Worth 10 points please help me ASAP

78. Use properties of exponents to rewrite each expression as either an integer or as a quotient of integers p/q to show the exp

kolezko [41]

Answer:

4√2 × 4√8 = 64, an integer.

Step-by-step explanation:

a) 4√2 × 4√8

First let's remember that a square root can be rewritten as a 1/2 exponent,

Therefore the expression we have can be rewritten as

$4(2^{1/2} )4(8^{1/2})$

We are going to write all numbers in their prime factor expressions:

<u>*Note: Remember that when we multiply two numbers with the same base but different exponents we sum up the exponents*</u>

<u>*Also, when we elevate one exponent to another exponent, we multiply the exponents*</u>

$4(2^{1/2} )4(8^{1/2})\\=2^2 (2^{1/2})2^2 (2^{3})^{1/2} \\ =2^2 (2^{1/2})2^2 (2^{3/2})\\=2^22^2(2^{1/2}2^{3/2})\\=16(2^{4/2})\\=16(2^2)\\=16(4)\\=64$

Therefore, the expression 4√2 × 4√8 = 64 and therefore is an integer

4 0

3 years ago

What are the next 3 numbers in this pattern of integers -2, -1, -1, 0, -1, 1, -2

sashaice [31]

Answer:

The next 3 numbers to the given pattern of integers is -2,-1,-1,0,-1,1,-2 are 3,-5,8

Step-by-step explanation:

Given pattern of integers is -2,-1,-1,0,-1,1,-2

To find their next 3 numbers of the given pattern :

Let $a_{1}=-2$

$a_{2}=-1$

$a_{3}=a_{1}-a_{2}$

$=-2-(-1)$

$=-2+1$

Therefore $a_{3}=-1$

$a_{4}=a_{2}-a_{3}$

$=-1-(-1)$

$=-1+1$

Therefore $a_{4}=0$

Similarly we have $a_{5}=-1$ , $a_{6}=1$ , $a_{7}=-2$

The general form to the given pattern is

$a_{n}=a_{n-2}+a_{n-1}$ for $n={\{1,2,3,4,5,6,7,8,9,10}\}$

Therefore to find the $a_{8},a_{9},a_{10}$

Put n=8 in $a_{n}=a_{n-2}-a_{n-1}$

$a_{8}=a_{8-2}-a_{8-1}$

$=a_{6}-a_{7}$

$=1-(-2)$

$a_{8}=3$

Put n=9 in $a_{n}=a_{n-2}-a_{n-1}$

$a_{9}=a_{9-2}-a_{9-1}$

$=a_{7}-a_{8}$

$=-2-(3)$

$a_{9}=-5$

Put n=10 in $a_{n}=a_{n-2}-a_{n-1}$

$a_{10}=a_{10-2}-a_{10-1}$

$=a_{8}-a_{9}$

$=3-(-5)$

$a_{10}=8$

Therefore the next 3 numbers are 3,-5,8

4 0

3 years ago

What is 0.7 as a fraction in simplest form

mote1985 [20]

The answer is 7/10

the 7 is in the tenth place making the denominator a 10 and no same number goes into both 7 and 10.

7 0

4 years ago

Read 2 more answers

Seema deposited $800 in a saving account earning 2.88% compounded annually. To the nearest cent, how much will she have in 16 ye

ehidna [41]

Answer:

1260.04

Step-by-step explanation:

The formula for compound interest is:

A = P(1+ $\frac{r}{n}$ $)^{nt}$ where A is the final amount, P is the initial principal balance, r is the interest rate, n is the number of times interest applied per time period and t is the number of time periods elapsed. Since the deposit was compounded annually, just like the interest, we can omit the n in the equation.

Applying the formula to question:

800(1+ $\frac{2.88}{100}$ $)^{16}$ = 1260.04 (rounded off to nearest cent since it's money)

5 0

3 years ago

Every that is fully readable

n200080 [17]

10)
60in=60in × (1ft/12in) = 5ft
30in= 30in × (1ft/12in) = 2.5ft
12in = 12in × (1ft/12in) = 1ft
answer is = 5ft × 2.5ft× 1ft =12.5 ft^3 = a

11)
dozen = 12 hammers
12 hammers = 20 pounds
therefore 1 hammer= 20/12 = 1.6666 lb

21 hammers ×1.666 = 35 = c

12)
convert qt to gal
600 gal × 4 qt/gal = 2400 qt

2400 qt ÷ 120 qt/min
=20 min = d

13)
Carla is 12
rob is 12+5= 17
cousin is 12-7 = 5

12+17+5= 34 =a

15)
convert 60ft into yards
60 ft × 0.333 yd/ft =20 yd

diameter = 20 yd

area of circle = (pi/4)×d^2
(pi/4)×20^2= 314.16 = b

8 0

4 years ago