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irina [24]
3 years ago
12

Simplify the following expression and state the excluded values m+7/m^2+4m-21

Mathematics
2 answers:
insens350 [35]3 years ago
7 0
Answer:     1 / (m−3) ;  m ≠ -3, 7 .
_____________________________________
Explanation:
________________________________________
Given:
________________________________________
<span>(m+7) / (m</span>² <span>+ 4m</span> − 21) ; Simplify the expression ;
____________________________________________
In the "denominator" :  " m² + 4m − 21 "  ; see if we can factor out an 
  "(m+7)" which is in the 'numerator' ;
________________________________________
        m² + 4m − 21 = (m+7) (m−3) ;  Yes!
___________________________________________
So, rewrite the original problem as:
___________________________________________
       (m+7) / [(m+7)(m−3)] ; and the "(m−7)" in both the numerator AND the denominator "cancel out" to "1";  since anything divided by that same number equals "1" ;
___________________________________________

So we rewrite the expression:
__________________________________________
   1 / (m−3) ; m ≠ -3, 7 .
_____________________________________________

erastova [34]3 years ago
4 0
5m-14/(m+1)(m-1)

excluded values: 1,-1
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Answer:

Using 5.25 cups of flour would make 3 batches of cookies. He made 180 cookies.

Step-by-step explanation:

To see how many batches you make all you do is take the 5.25 and divide it by 1.75 because thats how much it takes to make 1. When you divide it you get 3. If there are 5 dozen in each batch thats 60 cookies because 1 dozen is 12. Then,since he made 3 batches you multiply the 60 by 3 and you get 180.

Hope this helps!

4 0
3 years ago
Ginny is studying a population of frogs. She determines that the population is decreasing at an average rate of 3% per year. Whe
svp [43]

Answer:

Step-by-step explanation:

This is exponential, of the form

y=a(b)^x where a is the initial amount and b is the growth/decay rate. If Ginny begins the study with 1200 frogs in the population, our a value is 1200.

If the population is decreasing 3% per year, it is decreasing 100% - 3% = 97% which, as a decimal, is .97. Our exponential function, then, is

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6 0
3 years ago
Evaluate C_n.xP^xQn-x For the given n=7, x=2, p=1/2
r-ruslan [8.4K]

Answer:

The value of given expression is \frac{21}{128}.

Step-by-step explanation:

Given information: n=7, x=2, p=1/2

q=1-p=1-\frac{1}{2}=\frac{1}{2}

The given expression is

C(n,x)p^xq^{n-x}

It can be written as

^nC_xp^xq^{n-x}

Substitute n=7, x=2, p=1/2 and q=1/2 in the above formula.

^7C_2(\frac{1}{2})^2(\frac{1}{2})^{7-2}

\frac{7!}{2!(7-2)!}(\frac{1}{2})^2(\frac{1}{2})^{5}

\frac{7!}{2!5!}(\frac{1}{2})^{2+5}

\frac{7\times 6\times 5!}{2\times 5!}(\frac{1}{2})^{2+5}

21(\frac{1}{2})^{7}

\frac{21}{128}

Therefore the value of given expression is \frac{21}{128}.

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3 years ago
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3 years ago
What is the sum of all integers x that satisfy 1 &lt; (pi -1 )x &lt; 10?
DedPeter [7]

Answer:

10

Step-by-step explanation:

pi is 3.14...

pi - 1 is 2.14...

question becomes 1<2.14x and 2.14x < 10

1/2.14 < x, 0.46... < x

x < 10/2.14, x < 4.67...

combining

0.46< x < 4.67

x can be 1, 2, 3, 4

3 0
3 years ago
Read 2 more answers
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