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podryga [215]
2 years ago
6

The work of a student to solve a set of equations is shown: Equation A: y = 4 − 2z Equation B: 4y = 2 − 4z Step 1: −4(y) = −4(4

− 2z) [Equation A is multiplied by −4.] 4y = 2 − 4z [Equation B] Step 2: −4y = 4 − 2z [Equation A in Step 1 is simplified.] 4y = 2 − 4z [Equation B] Step 3: 0 = 6 − 6z [Equations in Step 2 are added.] Step 4: 6z = 6 Step 5: z = 1 In which step did the student first make an error? (5 points)​
Mathematics
2 answers:
mina [271]2 years ago
8 0

Answer:

step 2.

Step-by-step explanation:

dem82 [27]2 years ago
4 0

Answer:

The student made the first mistake in step 2.

Step-by-step explanation:

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Find a positive number for which the sum of it and its reciprocal is the smallest​ (least) possible. Let x be the number and let
Allisa [31]

Answer:

S(x) = x + \frac{1}{x} --- Objective function

Interval = \{x:x=1\}

Step-by-step explanation:

Given

Represent the number with x

The required sum can be represented as:

x + \frac{1}{x}

Hence, the objective function is:

S(x) = x + \frac{1}{x}

To get the the interval, we start by differentiating w.r.t x

<em>Using first principle, this gives:</em>

S'(x) = 1 - \frac{1}{x^2}

Equate S'(x) to 0 in order to solve for x

0 = 1 - \frac{1}{x^2}

Subtract 1 from both sides

0 -1 = 1 -1 - \frac{1}{x^2}

-1 = - \frac{1}{x^2}

Multiply both sides by -1

1 = \frac{1}{x^2}

Cross Multiply

x^2 * 1 = 1

x^2  = 1

Take positive square root of both sides because x is positive

\sqrt{x^2} = \sqrt{1

x = 1

Representing x using interval notation, we have

Interval = \{x:x=1\}

To get the smallest sum, we substitute 1 for x in S(x) = x + \frac{1}{x}

S(1) = 1 + \frac{1}{1}

S(1) = 1 + 1

S(1) = 2

<em>Hence, the smallest sum is 2</em>

3 0
3 years ago
If the start time is 8:34 amd the elapsed timne is 3 hours and 18 minutes what is the end time
mr_godi [17]
Forget the '34' part of 8:34 and the '18' minutes from 3 hours and 18 minutes for now.

Just add 3 hours on to 8, to get 11. Then, bring back the 34 and 18 and add them together. 34 + 12 = 52. Now put that 52 on the end of the 11, and you get 11:52 as the end time. 
3 0
3 years ago
Read 2 more answers
Solve the following dividend problem.
brilliants [131]

A.

To get dividend per share, we need to divide total dividend by total numbers of shares outstanding.

Dividend per share = \frac{40,000}{50,000}=0.8 dollars.


B.

Since per share you get $0.8, for 100 shares you will get 0.8*100=80 dollars.

Also, that is \frac{80}{40,000}*100=0.2 percent of the total dividends.


ANSWER:

A. $0.8 per share

B. $80 (and that is 0.2% of total dividend)

7 0
3 years ago
Read 2 more answers
What its two plus two
anastassius [24]

4 what do you think it is 1000000000

7 0
3 years ago
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[20 pts] evaluate the logarithm log(6)1/36​, show work pls!
Delvig [45]

Answer:

\large\boxed{\log_6\dfrac{1}{36}=-2}

Step-by-step explanation:

\text{We know:}\\\\\log_ab=c\iff a^c=b\\\\\log_6\dfrac{1}{36}\qquad\text{use}\ a^{-1}=\dfrac{1}{a}\\\\=\log_636^{-1}=\log_6(6^2)^{-1}\qquad\text{use}\ (a^n)^m=a^{nm}\\\\=\log_66^{(2)(-1)}=\log_66^{-2}\qquad\text{use}\log_ab^n=n\log_ab\\\\=-2\log_66\qquad\text{use}\ \log_aa=1\\\\=-2(1)=-2

\log_6\dfrac{1}{36}=-2\ \text{because}\ 6^{-2}=\dfrac{1}{6^2}=\dfrac{1}{36}

8 0
3 years ago
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