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2 years ago

Express the area of the entire rectangle. Your answer should be a polynomial in standard form.

Mathematics

1 answer:

weeeeeb [17]2 years ago

8 0

Answer: A=x²+6x+8

Step-by-step explanation:

Since we are looking to find the area of the entire rectangle, we would use the formula $A=lw$ . $l$ is length and $w$ is width. You would approach this problem like any other area of the rectangle problem, except you are dealing with polynomials instead.

$A=(x+2)(x+4)$

$A=x^2+4x+2x+8$

$A=x^2+6x+8$

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OlgaM077 [116]

Answer:

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100+40+20=160

3 0

3 years ago

estimate each product. tell whether the estimate is greater than or less than the actual product. $224×12= 372×36= 488×85= 515×4

Jobisdone [24]

<span>224*12=2600(less than actual Product) 372*36=13400(greater than actual Product) 488*85=41500(greater than actual Product) 515*41=21100(less than actual Product)</span>

6 0

3 years ago

Solve/answer the question and help me understand this question please

faltersainse [42]

Answer:

5.25 m

Step-by-step explanation:

A diagram can help you understand the question, and can give you a clue as to how to find the answer. A diagram is attached. The problem can be described as finding the sum of two vectors whose magnitude and direction are known.

<h3>understanding the direction</h3>

In navigation problems, direction angles are specified a couple of different ways. A <em>bearing</em> is usually an angle in the range [0°, 360°), <em>measured clockwise from north</em>. In land surveying and some other applications, a bearing may be specified as an angle east or west of a north-south line. In this problem we are given the bearing of the second leg of the walk as ...

N 35° E . . . . . . . 35° east of north

Occasionally, a non-standard bearing will be given in terms of an angle north or south of an east-west line. The same bearing could be specified as E 55° N, for example.

<h3>the two vectors</h3>

A vector is a mathematical object that has both magnitude and direction. It is sometimes expressed as an ordered pair: (magnitude; direction angle). It can also be expressed using some other notations;

magnitude∠direction
magnitude <em>cis</em> direction

In the latter case, "cis" is an abbreviation for the sum cos(θ)+i·sin(θ), where θ is the direction angle.

Sometimes a semicolon is used in the polar coordinate ordered pair to distinguish the coordinates from (x, y) rectangular coordinates.

The first leg of the walk is 3 meters due north. The angle from north is 0°, and the magnitude of the distance is 3 meters. We can express this vector in any of the ways described above. One convenient way is 3∠0°.

The second leg of the walk is 2.5 meters on a bearing 35° clockwise from north. This leg can be described by the vector 2.5∠35°.

<h3>vector sum</h3>

The final position is the sum of these two changes in position:

3∠0° +2.5∠35°

Some calculators can compute this sum directly. The result from one such calculator is shown in the second attachment:

= 5.24760∠15.8582°

This tells you the magnitude of the distance from the original position is about 5.25 meters. (This value is also shown in the first attachment.)

You may have noticed that adding two vectors often results in a triangle. The magnitude of the vector sum can also be found using the Law of Cosines to solve the triangle. For the triangle shown in the first attachment, the Law of Cosines formula can be written as ...

a² = b² +o² -2bo·cos(A) . . . . where A is the internal angle at A, 145°

Using the values we know, this becomes ...

a² = 3² +2.5² -2(3)(2.5)cos(145°) ≈ 27.5373

a = √27.5373 = 5.24760 . . . . meters

The distance from the original position is about 5.25 meters.

_____

<em>Additional comment</em>

The vector sum can also be calculated in terms of rectangular coordinates. Position A has rectangular coordinates (0, 3). The change in coordinates from A to B can be represented as 2.5(sin(35°), cos(35°)) ≈ (1.434, 2.048). Then the coordinates of B are ...

(0, 3) +(1.434, 2.048) = (1.434, 5.048)

The distance can be found using the Pythagorean theorem:

OB = √(1.434² +5.048²) ≈ 5.248

7 0

1 year ago

Work out the area of this circle. Take pi to be 3.142 and give your answer to 1 decimal place

Rashid [163]

Step-by-step explanation:

<em>I think you have forgotten to attach the question. </em>

<em>Anyways....</em>

In order to find the area of a circle use the formula:

π $r^{2}$ Where r is the radius

For example the radius is 3cm. The area of the circle will be:

π × $3^{2}$

Since you have taken pi as 3.142...

3.142 × $3^{2}$

3.142 × 9

= 28.278

In order to find the answer to 1 decimal place, check the number next to the number right after the decimal. Is it a number greater than or equal to 5? then add +1 to the number.

= 28.3 $cm^{2}$