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MrRa [10]
3 years ago
14

Which statement is true about the extreme value of the given quadratic equation? A. The equation has a maximum value with a y-co

ordinate of -21. B. The equation has a maximum value with a y-coordinate of -27. C. The equation has a minimum value with a y-coordinate of -21. D. The equation has a minimum value with a y-coordinate of -27.
Mathematics
1 answer:
insens350 [35]3 years ago
3 0

Answer:

A. The equation has a maximum value with a y-coordinate of -21.

Step-by-step explanation:

From the given equation:

\mathbf{y = -3x^2 + 12x -33}

This parabola is vertical and is goes downward via the negative path

Where the vertex represents the maximum value;

\mathbf{y = -3 (x^2 + 4x) -33}

Using completing the square method;

\mathbf{y = -3 (x^2 + 4x+2^2) -33+12}

\mathbf{y = -3 (x^2 + 4x+4) -21}

To perfect square:

\mathbf{y = -3 (x-2)^2 -21}

The vertex point is (2, -21)

Hence ; the equation has a maximum value with a y-coordinate of -21.

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What are the solutions to the system of equations?
svet-max [94.6K]

Answer:the third option is correct

Step-by-step explanation:

The system of equations are

y = 2x^2 - 5x - 7 - - - - - - - - - - -1

y = 2x + 2 - - - - - - - - - - - - - 2

We would equate equation 1 and equation 2. It becomes

2x^2 - 5x - 7 = 2x + 2

2x^2 - 5x - 2x - 7 - 2 = 0

2x^2 - 7x - 9 = 0

We would find two numbers such that their sum or difference is -7x and their product is - 18x^2. The two numbers are 2x and - 9x. Therefore

2x^2 + 2x - 9x - 9 = 0

2x(x + 1) - 9(x + 1) = 0

2x - 9 = 0 or x + 1 = 0

2x = 9 or x = - 1

x = 9/2 = 4.5

Substituting x = 4.5 or x = -1 into equation 2, it becomes

y = 2 × 4.5 + 2 or y = 2 × - 1 + 2

y = 11 or y = 0

Therefore, the solutions are

(4.5, 11) (- 1, 0)

6 0
3 years ago
What is (766*67*89*8*9*87656*7*908786*5*687*78*87*797*87897*8989*089*7654*4*367567*98097987567544*535*567*9*8*6787)0(5*64543534*
romanna [79]

Answer:

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Step-by-step explanation:

4 0
3 years ago
Read 2 more answers
How do I solve x+y=-5 using y=mx+b
andrew-mc [135]
To put in into y=mx+b format, you have to subtract the x on both sides.

y=-x-5
This would be the answer.

5 0
3 years ago
Calculate the surface area of this box.
julia-pushkina [17]

Answer:

36 cm^2

Step-by-step explanation:

S.A. = 2 (lw + wh + lh)

S.A. = 2 ((4)(2) + (2)(2) + (4)(2))

S.A. = 2 (8 + 4 + 6)

S.A. = 2 (18)

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4 0
2 years ago
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Given T5 = 96 and T8 = 768 of a geometric progression. Find the first term,a and the common ratio,r.
Alona [7]

Answer:

Of the given geometric sequence, the first term a is 6 and its common ratio r is 2.

Step-by-step explanation:

Recall that the direct formula of a geometric sequence is given by:

\displaystyle T_ n = ar^{n-1}

Where <em>T</em>ₙ<em> </em>is the <em>n</em>th term, <em>a</em> is the initial term, and <em>r</em> is the common ratio.

We are given that the fifth term <em>T</em>₅ = 96 and the eighth term <em>T</em>₈ = 768. In other words:

\displaystyle T_5 = a r^{(5) - 1} \text{ and } T_8 = ar^{(8)-1}

Substitute and simplify:

\displaystyle 96 = ar^4 \text{ and } 768 = ar^7

We can rewrite the second equation as:

\displaystyle 768 = (ar^4) \cdot r^3

Substitute:

\displaystyle 768 = (96) r^3

Hence:

\displaystyle r = \sqrt[3]{\frac{768}{96}} = \sqrt[3]{8} = 2

So, the common ratio <em>r</em> is two.

Using the first equation, we can solve for the initial term:

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7 0
2 years ago
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