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4 years ago

What is the greatest common factor of 24 and 54?

1 answer:

5 0

$24|2 \\ 12|2 \\ 6 \ |2 \\ 3 \ | 3 \\ 1 \\ \\ 24=2^3*3 \\ \\ 54|2 \\ 27|3 \\ 9 \ |3 \\ 3 \ |3 \\ 1 \\ \\ 54=2*3^3 \\ \\ \\ G.C.M(27;54)=2*3=6$

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A rectangular field measures 400yds x 600yds. Find the length of the diagonal of the field.

Fed [463]

That would be 1000 yards - add the both together

3 0

3 years ago

What is the x-component of the electric field at (x, y) = (0 m, 4 m)??

Elza [17]

(a)Two charges are placed on the x-axis: one is placed at x = 3 m and the other is at x = -3 m. The magnitude of both charges is 2.3 µC but the blue one (at x = -3 m) is positive while the red one (at x = +3 m) is negative.

What are the x- and y-components of the electric field at (x, y) = (0 m, +4 m)?

(b) Now the positive and negative charge switch places. The magnitude of the charges is still 2.3 µC where the blue one (now at x = +3 m) is positive and the red one (now at x = -3 m) is negative.

What are the x- and y-components of the electric field at (x, y) = (0 m, +4 m)?

(c) Now both charges (still at x = -3 m and x = +3 m) are positive. The magnitude of both charges is still 2.3 µC.

What are the x- and y-components of the electric field at (x, y) = (0 m, +4 m)?

(d) Finally, both charges (still at x = -3 m and x = +3 m) are negative. The magnitude of both charges is still 2.3 µC.

8 0

3 years ago

Jason and Eddy are traveling from Jacksonville to Miami, which is a distance of 382 miles. According to the American Automobile

wolverine [178]

Answer:

The value is $v = 49.23 \ mph$

Step-by-step explanation:

From the question we are told that

The distance from Jacksonville to Miami is d = 382 miles

The time it take to travel from Jacksonville to Daytona is $t_1 = 1 \ hour\ and\ 54\ minutes = 1 + \frac{54}{60} = 1.9 \ hours$

The time it take to travel from Daytona Beach to Fort Pierce is $t_2 = 2\ hours\ and\ 51\ minutes= 2 + \frac{51}{60} = 2.85 \ hours$

The time it take to travel from Fort Pierce to West Palm Beach is

$t_3 = 1\ hour\ and\ 23\ minutes= 1 + \frac{23}{60} = 1.38 \ hours$

The time it take to travel from West Palm Beach to Miami $t_4 = 1\ hour\ and\ 38\ minutes= 1 + \frac{38}{60} = 1.63 \ hours$

Generally the average speed is mathematically represented as

$v = \frac{d}{t_1 + t_2 +t_3 + t_4 }$

=> $v = \frac{382}{1.9 + 2.85 +1.38 + 1.63 }$

=> $v = 49.23 \ mph$

6 0

3 years ago

A combined total of 39000 is invested in two bonds that pay 5% and 6.5% simple interest. The annual interest is 235500 how much

dolphi86 [110]

Answer:

$12000 at 5%

$27000 at 6.5%.

Step-by-step explanation:

Let x represent amount invested at 5% and y represent amount invested at 6.5%.

We have been given that a combined total of 39000 is invested in two bonds. We can represent this information in an equation as:

$x+y=39000...(1)$

We are also told that the annual interest rate is 2355.00. We can represent this information in an equation as:

$0.05x+0.065y=2355...(2)$

Upon substituting equation (1) in equation (2), we will get:

$0.05x+0.065(39000-x)=2355$

$0.05x+2535-0.065x=2355$

$-0.015x+2535=2355$

$-0.015x=2355-2535$

$-0.015x=-180$

$\frac{-0.015x}{-0.015}=\frac{-180}{-0.015}$

$x=12000$

Therefore, an amount of $12,000 is invested at 5%.

Upon substituting $x=12000$ in equation (1), we will get:

$12000+y=39000$

$y=39000-12000$

$y=27000$

Therefore, an amount of $27,000 is invested at 6.5%.

4 0

3 years ago

Find four consecutive numbers whose sum equals 218

Softa [21]

Answer: 53, 54, 55, and 56

Step-by-step explanation: This problem states that the sum of 4 consecutive numbers is 218 and it asks us to find the numbers.

4 consecutive numbers can be represented as followed.

X ⇒ first number

X + 1 ⇒ second number

X + 2 ⇒ third number

X + 3 ⇒ fourth number

Since the sum of our 4 consecutive numbers is 218, we can set up an equation to represent this.

X + X + 1 + X + 2 + X + 3 = 218

On the left side of the equation, we can combine our x's and our numbers.

4x + 6 = 218

-6 -6 ← subtract 6 from both sides of the equation

4x = 212

÷4 ÷4 ← divide both sides of the equation by 4

X = 53

X ⇒ first number = 53

X + 1 ⇒ second number = 54

X + 2 ⇒ third number = 55

X + 3 ⇒ fourth number = 56

Therefore, our 4 consecutive numbers are 53, 54, 55, and 56.

4 0

4 years ago