I have these problems,need help with ans.:
1. -6(2x-9)-4x+5 (simplify)
2. x-6/y-5 (simply)
3. (x/6) to the 3rd. (simplify)
4. y-7x/6x+xy given x=1 & y=3 (evaluate)
5. 8x+7 given x=3 (evaluate)
6. -(8z-7w+2y) (simplify)
7. 6 sq. root sign over 7 + 3 sq. root sign over 7 (simplify)
8. 19/sq. root sign over 19 (simplify)
9. 5 to the 4th dot 5 to the 8th (simplify)
10. 7 0 power (simplify)
11. determine whether 15>16 (true or false)
12. sq. root sign 100/9 (simplify)
13. 2+6(x-2) to the 3rd. given x=4 (evaluate)
14. (x neg. 5th power)neg. 3rd (simplify)
15. express &evaluate the distance between the number 84 and neg. 34 using absolute value?
1.) -6*(2x - 9) - 4x + 5
-12x + 54 - 4x + 5
-16x + 59
2.) x - 6/y - 5 is already simplified; perhaps you mean (x - 6)/(y - 5) which is also simplified..unless you want to expand it to x/(y - 5) - 6/(y - 5) ..
3.) (x/6)^3
x^3/216
4.) Evaluate y - 7x/6x + xy : (1,3)
Well, I'm not sure if you mean what you have written, or (y - 7x)/(6x + xy).. or.. who knows.
Any way, what you have:
3 - 7(1)/6(1) + (1)(3) = 3 - 7/6 + 3 = 6 - 7/6 = 29/6
Or, if you meant what I have:
(3 - 7(1))/(6(1) + (1)(3)) = -4/9
5. Evaluate 8x + 7 : x = 3
8(3) + 7 = 24 + 7 = 31
You need to know the following rules:
(In the following, m and n are integers, and a and b are real numbers not equal to 0.)
a^n = a*a*...*a (n times)
a^0 = 1
a^n * a^m = a^(n + m)
(a^n)^m = a^(n*m)
a^(-n) = 1/(a^n)
sqrt(a) = a^(1/2)
a^n * b^n = (ab)^n
So.
3. (x/6) to the 3rd = (x/6)^3 = (x^3)/(6^3) = (x^3)/216
9. 5 to the 4th dot 5 to the 8th = 5^4 * 5^8 = 5^(4 + 8) = 5^12
10. 7 0 power
I presume this is 7^0 = 1?
12. sq. root sign 100/9 = sqrt(100/9) = sqrt(100)/sqrt(9) = 10/3
(Or:
sqrt(100/9) = (100/9)^(1/2) = [100^(1/2)]/[9^(1/2)] = [(10^2)^(1/2)]/[(3^2)^(1/2)]
= 10/3)
14. (x neg. 5th power)neg. 3rd = (x^5)^(-3) x^(5*(-3)) = x^(-15) = 1/(x^15)
-Dan
6.) Simplify -(8z - 7w + 2y)
Distribute the negative:
-8z + 7w - 2y, and this is simplified.
7.) Simplify 6*sqrt(7) + 3*sqrt(7) <-- that?
If so, then 9*sqrt(7).
8.) Simplify 19/sqrt(19)
Multiply by sqrt(19)/sqrt(19) (which is multiplying by 1), and then
19*sqrt(19)/19 = sqrt(19)
9.) Simplify 5^4 "dot" 5^8. By "dot" I doubt you mean dot product, and instead multiplication. Thus, add exponents since bases are the same:
5^12
10.) 7 0 power (simplify) <-- Um, 7^(0) ?
If so, any non-neg. integer raised to the 0th power is always 1.
Therefore, 7^0 = 1
11, 15 done already.
Well, a comment on 11:
"Determine whether 15 > 16"
Do you know what > means? What comes first...15...or 16? I'll let you figure that out.
12.) sqrt(100)/9 <-- that? Or, sqrt(100/9);
If it's the penultimate, then 10/9; if it's the latter, then 10/3.
13.) Evaluate 2 + 6(x - 2)^3 : x = 4
2 + 6(4 - 2)^3 = 2 + 6(2)^3 = 2 + 6*8 = 2 + 48 = 50.
14.) Simplify x^(-5)*"neg. 3rd"
What is neg. 3rd?
[x^(-5)]^(-3) ? If so:
x^(-5) = 1/(x^5); and then,
(1/(x^5))^(-3) = 1/(x^(-15)) = x^15