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2 years ago

5x - y + z = -6 2x + 7y + 3z = 8 x + 2z = 6

Mathematics

1 answer:

BabaBlast [244]2 years ago

5 0

Answer:

Step-by-step explanation:

The system of equations given are:

5x - y + z = -6 ------------- i

2x + 7y + 3z = 8 ---------- ii

x + 2z = 6 ----------------- iii

Let us deal with equation i and ii first since they have 3 variables x, y and z;

5x - y + z = -6 x 7

2x + 7y + 3z = 8 x 1

35x - 7y + 7z = -42 ---- iv

2x + 7y + 3z = 8 ---- v

Add equation iv and v;

37x + 10z = -34 ------vi

So, let us solve equation vi and iii:

x + 2z = 6 - ---------- iii x 10

37x + 10z = -34 --- iv x 2

10x + 20z = 60 vi

74x + 20z = -68 vii

Subtract vi - vii;

-64x = 128

x = -2

So; put x = -2 into iii;

x + 2z = 6

-2 + 2z = 6

2z = 6 + 2 = 8

z = 4

Put x = -2 and z = 4 into equation i;

5(-2) - y + 4 = - 6

-10 -y +4 = -6

-6 - y = -6

-y = 0

y = 0

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After breaking your penny bank, you notice that you have $4.87 in quarters ($0.25), dimes ($0.10), nickels ($0.05), and pennies

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Answer: Option 'c' is correct.

Step-by-step explanation:

Let the number of dimes be 'x'.

Let the number of nickels be ' $\dfrac{3}{2}x$ '.

Let the number of pennies be $\dfrac{3}{2}\times 2x=3x$

Let the number of quarters be '3x-34'.

As we know that

1 quarter = $0.25

1 dime = $0.10

1 nickel = $0.05

1 penny = $0.01

According to question, we get that

$0.10x+0.05\times \dfrac{3x}{2}+0.01\times 3x+0.25(3x-34)=4.87\\\\0.10x+0.075x+0.03x+0.75x-8.5=4.87\\\\\\0.955x=4.87+8.5\\\\0.955x=13.37\\\\x=\dfrac{13.37}{0.955}\\\\x=14$

So, the number of pennies is given by

$3x=3\times 14=42$

Hence, Option 'c' is correct.

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2 years ago

a carpet store charges 150 to install 12 square yards of carpet how much would it be for 24 square yards

ivanzaharov [21]

Answer:

$300

Step-by-step explanation:

150/12 to figure out how much to install one yard ($12.50)
24•12.50=300

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2 years ago

Given the matrices: 1 2 A= 1 -1 2 1 1 B= 3 4 Calculate AB: C11 C12 [2.1] х 1 2 3 4 C21 C22 C11 = C12 = -2 C22 - C215 DONE

eduard

Answer:

$\:c_{11}=-2,\:\:\:c_{12}=-2$

$\:c_{21}=5,\:\:\:c_{22}=8$

Step-by-step explanation:

Given the matrices

$A=\begin{pmatrix}1&-1\\ 2&1\end{pmatrix}$

$B=\begin{pmatrix}1&2\\ \:3&4\end{pmatrix}$

Calculating AB:

$\begin{pmatrix}1&-1\\ \:\:2&1\end{pmatrix}\times \:\begin{pmatrix}1&2\\ \:\:3&4\end{pmatrix}=\begin{pmatrix}c_{11}&c_{12}\\ \:\:\:c_{21}&c_{22}\end{pmatrix}$

Multiply the rows of the first matrix by the columns of the second matrix

$=\begin{pmatrix}1\cdot \:1+\left(-1\right)\cdot \:3&1\cdot \:2+\left(-1\right)\cdot \:4\\ 2\cdot \:1+1\cdot \:3&2\cdot \:2+1\cdot \:4\end{pmatrix}$

$=\begin{pmatrix}-2&-2\\ 5&8\end{pmatrix}$

Hence,

$\begin{pmatrix}c_{11}&c_{12}\\ \:\:\:c_{21}&c_{22}\end{pmatrix}=\begin{pmatrix}-2&-2\\ \:5&8\end{pmatrix}$

Therefore,

$\:c_{11}=-2,\:\:\:c_{12}=-2$

$\:c_{21}=5,\:\:\:c_{22}=8$

5 0

2 years ago

Read 2 more answers

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2 years ago

Find the common ratio of the geometric sequence 18,-72,288,...

tamaranim1 [39]

Answer:

<em>The common ratio of the geometric sequence is -4</em>

Step-by-step explanation:

<u>Geometric Sequence</u>

A geometric sequence is defined as a series of numbers that follow a fixed pattern: Each term equals the previous term times a fixed number called the common ratio. The recursive formula is:

$a_n=a_{n-1}*r$

Where r is the common ratio.

We are given three terms of a geometric sequence:

18,-72,288,...

To find the common ratio, just divide each term by the previous term:

$\displaystyle r=\frac{-72}{18}=-4$

Make sure it's a fixed number and test with the third term:

$\displaystyle r=\frac{288}{-72}=-4$

Since both numbers coincide, the common ratio of the geometric sequence is -4

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2 years ago