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3 years ago

Write the prime factorization for 168

Mathematics

1 answer:

11Alexandr11 [23.1K]3 years ago

7 0

$168|2\\.\ 84|2\\.\ 42|2\\.\ 21|3\\.\ \ 7|7\\.\ \ 1|\\\\168=2\cdot2\cdot2\cdot3\cdot7$

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Dwayne drove 18 miles to the airport to pick up his father and then returned home. On the return trip he was able to drive an av

Nesterboy [21]

Answer:

30 mph

Step-by-step explanation:

Let d = distance (in miles)

Let t = time (in hours)

Let v = average speed driving to the airport (in mph)

⇒ v + 15 = average speed driving from the airport (in mph)

Using: distance = speed x time

$\implies t=\dfrac{d}{v}$

Create two equations for the journey to and from the airport, given that the distance one way is 18 miles:

$\implies t=\dfrac{18}{v} \ \ \textsf{and} \ \ t=\dfrac{18}{v+15}$

We are told that the total driving time is 1 hour, so the sum of these expressions equals 1 hour:

$\implies \dfrac{18}{v} +\dfrac{18}{v+15}=1$

Now all we have to do is solve the equation for v:

$\implies \dfrac{18(v+15)}{v(v+15)} +\dfrac{18v}{v(v+15)}=1$

$\implies \dfrac{18(v+15)+18v}{v(v+15)}=1$

$\implies 18(v+15)+18v=v(v+15)$

$\implies 18v+270+18v=v^2+15v$

$\implies v^2-21v-270=0$

$\implies (v-30)(v+9)=0$

$\implies v=30, v=-9$

As v is positive, v = 30 only

So the average speed driving to the airport was 30 mph

(and the average speed driving from the airport was 45 mph)

8 0

1 year ago

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WILL GIVE BRAINLIEST

scZoUnD [109]

Answer:

it is d

Step-by-step explanation:

6 0

2 years ago

A color printer can print 36 pages in three minutes in 108 pages in nine minutes if the number of pages varies directly with the

nignag [31]

Answer:

12 pages per minutes

Step-by-step explanation:

36 pages in 3 minutes, so each minutes can print 12 pages

And 108 pages in 9 minutes, which is still 12 pages

So 12 pages per minute

7 0

2 years ago

Lamy can paint 84 portraits in 6 weeks. at this rate , how many portraits can he paint in 2 weeks

lilavasa [31]

Answer:

28 portraits

Step-by-step explanation:

Let's first figure out how many portraits Lamy can paint in 1 week, which is his unit rate. To calculate this, we just have to divide the number of portraits he paints by the amount of time it takes him to paint them.

In this case, the former quantity is 84 portraits, and the latter quantity is 6 weeks, so his unit rate is $\frac{84 \text \: portraits}{6 \text \: weeks}$ = 14 paintings per week.

Now, we know that in 1 week, Lamy can paint 14 portraits. Therefore, since this is a directly proportional relationship, all we have to do to find how many portraits he can paint is 2 weeks is double the unit rate. This is because in a directly proportional relationship, if you multiply one variable by a number, you have to multiply the other by the same number to maintain equality, and here we are multiplying weeks by 2 so we need to multiply paintings by 2 as well.

Thus, Lamy can paint 14 · 2 = 28 paintings in 2 weeks.

Hope this helps!

7 0

1 year ago

Complete the statement by typing the letter of the angle. m∠ =54º

tekilochka [14]

Answer:

x = 16

∠A = 39

∠B = 54

∠C = 87

Step-by-step explanation:

Make a equation of all of the angles added together is equal to 180 since the angles of a triangle added together is 180

(4x-10)+(2x+7)+(7x-25)=180

combine like terms

4x+2x+7x-10+7-25 = 180

13x-28=180

solve for x

13x=208

x = 16

plug in x to find the measure of the angle

∠A = 2(16) + 7 = 39

∠B = 4(16) - 10 = 54

∠C = 7(16) - 25 = 87

Add them together to double check your answer

39 + 54 + 87 = 180

hope this helps

3 0

2 years ago

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