Using the properties of Integer exponents, match each expression with its equivalent expression.
Answers
The -5⁻³ matches with -1/125, (-5⁻³)⁻¹ matches with -125, and (-5⁻³)⁰ matches with 1.
What is integer exponent?In mathematics, integer exponents are exponents that should be integers. It may be a positive or negative number. In this situation, the positive integer exponents determine the number of times the base number should be multiplied by itself.
5⁻³ = 1/5³ = 1/125
-5⁻³ = -1/5³ = -1/125
(-5⁻³)⁻¹ = (-1/5³)⁻¹ = (-1/125)⁻¹ = -125
(-5⁻³)⁰ = 1 [tex]\rm (a^0 = 1)[/tex]
Thus, the -5⁻³ matches with -1/125, (-5⁻³)⁻¹ matches with -125, and (-5⁻³)⁰ matches with 1.
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Answer:
[tex]\sf{1)\ 5^{-3}={\dfrac{1}{5^3}={\dfrac{1}{125}[/tex]
[tex]\sf{2)\ -5^{-3}={\dfrac{1}{-5^3}=-{\dfrac{1}{125}[/tex]
[tex]\sf{3)\ \left(-5^{-3}\right)^{-1}=\left(-5^{-3\times-1}\right)=-5^{3}=-125}[/tex]
[tex]\sf{4)\ \left(-5^{-3}\right)^{0}=1[/tex]
Step-by-step explanation:
Exponent Property Rules:
⟹ Zero Exponent Property - ex: x⁰ = 1
An integer (excluding 0) with an exponent of zero equals one.
⟹ Negative Exponent Property - ex: x⁻ⁿ = [tex]{\dfrac{1}{x^n}[/tex]
Any number raised to a negative power is equivalent to the reciprocal of the number's positive exponent.
⟹ Power of Product Property - ex: (xy)ⁿ = xⁿ × yⁿ
To find the power of a product, multiply the power of each factor.
[tex]\sf{1)\ 5^{-3}={\dfrac{1}{5^3}={\dfrac{1}{125}[/tex]
[tex]\sf{2)\ -5^{-3}={\dfrac{1}{-5^3}=-{\dfrac{1}{125}[/tex]
[tex]\sf{3)\ \left(-5^{-3}\right)^{-1}=\left(-5^{-3\times-1}\right)=-5^{3}=-125}[/tex]
[tex]\sf{4)\ \left(-5^{-3}\right)^{0}=1[/tex]
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Related Questions
A system of equations is graphed on the coordinate plane.
y = 1/2+2
y = x + 1
What is the solution to the system of equations?
Answers
Answer:
y=2.5, x=1.5
Step-by-step explanation:
y=1/2+2 ---(1)
y=x+1 ---(2)
y=1/2+2=2.5
Substitute y=2.5 into equation (2)
y=x+1
2.5=x+1
2.5-1=x
x=1.5
What is the volume of a sphere with a diameter of 32.5 m, rounded to the nearest tenth of a cubic meter?
Answers
Answer:
17,964.9 cubic meters
Step-by-step explanation:
Hey there!
The formula for finding the area of a sphere is:
[tex]V=(4/3)\pi r^3[/tex]
Where V is volume, and r is radius
The question already tells us that the diameter is 32.5m
*Remember, the diameter isn't the radius. It is the radius times two*
Now, we have to divide 32.5 by 2 to get the radius
32.5/2 is 16.25
Now we can plug this into the formula
16.25 cubed is 4291 after being rounded to the nearest tenth
Now we multiply 4291 by 3.14 (pi)
4291 x 3.14 is 13473.7 after being rounded to the nearest tenth
Now multiply 13473.7 by 4/3 and then you will get the volume to the sphere
13473.7 x 4/3 is 17964.93333333...
Since it is asking us to round to the nearest tenth of a cubic meter;
The volume of the sphere will be 17,964.9 cubic meters
[tex]\rule{300}{1}[/tex]
[tex]\dashrightarrow\large\blue\textsf{\textbf{\underline{Given question:-}}}[/tex]
What is the volume of a sphere with a diameter of 32.5 m, rounded to the nearest tenth of a cubic meter (m³)?
[tex]\dashrightarrow\large\textsf{\textbf{\underline{Answer and how to solve:-}}}[/tex]
We are asked to find the volume of a sphere, which we can find using the following formula:-
[tex]\bold{V=\dfrac{4}{3} \pi r^3}[/tex]
Where:-V=volumeπ=pi (3.14…)r=radiusProvided information:-diameter (d)=32.5 mWhat we need in order to find the volume:-radiusWhat we need in order to find the radius:-Since the radius is exactly one-half of the diameter, we divide the diameter by 2 in order to find the radius:-[tex]\bold{r=d\div2}[/tex]
Replace d with 32.5:-
[tex]\bold{r=32.5\div2}[/tex]
Therefore, the sphere's radius is as follows:-
[tex]\bold{r=16.25}[/tex] m
[tex]\rule{300}{1}[/tex]
Now, let's find the sphere's volume, which, as I mentioned earlier, can be found with the help of this formula:-
[tex]\bold{V=\dfrac{4}{3} \pi r^3}[/tex]
Replace r with 16.25:-
[tex]\bold{V=\dfrac{4}{3} \pi (4291)}[/tex] Next, we replace π with 3.14:-
[tex]\bold{V=\dfrac{4}{3} \times3.14\times4291}[/tex]
On simplification,
[tex]\bold{V=\dfrac{4}{3} \times13,473.74}[/tex]
On further simplification,
[tex]\bold{V=17,964.9\:m^3}\Longleftarrow\sf{volume\:of\:the\:sphere}[/tex]
Good luck with your studies.[tex]\rule{300}{1}[/tex]
Layla walked a total of 12 kilometers by making 4 trips to school. After 5 trips to school, how many kilometers will Layla have walked in total? Assume the relationship is directly proportional.
Answers
Answer:
[tex]=15km[/tex]
Explanation:
[tex]12[/tex] [tex]km[/tex] ÷ [tex]4[/tex]
[tex]=3[/tex] [tex]km[/tex] per trip to school
Now that we know that Layla walks 3 km to walk to school, we multiply that by 10
[tex]3[/tex] [tex]km[/tex] × [tex]5[/tex] [tex]trips[/tex]
[tex]=15[/tex] [tex]km[/tex]
∴ Layla walked 15 km in total
Geometry problem help, will reward brainly! both dont have to be solved, but id really appreciate it.
Answers
Answer:
height: 8 mslant height: 5 inStep-by-step explanation:
The parameter of interest can be found by putting the given values into the appropriate volume or area formula for a pyramid, then solving for the unknown. The relevant formulas are ...
V = 1/3s²h . . . . . s is the base length; h is the height
A = s(s +2h) . . . . s is the base length; h is the slant height
__
height given volumeUsing the given values for the volume and the length of the base, the formula becomes ...
V = 1/3s²h
96 m³ = 1/3(6 m)²h . . . . . . . . . . use the given values for V, s
(96 m³)/(12 m²) = 8 m = h . . . . . divide by the coefficient of h
The height of the pyramid is 8 meters.
__
slant height given areaUsing the given values for area and the length of the base, the formula becomes ...
A = s(s +2h)
47.25 in² = (3.5 in)(3.5 in + 2h) . . . . use the given values for A, s
13.5 in = 3.5 in + 2h . . . . . . . . . . . divide by 3.5 in
10 in = 2h . . . . . . . . . . . . . . . . . subtract 3.5 in
5 in = h . . . . . . . . . . . . . . . . divide by 2
The slant height of the pyramid is 5 inches.
PLSSS HELP IF YOU TURLY KNOW THISS
Answers
Answer:
A or 2
Step-by-step explanation:
Reason:
The 5's cancel out leaving the 2 behind as the final answer.
Another way to look at it is that the 5*2 up top multiplies to 10, then we divide that by the 5 in the denominator to end up with 10/5 = 2
If you are a visual learner, then draw a circle and divide it into 5 equal slices. Do this a total of five times. Each pizza having 2 slices, and 5 pizzas total, gives 2*5 = 10 slices overall. These ten slices can be rearranged into making 2 full pizzas.
See below.
Jeremiah paid $5.76 for some pencils at the school store. if each pencil cost $0.18, how many pencils did jeremiah buy?
Answers
Answer:
They bought 32 pencils
Step-by-step explanation:
5.76 divided by 0.18 = 32
10 units
What is the approximate area of the circle?
Answers
Because pi r ^2
What is the slope of the line that passes through the points (-8, 6) and (-8, 2)?
Write your answer in simplest form.
Answers
Answer: Undefined or Vertical Slope.
Round 418 to the nearest ten.
Answers
Answer:
The answer should be 420.
~
Step-by-step explanation:
PLEASE HELP ASAP!!
Describe the transformations from the parent function, and define the function of the following graph.
Answers
Answer: Vertical stretch by a factor of 5.8 , reflection across x-axis ⇒ answer B
Step-by-step explanation:
* Lets revise the vertical and horizontal stretch with reflection
- A vertical stretching is the stretching of the graph away from the
x-axis
- If k > 1, the graph of y = k•f(x) is the graph of f(x) vertically stretched
by multiplying each of its y-coordinates by k.
- If k should be negative, the vertical stretch is followed by a reflection
across the x-axis
- A horizontal stretching is the stretching of the graph away from
the y-axis
- If 0 < k < 1 (a fraction), the graph of y = f(k•x) is f(x) horizontally
stretched by dividing each of its x-coordinates by k.
- If k should be negative, the horizontal stretch or shrink is followed
by a reflection in the y-axis
* Lets solve the problem
∵ G(x) = sin x
∵ F(x) = -5.8 sin x
∴ F(x) = -5.8 G(x)
- From the rule above
∴ G(x) is stretched vertically by scale factor -5.8
∵ The scale factor is negative
∴ The vertical stretch is followed by a reflection across the x-axis
* The transformation is:
Vertical stretch by a factor of 5.8 , reflection across x-axis
help answer this pls
Answers
Base X Height
So 20 X 4 = 80
Hope this helps!!
What is the difference of the y coordinate (0,3) and the y coordinate (4,0)
Answers
Answer:
3
Step-by-step explanation:
The difference of the two y-coordinates is found by ...
a) identifying the y-coordinates
b) computing their difference.
__
Each ordered pair lists the y-coordinate second.
(0, 3) ⇒ y-coordinate = 3
(4, 0) ⇒ y-coordinate = 0
The difference of the y-coordinates is ...
3 -0 = 3
students from a class of 15 are going to be chosen to be on the dance committee. Find the number of different 4-person committees that can be made.
Answers
we know that
The formula for combinations is
[tex]C=n!/[(n-r)!*r!][/tex]
where
[tex]n[/tex] is the total number of objects you choose from
[tex]r[/tex] is the number that you choose to arrange
in this problem
[tex]n=15[/tex] students
[tex]r=4[/tex] students
[tex]C=15!/[(15-4)!*4!][/tex] → [tex]C=15!/[11!*4!][/tex] → [tex](15*14*13*12*11!)/(11!*4*3*2*1)[/tex]
[tex]C=(15*14*13*12)/(24)[/tex] → [tex]C=1365[/tex]
the answer is
1,365
#76 will give brainliest! please help
Answers
Answer:
2nd option, (6x + 8)(x - 1) = 0
Step-by-step explanation:
Answer:
[tex](6x+8)(x-1)[/tex]
Step-by-step explanation:
We can separate the 2x into -6x + 8x. Then this will give us [tex]6x^2 - 6x + 8x - 8 = 0[/tex]. Now we can factor out a 6x and an 8 to give us [tex]6x(x-1) + 8(x-1) = (6x+8)(x-1)[/tex] by the distributive property.
Hope this helps! :)
If humans have infinity magnetite why cant we think of a another colur
Answers
Which climate has moderate rainfall, nutrient rich soils, and has a relatively thick layer of topsoil?
A. Desert
B. Arctic
C. Tropical rainforest
D. Grassland
Answers
Move a phrase and number to the blanks to complete the sentence.
Answers
2nd blank- 75 min
Answer:
The sophomore in her school is 75
Step-by-step explanation:
Solution
The plot shows the distribution of 30 sophomores
We can see that there are 3 main vertical
line in red pen in the picture above.( distribution)
The first line means Minimum
The third line means the maximum
The second line means the medium
So the Medium is 75. And 30 sophomores in her
School took the survey.
So the medium belongs to them
22.
Round 203.497 to the nearest whole number
Answers
Answer:
≈ [tex]\sf 203[/tex]
i need help can u guys help ;-;
Answers
Answer:
The answer for x and y will be x = Y + 7 and Y = 6x + 7Step-by-step explanation:
Y=6x - 7
6x - 7 = Y
6x = Y + 7
6x/6 = Y + 7/6
X = Y + 7
Plsssss helpppppoooooooooopppppppppppppppppppppp
Answers
Answer:
4
Step-by-step explanation:
length of a rectangular garden is 9m and breadth is 6m calculate it's area in mm2
Answers
Given
Length =9 m
Breadth =6 m
Area of the rectangle= (length × breadth) sq. units
=(9×6) m
2
=54 m
2
Was this answer helpful?
Find out if the lengths form a right triangle
Answers
Answer:
The triangle is a right triangle.
Step-by-step explanation:
Since The Pythagorean Theorem only works on right triangles, we can use this knowledge to prove whether this triangle is right:
[tex]a^2 + b^2 = c^2\\10^2 + (2\sqrt{39})^2 = 16^2\\100 + (4 \times 39) = 256\\100 + 156 = 256\\256 = 256[/tex]
Therefore, the triangle is right.
A merchant bought 1000 electric bulbs at the rate of Rs.150 each. 50 of them were broken on the way and the remaining he sold at the profit of 5%.What was the selling price of each bulb?
Answers
Answer:
₹165.79
Step-by-step explanation:
Given:-
No. of electric bulbs = 1000
cost of each electric bulb = ₹ 150
No. of bulbs broken = 50
Selling price of each bulb = x
Profit percentage = 5%
To Find:-
The selling price of each bulb.
Solution:-
Cost price of 1000 electric bulbs,
= 1000 × ₹150
= ₹1,50,000
5% profit on the total cost price,
= {5}/{100}× ₹150000
= ₹7500
Total selling price = ₹157500
No. of bulbs remaining = 950
Therefore, selling price of each bulb,
= {₹157500}/{950}
= ₹165.79
Therefore,
Selling price of each bulb = ₹165.79
1.1 solve for x, where 0°< x 90°. write your answer to one decimal place. 1.1.1 tanx=sin38° 1.1.2cosec( x+10°)=1.345
Answers
The value of x in tan(x)=sin38° is 31.6 and the value of x in cosec(x+10°)=1.345 is 38.0
How to solve the trigonometry ratios?The equations are given as:
tan(x)=sin38°
cosec( x+10°)=1.345
In tan(x)=sin38°, we have:
tan(x)=0.6157
Take the arc tan of both sides
x = 31.6
Also, we have:
cosec(x+10°)=1.345
Take the inverse of both sides
sin(x+10°) = 0.7434
Take the arc sin of both sides
x+10 = 48.0
Subtract 10 from both sides
x = 38.0
Hence, the value of x in tan(x)=sin38° is 31.6 and the value of x in cosec(x+10°)=1.345 is 38.0
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what is the surface area of a rectangular prism that has a length of 5 cm, a height of 14 cm, and a width of 12 cm? a. 298 cm2 b. 378 cm2 c. 616 cm2 d. 596 cm2
Answers
Answer:
sorry for being late but the answer is c 616 cm
Step-by-step explanation:
Determine the interquartile range for the following data 1,15,16,16,19,24,25
Answers
Answer:
IQR = 9
Step-by-step explanation:
Q3 = 24
Q1 = 15
24-15=9
Give brainliest, please!
Hope this helps :)
Part 1. Using the two functions listed below, insert numbers in place of the letters a, b, c, and d so that f(x) and g(x) are inverses. f(x)= x+a b g(x)=cx−d Part 2. Show your work to prove that the inverse of f(x) is g(x). Part 3. Show your work to evaluate g(f(x)). Part 4. Graph your two functions on a coordinate plane. Include a table of values for each function. Include five values for each function. Graph the line y = x on the same graph. Task 2 Part 1. Create two radical equations: one that has an extraneous solution, and one that does not have an extraneous solution. Use the equation below as a model: a√x+b+c=d Use a constant in place of each variable a, b, c, and d. You can use positive and negative constants in your equation. Part 2. Show your work in solving the equation. Include the work to check your solution and show that your solution is extraneous. Part 3. Explain why the first equation has an extraneous solution and the second does not.A newspaper started an online version of its paper 14 years ago. In a recent presentation to stockholders, the lead marketing executive stated, “The revenues for online ads are more than double that of the revenues for printed ads.” Use the graph below to justify the lead executive’s statement. Determine the approximate year that the two ad revenues were equal. See Text Version Two ocean beaches are being affected by erosion. The table shows the width, in feet, of each beach measured at high tide where 1995 is represented by year 0: Year number Western Beach width (in feet) Dunes Beach width (in feet) 0 100 20 5 90 45 10 80 70 11 78 75 12 76 80 15 70 95 Describe the patterns shown by the erosion data measurements shown for each of the beaches in the table. Between which years will the beaches have approximately the same width? Assuming these rates remain constant, what can you do to get a better approximation of when the two beaches will have the same width?
Answers
Answer: 5+10-15=30
5=35
=7
х=49
5√49+10-15=30
30=30
+1+7=4
=-4
it is no solution
Step-by-step explanation:
answer that for me xx
Answers
Hope it helps.
Refer attachments
I hope this helps!
simplify square root of 10,000,000 using powers of ten
Answers
using Indices we can simplify the square root of 10,000,000 using powers of ten is: [tex]10^{7/2}[/tex]
Meaning of IndicesIndices in mathematics can be defined as a value that takes up in index form but still retain its magnitude.
It is writing big or complicated values in a simpler and smaller way.
Indices is so important for simplicity purposes.
in conclusion, using Indices we can simplify the square root of 10,000,000 using powers of ten is: [tex]10^{7/2}[/tex]
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Multiply. 2 5/8⋅(−4 3/4)
A. −12 15/32
B. −8 15/32
C. −7 3/8
D. −2 1/8
Answers
option b
see attachment for solution
hope it helps...!!!