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3 years ago

Solve the following system algerbraically: y=-3(x-2) squared+4 y=-6x+16

1 answer:

8 0

$y = - 3(x - 2) ^{2} + 4$
$y = - 6x + 16$
distribute the -3 and the square into the first equation
$y = - 3x ^{2} + 12x - 8$
$y = - 6x + 16$
multiply the second equation by 2
$y = - 3x ^{2} + 12x - 8$
$y = - 12x + 32$
add the equations together
$y = - 3x ^{2} + 24$
factor out -3
$y = - 3(x ^{2} - 8)$
factor inside parenthesis
$y = - 3(x + \sqrt{8} )( x - \sqrt{8})$
refine
$y = - 3(x + 2 \sqrt{2} )(x - 2 \sqrt{2} )$

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Lady bird [3.3K]

Hello!
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3 years ago

Solve this proportion: 8/x = 2/5. x =

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8/x= 2/5

8•5= 2•x

40=2x

40/2= x

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3 years ago

Write an expression for the product of z and 113, minus 300.

padilas [110]

Answer:

z*113 -300

Step-by-step explanation:

(z*113) -300

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3 years ago

Jason owns a small textile company that produces shirts. On a particular day, Jason has one worker come into the shop to make sh

Vesna [10]

Answer:

Variables:

$x$ → The number of hours the worker worked

$y$ → The number of shirts the worker made.

System fo equations:

$\left \{ {{25x+1.75 y=270} \atop {y=5x}} \right.$

Step-by-step explanation:

Let be $x$ the number of hours the worker worked and $y$ the number of shirts the worker made.

Since:

Jason must pay the worker $25 per hour (which can be represented with $25x$ ).
He must pay $1.75 per shirt for material costs (which can be represented with $1.75y$ ).
The total expenses were $270.

You can write the following equation:

$25x+1.75 y=270$

Knowing that the worker created an average of 5 shirts per hour, you can write the other equation:

$y=5x$

Therefore, with this equations you can set up the following system of equations, which could be used to determine the number of hours the worker worked and the number of shirts the worker made:

$\left \{ {{25x+1.75 y=270} \atop {y=5x}} \right.$

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2 years ago

Suppose the sediment density (g/cm) of a randomly selected specimen from a certain region is normally distributed with mean 2.65

Verizon [17]

A) 0.9803; 0.4803
B) 32

We calculate the z-score for this problem by using the formula:

$z=\frac{X-\mu}{\frac{\sigma}{\sqrt{n}}}$

Using our formula, we have:

$z=\frac{3.00-2.65}{\frac{0.85}{\sqrt{25}}}=2.06$

Using a z-table (http://www.z-table.com) we see that the area to the left of, less than, this score is 0.9803.

To find the probability it is between the mean and this, we subtract the probability associated with the mean (0.5) from this:
0.9803 - 0.5 = 0.4803.

To find B, we first find the z-score for this. Using a z-table (http://www.z-table.com) we see that the closest z-score would be 2.33. We then set up our equation as

$2.33=\frac{3.00-2.65}{\frac{0.85}{\sqrt{n}}}=\frac{0.35}{\frac{0.85}{\sqrt{n}}}
\\
\\2.33=0.35\div \frac{0.85}{\sqrt{n}}=0.35\times \frac{\sqrt{n}}{0.85}$

Multiplying both sides by 0.85 we have
2.33(0.85) = 0.35√n
1.9805 = 0.35√n

Divide both sides by 0.35:
1.9805/0.35 = √n

Square both sides:
(1.9805/0.35)² = n
32 ≈ n

8 0

3 years ago