parallelogram has an area of 60 square inches. If the base of the parallelogram is 12 inches, what is the height of the parall

Vikentia [17]

How to find the area of a parallelogram is length times height. 12 times what gets you to 60? 5 does. 12 times 5 is 60.

HEIGHT: 5

8 0

3 years ago

There are nickels, dimes, quarters in a large piggy bank, for every 2 nickels there are 3 dimes, for every 2 dimes there are 5 q

Alex

There are 80 nickels and 120 dimes and 300 quarters in piggy bank

Solution:

Given that,

For every 2 nickels there are 3 dimes ,

So, ratio of nickel to dime will be 2 : 3

Also for every 2 dimes there are 5 quarters

So, ratio of dime to quarters is 2 : 5

Let us first find the ratio of nickles to dimes to quarters

nickel : dime = 2 : 3

dime : quarters = 2 : 5

$\frac{nickel}{dime} = \frac{2}{3}$

$nickel = \frac{2}{3} dime$

$\frac{dime}{quarter} = \frac{2}{5}$

$quarter = \frac{5}{2}dime$

So,

$nickel : dime : quarter = \frac{2}{3}dime : dime : \frac{5}{2}dime\\\\nickel : dime : quarter = \frac{2}{3} : 1 : \frac{5}{2}\\\\nickel : dime : quarter = 4 : 6 : 15$

Thus nickel : dime : quarters = 4 : 6 : 15

Now, let the number of nickel be 4x

Let the number of dimes be 6x

Let the number of quarters be 15x

From given question,

There are 500 coins in all.

number of nickel + number of dimes + number of quarters = 500

4x + 6x + 15x = 500

25x = 500

x = 20

Thus,

number of nickel = 4x = 4(20) = 80

number of dimes = 6x = 6(20) = 120

number of quarters = 15x = 15(20) = 300

Thus there are 80 nickels and 120 dimes and 300 quarters in piggy bank

3 0

3 years ago

Ratio Question;

SashulF [63]

*Given

Money of Phoebe - 3 times as much as Andy

Money of Andy - 2 times as much as Polly

Total money of Phoebe, - £270

Andy and Polly

*Solution

Let

B - Phoebe's money

A - Andy's money

L - Polly's money

1. The money of the Phoebe, Andy, and Polly, when added together would total £270. Thus,

B + A + L = £270 (EQUATION 1)

2. Phoebe has three times as much money as Andy and this is expressed as

B = 3A

3. Andy has twice as much money as Polly and this is expressed as

A = 2L (EQUATION 2)

4. This means that Phoebe has ____ as much money as Polly,

B = 3A

B = 3 x (2L)

B = 6L (EQUATION 3)

This step allows us to eliminate the variables B and A in EQUATION 1 by expressing the equation in terms of Polly's money only.

5. Substituting B with 6L, and A with 2L, EQUATION 1 becomes,

6L + 2L + L = £270

9L = £270

L = £30

So, Polly has £30.

6. Substituting L into EQUATIONS 2 and 3 would give us the values for Andy's money and Phoebe's money, respectively.

A = 2L

A = 2(£30)

A = £60

Andy has £60

B = 6L

B = 6(£30)

B = £180

Phoebe has £180

Therefore, Polly's money is £30, Andy's is £60, and Phoebe's is £180.

3 0

3 years ago