which expressions are equivalent to the first one? I don't understand how to determine that so please explain. Thanks!​

9514 1404 393

Answer:

  (a) -(x+7)/y

  (b) (x+7)/-y

Step-by-step explanation:

There are several ways you can show expressions are equivalent. Perhaps the easiest and best is to put them in the same form. For an expression such as this, I prefer the form of answer (a), where the minus sign is factored out and the numerator and denominator have positive coefficients.

The given expression with -1 factored out is ...

  [tex]\dfrac{-x-7}{y}=\dfrac{1(x+7)}{y}=\boxed{-\dfrac{x+7}{y}} \quad\text{matches A}[/tex]

Likewise, the expression of (b) with the minus sign factored out is ...

  [tex]\dfrac{x+7}{-y}=\boxed{-\dfrac{x+7}{y}}[/tex]

On the other hand, simplifying expression (c) gives something different.

  [tex]\dfrac{-x-7}{-y}=\dfrac{-(x+7)}{-(y)}=\dfrac{x+7}{y} \qquad\text{opposite the given expression}[/tex]

__

Another way you can write the expression is term-by-term with the terms in alpha-numeric sequence (so they're more easily compared).

  Given: (-x-7)/y = (-x/y) +(-7/y)

  (a) -(x+7)/y = (-x/y) +(-7/y)

  (b) (x+7)/(-y) = (-x/y) +(-7/y)

  (c) (-x-7)/(-y) = (x/y) +(7/y) . . . . not the same.

__

Of course, you need to know the use of the distributive property and the rules of signs.

  a(b+c) = ab +ac

  -a/b = a/(-b) = -(a/b)

  -a/(-b) = a/b

__

Summary: The given expression matches (a) and (b).

_____

Additional comments

Sometimes, when I'm really stuck trying to see if two expressions are equal, I subtract one from the other. If the difference is zero, then I know they are the same. Looking at (b), we could compute ...

  [tex]\left(\dfrac{-x-7}{y}\right)-\left(\dfrac{x+7}{-y}\right)=\dfrac{-y(-x-7)-y(x+7)}{-y^2}\\\\=\dfrac{xy+7y-xy-7y}{-y^2}=\dfrac{0}{-y^2}=0[/tex]

Yet another way to check is to substitute numbers for the variables. It is a good idea to use (at least) one more set of numbers than there are variables, just to make sure you didn't accidentally find a solution where the expressions happen to be equal. We can use (x, y) = (1, 2), (2, 3), and (3, 5) for example.

The given expression evaluates to (-1-7)/2 = -4, (-2-7)/3 = -3, and (-3-7)/5 = -2.

(a) evaluates to -(1+7)/2 = -4, -(2+7)/3 = -3, -(3+7)/5 = -2, same as given

(b) evaluates to (1+7)/-2 = -4, (2+7)/-3 = -3, (3+7)/-5 = -2, same as given

(c) evaluates to (-1-7)/-2 = 4, different from given

what is 14/25 as a decimal and as a percent?
​

Please help me ASAP, Im so stuck.

A baseball pitcher won 60% of his games. How many did he win if he pitched 35 games?

9. What is the best model for the data?
Answer choices:
Linear
Exponential
Quadratic

Can someone help me do this.

-unnecessary comments will be reported

Which linear function represents the line given by the point-slope equation y + 7 = -2/3 (x+6)?
O f(x) = -x-11
O fx) = x-1
O f(x) = 2x+3
O fx) = 2x + 13

29) Which equation describes this graph?

graph that contains the points (-2,0) and (8,-10)

A. y=−2x−2
B. y=2+x
C. y=−x
D. y=−2−x

Simplify
6(-5n + 7 thank you

When the balloon touched the wall, it stayed there. What is the best explanation for the balloon staying on the wall? ​

scenario a: get $2,000 deposited into your bank account today, and $50 added each month for a year? make a f(×) function pls​

pls help, i need this in 5 mins!

If 2^3x-1 = 32 then x = (image included)
a. 5
b. -2
c. 2
d. 4/3
e. -4

15-a=20 what value would make this true

BRAINLIEST ASAP NEED HELP ez points
What expression represents the value of v?
A: v=√zy
B: v=√wz
C: v=√w(w+z)
D: v=√z(w+z)

The cost to park a car in a parking lot is $3.45 per hour. Maleek parked his car for 4 hours on Monday and 3 hours on Tuesday. How much did he spend on parking on Monday and Tuesday? Type your answer AND do your best to EXPLAIN why you did the math you did. *

No idea how to do this o

Question
If f(x) = x^2 + 7x and g(x) = 3x - 1, what is f(g(x))?
O 9x2 + x + 1
9x2 + 15x - 6
9x2 + 21x-6
9x2 - 27x
Help please

At the same time of day, a tree and a flagpole cast shadows as shown below.
How tall is the tree?

simplify the expression (-6i)(-6i)​

need help asap please

Find the missing side or angle.
Round to the nearest tenth.
B=18°
C=152°
b=4
c=[ ? ]

The Equation of line K is y=8/7x+3 perpendicular to line k is line L which passes through (-8,3) what is the slope of the equation of line l

I will mark brainliest please help ​

what is the GCF of 4x - 7​

What is the length of segment DB?

what is the slope of the line represented by the equation? ​

What does k equal?
As in y=kx
Pls help

Let p=x^2-2 which equation is equivalent to (x^2-2)^2+18=9x^2-18 in terms of p

Anita made these two statements.
The number 2 is its own opposite.
The opposite of the opposite of 1.5 is 1.5

Fill in the blanks to explain whether theses statements are true or false.

The opposite of 2 is

If you determined that the "k" value of your newly purchased tires is 1.0471264 and your odometer indicates that you have traveled 20,000 miles and you have not recalibrated your cars axle system, how far have you really driven?
A) 19,100 miles
B) 20, 942 miles
C) 209,420 miles
D) 2094.2 miles