4. The area of the rectangular field is 160cm^2and its length is twice its width. Find the dimensions of the field.
5. The hypotenuse of a right triangle is 17 cm. How long are the legs if one is 7 cm longer than the other.
6. If the square of a number is added to eight times the number, the sum is 105. Find the number.
7. The difference between two numbers is 8 while their product is 128. Find the two numbers.
8. A number is 1/10less than its multiplicative inverse. Find the number.
9. The length of a rectangle is 3 cm more than its width when its area is 28cm^2.Find the dimensions.
10. When 8 is divided by a certain number, the result is the same as when 12 is subtracted from the number and the difference is divided by 8. Find the number.
Answers
Answer :
4. Therefore the dimensions of the field are: Length = 8√5 m. Breadth = 4√5 m.
5. In a right triangle, either of the legs can be the base and the other leg is the height. You know one of the legs equals 7 cm. You can find the other leg using the Pythagorean Theorem: √(172 - 72).
6. To solve this problem you will need to set up an equation using X for all of the unknown variables.
X2+8x=105
From here, solve for X as you normally would.
X2+8x-105=0
(x-7)+(x+15)=0
x= -4
Plug -4 back into the equation to check:
(-4-7)+(-4+15)=0
-11+11=0
7. Let the 1st number be F, and the 2nd S
Since their product is 128, we can say that FS = 128 -------- (i)
Also, since their quotient is 8, then we can say that F%2FS+=+8------ (ii)
Solving for F in eq (ii), we get: F = 8S
Substituting 8S for F in eq (i), we get: 8S(S) = 128
8S%5E2+=+128-------- 8S%5E2+-+128+=+0
8%28S%5E2+-+16%29+=+8%280%29-------- Factoring out GCF, 8
S%5E2+-+16+=+0-------- (S - 4)(S + 4) = 0
Therefore, S, or the 2nd number is 4, or - 4
If the 2nd number is 4, then the 1st number is F(4) = 128, which makes F = 32
If the 2nd number is -4, then the 1st number is F(-4) = 128, which makes F = -32
Therefore, the numbers are either highlight_green%284_and_32%29, or highlight_green%28-4_and_-32%29.
8. a number is 1/10 less than its multiplicative inverse .find the number
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x = (1/x)-(1/10)
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10x^2 = 10 - x
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10x^2 + x - 10 = 0
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x = [-1 +- sqrt(1-4*10*-10)]/20
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x = [-1 +- sqrt(401)]/20
x = 0.95
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Cheers,
Stan H.
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I HOPE THIS WILL HELP YOU
sorry I don't know the answer of 9 and 10 .
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