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3 years ago

Twice a number is equal to 35 more than 7 times the number. Find the number.

Mathematics

2 answers:

masya89 [10]3 years ago

7 0

Answer:

-7

Step-by-step explanation:

make an equation-

2x=35+7x

-5x=35

x=-7

nikklg [1K]3 years ago

7 0

Answer:

-7

Step-by-step explanation:

number - n

Twice a number - 2n

Seven times the number - 7n

2n = 7n +35

7n-2n = -35

5n = -35

n = - 7

Check:

2(-7) = 7(-7) +35

-14 = -49 + 35

-14 = -14 True

The number is (- 7).

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

natulia [17]

The answer is: " 91 " .
___________________________________________________
→ " B = 91 " .
__________________________________________________

Explanation:
__________________________________________________
Given:
__________________________________________________
" A + B = 180 " ;

"A = -2x + 115 " ; ↔ A = 115 − 2x ;

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

(115 − 2x) + (169 − 6x) =

115 − 2x + 169 − 6x = ?

→ Combine the "like terms" ; as follows:

+ 115 + 169 = + 284 ;

− 2x − 6x = − 8x ;
_________________________________________________________
And rewrite as:

" − 8x + 284 " ;
_________________________________________________________
→ " - 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
__________________________________________________________
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 " .
____________________________________________________
Now; let us check our answer:
____________________________________________________
→ A + B = 180 ;
____________________________________________________
Plug in our "solved answer" ; which is "91", for "B" ; as follows:
________________________________________________________

→ A + 91 = ? 180? ;

↔ A = ? 180 − 91 ? ;

→ A = ? -89 ? Yes!
________________________________________________________
→ " 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!
_________________________________________________
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" } ;
__________________________________________________________
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:
________________________________________________________
→ " − 1(115 − 2x) " ;
________________________________________________________

→ " − 1(115 − 2x) " = (-1 * 115) − (-1 * 2x) ;

= -115 − (-2x) ;

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

→and rewrite:
_____________________________________________________

→ B = 180 − 115 + 2x ;

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

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

1. Determine if the two expressions are equivalent and explain your reasoning.

Elena-2011 [213]

1. Yes because of the constant and coefficient if you add it. Like the answer is 5m +4.

6 0

3 years ago

How many tiles are added to each figure in the tile pattern shown above

DENIUS [597]

Answer:

4 tiles are added to each figure in the tile pattern.

6 0

3 years ago

The area of the regular pentagon is 6.9 cm2. What is the perimeter? 2 cm 5 cm 10 cm 20 cm

disa [49]

Given

Area of the regular pentagon is 6.9 cm².

Find out the perimeter of a regular pentagon

To proof

Formula

Area of regular pentagon is

$= \frac{1}{4}\sqrt{5(5+2\sqrt{5})}\ a^{2}$

As given in the question

area of regular pentagon = 6.9 cm²

now equating the area value with the area formula.

$6.9 =\frac{1}{4}\sqrt{5(5+2\sqrt{5})} a^{2}$

Now put

√5 = 2.24 ( approx)

put in the above equation

$\frac{6.9\times 4}{\sqrt{5(5+2\times2.24)}}=a^{2}\\\frac{27.6}{\sqrt{47.4}}=a^{2}\\\frac{27.6}{6.88}=a^{2}$

thus

a² = 4.01

a = √ 4.01

a = 2.0 cm ( approx)

As perimeter represented the sum of all sides.

i.e regular pentagon have five sides of equal length.

Thus

perimeter of the regular pentagon = 5 × side length

= 5 ×2.00

therefore the perimeter of the regular pentagon = 10cm

option c is correct

Hence proved

3 0

3 years ago

Read 2 more answers

Write a division expression that could also be solved by using 1/2x9?

aleksandrvk [35]

Answer:

18 divided by 4.

Step-by-step explanation:

1/2x9= 4 1/2 and when you divide 18 divided by 4 you get 4 1/2 (4.5)

8 0

3 years ago