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zzz [600]
2 years ago
9

Find the missing term.

Mathematics
1 answer:
igor_vitrenko [27]2 years ago
5 0

Equations are used to relate equal expressions.

The missing term is: \mathbf{  m -1}

The equation is given as:

\mathbf{\frac{m - n}{m^2 - n^2} + \frac{?}{(m -1)(m -n)} = \frac{2m}{m^2 - n^2}}

Express \mathbf{m^2 - n^2\ as\ (m - n)(m + n)}

So, we have:

\mathbf{\frac{m - n}{(m - n)(m + n)} + \frac{?}{(m -1)(m -n)} = \frac{2m}{(m - n)(m + n)}}

Multiply through by \mathbf{m - n}

\mathbf{\frac{m - n}{m + n} + \frac{?}{m -1} = \frac{2m}{m + n}}

Collect like terms

\mathbf{ \frac{?}{m -1} = \frac{2m}{m + n} - \frac{m - n}{m + n}}

Take LCM

\mathbf{ \frac{?}{m -1} = \frac{2m - m + n}{m + n} }

\mathbf{ \frac{?}{m -1} = \frac{m + n}{m + n} }

Divide \mathbf{ \frac{m + n}{m + n} }

\mathbf{ \frac{?}{m -1} = 1}

Cross multiply

\mathbf{ ? =(m -1)\times 1}

\mathbf{ ? =m -1}

Hence, the missing term is: \mathbf{  m -1}

Read more about equations at:

brainly.com/question/15668451

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Find the exponential function that satisfies the given conditions: Initial value = 64, decreasing at a rate of 0.5% per week
mrs_skeptik [129]

Answer:

Step-by-step explanation:

An exponential function is of the form

y=ab^x

where a is the initial value and b is the growth/decay rate.  Our initial value is 64.  That's easy to plug in.  It goes in for a.  So the first choice is out.  Considering b now...

If the rate is decreasing at .5% per week, this means it still retains a rate of

100% - .5% = 99.5%

which is .995 in decimal form.

b is a rate of decay when it is greater than 0 but less than 1; b is a growth rate when it is greater than 1.   .995 is less than 1 so it is a rate of decay.  The exponential function is, in terms of t,

f(t) = 64(.995)^t

4 0
3 years ago
X/a+x/b=1<br>make x the subject of the formular​
monitta

Answer:

x = \frac{ab}{b+a}

Step-by-step explanation:

Given

\frac{x}{a} + \frac{x}{b} = 1

Multiply through by ab to clear the fractions

bx + ax = ab ← factor out x from each term on the left side

x(b + a) = ab ← divide both sides by (b + a)

x = \frac{ab}{b+a}

8 0
3 years ago
Which describes the graph of y=(x+3)^2-4?
worty [1.4K]
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8 0
3 years ago
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I need help with the equation.
natulia [17]

Answer:

(x - 3)² + (y + 9)² = 25

Step-by-step explanation:

The equation of a circle in standard form is

(x - h)² + (y - k)² = r²

where (h, k ) are the coordinates of the centre and r is the radius

Given area = 25π , that is

πr² = 25π ( divide both sides by π )

r² = 25 ( take the square root of both sides )

r = \sqrt{25} = 5

With centre (h, k) = (3, - 9 ) and r = 5 , then

(x - 3)² + (y - (- 9) )² = 5² , that is

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8 0
3 years ago
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A number m is no less than –1 or less than or equal to −5.
Law Incorporation [45]

Answer:

-1 < m ≤ - 5

Step-by-step explanation:

Your expression includes: m, -1, -5, >, ≤

m is the value being compared so it will be in the middle.

# sign m sign #

m is no less than -1: no less than means it is greater than -1, but does not include -1. Therefore, our sign is >

m > -1

m is less than or equal to -5. This means we use ≤ because it can equal -5.

m ≤ -5

Now combine the two expressions

m > -1 – This can also be written as -1 < m.

m ≤ -5

-1 < m ≤ - 5

7 0
3 years ago
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