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3 years ago

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2(8a + 5b) -(2a + 3b) Part A: Simplify the expression shown above, and include all necessary work to support your answer. Part B

: If a represents apples that cost $0.25 each and b represents bananas that cost SO. 15 each, what is the total cost based on the expression above? Include all necessary work to support

1 answer:

Alex17521 [72]3 years ago

6 0

Answer:

Total cost = <em>$</em> 4.55

Step-by-step explanation:

2(8a + 5b) -(2a + 3b)

<em>Part A: Simplify the expression shown above</em>

Exapanding the brackets;

16a + 10b - 2a - 3b

Collecting like terms;

16a - 2a + 10b - 3b

14a + 7b

<em>Part B: If a represents apples that cost $0.25 each and b represents bananas that cost SO. 15 each, what is the total cost based on the expression above?</em>

a = 0.25

b = 0.15

14a + 7b

Inserting the values into the equation;

14 (0.25) + 7(0.15)

Total cost = <em>$</em> 4.55

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<em>Observe attached image</em>

<em>Function zeros:</em>

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Step-by-step explanation:

<u>First factorize the function</u>

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<em>Now factor the expression $x ^ 2 -8x +15$ </em>

You must find two numbers that when you add them, obtain the result -8 and multiplying those numbers results in 15.

These numbers are -5 and -3

Then we can factor the expression in the following way:

$f (x) = -2(x-5)(x-3)$

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Now we find the coordinates of the vertex.

For a function of the form $ax ^ 2 + bx + c$ the x coordinate of its vertex is:

$x = \frac{-b}{2a}$

In the function $f (x) = -2x ^ 2 + 16x-30$

$a = -2\\b = 16\\c = 30$

<u>Then the vertice is:</u>

$x = \frac{-16}{2(-2)}\\\\x = 4$

The y coordinate of the symmetry axis is

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<u>Then the axis of symmetry is the line</u>

$x = 4$

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Answer:

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c. True

d. True

e. False

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Hi,

We have certain properties for matrices,<em> (where A and B are nxn matrices and I is the identity matrix) </em>:

${(A^{-1})}^{-1} = A$

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None of the properties help verify this statement. We ca use an example for counter:

Let $A =\left[\begin{array}{cc}1&2\\2&0\\\end{array}\right]$ and $B = \left[\begin{array}{cc}5&1\\3&2\end{array}\right]$ , we calculate the L.H.S:

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The square of (A+B):

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Lets calculate the R.H.S:

$A^{2} =\left[\begin{array}{cc}1&4\\4&0\\\end{array}\right]\\B^{2} = \left[\begin{array}{cc}25&1\\9&4\end{array}\right]\\2AB = \left[\begin{array}{cc} (1 \times 5) + (2 \times 3) &(1 \times 1) + (2 \times 2)\\(2 \times 5) + (0 \times 3)& (2 \times 1) + (0 \times 2)\end{array}\right]\\= \left[\begin{array}{cc} 11 &5\\10& 2\end{array}\right]$

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This proves that: L.H.S ≠ R.H.S

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B. False

This can only hold when the eigenvalues for A are real.

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C. True

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D. True

The property that inverse is possible for any "n" value of the matrix.

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