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rusak2 [61]
3 years ago
14

Find the midpoint of the segment with the given endpoints. (3,- 9) and (4, -8)

Mathematics
1 answer:
frez [133]3 years ago
3 0
  • (3,-9)
  • (4,-8)

\boxed{\sf (x,y)=\left(\dfrac{x_1+x_2}{2},\dfrac{y_1+y_2}{2}\right)}

\\ \sf\longmapsto \left(\dfrac{3+4}{2},\dfrac{-9+8}{2}\right)

\\ \sf\longmapsto \left(\dfrac{7}{2},\dfrac{-1}{2}\right)

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Find the values of x for which the combined function h(x) = is undefined if f(x) = 5x + 1 and g(x) = x2 - 9.
Rama09 [41]
We need to know the definition of the "combined function" h(x).  I'm going to guess--by looking at answers--that the function is h(x)=\frac{f(x)}{g(x)} making it

h(x)=\frac{5x+1}{x^2-9}

This function is undefined wherever the denominator is equal to 0 (division by zero is undefined).  Factor the denominator.

h(x)=\frac{5x+1}{(x+3)(x-3)}

The two values of x that make the denominator 0 are 3 and -3, otherwise written x=\pm 3.
5 0
3 years ago
Which of the following could be the equation of the graph shown below? Check all that apply.
Mashutka [201]

Answer:

y = -2x + 5

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2x + y = 4

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8 0
3 years ago
Prove by mathematical induction that 1+2+3+...+n= n(n+1)/2 please can someone help me with this ASAP. Thanks​
Iteru [2.4K]

Let

P(n):\ 1+2+\ldots+n = \dfrac{n(n+1)}{2}

In order to prove this by induction, we first need to prove the base case, i.e. prove that P(1) is true:

P(1):\ 1 = \dfrac{1\cdot 2}{2}=1

So, the base case is ok. Now, we need to assume P(n) and prove P(n+1).

P(n+1) states that

P(n+1):\ 1+2+\ldots+n+(n+1) = \dfrac{(n+1)(n+2)}{2}=\dfrac{n^2+3n+2}{2}

Since we're assuming P(n), we can substitute the sum of the first n terms with their expression:

\underbrace{1+2+\ldots+n}_{P(n)}+n+1 = \dfrac{n(n+1)}{2}+n+1=\dfrac{n(n+1)+2n+2}{2}=\dfrac{n^2+3n+2}{2}

Which terminates the proof, since we showed that

P(n+1):\ 1+2+\ldots+n+(n+1) =\dfrac{n^2+3n+2}{2}

as required

4 0
3 years ago
On the day of his 18th birthday harry decided to start saving money regularly
Veseljchak [2.6K]

We have been given that on the day of his 18th birthday Harry decided to start saving money regularly . Starting on that day, he could save 30.00 on the same date every month. We are asked to find the amount saved by the day before Harry's 60th birthday.

First of all, we will find years from 18 years to 60 years.

\text{Years}=60-18=42

We know that 1 year equals 12 months.

\text{42 years}=12\times 42\text{ Months}=504\text{ Months}

To find total amount saved, we will multiply 504 months by amount saved per month.

\text{Total amount saved}=\$30\times 504

\text{Total amount saved}=\$15,120

Therefore, Harry would have saved \$15,120 by the day before his 60th birthday.

3 0
3 years ago
Kory calculated several numbers in his calculator. The result displayed 1.3E-2 on the calculator screen. Which equivalent number
frosja888 [35]

Answer:

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Step-by-step explanation:

Many calculators use "E" to signify "×10^( )". Thus ...

... 1.3E-2 = 1.3×10^(-2)

This number in scientific notation is equivalent to the standard form number ...

... 1.3×0.01 = 0.013

5 0
3 years ago
Read 2 more answers
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