The work of a student to solve the equation 3(3y - 8) = 10 + 3y is shown below:
Step 1: 3(3y - 8) = 10 + 3y
Step 2: 6y - 5 = 10 + 3y
Step 3: 3y - 5 = 10
Step 4: 3y = 15
Step 5: y = 5
In which step did the student first make an error and what is the correct step?
Step 2: 9y - 24 = 10 + 3y
Step 2: 6y + 11 = 10 + 4y
O Step 3: 6y - 8 = 3(6 + y)
O Step 3: 3(3y - 8) = 7 + y
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Answer:

no...

8s -32 is the distributive property

Step-by-step explanation:

Answer:

20,000 pairs of barber scissors.

Step-by-step explanation:

The sales volume V for barber scissors is directly proportional to the size S of the sales force and inversely proportional to the price P of the scissors.

In other words, we can write that:

[tex]\displaystyle V = \frac{kS}{P}[/tex]

Where k is the constant of proportionality.

19,440 pairs were sold in 2013, when there was 54 salespeople and the price was $20 a pair. Hence, V = 19440 when S = 54 and P = 20. Substitute and determine the value of k:

[tex]\displaystyle \begin{aligned} (19440) &= \frac{k(54)}{(20)} \\ \\ 19440 &= \frac{27}{10}k \\ \\ k &=\frac{10}{27}(19440) = 7200 \end{aligned}[/tex]

Hence, our equation is:

[tex]\displaystyle V = \frac{7200S}{P}[/tex]

We want to determine the sales forecast with 50 salespeople and a price of $18 a pair. Hence, S = 50 and P = 18:

[tex]\displaystyle \begin{aligned} V&= \frac{7200(50)}{(18)} \\ \\ &= 20000\end{aligned}[/tex]

In conclusion, 20,000 pairs of barber scissors can be expected to be sold.

Answer:

4z

Step-by-step explanation:

-2z² + 4z + 2z²

Combine like terms

-2z^2  + 2z^2   +4z

0z^2 +4z

4z

[tex]\\ \sf\longmapsto -2z^2+4z+2z^2[/tex]

[tex]\\ \sf\longmapsto -2z^2+2z^2+4z[/tex]

[tex]\\ \sf\longmapsto (-2+2)z^2+4z[/tex]

[tex]\\ \sf\longmapsto 0z^2+4z[/tex]

[tex]\\ \sf\longmapsto 4z[/tex]

Step-by-step explanation:

x<1

x<(1/3)

yes this is the answer

Answer:

k=2

Step-by-step explanation:

Find the zeros of the factor

2x+1=0

x=-½

Plug x=-½ into the function and equate to 0

2(-½)³+(-½)²-k(-½)-1=0

2(-1/8)+¼+½k-1=0

-¼-1+¼+½k=0

-1+½k=0

½k=1

k=2

Step-by-step explanation:

2x+1=0

x=-1/2

Now p(x)= 2x^3 + x^2 -kx-1

subtitute value of x:

p(-1/2)= 2(-1/2)^3 + (-1/2)^2 -k(-1/2)-1

p(-1/2)=2*-1/8+1/4+k/2-1

p(-1/2)=-1/4+1/4+k/2-1

p(-1/2)=k/2-1

2x+1 is the factor of p(x) so

k/2-1=0

k/2=1

k= 2

Answer:

13, 14, 15

Step-by-step explanation:

13 + 14 + 15 = 42

Better explanation:

n + (n+1) + (n+2) = 42

42 - 2 - 1 = 39

n + n + n = 39

3n = 39  divide by 3 to isolate n

n = 13

So it starts with 13 and goes up from there.

Answer:

[tex]2x - x + 25 - x = x \: terms \: togther \\ 2x - x - x + 25 \\ = 0x + 25 \\ = 25 \\ thank \: you[/tex]

Answer:

2×12-12+25-12

24-12+13

24+13-12

37-12

25

Answer:  approximately 4.7368 minutes

This decimal value is the result of computing 90/19

=====================================================

Explanation:

Let's find the LCM of 6, 9 and 15. First, list out the prime factorization of each value.

The unique prime factors are 2, 3, and 5. We have 2 show up at most once, 3 show up at most twice, and 5 show up at most once. The LCM is 2^1*3^2*5^1 = 2*9*5 = 18*5 = 90.

We'll use this LCM value to set up an example below.

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

Consider the tank to be 90 gallons. If we only use tap A, keep tap B closed, and don't open pipe C, then tap A fills the tank at a rate of 90/6 = 15 gallons per minute since it needs 6 minutes to completely fill the tank.

If we have tap B do all the work (keep tap A and pipe C closed), then the rate is 90/9 = 10 gallons per minute for this tap.

Keeping pipe C closed, the two taps A and B work together to have a combined rate of 15+10 = 25 gallons per minute.

Now we consider pipe C being opened. This drains the tank and can do so in 15 minutes (assume the taps A and B aren't open). If we're dealing with a full 90 gallon tank, then its rate is 90/15 = 6 gallons per minute.

The net rate is 25-6 = 19 gallons per minute. We can think of it as a tug of war where the taps A and B ultimately win out despite the fact that pipe C is draining the water. The two taps fill the tank faster than the pipe can drain the tank.

In other words, the tank ultimately gets filled up rather than drained out over the long run. That net speed is at 19 gallons per minute.

The amount of time needed is approximately 90/19 = 4.7368 minutes.

Side note: you can start with any size tank. It doesn't have to be 90 gallons. I picked on this value because it works cleanly with the original given numbers 6, 9 and 15.

Answer:

[tex]x=\frac{90}{19}[/tex] = 4.73 minutes

[tex]\frac{1}{6}x +\frac{1}{9}x - \frac{1}{15} x = 1[/tex]

[tex]\frac{135}{810}x +\frac{90 }{810}x - \frac{54}{810} x = 1[/tex]

[tex]\frac{171}{810}x = 1[/tex]

x = 4.73 minutes

Step-by-step explanation:

Answer:

-13

Step-by-step explanation:

expression =4a-|3b+2c|

subtitute all values in the expression:

=4(-2) -|3(-3)+2(2)|

=-8-|-9+4|

=-8-|-5|

=-8-(5)

=-8-5

=-13

Note:if you need to ask any question please let me know.

The value of the expression from the variables  is -13

From the question, we have the following parameters that can be used in our computation:

4a - |3b + 2cl

Also, we have

a = - 2, b = -3, c = 2, x = 2.1, y = 3, and z = - 4.2.

substitute the known values in the above equation, so, we have the following representation

4a - |3b + 2cl = 4 * -2 - |3 * -3 + 2 * 2|

Evaluate

4a - |3b + 2cl = -13

Hence, the expression from the variables  is -13

Read more about expressions at

https://brainly.com/question/30492964

#SPJ3

Answer:  C)  4

==========================================================

Explanation:

Let's isolate t

-3 > -3t + 6

-3+3t > 6

3t > 6+3

3t > 9

t > 9/3

t > 3

This means any value can replace t such that it's larger than 3.

Something like t = 1/3 = 0.33 won't work since it's not larger than 3.

But something like t = 4 would work because it makes t > 3 true.

That's why choice C is the final answer.

Answer:

Specifically, Earth rotates faster at the Equator than it does at the poles. Earth is wider at the Equator, so to make a rotation in one 24-hour period, equatorial regions race nearly 1,600 kilometers (1,000 miles) per hour. Near the poles, Earth rotates at a sluggish 0.00008 kilometers (0.00005 miles) per hour.

Step-by-step explanation:

I hope this will help you :-)

Answer:

[tex] \frac{x + 19}{ - 2} = 5 \\ x + 19 = 5 \times ( - 2) \\ x + 19 = - 10 \\ x = - 19 - 10 \\ \boxed{x = - 29 }[/tex]

Answer:

r = 6

Step-by-step explanation:

– 36 – 4r = -2(-6 + 6r)

+36               +36

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

-4r = -12r + 48

+12r     +12r

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

8r = 48

/8     /8

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

r = 6

Answer:

r = 6

Step-by-step explanation:

– 36 – 4r = -2(-6 + 6r)

-36 - 4r = 12 - 12r

-48 - 4r = -12r

-48 = -8r

r = 6

Answer:

27 ft^2

Step-by-step explanation:

r = 3 ft (that's the radius)

and pi = 3

A = pi r^2

or

3 * r^2

plug in r = 3

so 3 * 3^2 = 3 * 9 = 27 ft^2

(note: 3^2 = 3 * 3. Squaring means we multiply the number by itself)

Answer:

It's b I'm pretty sure.

Step-by-step explanation:

Answer:

y = 2 2/5

Step-by-step explanation:

1 7/8y = 4 1/2

Change to improper fractions

1 7/8 = (8*1+7)/8 = 15/8

4 1/2 = (2*4+1)/2 = 9/2

15/8 y = 9/2

Multiply each side by 8/15

8/15 * 15/8y = 9/2 * 8/15

y = 9/15 * 8/2

y = 3/5 *4

y = 12/5

Changing back to a mixed number

y = 2 2/5

Answer:

20000

Step-by-step explanation:

This is because when you round to the signifigant figure, you basically look at any digits at the start of the number, which isn't zero. In this case it would be in the ten thousand 19340. So you round 19340 to the nearest 10 thounsand, which, would be 20000

Answer:

Step-by-step explanation:

[tex] {x}^{2} - 3x + 8[/tex]

(Putting value of x = 4)

[tex] = {4}^{2} - 3 \times 4 + 8[/tex]

= 16 - 12 + 8

= 24 - 12

= 12 (Ans)

Answer:

It is 12

Step-by-step explanation:

[tex]f(x) = {x}^{2} - 3x + 8[/tex]

When x is 4, substitute x as 4:

[tex]f(4) = {(4)}^{2} - 3(4) + 8 \\f(4) = 16 - 12 + 8 \\ f(4)= 12[/tex]

Answer:

Given;

120,000 people voted in 2015.

In 2015, 20% more people voted than 2014.

Therefore:

How many more people voted in 2015 = 20% of 120,000

= 24,000

Total number of people voted in 2014 = 120,000 - 24,000

= 96,000

Ans) 96,000 people voted in 2014.

Find the inverse of each of the given functions. f(x) = 4x − 12 f−1(x) = x +

first one is 1/4

second one is 3

Answer:

first box is 1/4
second box is 3

for the next question on the page ( h(x) = (2x-4)/3 ) the answer is C (h^-1(x) = (3x+4)/2 )

Step-by-step explanation:

Answer:

9

Step-by-step explanation:

Probability is 3/7

that 7 represent all shots and 3 represents successful ones

so,

sarah shots 21 times that means 9 of them would hit the target.

Answer:

$46,571.67

Step-by-step explanation:

if your description is right and complete, she sold cars on the first 2 days as average for $46975.

and on the third day for $45765

to calculate the total average we need to know the total amount of sales and then divide it by the observation period length (3 days).

how do we get the total sales ?

we know the average of the first 2 days. we don't need to find the exact value for every day, but we know the exact value for these first 2 days : 2×46975 = $93950

as the average of these 2 days = (day1 + day2)/2

46975 = (day1 + day2)/2

day1 + day2 = 2×46975 = 93950

it is not important what two (day) numbers created 93950. we know that this was the total sum of the first two days. and that is enough.

so, we have in total

$93950 on the first 2 days

$45765 in the third day

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

$139715 for all 3 days

the average per day is then

139715 / 3 = $46,571.67

Answer:

2x + 3y = -21

Step-by-step explanation:

Parallel lines have same slope.

2x + 3y = -21

      3y = - 2x - 21

y = [tex]y = \dfrac{-2}{3}x-\dfrac{21}{3}\\\\y=\dfrac{-2}{3}x-7[/tex]

Answer: 31.5

Step-by-step explanation:

Answer: 31.5

Concept:

When encounter questions that ask for operation on algebraic expressions, using BODMAS or PEMDAS method would be easier. Since this question asked for using BODMAS, then it is:

Solve:

Given

2 × 3 + 45 ÷ 2 - 6 + 9

Simplify by division

=2 × 3 + 22.5 - 6 + 9

Simplify by multiplication

=6 + 22.5 - 6 + 9

Simplify by addition

=28.5 + 9 - 6

=37.5 - 6

Simplify by subtraction

=31.5

Hope this helps!! :)

Please let me know if you have any questions

Answer:

buy for $20 and sell for $40

is 100% mark-up

Step-by-step explanation:

Answer:

5.975

Step-by-step explanation: