MATHEMATICS COLLEGE

1/3 x− 1/8 y=3
7y+9x=−2
please solve the system
45 points for who does

Answers

Answer 1

Answer:

Answer:

$x=6\ny=-8$

Step-by-step explanation:

$(1)/(3)x-(1)/(8)y=3\n 7y+9x=-2$

One method could be rewriting the second equation as x in terms of y and solving by replacing in the first equation.

$7y+9x=-2\n9x=-2-7y\nx=(-7y-2)/(9)$

Replace...

$(1)/(3)x-(1)/(8)y=3$

$(1)/(3)((-7y-2)/(9))-(1)/(8)y=3$

$(-7y-2)/(27)-(1)/(8)y=3$

$-(7)/(27)y-(2)/(27)-(1)/(8)y=3$

add $(2)/(27)$ on both sides.

$-(7)/(27)y-(1)/(8)y=3+(2)/(27)$

Combine like terms

$((-7)(8)-(1)(27))/((27)(8)) y=((3)(27)+2)/(27)$

$(-56-27)/(216) y=(81+2)/(27)$

$(-83)/(216)y =(83)/(27)$

Now, to get rid of the fraction and isolate y, multiply by the reciprocal or the inverted fraction.

$((216)/(-83)) (-83)/(216)y =(83)/(27)((216)/(-83))$

$y=(216)/(-27)$

Simplify

$y=-8$

Now replace the value of y in either equation to find x.

$7y+9x=-2\n7(-8)+9x=-2\n-56+9x=-2$

add 56

$56-56+9x=-2+56\n9x=54\n$

Divide by 9

$(9x)/(9)=(54)/(9)\n x=6$

To check whether these values are accurate, replace in either equation both values and you should have an equality. In this case I'll do it in both equations.

$(1)/(3)x-(1)/(8)y=3$

$(1)/(3)(6)-(1)/(8)(-8)=3$

$2-(-1)=3\n2+1=3\n3=3$

-----------------------------------------------------------------

$7y+9x=-2\n7(-8)+9(6)=-2\n-56+54=-2\n-2=-2$

Related Questions

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Simplify 2^3 + 6^1 =
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Find the critical numbers of the function f(x) = x6(x − 2)5.x = (smallest value)x = x = (largest value)(b) What does the Second Derivative Test tell you about the behavior of f at these critical numbers?At x = the function has ---Select--- [a local minimum, a local maximum, or neither a minimum nor a maximum].(c) What does the First Derivative Test tell you that the Second Derivative test does not? (Enter your answers from smallest to largest x value.)At x = the function has ---Select--- [a local minimum, a local maximum, or neither a minimum nor a maximum].At x = the function has ---Select--- [a local minimum, a local maximum, or neither a minimum nor a maximum].
Which quadrant would 6,-4 be in ?

Find the domain of f and f −1 and its domain. f(x) = ln(ex − 3). (a) Find the domain of f. (Enter your answer using interval notation.) (−2,[infinity]) (b) Find f −1. f −1(x) = x+ln(3)

Answers

Answer:

a.Domain of f=(1.099, $\infty)$

b. $f^(-1)(x)=ln(e^x+3)$

Step-by-step explanation:

Let $y=f(x)=ln(e^x-3)$

We know that domain of ln x is greater than zero

$e^x-3>0$

Adding 3 on both sides of inequality

$e^x-3+3>0+3$

$e^x>3$

Taking on both sides of inequality

$lne^x>ln 3$

$x>ln 3$ =1.099

By using $lne^x=x$

Domain of f=(1.099, $\infty)$

Let $y=f^(-1)(x)=ln(e^x-3)$

$e^y=e^x-3$

By using property $lnx=y\implies x=e^y$

$e^x=e^y+3$

Taking ln on both sides of equality '

$lne^x=ln(e^y+3)$

$x=ln(e^y+3)$

Replace x by y and y by x

$y=ln(e^x+3)$

Substitute y= $f^(-1)(x)$

$f^(-1)(x)=ln(e^x+3)$

Which property is shown in the matrix addition below?
[-6 15 -2 ] + [6 -15 2 ] = [0 0 0

Answers

Answer:

The property shown in matrix addition given is "Additive Inverse Property"

Step-by-step explanation:

First of all lets define what a matrix is.

A matrix is an array of rows and columns that consists of numbers. There are several types of matrices. The one in our question is a row matrix which consists of only one row.

There are several addition properties for matrices.

One of them is additive inverse property. The additive inverse of a matrix consists of the same elements but their signs are changed.

Additive inverse property states that the sum of a matrix and its additive inverse is a zero matrix.

$\left[\begin{array}{ccc}-6&15&-2\end{array}\right] + \left[\begin{array}{ccc}6&-15&2\end{array}\right] = \left[\begin{array}{ccc}0&0&0\end{array}\right]$

Hence,

The property shown in matrix addition given is "Additive Inverse Property"

Write 1/10 as a decimal number

Answers

Answer:

0.1

Step-by-step explanation:

hope this helps

22. Find the balance in an account with $900 earning 6.5% compounded
quarterly after 4 years

Answers

Answer:

$1,164.80

Step-by-step explanation:

Lets use the compound interest formula provided to solve this:

$A=P(1+(r)/(n) )^(nt)$

P = initial balance

r = interest rate (decimal)

n = number of times compounded annually

t = time

First, we need to change 6.5% into a decimal:

6.5% -> $(6.5)/(100)$ -> 0.065

Since the interest is compounded quarterly, we will use 4 for n. Lets plug in the values now:

$A=900(1+(0.065)/(4))^(4(4))$

$A=1,164.80$

The balance after 4 years will be $1,164.80

This pattern repeats every 5 terms. The pattern is rectangle, pentagon, square, hexagon, pentagon. What is the 19th term of this pattern? Answers Square
Pentagon
Hexagon
Rectangle

Answers

Since the pattern repeats every 5 terms, we can find the remainder when 19 is divided by 5 to determine which term in the pattern the 19th term corresponds to.

19 ÷ 5 = 3 with a remainder of 4

Since there are 5 terms in the pattern, the 19th term is equivalent to the 4th term in the pattern. Therefore, the 19th term is a square.

4(12+3) distributive property