Answers
Answer:
1) 6a
2) 8
3) 18a
Step-by-step explanation:
1) [tex] \sf {2a}^{ - 1} \times {3a}^{2} [/tex]
Simplify using exponent rule with the same base
[tex] \sf \: 2 \times {3a}^{ - 1 + 2} [/tex]
Multiply the monomials
[tex] \sf \: 6a {}^{ - 1 + 2} [/tex]
Calculate the sum or difference.
[tex] \sf \: {6a}^{1} [/tex]
Calculate the power
[tex] \sf \: 6a[/tex]
2) [tex] \sf( \frac{1}{2} ) {}^{ - 3} [/tex]
simplify using negative exponents rule [tex] \sf {a}^{-n} = \frac{1}{{a}^{n}} [/tex]
[tex] \sf {2}^{3} [/tex]
calculate the power
[tex] \sf \: 8[/tex]
3) [tex] \sf {2a}^{ - 1} \times {(3a)}^{2} [/tex]
Simplify using exponents rule with the same exponent
[tex] \sf {2a}^{-1} × {3}^{2} × {a}^{2}[/tex]
Simplify using exponents rule with the same base a ^ n + a ^m = a ^n+m
[tex] \sf 2×{3}^{2} ×{a}^{-1+2} [/tex]
Calculate the power
[tex] \sf 2 × 9a {}^{-1+2}[/tex]
[tex] \sf 18a[/tex]
2(I) We round a number to three significant figures in the same way that we would round to three decimal places. We count from the first non-zero digit for three digits. We then round the last digit. We fill in any remaining places to the right of the decimal point with zeros.
8348 = 8350(rounded to 3 SF)
2(ii) 0.00796 = 0.0080
2(II) 6.329 = 6
2(III) 0.05684 = 0.0568
Step-by-step explanation:
1.i
2a^-1 × 3a²
remember, when we multiply factors with the same base value or variable, we keep that base value or variable and simply add the exponents.
-1 + 2 = 1
so, we get
2×3 × a¹ = 6a
1.ii
(1/2)^-3
remember, the "-" on the exponent just means 1/...
so, it is actually
1 / (1/2)³ = 1 / 1/8 = 8
1.iii
2a^-1 × (3a)²
similar to the first one, but remember, when we put the product of factors to a certain power, we need to do this for every factor of the inner multiplication :
2a^-1 × 9a² = 2×9 × a¹ = 18a
2.
the first significant figure is the first digit in the number reading from the left, that is not 0. it can be before or after the decimal point.
any digit (now continuing to read further to the right) after the first significant figure is again a significant figure even if it is 0.
i.
8.348 is rounded to 3 significant figures : 8.35
ii.
0.00796 is rounded to 2 significant figures :
0.0080 or 0.008 (because if the last digit after the decimal point is a 0, we can ignore it).
iii.
6.329 is rounded to 1 decimal place : 6.3
iv.
0.05684 is rounded to 3 decimal places : 0.057
3.
the sum of interior angles in a polygon is (n − 2) × 180°. where n is the number of sides.
as deca stands for 10, a decagon has 10 sides and 10 vertexes.
the sum of its inner angles is
(10 - 2) × 180° = 8 × 180° = 1440°
1170° of that is already covered by the first 7 angles.
so, we have left
1440 - 1170 = 270°
for the remaining 3 angles (that are all equal).
so,
270 = 3×angle
angle = 270/3 = 90°.
so, all of the 3 remaining angles are 90°.
Related Questions
The cost per unit of an item is called the
Answers
Answer:
breakeven point,
Step-by-step explanation:
factorise completely m^2n-mn^2
Answers
Answer: nm(m-n)
Step-by-step explanation:
m^2n-mn^2=
n*m(m)-m*n(n)=
n*m(m-n)=nm(m-n)
8xy(x^3 y) fully simplify
Answers
Answer:
8x^4y^2
Step-by-step explanation:
Just plug it in to the calculator and that will be your result.
Say that you own property with a market price of $74,000. the state tax assessors have given it an assessed value of 48% of that amount. if your state’s property tax rate is 0.031, how much do you owe in property tax, to the nearest dollar? a. $1,101 b. $2,294 c. $35,520 d. $1,193 please select the best answer from the choices provided a b c d
Answers
Option a. $1101 is the amount one owes in property tax
The market price of the property = $74000
The assessed value of the property as per the state tax assessors= 48%
So, assessed value in terms of dollars = (48/100)*74000 = $35520
Property tax is calculated on the assessed value of the property. Therefore we will calculate the property tax as follows:
Property tax rate in the state= 3.1%
So, property tax on the owned property will be = (3.1/100)*35520 = 1101.12 or 1101
Therefore, option a. $1101 is the correct answer for the given question
Hence, one needs to pay $1101 in property tax to the state
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How many whole numbers lie between 237 and 143?
Answers
Answer:
93
Step-by-step explanation:
143 —————>233 = 90
233 —————>237 = 3
90 + 3 = 93
The number of the whole numbers lying between 237 and 143 will be 94.
What is Algebra?The analysis of mathematical representations is algebra, and the handling of those symbols is logic.
Zero, a consistently positive number, or a negative integer denoted by a minus sign are all examples of integers. The inverse additives of the equivalent positive values are negative in value. The set of integers is frequently represented in mathematical notation by the big bold letters Z.
The number of the whole numbers lying between 237 and 143 will be given by the subtraction of the numbers from 237 to 143. Then we have
⇒ 237 - 143
⇒ 94
The number of the whole numbers lying between 237 and 143 will be 94.
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What is the letter name of the point of (1, 4)?
Answers
Answer: u
Step-by-step explanation: go over 1 up 4
During the school year, each student planted
1.2 x 10^2 flowers as part of a community
service project. If there are 1.5 x 10³
students in the school, how many flowers did
they plant in total?
Answers
Answer:
18000
Step-by-step explanation:
We can multiply the number of students by the number of flowers per student.
[tex](1.2 \times 10^2)(1.5 \times 10^3) \\ \\ =(1.2)(1.5)(10^5) \\ \\ =1.8 \times 10^5 \\ \\ =18000[/tex]
Two customers spent the same total amount of money at a restaurant.
• The first customer bought 8 hot wings and left a $4 tip.
• The second customer bought 10 hot wings and left a $2.80 tip.
• Both customers paid the same amount per hot wing.
How much does one hot wing cost at this restaurant in dollars and cents?
Record your answer in the boxes below. Be sure to use the correct place value.
+/-
Answers
Explanation:
We’ll solve this with a set of equations since the price per wing is fixed and they paid the sam amount at the restaurant. Let x represent the cost of 1 wing.
8x + 4.00 = 10x + 2.80
4.00 = 2x + 2.80
1.20 = 2x
0.60 = x
So, we have found that one wing cost $0.60.
Cheers.
424 divided by 3243.6
Answers
The following are the weights of 10 young dogs, in pounds:
7, 5, 11, 8, 14, 19, 16, 15, 13, 27
what proportion of the measurements lie in the interval?
Answers
The proportion which falls within the range is 0.9.
Given that data:
x : 7, 5, 11, 8, 14, 19, 16, 15, 13, 27
Mean = Σx / n
Using calculator :
Mean (m) = 13.5
Standard deviation (s) = 6.433
Proportion that lies in mean ± 2s
Lower = Mean - 2s
13.5 - 2(6.433) = 0. 632
Upper = Mean + 2s
13.5 + 2(6.433) = 26.376
Mean ± 2(sd) = (0.632, 26.276)
The only digit from the data which falls outside the defined range = 27
Proportion within interval = 9 / n
Proportion which falls within range = 9/10 = 0.9
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What formula would you use to find 50 is what percent of 20?
a) p = rb
b) r = p/b
c) i = prt
d) b = p/r
Answers
We would use r = p/b formula to find 50 is what percent of 20.
The correct answer is an option (b)
For given question,
we need to find the formula which we use to find 50 is what percent of 20
We make the assumption that 20 is 100% since it is our output value.
Let the value we seek be m.
So, 100 % = 20 ...............(1)
m % = 50 ..............(2)
By simply dividing equation 1 by equation 2 and taking note of the fact that both the LHS
(left hand side) of both equations have the same unit (%); we have
[tex]\frac{100\%}{m\%}=\frac{2}{5}[/tex]
So, m = 250%
This means, 50 is 250% of 20
The formula PERCENTAGE p = rb – The result obtained when a number is multiplied by a percent.
The formula BASE ( b = p/r) – The whole in a problem. The amount you are taking a percent of.
The formula RATE (r = p/b) – The ratio of amount to the base. It is written as a percent.
Therefore, we would use r = p/b formula to find 50 is what percent of 20.
The correct answer is an option (b)
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A 2-cup bottle of glass cleaner costs $6.56. What is the price per fluid ounce?
Answers
Answer:
82 cents per ounce
Step-by-step explanation:
There are 8 oz in a cup so two cups = 16 ounces
$6 .56 / 8 oz = $ .82 / oz
Mia is building a fence using nails 2.5 in
long. She drives a nail through a board
that is 75 in. thick into a 4 in. square
fencepost. How much of the nail goes
into the post?
Answers
Answer:
jjajdawasdaw
Step-by-step explanation:
wsadwdasdawasdawdas
Describe and correct the error in using the diagram to find the value of x
Answers
Step-by-step explanation:
It's simple in the following diagram ( 13x + 45)° + (19x +3)° won't be equal to 180° as they are vertically opposite angle...... and are vertically opposite to each other...
So to find the value of x :
13x + 45° = 19x + 3°
13x - 19x = 3 - 45
-6x = - 42
x = -42 / -6
x = 7°
☘☘☘...
help i need some answers please
Answers
Answer:
1. -3x^2 +2x -5
a= -3 b= 2 c= -5
4. 2x^2 -2x -6
a= 2 ...
Step-by-step explanation:
Standard form: Ax^2 +bx +c
Subtract numbers from one side of the equation to make it equal to zero.Or distribute until the equation is in standard form.Identify the domain of the function shown in the graph.
Answers
Answer: B
Step-by-step explanation: B
Which of the following could be a real-world description of 5x − 18?
$18 in addition to the cost of 5 hot dog combos
The cost of 18 people splitting 5 hot dog combos
The cost of hot dog combos less an $18 coupon split by 5 people
$18 less than the cost of 5 hot dog combos
Answers
Answer:
$18 less than the cost of 5 hot dog combos
Step-by-step explanation:
First, we see from the minus sign that this will be subtraction. PEMDAS (order of operations) says we do the multiplication first, then the subtraction.
I need the answer to all of them Rolly quick Bc my phone is dying
Answers
Answer:
1: $5
2: 7
3: 18
4: 17
5: 2
6: 1,029
Step-by-step explanation:
A train covers 828 km in 9 hours what distance will it cover in 6 hours
Answers
Answer:
In 9 hr it covers a distance of 828 km
In 1 hr it will cover a distance of 828 Divided 9 km = 92
In 6 hr it will cover a distance of 92 × 6 km = 552 km
All Done!
Answer:
552 Km
Step-by-step explanation:
find the speed in Km per hour then multiply by 6
828 Km ÷ 9 hours = 92 Km per hour
then distance covered in 6 hours is
distance = 6 × 92 = 552 Km
help because i paay 30 a month 4 thisssd
Answers
Answer:
2c+2
The number that will go in the green box is 2.
Step-by-step explanation:
3c-1-c+3
Combine the like terms.
3c-1-c+3=2c+2
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A number is chosen at random from the numbers 1-10. What is the probability of selecting the number 7 or a number less than 4?
Answers
Answer:
3/25
Step-by-step explanation:
In 2008, the centers for disease control and prevention reported the average human life span in the united states as 76.8 years for men and 81.6 years for women. calculate how much longer, on average, u.s. women live than men in seconds.
Answers
On average, U.S women live more than men in 151,400,000 seconds.
Average:
Average is the ratio of the total value divided by the number of observation used.
Given,
In 2008, the centers for disease control and prevention reported the average human life span in the united states as 76.8 years for men and 81.6 years for women.
Here we need to calculate how much longer, on average, u.s. women live than men in seconds.
Here we know that,
Average life span for men = 76.8 years
Average life span for women = 81.6 years.
So, the women lived
=> 81.6 - 76.8
=> 4.8 years.
So, the average women lived 4.8 years more than the man.
Now we have to convert it into seconds,
We know that,
1 year = 31,536,000 seconds
So,
=> 4.8 x 31,536,000 seconds
=> 151,400,000 seconds.
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1/5v+gt =a Solve for V
Answers
Answer:
v = 5(a - gt) or
v = 5a - 5gt These both mean the same thing
Step-by-step explanation:
1/5 v + gt = a Subtract gt from both sides of the equation.
1/5 v = a - gt Multiply both sides by 5
v = 5(a - gt)
2
You can also use scientific notation for very small numbers. The
thickness of a dollar bill is about 0.0043 inches. Write this quantity in
scientific notation.
A. First move the decimal point to the right to get a number that is
greater than or equal to 1 but less than 10.
0.0043 The decimal point moves 3
places to the right.
Remove the extra zeros to get the first factor:
B. Since 0.0043 is less than 1, you moved the decimal point to the right,
so the exponent in the power of 10 will be negative.
-3
0.0043 = 4.3
X 10
Answers
the thickness in scientific notation is:
4.3* 10⁻³ inches
How to write the thickness in scientific notation?
Here we know that the thickness of a dollar bill is 0.0043 inches.
Now, scientific notation refers to the notation where we have a single digit at the left of the decimal point, and the order of the number is defined by a factor of a power of 10.
To write our number in scientific notation we need to count the number of zeros that we have before the first non-zero decimal, and we can see that it is equal to 3.
Then we can move all the digits 3 units to the left, and add a factor 10⁻³ to correct that, then we will get:
0.0043 = 4.3* 10⁻³
From this, we conclude that the thickness in scientific notation is:
4.3* 10⁻³ inches
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5 ➗ 1/7
Draw a model that represents the division expression
Answers
We have to draw the model for 5 divide 1/7 . In order to draw the model we use below steps.
Draw 1/7 boxes to represent 1/7 groups.
Assume 5 as the number which represents the total of these 1/7 groups.
Put a question mark at the first box.
Attached is the model to represents 5 divide 1/ 7 .
5/(1/7)
5*7
35
In the question mark we should put 35.
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The volume of the cone shown in the figure below is 1/3 the volume of the cylinder. In terms of h,
what is the volume of the
cone?
Answers
Answer:
It is the last answer [tex]\frac{16\pi }{3}[/tex]
Step-by-step explanation:
the volume of the cylinder is the area of the base times the height. The area of a circle is
a = [tex]\pi r^{2}[/tex] We are give the diameter is 8. The radius is 1/2 of the diameter so the radius is 4. [tex]4^{2}[/tex] = 16
a = 16[tex]\pi[/tex] If the cone is 1/3 of that, we divide this answer by 3 to get
a = [tex]\frac{16\pi }{3}[/tex]
Graph the equation. Plot at least five points on the graph and label them with their
coordinates.
Answers
3. (-1,-2), (0,-1), (1,0), (2,1), and (3,2)
3. (0,0), (-1,2), (1,2), (-2,4), and (2,4)
A rectangular sheet of tin measures 20 inches by 12 inches. suppose you cut a square out of each corner and fold up the sides to make an open-topped box. what size square should you cut out to maximize the box's volume? show all work to earn credit.
Answers
The volume of the box is maximized when a 6 x 6 inch or 10 x 10 inch square is cut from the corners of the rectangular sheet.
Volume of rectangle:
The volume of an object is the amount of space occupied by the object or shape, which is in three-dimensional space. It is usually measured in terms of cubic units.
The formula for Volume of the rectangle is
V = l x b x h
where
l represents the length
b represents the breadth
h represents the height.
Given,
A rectangular sheet of tin measures 20 inches by 12 inches. suppose you cut a square out of each corner and fold up the sides to make an open-topped box.
Here we need to find the volume of the box is maximized when a square is cut from the corners of the rectangular sheet.
Here we have the following values:
h = x
l = 20 - 2x
b = 12 - 2x.
Here we have to subtract two times of x value because in the question they said that we have to cut a square from it.
Apply the values on the volume formula then we get,
=> V = (20 - 2x) x (12 - 2x) x (x)
=> V = [240 - 40x - 24x + 4x²] x (x)
=> V = [240x - 64x² + 4x³]
Now differentiate:
=> V' = 240 - 64x + 4x²
Simplify and order the equation,
Then we get,
=> V' = x² - 16x + 60
When we factorize the equation then we get,
=> V' = x² - 6x - 10x + 60
Take the common term out of it,
=> V' = x (x-6) -10(x -6)
Therefore, the value of x is, either 6 or 10.
Now you need to look at your solutions.
At x=6, the volume is,
=> V = (20 - 2(6)) x (12 - 2(6)) x (6)
=> V = (20 - 12) x (12 - 12) x 6
=> V = 8 x 0 x 6
=> V = 0
our corner squares devour the entire piece of cardboard and you are left with zero volume; so that solution is a minimum.
Now at the value of x = 10,
The volume is
=> V = (20 - 2(10) x (12 - 2(10)) x (10)
=> V = (20 - 20) x (12 - 20) x 10
=> V = 0 x (-8) x 10
=> V = 0
So, in both cases we have 0 as minimum volume. So, we can take any one of the value to get the maximum out of it.
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the function f(x) is shown. the function g(x)= 2x - 6 compare slopes
Answers
Answer: The slope of f(x) is less than the slope of g(x) because the slope of f(x) is -3
Step-by-step explanation:
Define slope?
The slope of a line is the ratio of the amount that y increases as x increases some amount. Slope tells you how steep a line is, or how much y increases as x increases. The slope is constant (the same) anywhere on the line.
We can write:
m=(y2-y1) / (x2-x1)
If,
g(x) = 2x - 6
The slope of g(x), m = 2
Let, x1=0
y1=2
x2=-1
Y2=1
So, we take (x1, y1) and (x2, y2) Then consider (0, 2) and (-1, 1)
Solve it:
Replace with x1, y1 and x2, y2
m = [1-(-2)/(-1)]
m=[(1+2) /(-1) ]
m=3/(-1)
m=-3
Thus, the slope of f(x) is less than the slope of g(x) because the slope of f(x) is -3.
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Use the Angle Addition Postulate to find the measure of the unknown angle.
Answers
Answer:
Hey there!
Step-by-step explanation:
This is ur answer....
60 + 120 = 180DEF = 180Hope it helps!
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