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
Number 33, Im not sure how to start so if anyone could write the steps down in order or explain it, I would be so happy.
Answers
Answer:
A = 26 B = 82
Step-by-step explanation:
The angle A = 180 - ∅
So A is:
180 - (4x+10)
180 - 4x - 10
170 - 4x
The total angle of a triangle is 180, so A + B + C = 180
(170 - 4x) + (2x + 10) + 72 = 180
170 - 4x + 2x + 10 + 72 = 180
170 - 2x +82 = 180
252 - 2x = 180
252 - 180 = 2x
72 = 2x
72/2 = x
36 = x
A = (170 - 4x) = (170 - 4(36)) = 26
B = (2x + 10) = (2(36) + 10) = 82
C = 72
From nine cards numbered 1 through 9, two cards are drawn. consider the selection and classification of the cards as odd or even as an experiment. how many sample points are there for this experiment?
Answers
Probability= 5/9
Even cards = 2,4,6,8
Odd cards = 1,3,5,7,9
The number of ways of choosing one odd and one even number is 5C1 * 4C1
( 5!/ 1!* 4!) * (4!/1! * 3!)
5* 4= 20
Total number of ways of choosing 2 cards out of 9 = 9C2
9!/ 2! * (9-2)!
= 9!/ 2! * 7!
= 9*8/2
= 9 *4= 36
Thus, Probability is = 20/ 36
= 5/9
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twice the larger of two consecutive integers is equal to fifteen less than three times the smaller
Answers
The larger of the two integers is 18 and the smaller integer is 17.
Integers are collection of whole numbers and negative numbers. Integers are not fractional numbers or decimal. Some examples of integers are -5,-25,0,13,9 .
Let us consider the smaller integer be x.
As the integers are consecutive, the larger integer is (x+1).
Now according to the given condition:
Twice the large integer=2(x+1)
15 less than the 3 times the smaller integer=3x-15
Now the value of these two expressions is equal.
Therefore: [tex]2(x+1)=3x+-15[/tex]
Solving the above equation to find the value of x:
[tex]or,2(x+1)=3x-15\\or,2x+2=3x-15\\or,2x-3x=-15-2\\or,-x=-17\\or,x=17[/tex]
Therefore the smaller integer is 17.
Larger integer(x+1) : 17+1=18
Therefore the integers are 17 and 18.
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What is 0.29 as a fraction in simplest form ?
Answers
Answer:
Step-by-step explanation:
0.29 as a fraction is 29/100. Anytime you have a decimal, just turn it into a whole number and simplify it. However, 29/100 is already in its simplest form.
x - 4y=-20
x - 4y=-26
Answers
Answer:
x − 4y = −20x − 4y = −26
Step-by-step explanation:
Pls help me im not that smart !!
Answers
Work Shown:
5 times 2 = 10
5 times 13 = 65
5 times 2.13 = 10.65
This rounds to 10.7 when rounding to the nearest tenth, i.e. one decimal place.
Solve for the system:
-w+3z=18
5w+6z=15
Answers
need help pls it's due
Answers
Answer:
4. $216 gain
5. 30g
I hope this helps
Which of the following sentences contains a dangling modifier?
A. Exhausted and thirsty, Jack ran off the football field for a drink of water.
B. Embarrassed and humiliated, the singer ran off stage after forgetting the lyrics.
C. Heroically, the firefighter rescued the small child from the burning building.
D. Searching frantically, the homework was finally found and turned in.
Answers
Answer:
I'm pretty sure the answer is D
Step-by-step explanation:
I took the test
The sentence that contains a dangling modifier is D. Searching frantically, the homework was finally found and turned in.
What is a dangling modifier?A word or phrase that modifies a term that is not explicitly expressed in the sentence is known as a dangling modifier. A modifier provides a concept's definition, clarification, or more information.
A grammatical modifier that could be mistakenly understood as being connected to a word other than the one intended is known as a hanging modifier. A hanging modifier, which usually refers to a participle, has no subject.
Therefore, the sentence that contains a dangling modifier is Searching frantically, the homework was finally found and turned in.
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(3-x)² what is the standard form
Answers
Answer:
here is my answer........
Step-by-step explanation:
(3-x)^2 = 9 - 3x - 3x + X2
= X2 - 6x +9
Two trains leave stations 240 miles apart at the same time and travel toward each other. One train travels at 70 miles per hour while the other travels at 80
miles per hour. How long will it take for the two trains to meet?
Answers
Answer: get a verified 340
Step-by-step explanation:
2help me PLEASE THIS IS WORTH SO MANY POINTS PLEAS EHELP ME
Answers
Answer:
I would say A
Step-by-step explanation:
Because just because a quadrilateral has 4 congruent sides, does not make it a rhombus. Because a square has 4 congruent sides too.
6-x^2 what is it
please answer correctly to be awarded brainliest
Answers
Answer:
i think the question might be incorrect or the question is incomplete
This isn’t really solvable rationally if that’s what your trying to do but irrationally:
sqrt means square root
(-x + sqrt6) (x + sqrt6)
= -x^2-sqrt6x+sqrt6x+6
= -x^2 + 6
so x = -sqrt6 and sqrt6
hope this helped
Determine the smallest integer that makes -3x + 7 -5x < 15 true.
Answers
Step-by-step explanation:
-3x+7-5x<15
-5x-3x+7<15
-8x+7<15
-8x<15-7
-8x<8
The smallest integer is -3x.
2. y varies directly as the square root of x, and y = 12, when x = 49. Find the value of y when x = 225. 3. R is inversely proportional to the cube of S and R = 8 when S = 3. Find the value of R when S=6. 4. n varies directly as the square root of t and inversely as l. If n = 5 when t = 16 and 1 = 2, find t when n = 10 and 1 = 3.
Answers
We need to use the concept of proprotionality for the given question.The value of y is 25.7, value of R is 1 and value of t is 144.
It is given that y varies directly as the square root of x which means that y is directly proportional to x, we can write it as
y∝[tex]\sqrt{x}[/tex] which can again be written as y=[tex]\sqrt{x} k[/tex] where k is a proportionality constant,we need to find the value of k inorder to find the value of y.We know that y=12 when x=49
12=[tex]\sqrt{49} k[/tex]=7k⇒12=7k⇒k=[tex]\frac{12}{7}[/tex]
when x=225 then y=[tex]\sqrt{225}[/tex]×[tex]\frac{12}{7}[/tex]=15×[tex]\frac{12}{7}[/tex]=25.7
R is inversely proportional to the cube of S,we can write it as
R∝[tex]\frac{1}{S^{3} }[/tex] ⇒R=[tex]\frac{k}{S^{3} }[/tex]
We need to find the value of k inorder to find the value of R, it is given that R=8 when S=3
8=[tex]\frac{k}{27}[/tex]
k=27x8=216
Value of R when S=6 will be
R=[tex]\frac{216}{6^{3} } =\frac{216}{216} =1[/tex]
It is given that n varies directly as the square root of t and inversely as l,we can write it as
n∝[tex]\frac{\sqrt{t} }{l}[/tex] which can be again written as n=[tex]\frac{\sqrt{t} }{l} k[/tex] where k is a proportionality constant,we need to find the value of k first to find the value of t
We know that n=5 when t=16 and l=2
5=[tex]\frac{\sqrt{16} }{2}k=\frac{4}{2} k=2k[/tex]
k=[tex]\frac{5}{2}[/tex]
We know that n=10,l=3 and k=[tex]\frac{5}{2}[/tex] substituting these values we can get the value of t
t=[tex](\frac{nl}{k} )^{2}[/tex]=[tex](\frac{10.3.2}{5} )^{2} =12^{2} =144[/tex]
Thus we can see that using the concept of proportionality we found out the values of y,R and t. Value of y is 25.7, R is 1 and t is 144.
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Find the general solution of the given higher-order differential equation. y(4) y''' y'' = 0
Answers
The homogeneous linear ODE
[tex]y^{(4)} + y''' + y'' = 0[/tex]
has characteristic equation
[tex]r^4 + r^3 + r^2 = r^2 (r^2 + r + 1) = 0[/tex]
with a double root at [tex]r=0[/tex] and two complex roots
[tex]r^2 + r + 1 = 0 \implies r = -\dfrac{1 \pm i\,\sqrt3}2[/tex]
Hence the characteristic solution is
[tex]y = C_1 e^{0x} + C_2x e^{0x} + C_3 e^{((-1/2)-i(\sqrt3/2))x} + C_4 e^{((-1/2)+i(\sqrt3/2))x}[/tex]
[tex]y = C_1 + C_2x \\\\ ~~~~~~~~~~ + C_3 e^{-x/2} \left(\cos\left(\dfrac{\sqrt3}2x\right) - i\, \sin\left(\dfrac{\sqrt3}2x\right)\right) \\\\ ~~~~~~~~~~ + C_4 e^{-x/2} \left(\cos\left(\dfrac{\sqrt3}2x\right) + i\,\sin\left(\dfrac{\sqrt3}2x\right)\right)[/tex]
[tex]y = C_1 + C_2x + C_3 e^{-x/2} \cos\left(\dfrac{\sqrt3}2x\right) + C_4 e^{-x/2} \sin\left(\dfrac{\sqrt3}2x\right)[/tex]
Square root of 750 ..?
Answers
Answer: 27.3861278753
Step-by-step explanation:
√750 = 27.3861278753
В
2x – у = 3
19x - 6y = 6
Answers
Answer:
work is shown and pictured
Given f(n) = 6n - 5
Evaluate f(-3)
Is
Answers
Explanation:
f(-3) = 6(-3) - 5
= -18 - 5 = -23
Select all the data sets with a range greater than 10. (2 points)
4 5 6 7 13
1 5 7 8 14
10 11 14 17 18
5 7 9 21 23
11 11 11 11 11
Answers
The data sets with a range that is greater than 10 are:
1 5 7 8 14
5 7 9 21 23
What is the Range of a Data Set?The range of any given data set is the difference between the largest and the lowest data point in the data set.
Range for 4 5 6 7 13:
Range = 13 - 4 = 9
Range for 1 5 7 8 14:
Range = 14 - 1 = 13
Range for 10 11 14 17 18:
Range = 18 - 10 = 8
Range for 5 7 9 21 23:
Range = 23 - 5 = 18
11 11 11 11 11 has no range.
Therefore, the data sets with a range that is greater than 10 are:
1 5 7 8 14
5 7 9 21 23
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what is the MAD for 3,4,5,5,5,6,6,6,7,8
Answers
Answer:
1.1
Step-by-step explanation:
Find the mean of the data:(3+4+5+5+5+6+6+6+7+8)/10 = 5.5Step 2: Find the difference between each data and mean:Difference between 3 and 5.5 is 2.5Difference between 4 and 5.5 is 1.5Difference between 5 and 5.5 is 0.5Difference between 5 and 5.5 is 0.5Difference between 5 and 5.5 is 0.5Difference between 6 and 5.5 is 0.5Difference between 6 and 5.5 is 0.5Difference between 6 and 5.5 is 0.5Difference between 7 and 5.5 is 1.5Difference between 8 and 5.5 is 2.5Step 3: Add all the differences:2.5+1.5+0.5+0.5+0.5+0.5+0.5+0.5+1.5+2.5 = 11Step 4: Divide it by the number of data:11/10 = 1.1So, the MAD = 1.1
A 2. Given the plane DGF in the diagram, which points are collinear?
1. G, E, and F
2. D, E, and F
3. H, G, and D
4. G, D, and E
Answers
Answer:
B
Step-by-step explanation:
H,E on the line perpendicular to the plane
D,E,F on the horizontal line on the plane
Savior loves to make waffles for breakfast normally it takes nine minutes to make three waffles he had some friends sleepover last night and he wants to make 10 waffles this morning if the waffles cook at the same rate how many minutes will it take Xavier to make the waffles this morning
Answers
Answer:
30 Mins
Step-by-step explanation:
9 mins for 3 waffles is 3 mins per waffle. 9÷3=3
3 mins for each of 10 waffles is 30 mins. 3×10=30.
What is 5 x x I don’t know the answer please give me it!
Answers
Answer:
5i is an imaginary number and it's square is - 25.
by definition zero is considered to be both real and imaginary.
Step-by-step explanation:
#studywell #workhard #worksmart
A rectangle is 15 cm wide. Find the area and the perimeter of the rectangle if its width is 3/5 of its length
Answers
The area and perimeter of the rectangle are 80 cm and 375 cm² respectively.
How to find area and perimeter of a rectangle?The rectangle is 15 cm wide.
The width is 3 / 5 of its length
Therefore, the area and the perimeter of the rectangle can be found as follows:
area of a rectangle = lw
where
l = lengthw = widthTherefore,
w = 15 cm
15 = 3 / 5 × l
cross multiply
75 = 3l
l =75 / 3
l = 25 cm
Therefore,
area of the rectangle = 25 × 15 = 375 cm²
Perimeter of the rectangle = 2l + 2w
Perimeter of the rectangle = 2(l + w)
Perimeter of the rectangle = 2(25 + 15)
Perimeter of the rectangle = 2(40)
Perimeter of the rectangle = 80 cm
Therefore, the area and perimeter of the rectangle are 80 cm and 375 cm² respectively.
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Let x1, x2, x3 be three independent random variables with binomial distributions b(4,1/2), b(6,1/3), and b(12,1/6), respectively. find (a) p(x1 = 2,x2 = 2,x3 = 5).
Answers
0.00345 is the value of p(x).
What means binomial distribution?
When each trial has the same probability of achieving a given value, the number of trials or observations is summarized using the binomial distribution. The likelihood of observing a specific number of successful outcomes in a specific number of trials is determined by the binomial distribution.P(x₁= 2 , x₂ = 2 , x₃ = 5 )
p( x₁= 2) . p( x₂ = 2) . p( x₃ = 5) .........( as these are independent variable)
[c⁴₂ ( 0.5 )² ( 0.5 )² ] [ c⁶₂ ( 1/3)²(2/3)⁴ ] [ c¹²₅ (1/6)⁵ (5/6)⁷
= 0.375 × 0. 329 × 0.028
= 0.00345
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Due tomorrow Help Please
Answers
The radius of a circle is 12 miles. What is the circle's area?
Answers
Answer: 452.16
Step-by-step explanation:
area of circle= πr² where r is the radius
the value of the radius is squared and multiplied by pi, i.e.. 3.14.
a=452.39
Find the area of the region that lies inside both curves. r = 9 sin(), r = 9 cos()
Answers
The area of the region inside both curves r = 9 sin(θ) and r = 9 cos(θ) is 11.56 square units.
What is integration?It is defined as the mathematical calculation by which we can sum up all the smaller parts into a unit.
The curves are:
r = 9 sin(θ) and
r = 9 cos(θ)
On graphing the above curves:
From the graph:
A = (1/2)∫(9sin(θ))2dθ + (1/2)∫(9cos(θ)2dθ
The region is symmetrical about π/4,:
A = 81∫sin2(θ)dθ from 0 to π/4
After solving:
= 11.56 square unit
Thus, the area of the region inside both curves r = 9 sin(θ) and r = 9 cos(θ) is 11.56 square units.
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Which graph represents 7x - 2y < 5?
