Justify each step in the solution of the equation 5(x+2)=24-2x

Common difference = [tex]\frac{1}{5}[/tex]

Solution:

Given arithmetic sequence:

[tex]$-2,-1\frac{4}{5} ,-1\frac{3}{5} , -1\frac{2}{5} , ....[/tex]

Let us first convert the improper fraction into mixed fraction.

[tex]$-2,-\frac{9}{5} ,-\frac{8}{5} , -\frac{7}{5} , ....[/tex]

Difference between two numbers in an arithmetic sequence is the common difference.

[tex]$a_2-a_1=-\frac{9}{5}-(-2)=-\frac{9}{5}+2=\frac{1}{5}[/tex]

[tex]$a_3-a_2=-\frac{8}{5}-\left(-\frac{9}{5}\right)=-\frac{8}{5}+\frac{9}{5}=\frac{1}{5}[/tex]

[tex]$a_4-a_3=-\frac{7}{5}-\left(-\frac{8}{5}\right)=-\frac{7}{5}+\frac{8}{5}=\frac{1}{5}[/tex]

Common difference = [tex]\frac{1}{5}[/tex].

Hence the common difference of the arithmetic sequence is [tex]\frac{1}{5}[/tex].

Common difference of the given arithmetic sequence is equal to [tex]\frac{1}{5}[/tex]

The given arithmetic sequence is in mixed numbers. Converting them into proper fractions, we get:

[tex]First\ term = t_1 = -2\\\\Second\ term = t_2 = -1\frac{4}{5} = -\frac{(5\times1)+4}{5} = -\frac{9}{5}\\\\Third\ term = t_3 = -1\frac{3}{5} = -\frac{(5\times1)+3}{5} = -\frac{8}{5}\\\\Fourth\ term=t_4 = -1\frac{2}{5} = -\frac{(5\times1)+2}{5} = -\frac{7}{5}[/tex]

The sequence can thus be rewritten as [tex]-2, -\frac{9}{5}, -\frac{8}{5}, -\frac{7}{5}[/tex]

To find the common difference of the given arithmetic sequence, subtract any two consecutive numbers of the sequence. The difference between two consecutive numbers is always a constant and is termed as the common difference.

Hence,

[tex]d_1= t_2-t_1=(-\frac{9}{5} -(-2)= \frac{-9+10}{5}= \frac{1}{5} \\\\d_2=t_3-t_2= (-\frac{8}{5} -(-\frac{9}{5} )= \frac{-8+9}{5} = \frac{1}{5}\\\\d_3=t_4-t_3= (-\frac{7}{5} -(-\frac{8}{5} )= \frac{-7+8}{5} = \frac{1}{5}[/tex]

[tex]d_1=d_2=d_3 = d[/tex]

Common difference [tex]d=\frac{1}{5}[/tex]

Answer:

$153.75

Step-by-step explanation:

$71.75 / 7=$10.25

$10.25 x 15 =$153.75

Answer: 38

Step-by-step explanation:

Divide 38000/1000

Answer:

Step-by-step explanation: How many 10,000 are in 200,000

Answer:

The answer is A

Step-by-step explanation:

Since we are finding Tim's height in 6 months, you would have to plug the 6 into the expression.

Answer:

Step-by-step explanation: it A

0.5+6= 3

60+3= 63

Answer:

-0.22222222222

Step-by-step explanation:

Which is (B)

Answer:

12 choices

Step-by-step explanation:

2*3 = 6

6*2= 12

You would have to multiply the numbers to see the number of choices.

There are 12 different choices for coffee in the shop.

First, we need to find the selections, these are:

Now we need to find the number of options for each selection:

The total number of combinations is the product between the numbers of options:

C = 2*3*2 = 12

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Final answer:

The customer would need to have 25 small gifts to wrap in order for the costs to be the same, whether using the department store's service at $2 per gift or paying his niece the $50 flat fee.

Explanation:

To determine how many small gifts need to be wrapped to make the cost the same whether paying his niece the flat fee of $50 or paying the department store $2 per gift, we can set up a simple equation:

Let x represent the number of small gifts.
Then, the cost of wrapping at the department store is $2 per gift, which means the cost is 2x dollars.
The niece's flat fee is $50, regardless of the number of gifts.

The equation to find the breakeven point where both options cost the same is:
2x = 50

Solving for x gives us:

x = 50 / 2
x = 25 gifts

Thus, if the customer has 25 small gifts to wrap, it would cost the same to have them wrapped by his niece at a flat rate or by the department store per gift.

Answer:[tex]\frac{1}{12}[/tex]

Step-by-step explanation:

Okay, first, you want to find the probability of getting a head, which would be 1/2 because there are two options and we are only looking for one out of the two. Then, the probability of getting a 6 would be 1/6 because there is only one chance of getting a 6 and there are 6 options. Next, you would have to multiply both quantities to find out what the probability would be of getting both. So it would be [tex]\frac{1}{2}[/tex] ×[tex]\frac{1}{6}[/tex]=[tex]\frac{1}{12}[/tex]

Probability of getting a head followed by a 6 is 1/12

Step-by-step explanation:

There are 2 possible outcomes of tossing a coin a head and a tail.

The probability is 1 out of 2 each for head and tail.

Probability of getting a 6 when a dice is rolled is 1 out of 6 for each face i.e 1,2,3,4,5,6

So the probability of getting a head followed by 6 is 1/2*1/6 = 1/12

It can also be understood as below.

There can be 12 possible combinations once a coin is tossed and a die is rolled. Head-1, Head-2. Head-3, Head-4, Head-5, Head-6, Tail-1, Tail-2, Tail-3, Tail-4, Tail-5, Tail-6

In the list there is 1 outcome that we need. Head-6. This again gives us the chance of getting Head-6 as 1 out of 12.

Answer:

x=2

Step-by-step explanation:

5(6x-1)-10x+5=4(x+10)-4x

simplify both sides

30x-5-10x+5=4x+40-4x

Simplify even further

20x=40

x=2

Answer:

6/13 > 4/13

4/13 < 6/13

Step-by-step explanation:

Answer:

Step-by-step explanation:

1.609 km=1 mile

1 km=1/1.609 mile

[tex]4.8 km=\frac{4.8}{1.609} ~miles=\frac{4.8*5280}{1.609} \approx~15,751.40~ft[/tex]

Answer:

the answer is D 15,751.40

1 Kilometer is equal to 3,280.839895 feet which is approximately 3,281 feet.

multiply 3,281 feet by 4.8 = 15,748.8 which can be rounded to make 15,751.40.

In total making the correct answer choice D.

Answer:

43.5 ft

Step-by-step explanation:

Given: Julie is 6 feet tall

           She stands 15 feet from the flagpole.

           The edges of the square line up with the top and bottom of the flagpole.

Picture drawn to show side and angle formed by Julie and flagpole.

Lets assume the height of flagpole be "h".

As given, the edges of the square line up with the top and bottom of the flagpole.

∴ Angle and base of triangle are same then ratio of corresponding sides are also equal.

Now, finding the height of flagpole by using tangent rule.

we know, [tex]tan\theta= \frac{Opposite}{adjacent}[/tex]

Remember, both the angle are equal.

∴ Ratio of opposite and adjacent leg for both right angle triangle= [tex]\frac{6}{15} : \frac{h-6}{15}[/tex]

We can put it; [tex]\frac{6}{15} = \frac{15}{h-6}[/tex]

Solving the equation now

⇒ [tex]\frac{6}{15} = \frac{15}{h-6}[/tex]

Multiplying both side by 15

⇒[tex]6 = \frac{15\times 15}{h-6}[/tex]

Multiplying both side by (h-6)

⇒ [tex]6\times (h-6) = 15\times 15[/tex]

Distributive property of multiplication

⇒ [tex]6h-36= 225[/tex]

Adding both side by 36

⇒[tex]6h= 225+36[/tex]

Dividing both side by 6

⇒[tex]h= \frac{261}{6}[/tex]

∴ [tex]h= 43.5\ feet[/tex]

Hence, the height of flagpole is 43.5 feet.

The height of the flagpole is given by the length of the hypotenuse side

formed by the right triangle Julie forms with the cardboard.

Response:

The triangle formed by the edges of square lined up with the top and

bottom of the flagpole is a right triangle.

The altitude of the right triangle formed with the height of the flagpole as the base = 15 feet

Length of a leg of the right triangle = √(15² + 6²) = 3·√(29)

The other angle formed by the right triangle = (90° - arctan(15/6))

h × sin(arctan(15/6)) = 3·√29

[tex]h = \mathbf{\dfrac{3 \cdot \sqrt{29} }{sin(arctan(15/6))} } = 17.4[/tex]

Height of the flagpole, h = 17.4 feet

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Answer:

2/4 .   4/6 .   2/3

Step-by-step explanation:

Answer:

Step-by-step explanation:

2/4=1/4

4/6=2/3

5/8

3/6

6/9=3/6

Answer:

Step-by-step explanation:

2 3/4 = 11/4

11/4-1/3

11/4x3=33/12

1/3x4= 4/12

33-4=29

2 5/12

Answer:827

Step-by-step explanation:

Add 620 plus 207

Answer:

X=40 degrees

Step-by-step explanation:

Having trouble with RSM?

The value of angle x will be equal to 40 degrees.

According to the equivalent angle postulate, if a transversal meets two parallel lines, the corresponding angles must be congruent.

In other words, the corresponding angles will always be identical if a transversal intersects two parallel lines. In geometry, corresponding sides and corresponding angles of polygons are compared as part of the tests for congruence and resemblance.

In the diagram attached with the answer below apply the corresponding angle theorem to calculate the value of x.

The value of angle x by using corresponding angle theorem will be calculated as below:-

x = 180 - 65 - 75

x = 180 - 140

x = 40

Therefore, the value of angle x will be equal to 40 degrees.

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Answer:

4 and a half hours

Step-by-step explanation:

half an hour ((60 x 1) / 2) for 3 of the days (30 x 3) is 90 so 1 and a half hours. then, 2/3's of an hour ((60 x 2) / 3) for 3 days (40 x 3) is 120 so 2 hours. then, adding the last hour 1.5 + 2 + 1 is 4.5 or 4 and a half hours.

Assuming he spent $300 on specialty tools to make toy horses for children the number of   horses that  Samir sell in order to break even is 6 horses.

First step is to calculate his profit

Profit=$125-$75

Profit=$50

Now let determine how many horses does Samir sell in order to break even

Number of horse=$300/50

Number of horses=6 horses

Inconclusion the number of  horses that  Samir sell in order to break even is 6 horses.

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Answer:6

Step-by-step explanation:

There are 32 fluid ounces in 4 cups

In order to solve this problem, you need to know some facts:

[tex]1oz=0.125cups \\ \\ 1cup=8oz[/tex]

By knowing this, we can easily solve this problem by proportion:

[tex]Let: \\ \\ x:Fluid \ ounces \\ \\ \frac{x}{4}=\frac{1}{0.125} \\ \\ x=\frac{4}{0.125} \\ \\ x=32[/tex]

So there are 32 fluid ounces in 4 cups

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Answer:

Kira served 25 orders, Bill served 34 orders and Michael served 75 orders.

Step-by-step explanation:

Let Kira served x number of orders.

So, Bill served (x + 9) orders and Michael served 3x orders.

Now, it is given that Kira, Bill, and Michael served a total of 134 orders.

So, x + (x + 9) + 3x = 134

⇒ 5x + 9 = 134

⇒ 5x = 125

⇒ x = 25

Therefore, Kira served 25 orders, Bill served (25 + 9) = 34 orders and Michael served 3 × 25 = 75 orders. (Answer)

Answer:

$140

Step-by-step explanation:

Answer:

$140.00

Step-by-step explanation:

Gross pay is the pay before any deductions by taxes or other reason.

Simply multiply the five dollars by twenty-eight hours.

Answer:

Part 1) [tex]a=-\frac{1}{4c^6}[/tex]

Part 2) [tex]a=-\frac{1}{4c^{-6}}[/tex]

Step-by-step explanation:

Part 1) we have

[tex]a=2b^{3}[/tex] ----> equation A

[tex]b=-\frac{1}{2}c^{-2}[/tex] ----> equation B

substitute equation B in equation A

[tex]a=2(-\frac{1}{2}c^{-2})^{3}[/tex]

Applying property of exponents

[tex](x^{m})^{n}=x^{m*n}[/tex]

[tex]x^{-m} =\frac{1}{x^{m}}[/tex]

[tex]a=2(-\frac{1}{2}c^{-2})^{3}=2(-\frac{1}{2})^3(c^{-2})^{3}=2(-\frac{1}{8})(c^{-6})=-\frac{1}{4c^6}[/tex]

therefore

[tex]a=-\frac{1}{4c^6}[/tex]

Part 2) we have

[tex]a=2b^{3}[/tex] ----> equation A

[tex]b=-\frac{1}{2c^{-2}}=-\frac{c^{2}}{2}[/tex] ----> equation B

substitute equation B in equation A

[tex]a=2(-\frac{c^{2}}{2})^{3}[/tex]

Applying property of exponents

[tex](x^{m})^{n}=x^{m*n}[/tex]

[tex]x^{-m} =\frac{1}{x^{m}}[/tex]

[tex]a=2(-\frac{c^{2}}{2})^{3}=2(-\frac{c^{6}}{8})[/tex]

simplify

[tex]a=-\frac{c^{6}}{4}[/tex]

therefore

[tex]a=-\frac{1}{4c^{-6}}[/tex]

Answer:

Each person will be getting [tex]2\frac{2}{5}[/tex] pieces  of licorice

Step-by-step explanation:

If we have 12 pieces of licorice

To divide it equally among 5 people following formula will be used

Pieces to be given to each person = [tex]\frac{total\, pieces}{total\,people}[/tex]

                                                           = [tex]=\frac{12}{5} \\2.4\\[/tex]

So

Each person will be getting [tex]2\frac{2}{5}[/tex] pieces  of licorice

Keywords: Algebra

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I believe it's a 25% profit.

950+250= 1200

1500-1200= 300

300/1200= 0.25

0.25 x 100= 25%

Answer:

I want to say 20% I could be wrong

Step-by-step explanation:

$950 + $250 = 1,200

1,200 ÷ 1500 = 0.8

0.800 > 80.0

80%

100% - 80% = 20%

Net Profit Margin = 20%

Net Profit =$300

Profit Percentage = 25%

The speed of a boat in still water (b) is 50km/h. It takes the same time (t) for the boat to travel 10km (x) upstream as it does to travel 20km (y) downstream. Find the speed of the current.​

upstream speed (u) = speed in still water (b) - stream speed (s) = b-s = 50-s

downstream speed (d) = speed in still water (b) + stream speed (s) = 50+s

time (t) = x/u = y/d

10/(50-s) = 20/(50+s)

10(50+s) = 20(50-s)

500 + 10s = 1000 - 20s

30s = 500

stream speed (s) = 500/30 = 16.6 km/h

Answer:

Perpendicular

Step-by-step explanation:

Put all the points on a graph.

Parallel means that the lines that have the same slope and different y-intercepts. Lines that are parallel to each other will never intersect.

On the graph we made we can see that the lines will have to intersect because the points are in positions that no matter which points we chose to connect together, they would intersect with the other line.

Answer:

Step-by-step explanation:

3(x - 4)(x + 5) = 0

Dividing through by 3

(x - 4)(x + 5) = 0

(x - 4) = 0 or x + 5 = 0

x - 4 = 0 or x + 5 = 0

x = 4 or x = - 5

Answer:

4x^4

Step-by-step explanation:

Cubed and squared are the same thing

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