We have 30 miles of fencing which can be used to enclose a rectangular piece of grazing land along a straight portion of a river. No fence is required along the river. The grazing land will be subdivided into two sections by means of a fence parallel to the sides and perpendicular to the river. Write a function that expresses the total area in terms of the width x of the side of the grazing area perpendicular to the straight river.
Answers
Answer:
The area of the gazing land is square miles.
Step-by-step explanation:
Given that, 30 miles of fencing can be used to enclose a rectangular piece of grazing land along a straight piece of river.
Let the length of the rectangular piece of gazing which is along the river be y and the width of the rectangular piece of gazing be x.
Along the river side, no fence is required.
Therefore total length of fence is = 2(x+y)-x
=2y+x
∴2y+x=30
⇒2y=30-x
The area of the rectangular piece of gazing is = Length×width
=xy
square miles.
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answer in scientific notation
Answers
= 96.2x10^6
Explanation:
To make the calculations easier, factor the expression:
= (9.87x10-2.5)x10^6
= 96.2x10^6
Final answer:
To subtract numbers in scientific notation, both terms must be expressed in the same form. Convert 9.87 x 10^7 to 98.7 x 10^6, subtract 2.5 x 10^6 to get 96.2 x 10^6, and then convert this back to 9.62 x 10^7.
Explanation:
To solve the given problem 9.87 x 10^7 - 2.5 x 10^6, we need to make sure that both terms are in the same form of scientific notation. Here, the base (10) and the exponent (7 and 6) are already in the form of scientific notation. The next step is to perform the subtraction.
Because the two terms are not in the same order of magnitude, we cannot subtract directly. First convert them into the same form: 9.87 x 10^7 is the same as 98.7 x 10^6. Now, we can perform the subtraction: 98.7 x 10^6 - 2.5 x 10^6 = 96.2 x 10^6.
However, the typical form of scientific notation has just one digit before the decimal point, thus convert 96.2 x 10^6 back to 9.62 x 10^7.
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2
4
1
3
Answers
Answer:
2
Step-by-step explanation:
example A(2a,0),B(2b,0)
C(2b,2c),D(2a,2c)
mid point of AC=((2a+2b)/2,(0+2c)/2)=(a+b,c)
mid point of BD=((2b+2a)/2,(0+2c)/2)=(a+b,c)
∴midpoint of diagonals same or diagonals bisect each other.
Answers
Answer:
–9 < x – 4 < 9
Answers
Answer:
Step-by-step explanation:
The movement of the minute hand of the clock is circular. This means that a complete movement of the minute hand of the clock is the same as the angle formed at the center of the circle. The sum of the angles at a point is 360 degrees. The minute hand travels 360 degrees in a 60 minutes. It means that the degrees travelled in a minute is
360/60 = 6 degrees
The hour hand travels 360 degrees in 60 minutes. Therefore, the angle that the hour hand travels in 1 minute is
360/6 = 6 degrees
Final answer:
The minute hand of a clock travels 6° in 1 minute. The hour hand travels 0.5° in 1 minute.
Explanation:
To answer this question, we first need to consider what a full rotation is. A complete circle, one full rotation, is 360°. The minute hand of a clock completes one full rotation, or 360°, every hour or 60 minutes.
In 1 minute, the minute hand would have covered 1/60 of a full rotation. To calculate this in degrees, we multiply 360° by 1/60, which gives us 6°. Therefore, the minute hand of a clock travels 6° in one minute.
The hour hand moves more slowly. It takes 12 hours to complete a full rotation or 360°. In 1 minute, the hour hand covers, 360° divided by (12 hours x 60 minutes), which gives us 0.5°. Therefore, the hour hand of a clock moves 0.5° in 1 minute.
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Answers
Answer: It depends on how you round but about 10.44 m.
Step-by-step explanation:
x²_9
x2 + 3x + 9
-2x² +8
Answers
Final answer:
A polynomial is prime if it cannot be factored into polynomials of lower degree. In this case, x² +9 and x² + 3x + 9 are prime polynomials while x² -9 and -2x² +8 are not.
Explanation:
In mathematics, a polynomial is said to be prime if it cannot be factored into polynomials of lower degree, at least one of which must be non-constant. To determine if a polynomial is prime, we try to factor it. In our case:
- x² +9 is a prime polynomial because it is a sum of squares and cannot be factored into real polynomials of lower degree.
- x² -9 is not a prime polynomial because it can be factored into (x-3)(x+3).
- x² + 3x + 9 is a prime polynomial because it cannot be factored into real polynomials of lower degree.
- -2x² +8 is not a prime polynomial as it can be factored into -2(x²-4).
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Answer: x^2+9 and x^2+3x+9
Step-by-step explanation: