The work of a student trying to solve the equation 2(2x − 3) = 6 + 2x + 4 is shown below:

Step 1: 2(2x − 3) = 6 + 2x + 4
Step 2: 4x − 3 = 10 + 2x
Step 3: 4x − 2x = 10 + 3
Step 4: 2x = 13
Step 5: x = 6.5

In which step did the student first make an error and what is the correct step? (4 points)

Group of answer choices

Step 3: 4x + 2x = 10 + 3
Step 2: 4x − 3 = 2 + 2x
Step 3: 4x − 2x = 10 - 3
Step 2: 4x − 6 = 10 + 2x

Answer:

Asha has 3x books

Step-by-step explanation:

Since we dont not know how many books Luna has we know it is "X" so luna will have 3 times as much as X so 3x which also represents 3 times x

Answer:

Step-by-step explanation:

Answer: 2.25

Step-by-step explanation: This is because 2.25*40 is 90

Hope this helps and brainliest would be appreciated

Answer:

12π

is the correct answer

Answer:

1) You can rely solely on your brakes because when doing so the car will just travel 250ft from the point you hit your brakes till the point the car stopped completely, leaving you 50ft away from the cow.

2) See attached picture.

j(t) represents the distance from the point you hit the brake t seconds after you hit it in feet

j'(t) represents the velocity of the car t seconds after the brakes have been hit in ft/s.

j"(t) represents the acceleration of the car t seconds after the brakes have been hit in [tex]ft/s^{2}[/tex]

3) yes, any time after t=5.28 will not accurately model the path of the car since at that exact time the car will reach a velocity of 0ft/s and unless another force is applied to the car, then the car will not move after that time.

4) [tex]j(t)=\left \{ {{95t-9t^{2}; 0\le t<5.28s} \atop {250.69; 5.28s\leq t \leq 10s}} \right.[/tex]

[tex]j'(t)=\left \{ {{95-18t; 0\leq t<5.28s} \atop {0 ; 5.28s\leq t \leq 10s}} \right.[/tex]

(see attached picture for graph)

Step-by-step explanation:

1) In this part of the problem we need to find the time when the speed of the car is 0. Gets to a complete stop. For this we will need to take the derivative of the position function so we get:

[tex]j(t)=95t-9t^2[/tex]

[tex]j'(t)=95-18t[/tex]

and we set the first derivative equal to zero so we get:

95-18t=0

and solve for t

-18t=-95

[tex]t=\frac{95}{18}[/tex]

t=5.28s

so now we calculate the position of the car after 5.28 seconds, so we get:

[tex]j(5.28)=95(5.28)-9(5.28)^{2}[/tex]

[tex]j(5.28)=250.69ft[/tex]

so we have that the car will stop 250.69ft after he hit the brakes, so there will be about 50ft between the car and the cow when the car stops completely, so he can rely just on the breaks.

2) For answer 2 I take the second derivative of the function so I get:

[tex]j(t)=95t-9t^{2}[/tex]

[tex]j'(t)=95-18t[/tex]

j"(t)=-18

and then we graph them. (See attached picture)

j(t) represents the distance from the point you hit the brake t seconds after you hit it in feet

j'(t) represents the velocity of the car t seconds after the brakes have been hit in ft/s.

j"(t) represents the acceleration of the car t seconds after the brakes have been hit in [tex]ft/s^{2}[/tex]

3)  yes, any time after t=5.28 will not accurately model the path of the car since at that exact time the car will reach a velocity of 0ft/s and unless another force is applied to the car, then the car will not move after that time.

4) [tex]j(t)=\left \{ {{95t-9t^{2}; 0\le t<5.28s} \atop {250.69; 5.28s\leq t \leq 10s}} \right.[/tex]

[tex]j'(t)=\left \{ {{95-18t; 0\leq t<5.28s} \atop {0 ; 5.28s\leq t \leq 10s}} \right.[/tex]

(see attached picture for graph)

Answer: lesser x = 1/5 greater x = 4

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:

5.573.75

Step-by-step explanation:

because math

Answer:

x = 14

x + 23 < 37 ( move constant to right-hand side and change its sign)

x<37-23 ( subtract numbers)

x < 14

Answer: -c= 157+X^2

Step-by-step explanation:

Answer:

formula is 1/2 *b * h

so h=8m

b=8m

Step-by-step explanation:

b*h=

8*8=64*1/2=

64divided by 2= 32m²

Step-by-step explanation:

1)

10(3) + 2(1) = 32/4 = 8 mph

2)

[3(1.5) + 0.5x]/2 = 4

(4.5 + 0.5x) = 8

0.5x = 3.5

x = 7mph

Answer:

It's B

Step-by-step explanation:

Answer:

B is a functional answer

Answer:

A. 78

Step-by-step explanation:

7 x 4 is the bottom and the bottom is the same as the top so I got 28 x 2 which is 56. 4 x 1 is one side. The other side is the same so I got 4 x 2 which is 8. 1 x 7 is the front and back. I got 7 x 2 is 14. i wrote 56 + 14 + 8 and got 78

hope this helps :)

Answer:

Equation of parabola:  8*(y - 2) = (x - 3)^2

or

y = (1/8)*(x - 3)^2 + 2

Step-by-step explanation:

focus at (3,4) and its directrix y = 0.

Focus equation:  (h, k + c) = (3, 4)

Directrix equation  y =  k - c = 0

so  h = 3,   k + c = 4,   k - c = 0

Solve  the system :  k + c = 4 and k - c = 0

add the equations together:     k + c + k - c = 4 + 0

2k = 4

k = 2

so   k + c = 4,    2 + c = 4,   c = 2

4c (y - k) = (x -  h)^2

4*2 *(y - 2) = (x - 3)^2

8*(y - 2) = (x - 3)^2

Answer:

m = 0

Step-by-step explanation:

Hope this helps:)

Answer:

A) The multiplier for this situation is 0.02.

B) The cost in 4 years will be $ 33,555.39.

C) 31,000 x 1.02 ^ N = X

Step-by-step explanation:

Since in 2012 the average cost for a new midsized car was about $ 31,000, and new car prices tend to go up about 2% every year, to determine what is the multiplier for this situation, what will the cost be in 4 years if this trend continues and to write an equation to calculate the cost in n years the following calculations must be performed:

A)

31,000 x 2/100 = X

31,000 x 0.02 = X

Thus, the multiplier for this situation is 0.02.

B)

31,000 x 1.02 ^ 4 = X

33,555.39 = X

Thus, the cost in 4 years will be $ 33,555.39.

C)

31,000 x 1.02 ^ N = X

Here, N represents the number of years over which the price increase will be calculated, and X represents the price after that number of years.

Answer:

About 207 inches

Step-by-step explanation:

The circumference of a circle is given by the formula ...

 C = πd . . . . . where d represents the diameter

The circumference of the tire is the distance the truck will move when the tire makes one revolution. That distance is ...

 C ≈ 3.1416×(66 in) ≈ 207.35

The truck will travel about 207 inches for each revolution of the tire.

Answer:

Step-by-step explanation:

Five students= 5x

They all got two more= 5x + 2(5)

5x + 10 = 30

     - 10    -10

5x = 20

    5

x = 4

Answer:

Step-by-step explanation:

w and d are the width and diagonal, respectively.

w = d/2 + 1 = (d+2)/2

Pythagorean theorem

w^2 + 8^2 = d^2

substitution

(d+2)^2/4 +64 = d^2

(d+2)^2 + 256 = 4d^2

d^2+4d+4 + 256 = 4d^2

3d^2-4d-260 = 0

Quadratic formula

d = [4±√( 4²-4(3)(-260))]/[2⋅3] = 10, -26/3

-26/3 is an extraneous solution, so d = 10 inches

w=d/2 +1 =6 inches

Ant‘s path = 8+6 = 14 inches

Beetle’s path = 10 inches

14 < 1.5(10)

Ant reaches food first.

Answer:

10 units

Step-by-step explanation:

Answer:

21

Step-by-step explanation:

simply

the square represents 90 degrees and 90 - 61 is 21

Answer:

70

Step-by-step explanation:

2 x (25 + 10) = 2 x 35 = 70

Answer:

5/15

(1/3 if u want it simplified)

(about 33.3 % if you want percentage)

Step-by-step explanation:

6 + 4 + 5 = 15 total marbles

There are 5 blue marbles.

9514 1404 393

Answer:

  (1, 55), (4, 220), (5, 275)

  times 55

Step-by-step explanation:

You know from life experience that the cost of tickets is often proportional to the number of tickets*. Here, you can check that by dividing the cost by the number of tickets for each of the table entries where both are given:

  110/2 = 55 = 165/3

This tells you the cost of 1 ticket is 55. It also tells you the cost of 4 tickets will be 4×55 = 220, and the cost of 5 tickets will be 5×55 = 275.

In short, the cost in dollars is the number of tickets times 55.

_____

* Your life experience will also tell you that sometimes there is a "processing fee" that makes the relation non-proportional. No such fee is evident here.

__

Alternate solution

Since the relation is proportional, you can find the cost of 1 ticket by dividing the cost of 2 tickets by 2: 110/2 = 55. You can find the cost of 4 tickets by doubling the cost of 2 tickets: 2×110 = 220. You can also find the cost of 5 tickets by adding the costs of 2 and 3 tickets: 110 +165 = 275.

9514 1404 393

Answer:

  b⁶

Step-by-step explanation:

The question tells you how to work it: use the relations you studied.

Here, you have the power of an expression with an exponent. The exponents multiply.

  [tex]\text{Rule: }(a^b)^c=a^{bc}\\\\\text{Appication: }(b^3)^2=b^{3\cdot2}=\boxed{b^6}[/tex]

_____

Additional comment

A coefficient is used to indicate repeated addition: 3x = x + x + x.

An exponent is used to indicate repeated multiplication: x³ = x·x·x.

This is still true when the exponent is applied to an expression with an exponent:

  (b³)² = (b³)(b³) . . . . the factor b³ is repeated 2 times as indicated by the exponent 2

Of course, each of these indicates repeated multiplication, so we really have ...

  (b³)(b³) = (b·b·b)·(b·b·b) = b·b·b·b·b·b

And this can be simplified using an exponent to show the repeated multiplication:

  = b⁶

Then, by going the long way around, we arrive at ...

  (b³)² = b⁶

Answer:

There is only one image

Step-by-step explanation: