A) I would make the positive integer x and then form an equation.
x + 30 = x^2 - 12
x + 42 = x^2
0 = x^2 - x - 42 this can be factorised
(x - 7) ( x + 6) Therefore x = 7 or x = -6
Since the question asks for a positive integer the answer is 7.
B) two positive numbers x and y.
X - y = 3
x^2 + y^2 = 117
Use these simultaneous equations to figure out each number.
Rearrange the first equation
x = y + 3
Then substitute it into the second equation.
(y+3)^2 + y^2 = 117
y^2 + 6y + 9 + y^2 = 117
2y^2 + 6y - 108 = 0
then factorise this.
(2y - 12) (y + 9)
This means that y = 6 or y = -9 but it’s 6 because that’s the only positive number.
Use y to find x
x = y + 3
x = 6 + 3
x = 9
So the answers are x = 9 and y = 6.
Answer:
6.5 x 10^6 To answer this question, you need to divide the mass of the sun by the mass of mercury. So 2.13525 x 10^30 / 3.285 x 10^23 = ? To do the division, divide the mantissas in the normal fashion 2.13525 / 3.285 = 0.65 And subtract the exponents. 30 - 23 = 7 So you get 0.65 x 10^7 Unless the mantissa is zero, the mantissa must be greater than or equal to 0 and less than 10. So multiply the mantissa by 10 and then subtract 1 from the exponent, giving 6.5 x 10^6 So the sun is 6.5 x 10^6 times as massive as mercury.
:}
Answer:
6. 16 meters^2, 16 meters
7. 100 milimieters^2, 40 milimeters
9. 56 centimeters^2, 30 centimeters
10. 49 inches^2, 28 inches
11. 9 meters^2, 12 meters
12. 72 yards^2, 36 yards
Step-by-step explanation:
s is for a square
A=s^2
P=4s
l+w is for a rectangle
A=lw
P=2l+2w
6. A=4^2
A= 16 meters^2
P=4*4
P= 16 meters
7. A=10^2
A=100 milimieters^2
P=4*10
P= 40 milimeters
9. A=8*7
A= 56 centimeters^2
P=2(8)+2(7)
P=30 centimeters
10. A=7^2
A=49 inches^2
P=4*7
P=28 inches
11. A= 3^2
A=9 meters^2
P=4*3
P= 12 meters
12.
A=12*6
A=72 yards^2
P= 2(12)+2(6)
P= 36 yards
Let me know if you have any questions. Also, don't forget units!
Answer:
51 cents for 17 inches of wire
Step-by-step explanation:
22 = 66
17 = x
22x = 66 * 17
22x = 1122
x = 51 cents
or
22 inches costs 66 cents
1 inch costs 3 cents (66 / 22 = 3 cents)
17 inches costs 51 cents (17 * 3 = 51 cents)
This is same as (4x-6)(2x), so you can distribute 2x into 4x-6 and you would get
(2x)4x - (2x)6 = 8x² - 12x
Final answer: 8x² - 12x
Hope this helps.
