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3 years ago

Find an ordered pair that satisfies the equation 81x + 18y = 9

Mathematics

2 answers:

ch4aika [34]3 years ago

4 0

We can solve using y = 0 and solving for x.

81x + 18(0) = 9

81x = 9

x = 1/9

Therefore, the point (1/9, 0) sastisfies the equation.

Best of Luck!

Murrr4er [49]3 years ago

4 0

Find either the x intercept or y intercept:

To find the y intercept, Set x to 0 and solve for y:

81(0) + 18y = 9

0 + 18y = 9

Divide both sides by 18:

Y = 9/18

Y = 1/2

One solution is (0,1/2)

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Novay_Z [31]

Answer:

The bird will take 0.88 seconds to reach a height of 40 feet in the air for the first time

Step-by-step explanation:

we have

$h=-16t^2+55t+4$

This is a vertical parabola open downward

The vertex represent a maximum

where

h is the height of the bird

t is the amount of time, in seconds, the bird had been in the air

For h=40 ft

substitute in the quadratic equation

$40=-16t^2+55t+4$

$-16t^2+55t+4-40=0$

$-16t^2+55t-36=0$

The formula to solve a quadratic equation of the form

$ax^{2} +bx+c=0$

is equal to

$x=\frac{-b\pm\sqrt{b^{2}-4ac}} {2a}$

in this problem we have

$-16t^2+55t-36=0$

$a=-16\\b=55\\c=-36$

substitute in the formula

$x=\frac{-55\pm\sqrt{55^{2}-4(-16)(-36)}} {2(-16)}$

$x=\frac{-55\pm\sqrt{721}} {-32}$

$x=\frac{-55+\sqrt{721}} {-32}=0.88\ sec$

$x=\frac{-55-\sqrt{721}} {-32}=2.56\ sec$

therefore

The bird will take 0.88 seconds to reach a height of 40 feet in the air for the first time

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Find the value of a1 for an infinite geometric series with S=12 and r=1/6

blondinia [14]

$S_n=a(1+r+\cdots+r^{n-1}+r^n)$
$rS_n=a(r+r^2+\cdots+r^n+r^{n+1})$
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When $|r|$ , we have

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as is the case here. Since $S=\lim\limits_{n\to\infty}S_n=12$ and $r=\dfrac16$ are given, we can find the first term $a$ immediately:

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