What is the solution to the system of equations?<br> {2x + 3y = 6<br> x+y=1

1. You can buy a 6-hour phone card for $5.00, but the fine print says that each minute actually costs you 1.5 minutes of time. W

Vilka [71]

Divide 5.00 by 1.5 and you get (it's pretty long) 3.3333333333333333333333333333333

7 0

3 years ago

If the second term of a geometric sequence of real numbers is -2 and the fifth term is 16 then what is the fourteenth term?

Agata [3.3K]

<h3>Given</h3>

A geometric sequence such that ...

$a_2=-2\quad\text{and}\quad a_5=16$

$a_{14}$

<h3>Solution</h3>

We can use the ratio of the given terms to find the common ratio of the sequence, then use that to find the desired term from one of the given terms. We don't actually need the common ratio (-2). All we need is its cube (-8).

$a_2=a_1r^{(2-1)}=a_1r^1\\a_5=a_1r^{(5-1)}=a_1r^4\\a_{14}=a_1r^{(14-1)}=a_1r^13=a_5r^9\\\\\dfrac{a_5}{a_2}=\dfrac{a_1r^4}{a_1r^1}=r^3=\dfrac{16}{-2}=-8\\\\r^9=\left(r^3\right)^3=(-8)^3=-512\\a_{14}=a_5(-512)\\\\a_{14}=-8192$

7 0

3 years ago

The set of ordered pairs represents a

Murrr4er [49]

Answer:

The rule that represents the function is $y=x^2+1$ therefore the function is $f(x)=x^2+1$

Step-by-step explanation:

We have 5 ordered pairs in the plane xy. This means that <em>every pair has the form (x, y).</em>

Then, we have 5 values of x, which will give us 5 values of y, using the rule that represents the function.

<u>The easy evaluation is that when x=0, the value of y is y=1,</u> and then we can evaluate the rule for x=-1, and x=1, <em>the value of y is the same, y=2</em>. We can see here that we have a parabolic function, that is not centered in the origin of coordinates because when x=0, y=1.

So <u>we propose the rule </u> $y=x^2+1$ <u> which is correct for the first 3 values of x.</u>

Now, <em>we evaluate the proposed rule when x=2, and when x=3</em>. This evaluations can be written as

$f(2)=2^2+1=5$

$f(3)=3^2+1=10$

Therefore, the rule is correct, and the function is

$f(x)=x^2+1$

8 0

3 years ago

At track practice, Coach Wilson told the team to split into groups of four for a special relay. The first runner had to run 1 la

amid [387]

You can multiply the number of laps each person ran by the yards in each lap and then add them together:

440 + 2(440) + 3(440) + 4(440)
= 440 + 880 + 1,320 + 1,760
= 4,440 yards

Or you can add the laps first, then multiply by the yards in each lap
(1 + 2 + 3 + 4)(440)
= 10 x 440
= 4,400 yards

7 0

3 years ago

Help me for this question please

stealth61 [152]

Answer:70 degrees and 150 degrees

Step-by-step explanation: The angles of a quadrilateral add up to 360. So the sum of the two angles is 360 - (55+ 85) = 220.

After that you can model the sum of the angles with an equation:

7x + 15x = 220

22x = 220

x = 10

then you plug in x for each angle 7(10) = 70 and 15(10) = 150

7 0

3 years ago

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What is the solution to the system of equations? {2x + 3y = 6 x+y=1