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4 years ago

What is the coordinates of the vertex in the equation: y = (x-3)^2 + 2?

Mathematics

1 answer:

SashulF [63]4 years ago

3 0

This equation is already in vertex form.
the vertex is when (x-3)=0, x=3
when x=3, y=2
so the vertex is (3,2)

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Which of the following mathematical operations can be used with functions?

Temka [501]

The correct answers among all the other choices are A) Addition, B) Subtraction, C) Multiplication, and D) Division. These mathematical operations can be used with functions. Thank you for posting your question. I hope this answer helped you. Let me know if you need more help.

6 0

4 years ago

An electronics company produces transistors, resistors, and computer chips. Each transistor requires 3 units of copper, 2 unit

Gala2k [10]

Answer:

475 transistors, 25 resistors and 50 computer chips can be produced.

Step-by-step explanation:

Let us consider, p = Number of transistors.

q = Number of resistors.

r = Number of computer chips.

The following three linear equations according to question,

$3\times p + 3\times q + 2\times r = 1600\\2\times p + 1\times q + 1\times r = 1025\\1\times p + 2\times q + 2\times r = 625$

The matrix form of any system, Ax = B

Where, A = Coefficient matrix

B = Constant vector

x = Variable vector

$A = \left[\begin{array}{ccc}3&3&2\\2&1&1\\1&2&2\end{array}\right], x = \left[\begin{array}{ccc}p\\q\\r\end{array}\right], B = \left[\begin{array}{ccc}1600\\1025\\625\end{array}\right]$

The inverse matrix, $A^{-1}$ can be found by using the following formula,

$A^{-1} = \frac{1}{det A}\times (C_{A}) ^{T}$

Where, det A = Determinant of matrix A.

$C_{A}$ = Matrix of cofactors of A

Now, applying this formula to find $A^{-1}$ ;

$det A = \left[\begin{array}{ccc}3&3&2\\2&1&1\\1&2&2\end{array}\right] = 3\times(2-2)-3\times(4-1)+2\times(4-1) = -3$

Here, $det A\neq 0$ , thus the matrix is invertible.

$C_{A} = \left[\begin{array}{ccc}(2-2)&-(4-1)&(4-1)\\-(6-4)&(6-2)&-(6-3)\\(3-2)&-(3-4)&(3-6)\end{array}\right] = \left[\begin{array}{ccc}0&-3&3\\-2&4&-3\\1&1&-3\end{array}\right] \\(C_{A}) ^{T} = \left[\begin{array}{ccc}0&-3&3\\-2&4&-3\\1&1&-3\end{array}\right] ^{T} = \left[\begin{array}{ccc}0&-2&1\\-3&4&1\\3&-3&-3\end{array}\right]$

$A^{-1} = \frac{1}{-3}\times\left[\begin{array}{ccc}0&-2&1\\-3&4&1\\3&-3&-3\end{array}\right] \\ So, x= \frac{1}{-3} \left[\begin{array}{ccc}0&-2&1\\-3&4&1\\3&-3&-3\end{array}\right]\times\left[\begin{array}{ccc}1600\\1025\\625\end{array}\right]= \frac{1}{-3} \left[\begin{array}{ccc}-1425\\-75\\-150\end{array}\right] = \left[\begin{array}{ccc}475\\25\\50\end{array}\right]$

So, p = 475, q = 25, r = 50.

7 0

3 years ago

What is the standard form of twenty-two ten thousandths?

insens350 [35]

Twenty-two ten thousandths is
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8 0

4 years ago

Read 2 more answers

The concentration C (in mg/dl), of an antibiotic in a patient’s bloodstream per hour, t, is given by: c(t) = (50t)/(t^2+25) In o

NARA [144]

Answer:

Step-by-step explanation:

<u>Functions </u>

The problem describes a function that expresses the concentration of an antibiotic in mg/dl vs time in hours as:

$\displaystyle c(t)=\frac{50\ t}{t^2+25}$

We need to find the first value of t such that

$\displaystyle c(t)\geq 4$

It means that

$\displaystyle \frac{50\ t}{t^2+25}\geq 4$

Operating with the inequality

$\displaystyle 50\ t\geq 4\ t^2+100$

Rearranging and dividing by 2, we have a polynomial inequality:

$\displaystyle 2t^2-25t+50\leq 0$

Factoring

$\displaystyle 2(t-10)\left (t-\frac{5}{2}\right )\leq 0$

There are two possible values for t, both valids because they are positive

$\displaystyle t=\frac{5}{2}=2.5, \ t=10$

We need to find the first value, i.e.

$t=2.5 \ hours$

Now for the graphic method, we plot the graph for the function and a horizontal line at c=4 to find the values of t.

The graph is shown in the image provided below. We can see both values where the funcion and C=4 intersect. Both values coincide with the previously analitically found values

4 0

3 years ago

Factor the trinomial below x^2+7x-30

Triss [41]

Answer:

(x + 10)(x - 7)

Step-by-step explanation:

It is 3 and 10 in some order. The difference is 7 and it is plus, so the larger number is +10 and the smaller one - 3

(x + 10)(x - 3) should be the answer

10x - 3x = 7x

5 0

4 years ago