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Taya2010 [7]
3 years ago
10

1. Simplify. 5–1(3–2)

Mathematics
2 answers:
Monica [59]3 years ago
5 0

1. 5^-1(3^-2) = (1/5)*(1/3^2) = 1/5*3^2 = 1/45

2. mn^-4/p^0q^-2 = m*q^2/n^4  

p^0 = 1

1/q^-2 = q^2

3. 0.0042 = 4.2*10^-3

multiply by 10^-3 is the same as divide by 1000; 4.2 divided by 1000 is 0.0042

4. 6.12 × 10^3 = 6.12*1000 = 6,120

5. 0.5*(8*10^5) = (0.5*8)*10^5 = 4*10^5

6. (9*10^3)^2 = 9^2* (10^3)^2 = 81 * 10^(3*2) = 81*10^6

7. 1/(2a^4) * b^2 for a = –2 and b = 4 = 1/(2*(-2)^4) *4^2 = 1/(2*16) *16 = 1/2

8. Sometimes a number raised to a negative exponent is negative. For example 1^(-2) = 1 and (-1)^(-1) = -1

9. (4xy^2)^3(xy)^5 = 4^3 * x^3 * (y^2)^3 * x^5 * y^5 = 64 * x^(3+5) * y^(2*3) * y^5  = 64*x^8* y^(6+5) = 64*x^8*y^11

10. (2t^(-3))^3 * (0.4r)^2 = 2^3 * t^(-3*3) * (0.4)^2 * r^2 = 8 * t^(-9) * 0.16 * r^2 = 1.28*r^2/t^9

konstantin123 [22]3 years ago
4 0

Answer with explanation:

Using following law of indices

1.x^a \times x^b=x^{a+b}\\\\2. (x^m)^n=x^{mn}\\\\ 3. x^{-n}=\frac{1}{x^n}\\\\4. \frac{x^m}{x^n}=x^{m-n}

1.5^{-1}\times 3^{-2}=\frac{1}{5}\times\frac{1}{3^2}\\\\=\frac{1}{5\times9}\\\\=\frac{1}{45}\\\\2. \frac{mn^{-4}}{p^0*q^{-2}}=\frac{mq^2}{n^4}\\\\ 3.0.0042=4.2\times 10^3\\\\4.6.12 \times 10^3=6.12 \times 1000=6120\\\\ 5.0.5 \times(8\times10^5})=\frac{1}{2}\times8 \times 10^5=4\times 10^5\\\\6. (9 \times 10^3)^2=9^2 \times (10^3)^2=81 \times 10^6\\\\7.( \frac{1}{2}a^{-4}\times b^2 )_{a=-2,b=4}{\text{or}}( \frac{1}{2}a^{4}\times b^{-2} )_{a=-2,b=4}=\frac{1}{2}\times (-2)^{-4}\times(4)^2{\text{or}}=\frac{1}{2}\times (-2)^{4}\times(4)^{-2}=\frac{16}{2\times16}=\frac{1}{2}

9. (4\times x\times y^2)^3\times (xy)^5=4^3\times x^3\times (y^2)^3\times x^5 \times y^5\\\\=64\times x^{3+5}\times y^{5+6}\\\\=64x^8y^{11}\\\\10.(2\times t^3)^3(0.4\times r)^2=2^3 \times (t^3)^3\times (0.4)^2 \times r^2=8\times t^9 \times 0.16 \times r^2=1.28r^2t^9

8. A number raised to a negative exponent is negative.

Explaining with the help of few examples

 1.2^{-3}=\frac{1}{2^3}=\frac{1}{8}\\\\ 2.(-3)^{-3}=\frac{1}{(-3)^{3}}=\frac{-1}{27}

Option C: Sometimes

1.Option B

2.Option A

3.Option C

4.Option A

5.Option D

6.  81 \times 10^6

7.Option B

8.Option C

9.Option A

10.Option  1.28 r^2 \times t^9

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I need help With Math Exponents (click for picture )
Murljashka [212]

Answer

25. 9^3,    729

26. 2^6,    64

27. 1^8,     1

28. 5^4,   625

29. 7^6,   1117,649

5 0
3 years ago
Y = 7/8u + 9, solve for u
vivado [14]

Answer:

u=\frac{8y-72}{7}

Step-by-step explanation:

Flip the equation.

\frac{7}{8}u+9=y

Add -9 to both sides

\frac{7}{8}u+9(-9)=y(-9)

\frac{7}{8}u=y-9

Divide both sides by 7/8

u=\frac{8y-72}{7}

hope this helps

3 0
3 years ago
The electrical charge on a metal plate is given
Katarina [22]

Answer:

after 10 seconds  the charge  is 1.624

Step-by-step explanation:

I think your question missed key information, allow me to add in and hope it will fit the orginal one.

The electrical charge on a metal plate is given  by the function below, where t is the time in  seconds. What is the charge after 10 seconds?

C (t) = 12e^{\frac{-t}{5} }

My answer:

Given the information:

C (t) = 12e^{\frac{-t}{5} }  

when t =10 we have:

C (10) = 12e^{\frac{-10}{5} }

<=>  C (10) = 12e^{-2}

<=>  C (10) = 12\frac{1}{e^{2} }

<=> C (10) = 12 * 0.1353

<=>  C (10) = 1.624

Hence, after 10 seconds  the charge  is 1.624

8 0
3 years ago
Renee is standing at point (1, 0) on a gigantic circular track of radius 1 mile with center (0, 0). She walks counterclockwise a
mafiozo [28]

Answer:

32

Step-by-step explanation: xbcjxnszHJCGewupearl had some beads She used 3/5 of them to make bracelets and 1/4 of the remainder to decorate her sweater if she had 300 beads left how many beads did she have at first jdks

7 0
3 years ago
3. The sum of three consecutive numbers<br> is 42. What are the numbers?
Zanzabum

Answer:

13 + 14 + 15

Step-by-step explanation:

n + (n + 1) + (n +2) =42

n + n + n + 1 + 2 = 42

3n + 3 = 42

(subtract 3 from both sides)

3n = 39

(divide both sides by 3)

n = 13

(solve)

n + (n + 1) + (n +2) =42

13 + (13 + 1) + (13 + 2) = 42

13 + (14) + (15) = 42

13, 14, 15

(Hope this helps, have a nice day!)

3 0
3 years ago
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