To find the correct polynomial, we can use the answers to help us out. The middle variable must be the sum of +2 and another number; the last number in the equation must be the product of +2 and the other number.
Knowing this information, we can use the process of elimination to find the exact polynomial that contains the factor (3x + 2).
A) This can't be it because to get -x as the middle variable, you would need to add -3 and +2. However, -3 x +2 doesn't equal -4.
B) This equation isn't the right one because to get +8 you need to add +6 + 2. However, the product of these two isn't -8.
C) Can't be correct because +2 and -7 = -5, but 2 x -7 = -14...not -9.
D) Is the correct answer because you can add 2 and -1 to get +1. (There is an understood +1 in front of the x in the equation.) The product of 2 and -1 equals -2, which happens to be the last number inside this equation. Therefore, this (D) is the correct answer choice.
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The area of the remaining board is [(L × B) - (l × b)].
According to the statement
We have to find that the area of the remaining board.
So, For this purpose, we know that the
Area of rectangle is the region occupied by a rectangle within its four sides or boundaries. The area of a rectangle depends on its sides.
From the given information:
Suppose the bigger rectangle is labelled as ABCD and the smaller rectangle is labelled as PQRS.
And
Consider that the length and breadth of the bigger rectangle are L and B respectively. And the length and breadth of the bigger rectangle are l and b respectively.
The area of any rectangle is:
Area = Length × Breadth
The area of the bigger rectangle is:
Area of ABCD = L × B
The area of the smaller rectangle is:
Area of PQRS = l × b
Then the area of the remaining board will be:
Area of remaining board = Area of ABCD - Area of PQRS
Area of remaining board= (L × B) - (l × b)
Thus, The area of the remaining board is [(L × B) - (l × b)].
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Question:
A rectangle is removed from the middle of a larger rectangular shaped board. What is the area of the remaining board?
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1. Use p to find the circumference of a circle 2. Use p to find the area of a circle 3. Find the area of a parallelogram 4. Find the area of a triangle 5. Convert square units In Section 4.2, we again looked at the perimeter of a straight-edged figure. The distance around the outside of a circle is closely related to this concept of perimeter. We call the perimeter of a circle the circumference. 341 Example 1 Finding the Circumference of a Circle A circle has a diameter of 4.5 ft, as shown in Figure 2. Find its circumference, using 3.14 for p. If your calculator has a key, use that key instead of a decimal approximation for p. p The circumference of a circle is the distance around that circle. Definitions: Circumference of a Circle Let’s begin by defining some terms. In the circle of Figure 1, d represents the diameter. This is the distance across the circle through its center (labeled with the letter O, for origin). The radius r is the distance from the center to a point on the circle. The diameter is always twice the radius. It was discovered long ago that the ratio of the circumference of a circle to its diameter always stays the same. The ratio has a special name. It is named by the Greek letter p (pi). Pi is approximately , or 3.14 rounded to two decimal places. We can write the following formula. 22 7 O d Radius Diameter Circumference Figure 1 C pd (1) Rules and Properties: Formula for the Circumference of a Circle NOTE The formula comes from the ratio p C d 4.5 ft Figure 2 342 CHAPTER 4 DECIMALS © 2001 McGraw-Hill Companies C 2pr (2) Rules and Properties: Formula for the Circumference of a Circle Example 2 Finding the Circumference of a Circle A circle has a radius of 8 in., as shown in Figure 3. Find its circumference using 3.14 for p. From Formula (2), C 2pr 2 3.14 8 in. 50.2 in. (rounded to one decimal place) 8 in. Figure 3 NOTE Because d 2r (the diameter is twice the radius) and C pd, we have C p(2r), or C 2pr. CHECK YOURSELF 2 Find the circumference of a circle with a radius of 2.5 in. NOTE Because 3.14 is an approximation for pi, we can only say that the circumference is approximately 14.1 ft. The symbol means approximately. NOTE If you want to approximate p, you needn’t worry about running out of decimal places. The value for pi has been calculated to over 100,000,000 decimal places on a computer (the printout was some 20,000 pages long). CHECK YOURSELF 1 A circle has a diameter of inches (in.). Find its circumference. 3 1 2 Note: In finding the circumference of a circle, you can use whichever approximation for pi you choose. If you are using a calculator and want more accuracy, use the key. There is another useful formula for the circumference of a circle. p By Formula (1), C pd 3.14 4.5 ft 14.1 ft (rounded to one decimal place) AREA AND CIRCUMFERENCE SECTION 4.4 343 © 2001 McGraw-Hill Companies Example 3 Finding Perimeter We wish to build a wrought-iron frame gate according to the diagram in Figure 4. How many feet (ft) of material will be needed? The problem can be broken into two parts. The upper part of the frame is a semicircle (half a circle). The remaining part of the frame is just three sides of a rectangle. Circumference (upper part) Perimeter (lower part) 4 5 4 13 ft Adding, we have 7.9 13 20.9 ft We will need approximately 20.9 ft of material. 1 2 3.14 5 ft 7.9 ft 5 ft 4 ft Figure 4 NOTE Using a calculator with a key, 1 2 5 p p Sometimes we will want to combine the ideas of perimeter and circumference to solve a problem. CHECK YOURSELF 3 Find the perimeter of the following figure. 6 yd 8 yd The number pi (p), which we used to find circumference, is also used in finding the area of a circle. If r is the radius of a circle, we have the following formula.
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The slope of the first equation has a slope of one and a y intercept of -4. The second equation has a y intercept of -2.3333 as seen when plugging in 0 for x, so the same y-intercept and same line are out of the question. This means either they have the same slope and thus are parallel or intersect at some point. A simple way to find out? Plug in 1 for x on the second. If it isn't -1.33333, which is a slope of positive 1 such as in the first equation, they WILL INTERSECT somewhere. When plugging in 1, we get
3y - 1 = -7
3y = -6
y = -2
(1, -2) is the next point after (0, -2.3333)
That means it is most certainly not the same slope, and thus they will intersect at some point. The two slopes are 1/1 and 1/3 if you weren't aware.
Answer: Question 1 :B,D.
Question 2:option B,
Question 3:Degree=5.
Question 4:option D.
Question 5: option c.
Step-by-step explanation:
1) A polynomial can not have any exponent as a variable or a fraction.
Options B and D are polynomials.
2) The polynomial is having 3 terms and is of degree 3.so it is a cubic trinomial Option B.
3) Degree is the highest power of the variables in the terms .The term 
has the power=3+2=5
So degree =5.
4)
Option D
5)
Simplifying like terms,
=
Option c.
