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4 years ago

How to solve this 4x-3(x-2)=21

Mathematics

1 answer:

Natasha_Volkova [10]4 years ago

4 0

We can start by getting rid of parenthesis:

4x-3x+6=21

Then we can combine like terms:

x=21-6

x=15

So our end product is x=15.

Hope I helped soz if I'm wrong ouo.

~Potato.

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The nth term of a sequence is n2+20a)What is the first three terms of the sequence?

notka56 [123]

$a_n=n^2+20\\\\a)\\a_1=1^2+20=1+20=21\\a_2=2^2+20=4+20=24\\a_3=3^2+20=9+20=29\\\\Answer:\ 21;\ 24;\ 29\\\\b)\\n^2+20 < 50\ \ \ |-20\\\\n^2 < 30\to n < \sqrt{30}\ \wedge\ n\in\mathbb{N^+}\to\ n\in\{1;\ 2;\ 3;\ 4;\ 5\}\\\\Answer:\ 5\ terms$

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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

15 is what percent of 500

TEA [102]

% of 15 in 500= (15÷500)×100
= 0.03×100
= 3 %

5 0

4 years ago

What is the answer to 2/3 of something equals 10

denis23 [38]

In math, when you see the word "of" it usually means "times".

So the question is:

<u>2/3 times something = 10</u>

Multiply each side of the equation by 3 :

2 times something = 30

Divide each side by 2 :

<em> something = 15</em>

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3 years ago

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When using "mean" does it mean average of something if not please explain, I'm a bit confused.

lesya [120]

Mean the the total of all values, divided by the number of values

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3 years ago

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