Part A: Find the LCM of 5 and 12. Show your work. (3 points)

Part B: Find the GCF of 72 and 81. Show your work. (3 points)

Part C: Using the GCF you found in Part B, rewrite 72 + 81 as two factors. One factor is the GCF and the other is the sum of two numbers that do not have a common factor. Show your work. (4 points)

Applying the required rule or theorem, it can be concluded that the second biker is farther from the parking lot. The distance of the bikers to the parking lot are:

i. First biker = 17.0 km

ii. Second biker = 20.22 km

The path of travel of both bikers would form a triangle. Applying the Pythagoras theorem to the path of the first biker would give his distance from the starting point. While applying the cosine rule to the path of second rider would gives his distance to the starting point.

Thus,

a. To determine the distance of the first biker from the parking lot.

Let the required distance be represented by x. Applying the Pythagoras theorem, we have:

[tex]hyp^{2}[/tex] = [tex]adj 1^{2}[/tex] + [tex]adj 2^{2}[/tex]

[tex]x^{2}[/tex] = [tex]8^{2}[/tex] + [tex]15^{2}[/tex]

   = 64 + 225

   = 289

x = [tex]\sqrt{289}[/tex]

  = 17

x = 17 km

Thus, the first biker is 17.0 km from the starting point.

b. To determine the distance of the second biker from the parking lot.

Let the required distance be represented by x. So that applying the cosine rule, we have:

[tex]c^{2}[/tex] = [tex]a^{2}[/tex] + [tex]b^{2}[/tex] - 2ab Cos θ

[tex]x^{2}[/tex] = [tex]8^{2}[/tex] + [tex]15^{2}[/tex] - 2(15*8) Cos (180 - 20)

    = 64 + 225 - 240 Cos 160

    = 289 - 240 * -0.5

[tex]x^{2}[/tex] = 289 + 120

   = 409

x = [tex]\sqrt{409}[/tex]

 = 20.2237

x = 20.22 km

Thus, the second biker is 20.22 km from the starting point.

Therefore, the second biker is farther from the parking lot.

A sketch of the path of travel for the two bikers is attached for more clarifications.

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Answer:

Step-by-step explanation:

4*4*__=48

16*__=48

48/16=3

3*4=12

Answer:

12 boxes on the right side

Step-by-step explanation:

4 going across and 3 rows so 12 boxes

48 divided by 3 is 16 but divided by 4 is 12

since there are 16 boxes at the top its a good inference that there's

only 3 flat rows meaning per every flat there would be 4 boxes and 3 rows

there would be 12 boxes on the right side.

Answer:

  66,000 kg·km/hr

Step-by-step explanation:

  p = mass × velocity

  p = (1200 kg) × (55 km/hr) = 66,000 kg·km/hr

_____

Additional comment

Here, we have used the standard metric units for momentum. The units you choose can be any mass·velocity units that meet your needs.

Answer: 2,343.3333 repeating, or just 2,343 1/3

Step-by-step explanation:

If you divide, your answer comes out to be 2,343.3333 repeating or 2,343 1/3.

The quantity of excess reserves that the Bank of Cheerton now hold is $210

From the attached table, the amount generated on the reserve is $4,200

If the Fed's reserve requirement is 5 percent, then the quantity of excess reserves that the Bank hold is given as:

Quantity of excess reserves = 5% of $4,200

Quantity of excess reserves = 0.05 * 4200

Quantity of excess reserves = $210

Hence the quantity of excess reserves that the Bank of Cheerton now holds is $210.

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Answer:

Petra would need to save for 12 weeks to get 126

126+34.75=160.75

Petra need to save $10.50 to have enough money to buy the electronic reader in 12 weeks.

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

Petra wants to buy an electronic reader that costs $160.75 including tax. She has saved $34.75.

Here, So far and plans to save an additional $10.50 each week.

Let number of weeks to save $10.50 to have enough money to buy the electronic reader = x

So, We can formulate;

⇒ 10.50x + 34.75 = 160.75

Solve for x;

⇒ 10.50x = 160.75 - 34.75

⇒ 10.50x = 126

⇒ x = 126/10.50

⇒ x = 12

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Answer:

x = 33

Step-by-step explanation:

11 - 4 = 7

You need to make that fraction equal 11

33/3 = 11

I hope this helps!

Answer:

17.41 Dollars

Step-by-step explanation:

First, you take the discount, which is 2 dollars, so now the cost without any additional costs is 22 dollars. Next, find 8 percent of 22 by multipling 22*0.08 and then you get 1.76. Subtract that from 22 and 20.24. Then take 14 percent of 20.24 by multiplying it by 0.14, which you get 2.8336. Round that down and you get 2.83. Subtract that from that and you get 17.41.

Answer:

5 m, 2 m, 2.5 m, 2 m, 2.5 m, 4 m.

Step-by-step explanation:

First find the length of the 2 missing sides. Remember that the picture is WAY out of proportion, so the sides won't be what they look like.

Since the left side is 4 and the right side is 8 cm, the missing left side is 4 cm.

Since the top side is 5 and the bottom side is 10 cm, the missing top piece is 5 cm.

So the sides starting at the bottom right and going clockwise are 10, 4, 5, 4, 5, 8 cm. Multiply each of these * 0.5 and call them meters.

5 m, 2 m, 2.5 m, 2 m, 2.5 m, 4 m.

Answer:

x=3

Step-by-step explanation:

Answer:

  15π/2 ft

Step-by-step explanation:

Arc length is given by the formula ...

  s = rθ . . . . . r = radius; θ = central angle in radians

A 135° arc has a radian measure of (135)(π/180) = 3π/4. The radius of a circle with a 20 ft diameter is (20 ft/2) = 10 ft. So, the arc length is ...

  s = (10 ft)(3π/4) = 30π/4 ft = 15π/2 ft

Answer:

The answer is B

Answer: D: (-∞, ∞)

               R: (-∞, ∞)

Step-by-step explanation:

Since the end points are arrows and have no set stopping point we can assume the answer is all real numbers, also known as infinity

The value of a in the equation is 10

The root of the equation is determined using the equation shown below:

[tex]x=\frac{-b\pm\sqrt{b^2-4ac} }{2a}[/tex]

Given the quadratic equation ax^2+x-24=0;

The product of the quadratic equation is c/a

Product = c/a

- 2 2/5 = -24/a

-12/5 = -24/a

-12a = 5 * -24

-12a = -120

a = 10

Hence the value of a in the equation is 10

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Compare to ax^2+bx+c

Product of roots=c/a

ATQ

[tex]\\ \tt\hookrightarrow \dfrac{c}{a}=-2\dfrac{2}{5}[/tex]

[tex]\\ \tt\hookrightarrow \dfrac{-24}{a}=\dfrac{-12}{5}[/tex]

[tex]\\ \tt\hookrightarrow \dfrac{24}{a}=\dfrac{12}{5}[/tex]

[tex]\\ \tt\hookrightarrow 12a=120[/tex]

[tex]\\ \tt\hookrightarrow a=10[/tex]

Answer:

Which Restaurant and aquarium

Step-by-step explanation:

If you tell the name I can answer it

The required angles from smallest to largest are m<M < m<L < m<K

Given the coordinate of the triangle KLM given as K(-2,-2), L(2, 6), M(7, -2)

Get the measure of KL, KM and LM using the distance formula as shown:

[tex]D=\sqrt{(x_2-x_1)^2+(y_2-y)_1)^2}[/tex]

For the length KL with coordinate points K(-2,-2), L(2, 6)

[tex]KL=\sqrt{(2-(-2))^2+(6-(-2))^2}\\KL=\sqrt{4^2+8^2}\\KL=\sqrt{16+64}\\KL=\sqrt{80}\\KL =4\sqrt{5}[/tex]

For the length KM with coordinate points K(-2,-2), M(7, -2)

[tex]KM=\sqrt{(7-(-2))^2+(-2-(-2))^2}\\KM=\sqrt{9^2+0^2}\\KM=\sqrt{81}\\KM=9[/tex]

The length LM with coordinate points L(2,6), M(7, -2)

[tex]LM=\sqrt{(7--2)^2+(-2-6)^2}\\LM=\sqrt{5^2+(-8)^2}\\LM=\sqrt{25+64}\\LM=\sqrt{89}[/tex]

From the distances, we can see that side LM > KM > KL. Hence the required angles from smallest to largest are m<M < m<L < m<K

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Answer: I Think you will make 100 time 2 divide 3

Step-by-step explanation:

i'm not sure, have a nice day

Answer:

In the document, Westing names the sixteen heirs present as his “nieces and nephews” and says that tomorrow his ashes “will be scattered to the four winds.” He then asserts that his life has been taken by one of his heirs, and he promises that the heir who finds something will receive the inheritance

Step-by-step explanation:

Westing names the sixteen heirs present as his “nieces and nephews” and says that tomorrow his ashes “will be scattered to the four winds.” He then asserts that his life has been taken by one of his heirs, and he promises that the heir who finds something will receive the inheritance.

The main events in the Westing Game include moving into Sunset Towers, the Halloween dare, the reading of Samuel Westing's will, and the pairing of teams. Finally, the solving of clues and ultimately solving the puzzle.

Several years after that, Turtle stays with Sandy/Westing (as Eastman) while he really dies. She finally wins the prize and goes to play chess with her niece Alice.

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Answer:

Step-by-step explanation:

=> 3x + 9 = 2x + 5

=> 3x - 2x = 5 - 9

=> x = - 4

Hence, x has only one solution that is, x = -4 (Ans)

Topic : Linear equations in one variable

Given :

Solution :

[tex]\qquad \sf \: { \dashrightarrow 3x + 9 = 2x + 5}[/tex]

Transposing variables on one side and constant terms on the other side, we get :

[tex]\qquad \sf \: { \dashrightarrow 3x - 2x = 5 - 9}[/tex]

[tex]\qquad \sf \: { \dashrightarrow x = - 4}[/tex]

Answer:

6x + 3y

Step-by-step explanation:

3(2x - y) + 6y ← distribute parenthesis by 3

= 6x - 3y + 6y ← collect like terms

= 6x + 3y

[tex]\huge\boxed{Hi\: there!}[/tex]

Here, we use the Distributive Property:

[tex]a(b+c)=ab+ac[/tex]

3(2x-y)+6y=6x-3y+6y

Combine like terms:

6x+3y

[tex]\huge\boxed{Therefore,\: our \:equation\: is:6x+3y}[/tex]

[tex]\huge\bf{Good \:luck \:with \:your \: studies! :)\\~Unknown Dreamer}[/tex]

ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff

b

Answer:

The retail price would be $93.6

Step-by-step explanation:

This is because you can divide 130 by 100 to find 1% of such, and you'll get 1.3. Then, multiply 1.3 by 72, which makes 72% of the original price, to come find your answer, $93.6. Hope this helps!

Answer:

the top right box

Step-by-step explanation:

Answer:

-g-8≥9

Step-by-step explanation:

Just ask.

Hope this helps. :)

Answer:

B.3/7

Step-by-step explanation:

Answer:

16 and 2

Step-by-step explanation:

16+2=18

16-2=14