4. Let the numbers be x - 2, x, and x + 2, where x is an odd number.
2(x² - 4) - 4x = (x + 2)² + 21
2x² - 8 - 4x = x² + 4x + 4 + 21
2x² - 4x - 8 = x² + 4x + 25
x² - 8x - 33 = 0
(x - 11)(x + 3) = 0
x = 11, or -3
When x = 11, x - 2 = 9, x + 2 = 13
When x = -3, x - 2 = -5, x + 2 = -1
Explanation: You are on the right track. However, rather than having three unknown variables, try to reduce your working out to one unknown variable. Since you know they are consecutive odd numbers, you can simply let x be the middle term and the other two be + and - 2, provided x is an odd number.
That will reduce your variable issues, and helps as the first and third provide a difference of two squares, and this works out very nicely.
Q5: is essentially the same process. Let your variables be something in the form of one unknown variable, and you should be okay from there. Let me know if you're stuck.
Answer:
x must equal 0 or - 10
and y must equal 1 or 6
so its 3 x 0 = 0 plus 6 x 1 = 6
or 3 x -10 = -30 plus 6 x 6 = 36 so -30 plus 36 is 6
Step-by-step explanation:
Answer:
50 blocks
Step-by-step explanation:
First of all, you need to label you're proportions, which can be mm/blocks.
Then, for 1 block, it is 20 mm because the block is 2 cm, which is equal to 20 mm. So for you're proportion, it is 20 mm/1 block.
Finally, you need to find the total amount of blocks that equals 1000 mm. So you can multiply the 20 mm by 50 to get the 1000 mm. What you do at the top, you do at the bottom, so you also have to do 1 block by 50 to get 50 blocks
So for you're final answer/proportion, it is mm/blocks = 20/1 = 1000/50 and you're final answer is 50 blocks
Hope this helps : )
Answer:
Please read all of this! Underlined things are the answers. The area of the entire circle is 19.625
Step-by-step explanation:
(This is a circle so the middle line is the diameter. According to the attachment, the diameter is 5 cm. To find the area, we have to multiply π and the radius squared. The radius is half of the diameter.
5 ÷ 2 = 2.5
2.5² = 6.25
π = 3.14
3.14 x 6.25 = 19.625)
Ignore the top I just realized what I'm supposed to do but I left it there just in case you need help!
<u>The right and left shaded regions areas are 6.28 each.</u>
4 ÷ 2 = 2
2² = 4
3.14 x 4 = 12.56
Since this is a semi circle, we cut it in half.
12.56 ÷ 2 = 6.28
To find the top and bottom shaded region's areas, repeat the same steps.
3 ÷ 2 = 1.5
1.5² = 2.25
3.14 x 2.25 = 7.065
7.065 ÷ 2 = 3.5325
<u>The areas of the the top and bottom shaded regions are 3.5325 each.</u>
