Complete the table. Use powers of 64 in the top row and radicals or rational numbers in the bottom row.
Answers
Applying the rules of exponents and radicals, the table can be completed as follows:
First column: [tex]64^1 = 64[/tex]
Second Column: [tex]\mathbf{64^\frac{1}{2} = 8}[/tex]
Third Column: [tex]\mathbf{64^\frac{1}{3} = 4}[/tex]
Fourth Column: [tex]\mathbf{64^0 = 1}[/tex]
Fifth Column: [tex]\mathbf{64^{-\frac{1}{2}} = \frac{1}{8}}[/tex]
Sixth Column: [tex]\mathbf{64^{-1} = \frac{1}{64}}[/tex]
The table to complete is attached below.
We will need to apply the knowledge of exponents and radicals of a number in order to fill out the table.
The numbers expressed as powers of 64 in the top row are equivalent to the numbers expressed as radicals or rational numbers in the corresponding cells in the bottom row.
Also, recall the following rules of exponents and radicals:
[tex]x^{\frac{a}{b}} = \sqrt[b]{x^{a}}[/tex][tex]x^{-a} = x^{\frac{1}{a} }[/tex][tex]x^{0} = 1[/tex]Appling the above rule, we would have the following:
First column:[tex]64^1 = 64[/tex]
Second Column:[tex]64^\frac{1}{2} = \sqrt[]{64} = 8\\\\\mathbf{64^\frac{1}{2} = 8}[/tex]
Third Column:[tex]64^\frac{1}{3} = \sqrt[3]{64} = 4\\\\\mathbf{64^\frac{1}{3} = 4}[/tex]
Fourth Column:[tex]\mathbf{64^0 = 1}[/tex]
Fifth Column:[tex]64^{-\frac{1}{2}} = \frac{1}{64^{\frac{1}{2}} } = \frac{1}{\sqrt{64} } = \frac{1}{8} \\\\\\\mathbf{64^{-\frac{1}{2}} = \frac{1}{8}}[/tex]
Sixth Column:[tex]64^{-1} = \frac{1}{64^1} } = \frac{1}{64 } \\\\\mathbf{64^{-1} = \frac{1}{64}}[/tex]
Therefore, applying the rules of exponents and radicals, the table can be completed as follows:
First column: [tex]64^1 = 64[/tex]
Second Column: [tex]\mathbf{64^\frac{1}{2} = 8}[/tex]
Third Column: [tex]\mathbf{64^\frac{1}{3} = 4}[/tex]
Fourth Column: [tex]\mathbf{64^0 = 1}[/tex]
Fifth Column: [tex]\mathbf{64^{-\frac{1}{2}} = \frac{1}{8}}[/tex]
Sixth Column: [tex]\mathbf{64^{-1} = \frac{1}{64}}[/tex]
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Related Questions
Find y'([tex]\sqrt[3]{3}[/tex]) where y = y(x) is an implicit function of x given by 2[tex]x^{3}[/tex]+[tex](x^{3}-3)[/tex]·sin(2πy)−3y = 0.
Answers
Given
2x³ + (x³ - 3) sin(2πy) - 3y = 0
we first notice that when x = ³√3, we get
2 (³√3)³ + ((³√3)³ - 3) sin(2πy) - 3y = 0
2•3 + (3 - 3) sin(2πy) - 3y = 0
6 - 3y = 0
3y = 6
y = 2
Differentiating both sides with respect to x gives
6x² + 3x³ sin(2πy) + 2π (x³ - 3) cos(2πy) y' - 3y' = 0
Then when x = ³√3, we find
6(³√3)² + 3(³√3)³ sin(2π•2) + 2π ((³√3)³ - 3) cos(2π•2) y' - 3y' = 0
6•³√9 + 3•3 sin(4π) + 2π (3- 3) cos(4π) y' - 3y' = 0
6•³√9 + 0 + 0 - 3y' = 0
3y' = 6•³√9
y' = 2•³√9
(that is, 2 times the cube root of 9)
Can you help me?????
Answers
Answer:
180 - (55+48) =77
180 -77 =103
Emerson is making costumes for the
school play. She needs 3 1/2 square
yards of fabric to make each costume.
If she uses a total of 46 2/3 square
yards of fabric, how many costumes
does she make?
Answers
9514 1404 393
Answer:
13 costumes
Step-by-step explanation:
The amount of fabric used is the product of the amount per costume and the number of costumes.
A = na . . . . . A = total area; n = number of costumes; 'a' = area per costume
46 2/3 = n(3 1/2)
n = (46 2/3)/(3 1/2) = (140/3)/(7/2) = (140/3)(2/7) = 40/3 = 13 1/3
Apparently there is some waste, as Emerson used more fabric than necessary to make 13 costumes.
Maria is 62 inches tall. If her sister Eva was 1.5 inches taller, she would be exactly half Maria's height. How tall is Eva? Enter your answer as a decimal in the box.
Answers
Answer:
Step-by-step explanation:
Let Eva's height be x
62* 0.5 = x + 1.5
31 = x + 1.5 Subtract 1.5 from both sides.
31 - 1.5 = x
x = 29.5
Eva is 29.5 inches tall.
Answer:
29.5
Step-by-step explanation: I took the test
6
What value of x makes the equation -5x - (-7.4x) = -2(3x + 4) true?
F
X = 3
G
* = 5
H
J
x
Answers
Step-by-step explanation:
-5x - (-7.4x) = -2(3x + 4)
-5x + 28x = -6x - 8
(-5 + 28 + 6)x = -8
29x = -8
x = -8/29
(d^8)^-2. Anyone help pls?
Answers
Answer:
1/d^16
Step-by-step explanation:
Hope this helped!
Can I get brainlist? If not that's okay!
The cost, C, in dollars to produce 3 pounds of chocolate candy
is represented by the linear function C (x) = 3.5x+ 800.
Find the number of pounds produced if the cost is $842.00.
Round to the nearest tenth of a pound.
469.1
h
O 3,747.0
38.5
12.0
o 1.2
Answers
Answer:
(c) 12 pounds
Step-by-step explanation:
The cost of production is given as ...
3.5x +800 = 842
3.5x = 42 . . . . . . . . subtract 800
x = 12 . . . . . . . . . . . divide by 3.5
The number of pounds produced is 12.
List the first 10 triangular numbers
Answers
0, 1, 3, 6, 10, 15, 21, 28, 36, 45
Write an equation for this linear
function.
f(3) = 7 and f(7) = 3
Answers
f(x)=-x+10
well looking at the difference on the x and y coordinates, it is a difference of 4 and-4, making the slope -1. because it is next to x on the function notation you can just say -x, then insert the y and x coordinates to solve for y intercept
Prius bought these items at the grocery store. Find each unit price.
A. 12 eggs for $3 how much is the cost per egg ?
Answers
Answer:
your answer would be 0.25 cents per egg
Step-by-step explanation:
What is the value of n in the equation?
7n + 2 = 5 × 6
A.25
B.4
C.6
D.28
Answers
Answer:
B. 4
Step-by-step explanation:
7n+2 = 5×6
7n+2 = 30
7n = 30-2
7n = 28
7n ÷ 7 = 28 ÷ 7
n = 4
Adam ran 3 miles in 30 minutes. If he continues at a
constant rate, how many miles can he run in 2
hours?
Answers
30 min = 3 miles
60 min = 6 miles
90 min = 9 miles
120 min = 12 miles
If p and q vary inversely and p is 4 when q is 12, determine q when p is equal to 8.
Answers
Answer:
24
Step-by-step explanation:
[tex]p = 8 \\ q = x \\ \\ q(8) = p(x) \\ \\ 12(8) = 4(x) \\ 96 = 4x \\ \frac{96}{4} = \frac{4x}{4 } \\ x = \frac{96}{4} \\ x = 24[/tex]
Frank’s mother gave him 25 to save. If he already had 38 saved, how much money does frank have save now
Answers
Answer:
Frank now has $63 saved.
Step-by-step explanation:
25 + 38 = 63
I hope this answered your question properly!
Joe bought a box of laundry detergent that contains 195 scoops each load of laundry uses 2 1/2 scoops the box of detergent was $24.96 how much is he paying for each load that was wash
Answers
Answer:
a) Number of laundry he can do with this box = 78 laundries.
b) Price he paying for each load = 0.256 $
Step-by-step explanation:
Total scoop contained in detergent box = 195 scoops.
Scoops used by each load of laundry = 2 1/2 = 2 * 2 + 1/2 = 5/2 scoops = 2.5 scoops
Number of laundry he can do with this box = 195/2.5 = 78 laundries.
Price of detergent box = 19.99 $
Price he paying for each load = Total price/ Number of loads
= 19.99/78
= 0.256 $
Select all possible solutions for 2x +7
[tex] 2x + 7\leqslant 3 \times - 5[/tex]
Answers
Answer:
Select all options of x greater than or equal to 12
Step-by-step explanation:
2x + 7 <= 3x - 5
7 + 5 <= 3x - 2x
12 <= x
x >= 12
please help will mark as brainliest pls show work
Answers
9514 1404 393
Answer:
y = 1/5x +8
Step-by-step explanation:
The slope of the perpendicular line will be the opposite reciprocal of the slope of the given line:
m = -1/(-5) = 1/5
The y-intercept (b) can be found from this and the given point:
b = y -mx
b = 9 -(1/5)(5) = 8
Then the slope-intercept equation can be written ...
y = mx +b . . . . . . line with slope m and y-intercept b
y = 1/5x +8
_____
Additional comment
Since the question asks for "an equation," the problem can be solved even more quickly using the point-slope form of the equation of a line.
y -k = m(x -h) . . . . . . line with slope m through point (h, k)
y -9 = 1/5(x -5) . . . . . an equation for line j
Evaluate (3x-2)/6 when x = 5
Answers
Answer:
13/6
Step-by-step explanation:
Substitue in 5 for x in 3x.
3x(5)= 15
15-2=13
13/6 or 2.16
Can someone please explain how to do this.
Answers
Answer: 9/30
Step-by-step explanation:
someone please just help me i cant fail this please
Answers
Aidan wants to rent a car while on a trip to Europe. He can rent a sedan that holds 70.1 liters of gasoline, or a sports car that holds 4,930 centiliters of gasoline. How many more liters of gasoline can the sedan hold?
Answers
A couple deposits $21,000 $ 21,000 into an account earning 5% 5 % annual interest for 30 30 years. Calculate the future value of the investment if the interest is compounded daily. Round your answer to the nearest cent.
Answers
Answer:
$94105.81
Step-by-step explanation:
[tex]21000( ({1 + .0512675})^{30} - 1) \\ = 73105.81 \\ 73105.81 + 21000 = 94105.81[/tex]
Future value of the investment if the interest is compounded daily is $94,105.80.
What is Compound Interest?Compound interest is defined as the amount of interest which has been calculated on the principal amount as well as the amount accumulated over the previous period is also included.
Given that,
Principal amount, P = $21,000
Rate of interest, r = 5% = 5/100 = 0.05
Time, t = 30 years
The final amount in a compound interest is,
A = P (1 + r/n)^(nt), where n is the number of times compounding is done in a year.
Here, n = 365
A = 21000 (1 + 0.05/365)^(365 × 30)
= 94,105.802
≈ 94,105.80
Hence the final amount is $94,105.80.
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Clifton spent $14.30 to buy his class 26 ice
cream sandwiches. How much did each ice
cream sandwich cost?
Answers
Answer:
$0.55
Step-by-step explanation:
All you have to do is divide $14.30 by 26 and that equals 0.55 so he spent 55 cents on each sandwich
–5(–2) = eeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee
Answers
Answer:
10
Step-by-step explanation:
-5 times -2= 10
Kevin has Oranges and grapefruits in a ratio of 40:18. How many oranges does he have if he has 9 grapefruits?
Answers
Answer:
20 oranges
Step-by-step explanation:
40:18 / 2 = 20:9
can you plz help out
Answers
Try this option:
1) q: What is the slope of the line and what does it mean in this situation?
a: the slope is 2.5 and it means 'ammount of the rain is 2.5 mm. per hour'.
2) the slope of the line is '2.5'
3) this means that '2.5' mm. of the rain falls every '1' hour.
Amir got 35% and fail by 20 marks and naveed got 45% marks and sucured 20 more marks than passing marks .what is the % of pass the exmanination?
Answers
Answer:
40%
Step-by-step explanation:
middle of 35 and 45
35 40 45
fail by 20 pass extra 20
and the total marks are
400
that means
every 1% is equivalent to 4 marks
Hero is in the bowling club. There are 14 students in the club. Of the 14 students, through will be picked at random to attend an award banquet. What is the probability that hero will not be paid to attend the banquet?
Answers
Find the inverse of the function f(x) = 2x^3 - 5
This is what I have so far
F(x) = 2x^3 - 5
Y = 2x^3 - 5
X = 2y^3 - 5
+5 +5
x + 5 = 2y^3
Answers
9514 1404 393
Answer:
f^-1(x) = ∛((x +5)/2)
Step-by-step explanation:
Continue to solve for y.
[tex]x +5=2y^3\qquad\text{so far so good}\\\\\dfrac{x+5}{2}=y^3\qquad\text{divide by 2}\\\\\sqrt[3]{\dfrac{x+5}{2}}=y\qquad\text{take the cube root}\\\\\boxed{f^{-1}(x)=\sqrt[3]{\dfrac{x+5}{2}}}\qquad\text{expressed in functional form}[/tex]
If you want to "rationalize the denominator", you can multiply both numerator and denominator by 4 inside the radical. This will simplify to ...
[tex]\displaystyle\boxed{f^{-1}(x)=\frac{1}{2}\sqrt[3]{4x+20}}[/tex]
[tex]\\ \rm\Rrightarrow y=2x^3-5[/tex]
Interchange y and x[tex]\\ \rm\Rrightarrow x=2y^3-5[/tex]
[tex]\\ \rm\Rrightarrow 2y^3=x+5[/tex]
Isolate y[tex]\\ \rm\Rrightarrow y^3=\dfrac{x+5}{2}[/tex]
[tex]\\ \rm\Rrightarrow y=\sqrt[3]{\dfrac{x+5}{2}}[/tex]
This is the inverse[tex]\\ \rm\Rrightarrow f^{-1}(x)=\sqrt[3]{\dfrac{x+5}{2}}[/tex]
what is x and y in the equation 9x + 20y > 120
Answers
Answer:
x= 120-20y/9
Step-by-step explantion:
