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Hatshy [7]
2 years ago
11

37. The sum of first three terms in an arithmetic progression is 24 and the sum of their squares is 224. Find the first three te

rms of this arithmetic progression.
​
Mathematics
1 answer:
Airida [17]2 years ago
8 0

Answer:

12, 8, and 4

Step-by-step explanation:

  • Given

a + d + a + a - d = 24

3a = 24   ⇒  [ a = 8 ]  

and (a + d)² + a² + (a - d)² = 224

3a² + 2d² = 224

2d² = 224 - 192 = 32

d² = 16

[ d = ±4 ]

∴ The first three terms to A.P are

a + d = 8 + 4 = 12

a  -  = 8

a - d = 8 - 4 = 4

∴ Three terms are 12 , 8, and 4

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It is known that 1.4< square root of 2 <1.5. Find all possible values of the expression 2-square root of 2. How do I find
horsena [70]

Answer:

0.5<2-√2<0.6

Step-by-step explanation:

The original inequality states that 1.4<√2<1.5

For the second inequality, you can think of 2-√2 as 2+(-√2).

Because of the "properties of inequalities", we know that when a positive inequality is being turned into a negative, the numbers need to swap and become negative. So, the original inequality becomes -1.5<-√2<-1.4. (Notice how the √2 becomes negative, too). This makes sense because -1.5 is less than -1.4.

Using our new inequality, we can solve the problem. Instead of 2+(-√2), we are going to switch "-√2" with both possibilities of -1.5 and -1.6. For -1.5, we would get 2+(-1.5), or 0.5. For -1.4, we would get 2+(-1.4), or 0.6.

Now, we insert the new numbers into the equation _<2-√2<_. The 0.5 would take the original equation's "1.4" place, and 0.6 would take 1.5's. In the end, you'd get 0.5<2-√2<0.6. All possible values of 2-√2 would be between 0.5 and 0.6.

Hope this helped!

4 0
3 years ago
What number can go in the box to make the number sentence true?
Len [333]
I believe it would be 4 lil man
6 0
3 years ago
Select the Like Terms in this expression
sesenic [268]

Answer:

5, 2x2 and 4

Step-by-step explanation:

Terms are expressions or characters that are separated by a plus or minus sign.

therefore, the terms are 3x, 5, 2x2 and 4

like terms have the same have the same variables or no variables attached to them.

like terms = 5, 2x2, and 4

Note: 2x2 = 4

8 0
3 years ago
Mr. Smith has 12 congruent boxes shaped like rectangular prisms in his office. If the length is 25 inches, the height is 2 feet,
Nana76 [90]

Answer:

width of one box = 1.25 inches

Step-by-step explanation:

Given data:

12 congruent boxes

Length = 25 inches

height = 2 feet

Volume = 9000 cubic inches

First change the height into inches

1 foot = 12 inches

therefore 2 feet = 24 inches

Volume = Length * width * height

9000 = 25 * width * 24

9000 = 600 * width

width = 9000/600

width = 15 inches

width of one box = width of all boxes / number of boxes

width of one box = 15/12

width of one box = 1.25 inches

4 0
3 years ago
Solve this one pleeaasssee
Tamiku [17]

Answer:

the answer is c

Step-by-step explanation:

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4 0
3 years ago
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