A 4 1/2 foot long wire is being cut into smaller pieces that are 1 1/4 feet long. What is the maximum number of smaller pieces of wire that can be cut from the original piece of wire?

Answer250

Step-by-step explanation:

Final answer:

To find when two balloons are at the same height, set up two equations equal to each other with the starting heights and rates of ascent, and solve for the time. The two balloons will be at the same height approximately 4.636 seconds after they start rising.

Explanation:

To determine when two balloons will be at the same height, we can set up an equation based on their starting heights and their rates of ascent. We have a red balloon that starts at 7.3 meters off the ground and rises at 2.6 meters per second, and a blue balloon that starts at 12.4 meters off the ground and rises at 1.5 meters per second.

Let's let t represent the time in seconds after the balloons begin to ascend. The height of the red balloon at any time t can be expressed as:

Height_red = 7.3 + 2.6t

Similarly, the height of the blue balloon at any time t is:

Height_blue = 12.4 + 1.5t

To find out when the balloons are at the same height, we set the two equations equal to each other:

7.3 + 2.6t = 12.4 + 1.5t

Now, we solve for t by subtracting 1.5t from both sides:

2.6t - 1.5t = 12.4 - 7.3

1.1t = 5.1

Next, we divide both sides by 1.1 to isolate t:

t = 5.1 / 1.1

t ≈ 4.636 seconds

Thus, the balloons will be at the same height approximately 4.636 seconds after they begin to ascend.

The total employment compensation of the employee is b. $70,970.

Arithmetic operations are the basic part of mathematics which combines the basic operations like addition, subtraction, multiplication and division.

Given that,

Annual salary of the employee = $51,300

Health insurance per year = $2,830

Paid time off per year = $4,600

Monthly expense for personal vehicle = $600

Yearly expense = 12 × $600 = $7200

Reimbursement for the vehicle = $0.54 per work mile

Reimbursement for vehicle for 36,000 miles for work for the year = $0.54 × 36,000 miles = $19,440

Total employment compensation = ($51,300 + $2,830 + $4,600 + $19,440) - $7200

= $70,970

Hence the employment compensation is $70,970.

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Answer:

  B.  3, 3, 2

Step-by-step explanation:

The triangle inequality requires the sum of the lengths of the two shortest sides exceed the length of the longest side. That is the case only for the lengths of selection B:

  2 + 3 > 3

Actually the answer is (-1,5)

x^2 – 4x – 5 = 0

x^2 – 4x = 5

x^2 – 4x + 4 = 5 + 4

(x – 2)^2 = 9

x – 2 = ± 3

x = 2 + 3 and x = 2 – 3

x = 5 and x = –1

{–1, 5}

Answer:

Step-by-step explanation:

When we are proving a proposition, it's important to have order in our 2-column proof.

So, we must have a left colum for Statements and a right colum for Reasons, that's the order we need to have.

In the statements colum we write our deductions. In the reasons column, we write the justification or reason about our deduction.

Therefore, the right answer is the third choice: Order.

Answer:

B) 16

Step-by-step explanation:

The dot product of a pair of vectors is the sum of the products of their corresponding parts. It is a scalar.

... a · b = (7i -4j) · (4i +3j) = 7·4 + (-4)·3

... = 28 -12 = 16

A real-world situation for the inequality 4x + 8 ≥ 32 could involve calculating the minimum hours required at a part-time job to earn $32. Subtracting 8 and dividing by 4, we find that at least 6 hours of work are needed.

A real-world example that could be solved by using the inequality 4x + 8 ≥ 32 might involve a situation where you need to determine how many hours you must work at a part-time job to earn at least a certain amount of money. Suppose you earn $4 per hour and you have already earned $8. You want to know the minimum number of hours you must work to have at least $32 in total.

To solve the inequality 4x + 8 ≥ 32, you would first subtract 8 from both sides, which gives you 4x ≥ 24. Then, you would divide both sides by 4 to find the number of hours (x) you need to work. Therefore, x ≥ 6. This means you must work at least 6 hours to earn $32 or more.

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Answer:

12 by 14

Step-by-step explanation:

took quiz

The quotient of 5 divided by 1/2 is greater than 5 because dividing by a number less than 1 results in a larger number. In this case, it is equivalent to multiplying 5 by 2, yielding 10.

To determine if the quotient of 5 and 1/2 is greater than or less than 5, we consider the operation of division. Dividing by a number less than 1 will result in a larger number, while dividing by a number greater than 1 will result in a smaller number. The number 1/2 is less than 1, so when 5 is divided by 1/2, the quotient is greater than 5. It is equivalent to multiplying 5 by 2 (since dividing by a fraction is the same as multiplying by its reciprocal), which is 10. Therefore, 5 divided by 1/2 equals 10, which is greater than 5.

Answer:

6% annum for 850 would be 955

Answer:

Step-by-step explanation:

We are given that: Two triangles are such that one triangle is inverted and they share a common vertex. The lower triangle has two angles at the base. The lower left angle is marked as 55 degrees. The lower right angle is marked as 30 degrees. The angle at the vertex of the inverted triangle at the top is marked as x degrees.

The figure of such a triangle is attached to the answer.

As we know that sum of all the angles of a triangle is equal to 180°.

⇒ 55°+30°+x=180°

⇒  85°+x=180°

⇒ x=180°-85°

⇒ x=95°

Hence, the angle at the vertex is 95°.

The measure of angle x in the inverted triangle formed by two triangles sharing a common vertex is 95 degrees .

Two triangles sharing a common vertex. The angles given are as follows:

Measure of the lower left angle of the lower triangle = 55 degrees.

Measure of the lower right angle of the lower triangle = 30 degrees.

The angle at the vertex of the inverted triangle (at the top) can be found by subtracting the sum of the angles in the lower triangle from 180 degrees .

Since the sum of angles in a triangle is always 180 degrees.

Sum of angles in the lower triangle

= 55 degrees + 30 degrees

= 85 degrees.

Now, subtract the sum of angles in the lower triangle from 180 degrees to find the angle at the vertex of the inverted triangle (x degrees):

x degrees = 180 degrees - 85 degrees

                 = 95 degrees.

Therefore, the measure of angle x is 95 degrees.

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Answer:Theres a article about that ont he internet

Step-by-step explanation: