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Lana71 [14]
3 years ago
11

If you know the number of yards for a measurement, you can change that measure to

Mathematics
1 answer:
otez555 [7]3 years ago
7 0

Answer:

f(x) = 0.9144x

Step-by-step explanation:

To convert 3 yards to meters by multiplying 3*0.9144 = 2.7432 meters. This can be done for any number of yards x by writing f(x) = 0.9144x.

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which expressions are equivalent to the first one? I don't understand how to determine that so please explain. Thanks!​
coldgirl [10]

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 ...

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

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

  \dfrac{x+7}{-y}=\boxed{-\dfrac{x+7}{y}}

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

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

__

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

__

<u>Summary</u>: The given expression matches (a) and (b).

_____

<em>Additional comments</em>

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 ...

  \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

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

3 0
2 years ago
There are 10 girls and 5 boys in a classroom. Of
Mazyrski [523]

Answer:

60%

Step-by-step explanation:

If there's 9 people wearing pink out of 15 then your answers 60%

3 0
2 years ago
How do you solve this
PilotLPTM [1.2K]
Since 3=30/10, (30+1)/10=31/10. 31s/10=(30+1)/5 ( we get 30 because 5*6=30) = 31/5. Multiplying both sides by 10, we get 31s=62 (since 5 is a factor of 10, we can do 10/5 =2 and multiply 2 by 31). Dividing both sides by 31, we get s =2
7 0
3 years ago
What does it mean “2 times the difference between 49.5 and 37.5?
TEA [102]

Hello from MrBillDoesMath!  


Answer:

See Discussion below


Discussion:

It means

"two"   "times"       "the difference between 49.5 and 37.5

2           *                   ( 49.5 - 37.5)

this equals 2 * (12) = 24

Thank you,

MrB

4 0
3 years ago
Which three of the following mixed numbers will produce a whole number when added?
Wewaii [24]

Answer:

4\frac{1}{8} , 4\frac{3}{8} , 2\frac{1}{2} = 11

6 0
2 years ago
Read 2 more answers
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