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2 years ago

Desperate for helllppp pls

Mathematics

1 answer:

beks73 [17]2 years ago

7 0

Answer:

B) - 1 < x < - 0.2

Step-by-step explanation:

<h3>Given inequality</h3>

|5x + 3| < 2

The LHS is absolute value so we look at two options:

<h3>Option 1</h3>

5x + 3 is positive, then the inequality becomes:

5x + 3 < 2
5x < 2 - 3
5x < - 1
x < - 1/5 or x < - 0.2

<h3>Option 2</h3>

5x + 3 is negative, then the inequality becomes:

- (5x + 3) < 2
5x + 3 > - 2
5x > - 2 - 3
5x > - 5
x > - 1

The solution is the combination of the two intervals:

x > - 1 and x < - 0.2 ⇒ - 1 < x < - 0.2

Correct choice is B

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Solve these linear equations by Cramer's Rules Xj=det Bj / det A:

timurjin [86]

Answer:

(a) $x_1=-2,x_2=1$

(b) $x_1=\frac{3}{4} ,x_2=-\frac{1}{2} ,x_3=\frac{1}{4}$

Step-by-step explanation:

(a) For using Cramer's rule you need to find matrix $A$ and the matrix $B_j$ for each variable. The matrix $A$ is formed with the coefficients of the variables in the system. The first step is to accommodate the equations, one under the other, to get $A$ more easily.

$2x_1+5x_2=1\\x_1+4x_2=2$

$\therefore A=\left[\begin{array}{cc}2&5\\1&4\end{array}\right]$

To get $B_1$ , replace in the matrix A the 1st column with the results of the equations:

$B_1=\left[\begin{array}{cc}1&5\\2&4\end{array}\right]$

To get $B_2$ , replace in the matrix A the 2nd column with the results of the equations:

$B_2=\left[\begin{array}{cc}2&1\\1&2\end{array}\right]$

Apply the rule to solve $x_1$ :

$x_1=\frac{det\left(\begin{array}{cc}1&5\\2&4\end{array}\right)}{det\left(\begin{array}{cc}2&5\\1&4\end{array}\right)} =\frac{(1)(4)-(2)(5)}{(2)(4)-(1)(5)} =\frac{4-10}{8-5}=\frac{-6}{3}=-2\\x_1=-2$

In the case of B2, the determinant is going to be zero. Instead of using the rule, substitute the values of the variable $x_1$ in one of the equations and solve for $x_2$ :

$2x_1+5x_2=1\\2(-2)+5x_2=1\\-4+5x_2=1\\5x_2=1+4\\ 5x_2=5\\x_2=1$

(b) In this system, follow the same steps,ust remember $B_3$ is formed by replacing the 3rd column of A with the results of the equations:

$2x_1+x_2 =1\\x_1+2x_2+x_3=0\\x_2+2x_3=0$

$\therefore A=\left[\begin{array}{ccc}2&1&0\\1&2&1\\0&1&2\end{array}\right]$

$B_1=\left[\begin{array}{ccc}1&1&0\\0&2&1\\0&1&2\end{array}\right]$

$B_2=\left[\begin{array}{ccc}2&1&0\\1&0&1\\0&0&2\end{array}\right]$

$B_3=\left[\begin{array}{ccc}2&1&1\\1&2&0\\0&1&0\end{array}\right]$

$x_1=\frac{det\left(\begin{array}{ccc}1&1&0\\0&2&1\\0&1&2\end{array}\right)}{det\left(\begin{array}{ccc}2&1&0\\1&2&1\\0&1&2\end{array}\right)} =\frac{1(2)(2)+(0)(1)(0)+(0)(1)(1)-(1)(1)(1)-(0)(1)(2)-(0)(2)(0)}{(2)(2)(2)+(1)(1)(0)+(0)(1)(1)-(2)(1)(1)-(1)(1)(2)-(0)(2)(0)}\\ x_1=\frac{4+0+0-1-0-0}{8+0+0-2-2-0} =\frac{3}{4} \\x_1=\frac{3}{4}$

$x_2=\frac{det\left(\begin{array}{ccc}2&1&0\\1&0&1\\0&0&2\end{array}\right)}{det\left(\begin{array}{ccc}2&1&0\\1&2&1\\0&1&2\end{array}\right)} =\frac{(2)(0)(2)+(1)(0)(0)+(0)(1)(1)-(2)(0)(1)-(1)(1)(2)-(0)(0)(0)}{4} \\x_2=\frac{0+0+0-0-2-0}{4}=\frac{-2}{4}=-\frac{1}{2}\\x_2=-\frac{1}{2}$

$x_3=\frac{det\left(\begin{array}{ccc}2&1&1\\1&2&0\\0&1&0\end{array}\right)}{det\left(\begin{array}{ccc}2&1&0\\1&2&1\\0&1&2\end{array}\right)}=\frac{(2)(2)(0)+(1)(1)(1)+(0)(1)(0)-(2)(1)(0)-(1)(1)(0)-(0)(2)(1)}{4} \\x_3=\frac{0+1+0-0-0-0}{4}=\frac{1}{4}\\x_3=\frac{1}{4}$

6 0

4 years ago

Can some one help me asap

zavuch27 [327]

It'd be easier to do #18 if y ou were to break it up:

14* (first term + 14th term)
Sum from n=1 to 14 of n = S = ---------------------------------
14 2

14(1+14)
= ---------------- = 7(15) = 105
2

The sum of twice that is 210. The sum of "1 from n=1 to n=14" is just 14.

The final sum is 210 + 14 = 224 (answer)

4 0

3 years ago

The cost of tuition at a 2 year school is $11,000 per academic year. Ming is eligible for $9,500 in financial aid to cover tuiti

goldenfox [79]

Answer:

$125

Step-by-step explanation:

11,000 - 9,500 = 1,500

1,500 / 12 = 125 (we use 12 because 12 months = 1 year)

8 0

3 years ago

Read 2 more answers

What is the answer? <br><br><br> A: 5/20<br><br> B:5/11<br><br> C: 19/20<br><br> D: 1 9/20

Kaylis [27]

The answer is D.
Find common factors of denominators.
15+10+4/20= 29/20= 1 9/20 :)

7 0

4 years ago

PLEASE HELP

UNO [17]

6.3-4.6=1.7%. You subtract the percentages to find the total percentage after the percentage dropped 4.6 from 6.3

4 0

3 years ago