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2 years ago

Solve the system by graphing. Y=2x-9 y=-2x-1

Mathematics

1 answer:

sattari [20]2 years ago

4 0

Answer:

(2,-5)

Step-by-step explanation:

See attachment

One can also solve this by calculation:

y=2x-9

y=-2x-1

Rearrange either equation to find x. I'll use the first:

y=2x-9

2x = y+9

x = (y+9)/2

Now use this value of x in the second equation:

y = -2x-1

y =-2((y+9)/2)-1

y = (-2y-18)/2)-1

y = -y -9 - 1

2y = -10

y = -5

Now use -5 for y in the rearranged equation:

y = -2x-1

-5 = -2x-1

-2x = -4

x = 2

Solution is (2,-5)

But the question wants a graph solution, which is also fun when you use DESMOS.

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Write a recursive formula for each sequence given or described below.

valentinak56 [21]

Answer:

$a_{n} =a_{n-1} +3000$ and a₁ =30000 for n = 2,3,4,5,6, ......

Step-by-step explanation:

Doug has joined a job with a starting salary of $30000 per year.

Hence, if a₁ is the salary of Doug in the first year, then

a₁ =30000

Now, each year Doug will receive a raise of $3000 in his salary.

Hence, in the 2nd year, his salary(a₂) will become ( a₁ +3000) per year.

Again, in the 3rd year, his salary(a₃) will become ( a₂ +3000) per year.

Therefor, in the similar manner the recursive formula for his salary in each year will be given as $a_{n} =a_{n-1} +3000$ and a₁ =30000 for n = 2,3,4,5,6, ...... {aₙ is the yearly salary of Doug in the nth year} (Answer)

7 0

3 years ago

You place the spring vertically with one end on the floor. You then drop a book of mass 1.50 kg onto it from a height of 0.900 m

Alex777 [14]

Answer:

The value of the maximum distance the spring will be compressed

x = 0.143 m= 14.3 cm

Step-by-step explanation:

Given data

Mass m = 1.5 kg

h = 0.9 m

k = 1500 $\frac{N}{m}$

Since the book is released from a height h = 0.9 m above the top of the spring. so the total distance

y = h + x

Now in that case for the spring

$mg y= \frac{1}{2} k x^{2}$

$mg(h +x) = \frac{1}{2} k x^{2}$

By rearranging the above equation we get

$k x^{2} - 2mgx - 2mg h = 0$

Put all the values in above equation we get

$1500x^{2} - 29.43 x - 26.48 = 0$

By solving the above equation we get

x = 0.143 m= 14.3 cm

This is the value of the maximum distance the spring will be compressed.

8 0

3 years ago

H represents the height of<br> H = 210 +33t<br> How fast does the tree grow

lisabon 2012 [21]

Answer:

243

Step-by-step explanation:

you just add

3 0

3 years ago

Express the function as the sum of a power series by first using partial fractions. f(x) = 8 x2 − 4x − 12 f(x) = ∞ n = 0 find th

alexandr1967 [171]

I'm guessing the function is

$f(x)=\dfrac8{x^2-4x-12}=\dfrac8{(x-6)(x+2)}$

which, split into partial fractions, is equivalent to

$\dfrac1{x-6}-\dfrac1{x+2}$

Recall that for $|x|$ we have

$\dfrac1{1-x}=\displaystyle\sum_{n=0}^\infty x^n$

With some rearranging, we find

$\dfrac1{x-6}=-\dfrac16\dfrac1{1-\frac x6}=\displaystyle-\frac16\sum_{n=0}^\infty\left(\frac x6\right)^n$

valid for $\left|\dfrac x6\right|$ , or $|x|$ , and

$\dfrac1{x+2}=\dfrac12\dfrac1{1-\left(-\frac x2\right)}=\displaystyle\frac12\sum_{n=0}^\infty\left(-\frac x2\right)^n$

valid for $\left|-\dfrac x2\right|$ , or $|x|$ .

So we have

$f(x)=\displaystyle-\frac16\sum_{n=0}^\infty\left(\frac x6\right)^n-\frac12\sum_{n=0}^\infty\left(-\frac x2\right)^n$

$f(x)=\displaystyle-\sum_{n=0}^\infty\left(\frac{x^n}{6^{n+1}}+\frac{(-x)^n}{2^{n+1}}\right)$

$f(x)=\displaystyle-\sum_{n=0}^\infty\frac{1+3(-3)^n}{6^{n+1}}x^n$

Taken together, the power series for $f(x)$ can only converge for $|x|$ , or $-2$ .

6 0

3 years ago

Paulita reads an average of 20 pages each day. She has 6 days to read 10^2 pages. Will she finish her reading in 6 days? Explain

MissTica

Yes, she would finish in time because 10^2=100, if she reads 20 pages per day, it'll take her 5 days to finish her reading before the 6 days

6 0

3 years ago