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3 years ago

Solve by completing a square r^2-8r+9

Mathematics

1 answer:

Tanzania [10]3 years ago

7 0

Solving $r^2-8r+9$ by completing a square gives $(r+4)^2-7$

Step-by-step explanation:

We need to solve the equation $r^2-8r+9$ by completing a square

The completing a square method requires: $a^2\pm 2ab +b^2=(a\pm b)^2$

Solving:

$r^2-8r+9\\=(r)^2-2(r)(?)+(?)^2+9$

We need to add and subtract (4)^2=16 to make the equation a complete square

$=(r)^2-2(r)(4)+(4)^2-(4)^2+9\\=(r)^2-2(r)(4)+(4)^2-16+9\\=(r)^2-2(r)(4)+(4)^2-7\\=(r+4)^2-7$

So, Solving $r^2-8r+9$ by completing a square gives $(r+4)^2-7$

Keywords: Solve by completing a square

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A department store sold 51 51 shirts one day. All short-sleeved shirts cost $14.00 $ 14.00 each and all long-sleeved shirts cost

Dmitrij [34]

Answer:

28 short-sleeved shirts were sold and 23 long-sleeved shirts were sold.

Step-by-step explanation:

We can solve this question by a system of equations.

I am going to say that:

x is the number of short-sleeved shirts sold.

y is the number of long-sleeved shirts sold.

A department store sold 51 shirts one day.

This means that $x + y = 51$

All short-sleeved shirts cost $14.00 each and all long-sleeved shirts cost $23.00 each. Total receipts for the day were $921.00.

This means that

$14x + 23y = 921$

How many of each kind of shirt were sold?

We have to solve the system of equations.

$x + y = 51$

$x = 51 - y$

--------------

$14x + 23y = 921$

$14(51 - y) + 23y = 921$

$714 - 14y + 23y = 921$

$9y = 207$

$y = \frac{207}{9}$

$y = 23$

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$x = 51 - y = 51 - 23 = 28$

28 short-sleeved shirts were sold and 23 long-sleeved shirts were sold.

7 0

3 years ago

A small fish is dropped by a pelican that is rising steadily at 0.50 m/s. How far below the pelican is the fish after 2.5 s? Ple

alexandr1967 [171]

The initial velocity of the fish is the same as that of the pelican and it is -0.50 m/s. The distance traveled by the object is given by the equation,
d = (V1)t + 0.5at²
where t is equal to 2.50s and the acceleration due to gravity, a, is 9.80 m/s². Substituting,
d = (-0.50 m/s)(2.5 s) + 0.5(9.8 m/s²)(2.50 s)²
d = 30.625 m
Thus, the answer is letter C.

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3 years ago

An observer (O) spots a plane flying at a 55° angle to his horizontal line of sight. If the plane is flying at an altitude of 21

mel-nik [20]

Angle of elevation is angle measured from horizontal line to line of sight, The distance from the plane to the observer is 25,636 feet approx

<h3>What is angle of elevation?</h3>

You look straight parallel to ground. But when you have to watch something high, then you take your sight up by moving your head up. The angle from horizontal line to the point where you stopped your head is called angle of elevation. See the figure where angle OPD is the angle when observer saw the plane. It is measured from the horizontal line OD.

Refer to the attached figure.

It is given that we have

Length of PD = |PD| = 21,000 feet

Angle ∠OPD = 55°

Assuming length of OP = |OP| = x feet, we get the sin ratio as

$sin(55^\circ) = \dfrac{|PD|}{|OP|} = \dfrac{21000}{x}\\\\x = \dfrac{21000}{\sin(55^\circ)} \approx 25636.27 \approx 25636 \: \rm feet$

(tan 55° was calculated from online calculator)

Thus,

The distance from the plane to the observer is 25,636 feet approx.

Learn more about trigonometric ratios here:
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3 years ago

Ruby started off her savings account with $100, and $0 in her checking account. She made $95 washing dishes and deposited it int

jarptica [38.1K]

Answer:

150+93=241

Step-by-step explanation:

I'm not sure if this is correct but i guess because she got 95 and deposited it into her checking she has 95 and judging on if she spent 2 dollars from her savings or checking i assumed it was savings which leaves it with 148 from 100 after depositing 50 - 2 = 148 so basically

edit: nvm i saw the note now im sure but something i dont understand is that if she made 95 how come the answer choices dont say 93 in checking so im guessing you meant 150+43=193

193 is your answer sorry lol took me a while to work this out or Answer choice C

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Vanyuwa [196]

Answer:

Step-by-step explanation:

5/12 * 300 = 125 times

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4 years ago

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