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son4ous [18]
3 years ago
15

Write 3x^2-18x-6 in vertex form

Mathematics
1 answer:
Vedmedyk [2.9K]3 years ago
6 0
The standard form of a quadratic equation is \displaystyle{ y=ax^2+bx+c, while the vertex form is:

                      y=a(x-h)^2+k, where (h, k) is the vertex of the parabola.

What we want is to write \displaystyle{ y=3x^2-18x-6 as y=a(x-h)^2+k

First, we note that all the three terms have a factor of 3, so we factorize it and write:

\displaystyle{ y=3(x^2-6x-2).


Second, we notice that x^2-6x are the terms produced by (x-3)^2=x^2-6x+9, without the 9. So we can write:

x^2-6x=(x-3)^2-9, and substituting in \displaystyle{ y=3(x^2-6x-2) we have:

\displaystyle{ y=3(x^2-6x-2)=3[(x-3)^2-9-2]=3[(x-3)^2-11].

Finally, distributing 3 over the two terms in the brackets we have:

y=3[x-3]^2-33.


Answer: y=3(x-3)^2-33
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What conclusions can be drawn about finding the quotient in scientific notation? Check all that apply.
irga5000 [103]

Answer:

B.The exponent of the solution is –12, the difference of the original exponents.

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D.The quotient is 3.0 ×

Step-by-step explanation:

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2 years ago
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Trigonometry
Mashcka [7]

The area of the triangle EFG is 7.4 square units.

Explanation:

Given that the measurements of the sides of the triangle are EF = 8, EG = 8 and m\angle E=22^{\circ}

We need to determine the area of the triangle EFG

<u>Area of the triangle:</u>

The area of the triangle EFG can be determined using the formula,

\text {Area}=\frac{1}{2} fg \sin E

Substituting the values, we get,

\text {Area}=\frac{1}{2} (5)(8) \sin 22^{\circ}

Simplifying the values, we have,

\text {Area}=\frac{1}{2}(40)(0.37)

Multiplying, we get,

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Dividing, we get,

\text {Area}=7.4

Hence, the area of the triangle EFG is 7.4 square units.

3 0
2 years ago
Adele opens an account with $100 and deposits $35 a month. Kent opens an account with $50 and also deposits $35 a month. Will th
Svetach [21]
Equations:

100 + 35m
50 + 35m

Steps:
100 + 35m = 50 + 35m <span>

<em>Set the equations equal to each other.</em>
</span>   <span />
<span>
100 + 35m = 50 + 35m <span>
-50              - 50
</span>
<em>Subtract 50 from both sides of equation to isolate the variable on one side</em>.

50+35m=35m
     -35m  -35m

<em>Subtract 35m from both sides of equation.</em>

50=m

In fifty months, they will have the same amount of money. They will each contain $1850 dollars.

Hope this helps.
</span>                      

7 0
3 years ago
determine the equation of the straight line which passes through the point 1 and 5 and is perpendicular to the line 3x + y is eq
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The straight line is perpendicular to y = -3x + 4.

Therefore, the gradient of the straight line must be 3.

The equation of the straight line is y = 3x + 2.

7 0
3 years ago
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