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3 years ago

PLEASE HELP ASAP!!! CORRECT ANSWER ONLY PLEASE!!!

Mathematics

1 answer:

Butoxors [25]3 years ago

5 0

Answer: $\bold{a_n=\dfrac{2^{n-1}}{3^{n+1}}}$

<u>Step-by-step explanation:</u>

The explicit rule for a geometric sequence is: $a_n=a_1(r)^{n-1}\quad \text{where}\ a_1\ \text{is the first term and r is the common ratio}$

Given the sequence {9, 6, 4, $\dfrac{8}{3}$ , ... } we know

the first term (a₁) is 9
the common ratio (r) is $\dfrac{6}{9}=\dfrac{2}{3}\ \text{when simplified}$

So, the explicit rule for the given sequence is:

$a_n=9\bigg(\dfrac{2}{3}\bigg)^{n-1}\\\\\\.\quad =3\cdot3\dfrac{(2)^{n-1}}{(3)^{n-1}}\\\\\\.\quad =3\dfrac{(2)^{n-1}}{(3)^{n}}\\\\\\.\quad =\dfrac{(2)^{n-1}}{(3)^{n+1}}$

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Here is a sketch of y=x^2+bx+c The curve intersects

atroni [7]

Answer:

y = 18 and x = -2

Step-by-step explanation:

y = x^2+bx+c To find the turning point, or vertex, of this parabola, we need to work out the values of the coefficients b and c. We are given two different solutions of the equation. First, (2, 0). Second, (0, -14). So we have a value (-14) for c. We can substitute that into our first equation to find b. We can now plug in our values for b and c into the equation to get its standard form. To find the vertex, we can convert this equation to vertex form by completing the square. Thus, the vertex is (4.5, –6.25). We can confirm the solution graphically Plugging in (2,0) :

y=x2+bx+c

0=(2)^2+b(2)+c

y=4+2b+c

-2b=4+c

b=-2+2c

Plugging in (0,−14) :

y=x2+bx+c

−14=(0)2+b(0)+c

−16=0+b+c

b=16−c

Now that we have two equations isolated for b , we can simply use substitution and solve for c . y=x2+bx+c 16 + 2 = y y = 18 and x = -2

4 0

2 years ago

A taxi driver had 27 fares to and from the airport last Monday. The price for a ride to the airport is $14, and the price for a

OLga [1]

Answer:

(15, 12)

Step-by-step explanation:

Let's generate two systems of equations that fit this scenario.

Number of trips to the airport = x

Number of trips from the airport = y

Total number of trips to and from the airport = 27

Thus:

$x + y = 27$ => equation 1.

Total price for trips to the Airport = 14*x = 14x

Total price of trips from the airport = 7*y = 7y

Total collected for the day = $294

Thus:

$14x + 7y = 294$ => equation 2.

Multiply equation 1 by 7, and multiply equation 2 by 1 to make both equations equivalent.

7 × $x + y = 27$

1 × $14x + 7y = 294$

Thus:

$7x + 7y = 189$ => equation 3

$14x + 7y = 294$ => equation 4

Subtract equation 4 from equation 3

-7x = -105

Divide both sides by -7

x = 15

Substitute x = 15 in equation 1

$x + y = 27$

$15 + y = 27$

Subtract both sides by 15

$y = 27 - 15$

$y = 12$

The ordered pair would be (15, 12)

7 0

3 years ago

Solve for x.

Daniel [21]

Answer:

$x=-\frac{9}{4} \\ or \:\\x = -2\frac{1}{4}$

Step-by-step explanation:

$-2 (x + 1/4)+1=5\\\\-2\left(x+\frac{1}{4}\right)+1=5\\\\\mathrm{Subtract\:}1\mathrm{\:from\:both\:sides}\\\\-2\left(x+\frac{1}{4}\right)+1-1=5-1\\\\Simplify\\-2\left(x+\frac{1}{4}\right)=4\\\\\mathrm{Divide\:both\:sides\:by\:}-2\\\frac{-2\left(x+\frac{1}{4}\right)}{-2}=\frac{4}{-2}\\\\Simplify\\x+\frac{1}{4}=-2\\\\\mathrm{Subtract\:}\frac{1}{4}\mathrm{\:from\:both\:sides}\\\\x+\frac{1}{4}-\frac{1}{4}=-2-\frac{1}{4}\\\\Simplify\\x=-\frac{9}{4}\\\\x = -2\frac{1}{4}$