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GarryVolchara [31]
3 years ago
10

What is the first step when rewriting y = 6x2 + 18x + 14 in the form y = a(x – h)2 + k?

Mathematics
2 answers:
musickatia [10]3 years ago
6 0
The first step in rewriting the equation given to the vertex form is to transpose first the constant term to the other side to simplify the procedure. It is done as follows:

<span>y - 14= 6x</span>²<span> + 18x )

Hope this answer the question.
</span><span>
</span>
Tatiana [17]3 years ago
5 0

Answer:

y = 6(x -(-3/2))^2 - 13/12

Step-by-step explanation:

Given: 6x^2 +18x + 14

We have to write in vertex form y = a(x -h)^2 + k

Step 1: <em><u>In the given function y = 6x^2 + 18x + 14, the coefficient of x^2 is 6, we need to make it 1, so we take out 6 and factor it.</u></em>

<em><u>y = 6(x^2 + 3x + 7/6)</u></em>

x^2 + 3x + 7/6, the value of b = 3, now divided 3 by 2, then square it.

(3/2)^2 = 9/4

Now add and subtract 9/4

y = 6(x^2 + 3x +9/4 -9/4 + 7/6)

y = 6(x +3/2)^2 -9/4+ 7/6

y = 6(x -(-3/2))^2 + (\frac{-27 + 14}{24} )

Here we simplified -9/4 + 7/6 taking the LCD as 12

y = 6(x - (-\frac{3}{2}))^2 +(\frac{-13}{12} ).

This can be written as

y = 6(x -(-\frac{3}{2} )^2 -\frac{13}{12}

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One watering system needs about three times as long to complete a job as another warning system when both systems operate at the
algol13

Answer:

One watering system requires 36 minutes to complete the job alone while another watering system requires 12 minutes to complete the job alone.

Step-by-step explanation:

Given:

Both the system can complete the job = 9 minutes

We need find the time required by each system to do the job.

Solution:

Let the time required by another watering system to complete the job be 'x' mins.

Now given:

One watering system needs about three times as long to complete a job as another watering system.

Time required by one watering system = 3x

Rate to complete the job by another watering system = \frac{1}{x}\ job/min

Rate to complete the job by One watering system = \frac{1}{3x}\ job/min

Rate at which both can complete the job = \frac{1}{9}\ job/min

So we can say that;

Rate at which both can complete the job is equal to sum of Rate to complete the job by another watering system and Rate to complete the job by One watering system.

framing in equation form we get;

\frac{1}{x}+\frac{1}{3x}=\frac19

Now taking LCM to make the denominator common we get;

\frac{1\times3}{x\times 3}+\frac{1\times1}{3x\times1}=\frac19\\\\\frac{3}{3x}+\frac{1}{3x}=\frac19\\\\\frac{3+1}{3x}=\frac{1}{9}\\\\\frac{4}{3x}=\frac{1}{9}

By Cross multiplication we get;

4\times9 =3x\\\\3x =36

Dividing both side by 3 we get;

\frac{3x}{3}=\frac{36}{3}\\\\x=12\ min

Time required by One watering system = 3x =3\times 12 =36\ min

Hence One watering system requires 36 minutes to complete the job alone while another watering system requires 12 minutes to complete the job alone.

6 0
3 years ago
Rewrite in simplest terms: -2(5d-9f)+7f-10(-9f-7d)
Afina-wow [57]

Answer:

= 5 ( 12d + 23f )

Step-by-step explanation:

-2(5d-9f)+7f-10(-9f-7d

Open parenthesis

= -10d + 18f + 7f + 90f + 70d

Collect like terms

= -10d + 70d + 18f + 7f + 90f

= 60d + 115f

Factorise

= 5 ( 12d + 23f )

Therefore,

-2(5d-9f)+7f-10(-9f-7d) in its simplest form is 5 ( 12d + 23f )

4 0
2 years ago
Help me pls guys! im being timed and need some help!
Agata [3.3K]

Answer:

B.

Step-by-step explanation:

she only has $60 to spend therefore, she has the option of spending all of it, or less. However she cannot spend money she doesn't have.

4 0
2 years ago
Read 2 more answers
Elizabeth has $10, $5, and $1 bills worth $101. she has five more five dollar bills than ten dollar bills and 4 times more 1 dol
vesna_86 [32]

Let x be number of $10 dollar bills

Let y be number of $5 dollar bills

Let z be number of $1 dollar bills

From the question, we can come up with three equations (so we can find the values of x, y & z) :

  • 10x + 5y + z = 101
  • y - x = 5
  • z = 4x

The first equation comes from finding the total money Elizabeth has, which is $101.

The second equation comes from value of y (number of $5 bills) is more than value of x (number of $10 bills) by 5 dollars.

The third equation comes from the value of z (number of $1 bills) being 4 times more than the value of x (number of $10 bills).

Now, we will begin to find the value of x, y & z.

From the first equation,

10x + 5y + z = 101

Substitute the third equation (z = 4x) into z:

10x + 5y + 4x = 101

Simplify this and you get,

14x + 5y = 101

Now, we use the second equation. The second equation is y - x = 5. If we try to make y as the subject, it becomes y = 5 + x.

Now, substitute this into the value of y of the last working we did:

14x + 5(5+x) = 101

Simplify that and it becomes:

x = 4

Then, substitute this value of x into the second and third equations to find y and z.

y - x = 5

y - 4 = 5

y = 9

z = 4x

z = 4(4)

z = 16

Finally, let's check these answers by substituting them into the first equation to try and see if the total value is <em>really</em> $101.

10x + 5y + z = 10(4) + 5(9) + 16

10x + 5y + z = 40 + 45 + 16

10x + 5y + z = 101

Thus, our answers are correct. Elizabeth has FOUR $10 bills, NINE $5 bills and SIXTEEN $1 bills.

6 0
2 years ago
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A worker's in a sliver mine descends 57 feet. Use an integer to represent to cahnge the worker's position
LenKa [72]
The change is -57 feet.
3 0
3 years ago
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