3 3
7
Which expression is equivalent to
7
-2
:
.?
4.
A
.
1 7
2 -2
27
1 2
2 7
B
1
-2
-1
D
2
-2

 The correct answer is:

______________

            →   Choice: [C]:  "   " .

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Step-by-step explanation:

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Note that this problem contains multiplication and division.

 WIth multiplication and division;

the order of operations we perform is from "left side to right side" in the expression;  in the order in which the operation occurs:

As such:

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The given problem:

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"   ÷ " ;

Is treated as:

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" ÷ " ;

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So, we start with:

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" " ;

______________

→ ;  

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Simplify:

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"   " ;

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          →  The "(-1)'s " cancel out:

              {since: "(-1)/(-1) = 1 "} ;

→ And we have:  " " ;

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Now, continue with the problem, and divide this value by: " " ;

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 " ÷ " ;

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Note that dividing by a number is the same as multiplying by the reciprocal of that said number:

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The reciprocal of " " ; is:  " : l

As such:

" ÷ " ;

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     =   "    "

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Now, let us simplify:

 Note:  The "8" and the "-8" ;

    The "8" can be changed to "1" ; and the "-8" can be changed to "-1" ;

since: "-8 ÷ 8 = 1 " ;  and since:  "8 ÷ 8 = 1 " ;

Note:  The "3" and the "21" ;

    The "3" can be changed to "1";  and the "21" can be changed to "7" ;

since: "21 ÷ 3 = 7 " ; and since:  "3 ÷ 3 = 1 " ;

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And we can we rewrite the expression:

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 → " " ;

which equals:  " 7 * -1 " ;  which equals " - 7 ".

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Now, the problem has 4 (four) answer choices.  Which expression [i.e. which answer choice] is equal to:  " -7 " ??

______________

Consider Choice [A]: " " ; which equals: " " ;

" ."

Rule out: "Choice [A]."

______________

Consider Choice: [B]: " " ; which equals: " ; " ."

Rule out: "Choice: [B]."

______________

Consider Choice: [C]: " " ; which equals: " ;  " ".  

 Choice [C]: seems correct!

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Consider Choice: [D]: " " ; which equals:

                           " ;

                                              → cancel out the "(-1)'s" ;

                                              → {since: "(-1) / (-1) = 1 " ;  

                                         to get:

                                              → " " ; which equals:

                                              → " " ;  " . "

 Rule out: "Choice: [D]."

______________

The correct answer is:

______________

Choice: [C]:  "   " .

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Hope this is helpful to you!

Wishing you the best!

______________

for any of you who need the translation here it is

step-by-step explanation:

find the angular size of the equatorial radius of the earth, if the horizontal parallax of the sun

1. f(x)=x²+10x+16

use the formula to find the vertex = (-b/2a, f(-b/2a)) , here in the above equation a=1(as, a> 0 the parabola is open upward), b=10. by putting the values.

-b/2a = -10/2(1) = -5

f(-b/2a)= f(-5)= (-5)²+10(-5)+16= -9

so, vertex = (-5, -9)

now, find y- intercept put x=0 in the above equation. f(0)= 0+0+16, we get point (0,16).

now find x-intercept put y=0 in the above equation. 0= x²+10x+16

x²+10x+16=0 ⇒x²+8x+2x+16=0 ⇒x(x+8)+2(x+8)=0 ⇒(x+8)(x+2)=0 ⇒x=-8 , x=-2

from vertex, y-intercept and x-intercept you can easily plot the graph of given parabolic equation. the graph is attached below.

2. f(x)=−(x−3)(x+1)

by multiplying the factors, the general form is f(x)= -x²+2x+3.

use the formula to find the vertex = (-b/2a, f(-b/2a)) , here in the above equation a=-1(as, a< 0 the parabola is open downward), b=2. by putting the values.

-b/2a = -2/2(-1) = 1

f(-b/2a)= f(1)=-(1)²+2(1)+3= 4

so, vertex = (1, 4)

now, find y- intercept put x=0 in the above equation. f(0)= 0+0+3, we get point (0, 3).

now find x-intercept put y=0 in the above equation. 0= -x²+2x+3.

-x²+2x+3=0 the factor form is already given in the question so, ⇒-(x-3)(x+1)=0 ⇒x=3 , x=-1

from vertex, y-intercept and x-intercept you can easily plot the graph of given parabolic equation. the graph is attached below.

3. f(x)= −x²+4

use the formula to find the vertex = (-b/2a, f(-b/2a)) , here in the above equation a=-1(as, a< 0 the parabola is open downward), b=0. by putting the values.

-b/2a = -0/2(-1) = 0

f(-b/2a)= f(0)= −(0)²+4 =4

so, vertex = (0, 4)

now, find y- intercept put x=0 in the above equation. f(0)= −(0)²+4, we get point (0, 4).

now find x-intercept put y=0 in the above equation. 0= −x²+4

−x²+4=0 ⇒-(x²-4)=0 ⇒ -(x-2)(x+2)=0 ⇒x=2 , x=-2

from vertex, y-intercept and x-intercept you can easily plot the graph of given parabolic equation. the graph is attached below.

4. f(x)=2x²+16x+30

use the formula to find the vertex = (-b/2a, f(-b/2a)) , here in the above equation a=2(as, a> 0 the parabola is open upward), b=16. by putting the values.

-b/2a = -16/2(2) = -4

f(-b/2a)= f(-4)= 2(-4)²+16(-4)+30 = -2

so, vertex = (-4, -2)

now, find y- intercept put x=0 in the above equation. f(0)= 0+0+30, we get point (0, 30).

now find x-intercept put y=0 in the above equation. 0=2x²+16x+30

2x²+16x+30=0 ⇒2(x²+8x+15)=0 ⇒x²+8x+15=0 ⇒x²+5x+3x+15=0 ⇒x(x+5)+3(x+5)=0 ⇒(x+5)(x+3)=0 ⇒x=-5 , x= -3

from vertex, y-intercept and x-intercept you can easily plot the graph of given parabolic equation. the graph is attached below.

5. y=(x+2)²+4

the general form of parabola is y=a(x-h)²+k , where vertex = (h,k)

if a> 0 parabola is opened upward.

if a< 0 parabola is opened downward.

compare the given equation with general form of parabola.

-h=2 ⇒h=-2

k=4

so, vertex= (-2, 4)

as, a=1 which is greater than 0 so parabola is opened upward and the graph has minimum.

hope this : )