9514 1404 393
Answer:
100
Step-by-step explanation:
A root is equivalent to a fractional power. A square root is a 1/2 power. A cube root is a 1/3 power. The index of the root is the denominator of the fraction.
Of course the usual rules of exponents apply in evaluating an expression.
(a^b)^c = a^(bc)
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Your expression can be simplified as follows.
[tex]\displaystyle\sqrt[3]{1000^2}=(1000^2)^{\frac{1}{3}}=1000^{\frac{2}{3}}=(10^3)^{\frac{2}{3}}=10^2=\boxed{100}[/tex]
It can also be simplified another way:
[tex]\displaystyle\sqrt[3]{1000^2}=\sqrt[3]{(10^3)^2}=\sqrt[3]{(10^2)^3}=10^2=100[/tex]
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Additional comments
A problem like this is simpler if you are familiar with the squares and cubes of small integers.
The area of a rectangle is 8w + 18 square feet. The length of the rectangle is 2 feet. Use factoring to write an expression to represent the width of the rectangle.
Answer:
4w + 9
Step-by-step explanation:
Area of rectangle = length x width (or base x height, depending on how you look at it).
It is given to you that:
Area = 8w + 18
Length = 2
Let: width = x
Plug in the corresponding terms with the corresponding words:
8w + 18 = 2x
Isolate the variable, x. Divide 2 from both sides of the equation:
(8w + 18)/2 = (2x)/2
x = (8w + 18)/2
w = (8w)/2 + (18)/2
w = 4w + 9
4w + 9 is the expression that represents the width of the rectangle.
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line R has the equation y=4x+7 Line P is parallel tone line R and intersects the y axis a (0,-5). write down the equation of line P in the form y=mx+c
Solve for h.
-4h - 10 = 10 - 9h
h = |
if 3/4 of a certain number is equal to 9 find the number
write the equation.
3/4n=9
now solve.
3/4n=9
/3/4 /3/4
n=12
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hope it helps
Answer:
x = 12
Step-by-step explanation:
1. Prove that the product of the second and third numbers out of four consecutive whole numbers is two greater than the product of the first and the fourth numbers.
2. Prove that the square of the second number out of three consecutive odd numbers is four greater than the product of the first and third numbers.
Answer:
1.
(x+1)(x+2)>x(x+3)
x^2+2x+x+2>x^2+3x
x^2+3x+2>x+3x
2>0
2.
(x+2)^2>x(x+4)
x^2+4x+4>x^2+4x
4>0
Step-by-step explanation:
1.
Suppose x is the lowest number in the set of 4 consecutive numbers, then x+1, x+2, and x+3 are then the next numbers in the sequence since they are the next whole numbers.
Then, to follow the conditions of the problem, we make the equation:
(x+1)(x+2)>x(x+3)
Using the formula of (a+b)(c+d)=ac+ad+bc+bd, we can expand both sides of the equation into this:
x^2+2x+x+2>x^2+3x
=x^2+3x+2>x^2+3x
We can then cancel x^2+2x from both sides and we are left with 2>0.
2.
Again, suppose x is the lowest value in the set of consecutive numbers. In this case, odd numbers increase by 2 each time so the series of numbers are:
x, x+2, x+4
Therefore, to follow the conditions of the problem, we make the equation:
(x+2)^2>x(x+4)=
(x+2)(x+2)>x(x+4)
Using the same formula of (a+b)(c+d)=ac+ad+bc+bd, we get:
x^2+4x+4>x^2+4x
Cancel x^2+4x from both sides and we are left with 4>0
Hope this helps!
Write an explicit formula for an the nth
term of the sequence 8, 48, 288
Answer:
Step-by-step explanation:
a₁ = 8
a₂ = 48
Common ratio r = a₂/a₁ =6
nth term = a₁rⁿ⁻¹
= 8×6ⁿ⁻¹
The first triangle is an enlargement of the second.
Calculate the size of the missing sides and angles.
Answer:
large triangle:
base = 6.64 cm
hypotenuse = 8.31 cm
small triangle:
base = 4 cm
Step-by-step explanation:
large triangle:
tan 37 = 5/base
0.7536 = 5/base
base = 6.64 cm
using the Pythagorean theorem:
hypotenuse² = 5² + 6.64²
hypotenuse² = 25 = 44.02 = 69.02
hypotenuse = 8.31 cm
small triangle:
using the Pythagorean theorem:
base² = 5² - 3²
base² = 25 - 9 = 16
base = 4 cm
Write an equation in point-slope form for the line that passes through (–2, 1) with a slope of 1/4. Giving brainliest!
Answer:
y=1/4x+1.5
Step-by-step explanation:
Slope is 1/4 and I figured out that the y-intercept point is 1.5y.
I am not exactly sure though
I don't know how to do these 3 circled problems. can you do it step by step?
Pls help you can do either one
Answer:
4. 20.8 in
5. 60 degrees
6. i cant see number 6 so yah
Step-by-step explanation:
Which expressions are equivalent to 4m + 12? Choose all that apply. Whoever answers fastest, I’ll mark the Brainliest!
Answer: 1st and 3rd
Step-by-step explanation:
Answer:
third one
Step-by-step explanation:
6m-2m =4m
Hence 4m+12
re-grouping strategy for solving 57 x 18?
Answer:
1026
Step-by-step explanation:
I would do 50 x 18 and then do 7 x 8... then add the two results...
Which of the following properties is always true for a parallelogram? *
Diagonals bisect each other.
Diagonals are perpendicular.
Diagonals are congruent.
Diagonals biscect opposite angles.
Answer:
Diagonals bisect each other
**GIVING BRAINLIEST**
out in the open ocean, a tsunami can travel 800 kilometers per hour but as it reaches the coast it has to compress and slow down. suddenly it is now traveling only 160 kilometers in 2 hours. what is the rate of speed?
find the slope of line through points (4,-4) and (9,-4)
Step-by-step explanation:
Slope is equal to the change in y over the change in x, or rise over run.
[tex]m = \frac{change \: in \: y}{change in \: x\: } [/tex]
The change in x is equal to the difference in x-coordinates (also called run), and the change in y is equal to the difference in y-coordinates (also called rise).
[tex]m = \frac{y2 - y1}{x2 - x1} [/tex]
Substitute in the values of x and y into the equation to find the slope.
[tex]m = \frac{ - 4 - ( - 4)}{9 - (4)} [/tex]
Simplify.
[tex]m = 0[/tex]
Therefor, The slope is 0.
Answer:
Slope: 0
Step-by-step explanation:
The formula to finding slope is [tex]\frac{y1-y2}{x1-x2}[/tex]
We have the points (4,-4) and (9,-4)
So plug in:
[tex]\frac{-4-(-4)}{4-9}[/tex]
Simplify:
[tex]\frac{0}{-5}[/tex]
Slope: 0
There are 1,560 students enrolled at Greenwood Middle School. If 85% of these students ride the bus, how many do not ride the bus?
Answer:
234 students do not ride the bus
Step-by-step explanation:
1560*0.15
Answer:
if 85% ride the bus, that leaves 15% not riding.
1560× .15= 234 students
?????Help help help help help
Answer:
trapezoid
Step-by-step explanation:
PLZ HELP IF CORECT WILL GIVE BRAINLIST
Answer:
65 meters
Step-by-step explanation:
you add all the side/numbers together
Reid bought 4 souvenirs during 2 days of vacation. How many days will Reid have to spend on vacation before he will have bought a total of 14 souvenirs?
Step-by-step explanation:
4/2=2 souvenirs per day
2x=14=>x=7 days time to buy 14 souvenirs
Hence the 6th day is the day before he buys 14 souvenirs.
You deposited $10,000 into a savings account that compounds quarterly. The account has an interest rate of 3%. What would be the value after 30 years?
Answer:
$24272.62
Step-by-step explanation:
Given data
Principal= $10,000
Rate= 3%
Time = 30 years
The expression for the compound interest is given as
A= P(1+r)^t
Substitute
A=10000(1+0.03)^30
A=10000(1.03)^30
A=10000*2.4272
A= 24272.62
Hence the final Amount A=$24272.62
help please what is the domain and range of S
S={(0,-2), (5,3), (-3,5), (1,1)}
Answer:
Domain: {0,5,−3,1}
Range: {2,3,5,1}
Step-by-step explanation:
a certain book has 396 pages the student has already read 3/8 of the pages and now picks up the book again at time x=0 minutes write the equation that describes the total number of pages of the book read as a function of the number of minutes of further reading
Answer: https://brainly.com/question/22630516?answering=true&answeringSource=feedPublic%2FhomePage%2F1
Step-by-step explanation: I hope this helps pls mark branily
which is a rational number
a) 1.4142135623
b) 3.6256256
c) 2 (pie)
d) squared 5
Answer:
Rational numbers can be expressed as a fraction
Squared 5 = 25
25 can be expressed as a fraction- 25/1, so d is correct.
Let me know if this helps!
5 squared is right im sorry i miss read it
Nichole's rotating sprinkler waters her lawn up to a radius of 7 feet. What is the maximum number of square feet of lawn Nichole can expect the sprinkler to cover?
Answer:
153.9 ft²
Step-by-step explanation:
Given that:
Radius of circular lawn = 7 feets
To obtain the maximum number of square feet of lawn Nichole can expect the sprinkler to cover ; find the area of the lawn
Area of a circle, A = πr²
A = π * 7 * 7
A = 153.93804
A = 153.9 ft²
Select all the true statements.
(1048 – 876) ÷ 4 is four times as large as (1048 – 876).
(1048 – 876) + 24 is 24 times as large as (1048 – 876).
(1048 – 876) – 17 is seventeen less than (1048 – 876).
1/2 × (1048 – 876) is half as large as (1048 – 876).
(1048 – 876) × 4 is four more than (1048 – 876).
Answer:
C and D are are the true statements
The equation below can be used to find how much Julie took to the mall (d), in dollars.
d - $44.00 = $22.00
How much did Julie take to the mall?
$968.00
$2.00
$66.00
$22.00
Answer:
$22.00
Step-by-step explanation:
the reason it's 22 dollars is because you take away 44 - 22 and it's 22
Hey, can anyone help me with this homework answer?
Answer:
x=10
Step-by-step explanation:
Answer: 10
Step-by-step explanation: 7x-11=x-49
7x - 11 = x - 49 so add 11 to both sides 7x = x -60
Then 7x - x = 6 so 60/6= 10
please help me ill mark you brainliest and please show your work :)
Answer:
12
Step-by-step explanation:
Multiply both sides of the equation by 8/5.
4x-16=32
Move 16 to the other side
4x=32+16
add numbers on the right side
4x=48
divide both sides by 4
x=12
please help!!!! will mark brainlest
Answer:
16.59
Step-by-step explanation:
πr^2/2
radius is 6.5/2 = 3.25
πx3.25x3.25/2= 16.59
What is the circumference of the circle? Use 3.14 for Pi.
Answer: Could we see the circle we need to find the circumference for?
Step-by-step explanation:
