MATHEMATICS HIGH SCHOOL

solve by substitution ( show steps)

y=3x+2

3x-y=2

Answers

Answer 1
Answer: \left\{\begin{array}{ccc}y=3x+2\n3x-y=2\end{array}\right\n\nsubstitute\n\n3x-(3x+2)=2\n3x-3x-2=2\n-2=2-FALSE\n\nAnswer:No\ solution
Answer 2
Answer: y=3x+2\n 3x-y=2\n\n 3x-(3x+2)=2\n 3x-3x-2=2\n -2=2\n x\in\emptyset \Rightarrow y\in\emptyset

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What is the 23rd term of the arithmetic sequence where a1 = 8 and a9 = 48?

Answers

Answer:

23rd term of the arithmetic sequence is 118.

Step-by-step explanation:

In this question we have been given first term a1 = 8 and 9th term a9 = 48

we have to find the 23rd term of this arithmetic sequence.

Since in an arithmetic sequence

T_(n)=a+(n-1)d

here a = first term

n = number of term

d = common difference

since 9th term a9 = 48

48 = 8 + (9-1)d

8d = 48 - 8 = 40

d = 40/8 = 5

Now T_(23)= a + (n-1)d

= 8 + (23 -1)5 = 8 + 22×5 = 8 + 110 = 118

Therefore 23rd term of the sequence is 118.

the population of mastertown was 23,000 in 2012. assume that mastertowns population increases at a rate of 2% per year. write an equation to model the population of mastertown (y) based on numbers of years since 2012 (x)

Answers

So, after one year will will have the new population of 23 000 * (100 %+2%)
(the 100 % is the old population and the 2% is the increase), that is:

23000*1.02=23460

(102 % can be represented as 1.02)

And for the next years, we have to repeat the procedure.

a more generic rule would be:

y=23000*1.02^(x) (x is the number of years passed)

The vertex of this parabola is at (-3, 6). Which of the following could be its equation? A. y = -3(x + 3)2 + 6
B. y = -3(x + 3)2 - 6
C. y = -3(x - 3)2 + 6
D. y = -3(x - 3)2 - 6

Answers

nice, already in vertex form
y=a(x-h)^2+k
(h,k) is vertex

therfor since (-3,6) is vertex
we are looking for something like
y=a(x-(-3))^2+6 simplified to
y=a(x+3)^2+6


A is ansre
So,

The vertex form of a parabola is:

y=a(x-h)^2+k

and the vertex is at (h,k).

Thus, the equation will have to look something like this:

y=a(x+3)^2+6

Only option A matches these criteria, so is must be the correct option.

What is the sum of the first 50 natural numbers? How to solve it without adding 50 digits?

Answers

1+2+3+4+5+\dots+50\n\n1;\ 2;\ 3;\ 4;\ 5;\dots;50\ are\ the\ terms\ of\ a\ arithmetic\ sequence\nwhere\ a_1=1\ and\ d=1\n\nSum:S_n=(a_1+a_n)/(2)\cdot n\n\nS_(50)=(1+50)/(2)\cdot50=51\cdot25=1275\leftarrow solution
Look at the first one and the last one:                  1 + 50 = 51
Look at the second one and the second-last one:  2 + 49 = 51
Look at the third one and the third-last one:           3 + 48 = 51

Every pair you construct in this way adds up to 51 .

There are ( 50/2 ) = 25 pairs.

They all add up to ( 25 pairs ) x ( 51 per pair ) = 1,275

If k = 23 and m
-14, what is ✓k + m?
Submit

Answers

Answer:

3

Step-by-step explanation:

Evaluate:

Sqrt of k = 32 + m = -14

Sqrt of 32-14 = 9

Sqrt of 9 = 3

Therefore, our answer is 3!

Btw sqrt means: square root

Hope this helps! Have a good day!

Add 3/7 + 4/5 please helppppp me

Answers

Answer: 43/35

Reasoning: You need the denominators to equal the same to add or subtract them
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