Which statement is true?

A student says that the graph of the equation y = 3(x + 8) is the same as the graph of y = 3x, only translated upwards by 8 unit

Wittaler [7]

Given:

A student says that the graph of the equation $y = 3(x + 8)$ is the same as the graph of $y = 3x$ , only translated upwards by 8 units.

To find:

Whether the student is correct or not.

Solution:

Initial equation is

$y=3x$

$f(x)=3x$

Equation of after transformation is

$y=3(x+8)$

$g(x)=3(x+8)$

Now,

$g(x)=f(x+8)$ ...(i)

The translation is defined as

$g(x)=f(x+a)+b$ ...(ii)

Where, a is horizontal shift and b is vertical shift.

If a>0, then the graph shifts a units left and if a<0, then the graph shifts a units right.

If b>0, then the graph shifts b units up and if b<0, then the graph shifts b units down.

From (i) and (ii), we get

$a=8\text{ and }b=0$

Therefore, the graph of $y=3x$ translated left by 8 units. Hence, the student is wrong.

8 0

2 years ago

8x + 7 equals -9 solve for x

Montano1993 [528]

The answer to this equation is
x= (1/4)

8 0

3 years ago

I need help with a problem with solving by square roots in quadratic equation.

Readme [11.4K]

To solve for x, first, we add 3 to the given equation:

$\begin{gathered} 2(x+5)^2-3+3=44+3, \\ 2(x+5)^2=47. \end{gathered}$

Dividing by 2, we get:

$(x+5)^2=\frac{47}{2}.$

Therefore:

$x+5=\pm\sqrt{\frac{47}{2}}.$

Finally, subtracting 5 we get:

$x=\pm\sqrt{\frac{47}{2}}-5.$

Answer:

$x=\operatorname{\pm}\sqrt{\frac{47}{2}}-5.$

4 0

1 year ago

What was the total production of gasoline and kerosene combined (in Barrels)

Elina [12.6K]

The amount of kerosene and gasoline produced is an illustration of equations.

44.4 million barrels of gasoline and kerosene are produced

Let

$x \to$ Proportion of kerosene

$y \to$ Proportion of Gasoline

So:

$x = 40\%$

$y = 34\%$

$Total = 60\ million$ ---- total barrels produced

The amount of Kerosene produced is:

$Kerosene =x \times Total$

$Kerosene =40\% \times 60\ million$

$Kerosene = 24\ million$

The amount of Gasoline produced is:

$Gasoline =y \times Total$

$Gasoline =34\% \times 60\ million$

$Gasoline =20.4\ million$

So, the total production of both is:

$Total = Kerosene + Gasolene$

$Total = 24\ million + 20.4\ million$

$Total = 44.4 million$

Hence, 44.4 million barrels of gasoline and kerosene are produced

Read more about equations at:

brainly.com/question/21105092

8 0

2 years ago

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

2 years ago