Which could be the first step in simplifying this expression? Check all that apply. (x cubed x Superscript negative 6 Baseline) squared (x Superscript negative 18 Baseline) squared (x Superscript negative 3 Baseline) squared (x Superscript negative 2 Baseline) squared x Superscript 6 Baseline x Superscript negative 12 Baseline x Superscript 5 Baseline x Superscript negative 4. Need Help ASAP!
Answers
Answer:
[tex](x^{-3} )^{2}[/tex]
[tex]x^6 x^{-12}[/tex]
Step-by-step explanation:
[tex](x^{3} x^{-6} )^{2}[/tex] is the expression given to be solved.
First of all let us have a look at 3 formulas:
[tex]1.\ p^a \times p^b = p^{(a+b)}\\2.\ (p^a \times q^b)^c = (p^{a})^c \times (q^{b})^c\\3.\ (p^a)^b = p^{a\times b}[/tex]
Both the formula can be applied to the expression([tex](x^{3} x^{-6} )^{2}[/tex]) during the first step while solving it.
Applying formula (1):
[tex](x^{3} x^{-6} )^{2}[/tex]
Comparing the terms of [tex](x^{3} x^{-6} )[/tex] with [tex]p^a \times p^b[/tex]
[tex]p=x, a =3, b=-6[/tex]
[tex]\Rightarrow x^{3+(-6)}\\\Rightarrow x^{3-6}\\\Rightarrow x^{-3}[/tex]
So, [tex](x^{3} x^{-6} )^{2}[/tex] is reduced to [tex](x^{-3} )^{2}[/tex]
Applying formula (2):
Comparing the terms of [tex](x^{3} x^{-6} )^{2}[/tex] with [tex](p^a \times q^b)^c[/tex]
[tex]p=q=x, a =3, b=-6, c=2[/tex]
[tex]\Rightarrow (x^{3})^2\times (x^{-6})^2\\\text{Applying Formula (3)}\\x^6 x^{-12}[/tex]
So, [tex](x^{3} x^{-6} )^{2}[/tex] is reduced to [tex]x^6 x^{-12}[/tex].
So, the answers can be:
[tex](x^{-3} )^{2}[/tex]
[tex]x^6 x^{-12}[/tex]
Answer:
b d
Step-by-step explanation:
Related Questions
rewrite the expression in the form 2n
Answers
Answer:
two times a number
Step-by-step explanation:
Can anyone help me with this?
Answers
Answer:
Yes it is 7 cuz it has the equation of 3-5a
Step-by-step explanation:
Answer:
D
Step-by-step explanation:
Plug in -3 as a
h(-3) = (3+15)/3
h(-3) = 18/3
h(-3) = 6
The triangles shown below must be congruent.
45°
45-
12
45°
45°
12
O A. True
B. False
Answers
Answer: True
Step-by-step explanation: The angles given are the same AND the side given us the same. The triangle has been reflected, but the reflection is still congruent.
The two triangles given are congruent according to the ASA congruence rule.
What is ASA congruence rule ?Two triangles are congruent if two angles and the included side of one triangle are equal to two angles and the included side of the other triangle.
Check whether the triangles are congruent :The given triangles are both right angled triangles.
The side 12 units is the included side between the angles 45° and 90° in both the triangles. This is the required condition for ASA congruence rule.
Hence we can say that the triangles are congruent according to the ASA congruence rule. The answer is A.True.
Learn more about congruence of triangles here:
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What is the value of 3/10 to the third power
Answers
Answer:
[tex]\frac{27}{1000}[/tex]
Step-by-step explanation:
=> [tex](\frac{3}{10} ) ^3[/tex]
=> [tex]\frac{(3)^3}{(10)^3}[/tex]
=> [tex]\frac{27}{1000}[/tex]
Answer:
It's 0.003.
Step-by-step explanation:
Use long division to solve:
69 )310.5
Answers
69)310.5
69)621/2
69*2/621
=2/9
HELP FAST! A cat spies a bird sitting at the top of a 32 foot pole. If the angle of elevation from the cat to the bird is 47°, then the cat is __________ feet from the base of the flagpole. Select one:
a. 29.880
b. 29.890
c. 29.820
d. 29.800
e. 29.840
Answers
Answer:
e. 29.840
Step-by-step explanation:
The cat, the floor and the foot pole form the shape of a right angled triangle.
The opposite is the height of the foot pole = 32 ft
The adjacent is the distance of the cat from the base of the foot pole.
The hypotenuse is the direct distance of the cat from the bird.
The angle of elevation, x, is 47°
To find the distance of the cat from the foot of the foot pole, we can use to TAN part of the trigonometric function SOHCAHTOA:
tan(x) = opposite / adjacent
=> tan(47) = 32 / adj
adj = 32 / tan(47)
adj = 29.840 ft
Therefore, the cat is 29.840 feet from the base of the foot pole.
HELP ASAP!!!!
what is the sum of the intimate geometric series
Answers
Answer:
[tex]-288[/tex]
Step-by-step explanation:
The sum of the infinite geometric series is defined as:
[tex]S=\frac{a_1}{1-r}[/tex]
Where [tex]a_1[/tex] is the first time and [tex]r[/tex] is the common ratio, where [tex]r[/tex] lies in the range of:
[tex]|r|<1[/tex]
[tex]S=\frac{-144}{1-\frac{1}{2}}=\frac{-144}{\frac{1}{2}}=-288[/tex]
What is the probability of selecting a boy or a blonde-haired person from 12 girls, 5 of whom have blonde-haired and 15 boys, 6 of whom have blonde-haired
Answers
Answer: 20/27
Step-by-step explanation:
So it is non- mutually exclusive;
Let B for the boys and H for the blond hair.
P(B) = 15/27; P(H) 11/27; P(B and H) = 6/27
Then, we have,
P(B or H) = 15/27 + 11/27 - 6/27
P(B or H) = 20/27
Therefore, the probability of selecting a boy or a blond-haired person is 20/27.
Cam is making a party hat, shown at left, in the shape of a cone for his
birthday. The circumference of the part of his head where the hat will
rest is 56 centimeters (cm). If the height of the hat is 25 cm, which of
the following is closest to the volume of Cam's hat, measured in cubic
centimeters (cm)?
Answers
Answer:
V≈2,080cm^3 Hope I helped :)
Step-by-step explanation:
The volume of a cone of radius r and height h is:
V=1/3πr^2h
Since the circumference of Cam's head is 56
2πr=56
r=56/2π
r=28/π
The volume of the hat is therefore:
V=1/3π(28/π )^2(25)
V=1/3((28)^2/π)(25)
V=1/3(19,600/π)
V≈2,080cm^3
The volume of the Cam's hat measured in cubic centimetres is 2081 cm³
Volume of a cone:The volume of a cone is as follows:
v = 1 / 3 π r²hwhere
h = height
r = radius
The circumference of the part of his head where the hat will rest is 56 cm. Let's find the radius
circumference = 2πr56 = 2 × π × rr = 28 / πh = 25 cm
V = 1 / 3 × π × (28 / π )² × 25
V = 1 / 3 × π × 784 / π² × 25
V = 19600 / 3π
V = 19600 / 9.42
V = 2080.67940552
V ≈ 2081 cm³
learn more on volume here : https://brainly.com/question/16048559?referrer=searchResults
Which expression best estimates 6 and three-fourths divided by 1 and two-thirds?
A) 7 divided by 2
B) 6 divided by 1
C) 8 divided by 3
D) 3 divided by 2
Answers
The expression that best estimates 6 3/4 divided by 1 2/3 is 7/2. 6 3/4 (or 6.75) divided by 1 2/3 (or 1.66...) comes out to 4 1/20 (or 4.05). The closest value to this in the options available is 7/2 (or 3.5). This answer is only .55 away from the correct value, while the rest of the options are far less close.
Answer:
7/2 or
7 dived by 2
Step-by-step explanation:
bruh A
The proof that is shown. Given: ΔMNQ is isosceles with base , and and bisect each other at S. Prove: Square M N Q R is shown with point S in the middle. Lines are drawn from each point of the square to point S to form 4 triangles. We know that ΔMNQ is isosceles with base . So, by the definition of isosceles triangle. The base angles of the isosceles triangle, and , are congruent by the isosceles triangle theorem. It is also given that and bisect each other at S. Segments _______ are therefore congruent by the definition of bisector. Thus, by SAS. NS and QS NS and RS MS and RS MS and QS
Answers
Answer:
MS and QS
Step-by-step explanation:
Finished the test!!! Hope u have a great day or night wherever u are :)
ΔMNQ is said to be an isosceles triangle, and a side is bisected at S, based on the definition of bisector, the segments that are congruent are: MS and QS.
What is the Isosceles Triangle Theorem?According to the isosceles triangle theorem, if two sides of a triangle are said to congruent or equal in length, then, the angles that are opposite to these two congruent sides are also congruent to each other.Thus, since ΔMNQ is said to be an isosceles triangle, and a side is bisected at S, based on the definition of bisector, the segments that are congruent are: MS and QS.
Learn more about isosceles triangle theorem on:
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what is the solution for the inequality -3x + 2 < 11?
Answers
Start by subtracting 2 from both sides.
This gives us -3x < 9.
Now, divide both sides by -3.
However, when you divide both sides of an inequality by a negative number, you must switch the direction of the inequality sign.
So we have x > -3.
Which reslts only in a horizontal compression of y=1/x by a factor of 6?
Answers
Answer:
y=1/6x
Step-by-step explanation:
y=1/x
the rule for horizontal compression is f(k.x) since we have the equation of y=1/x and k=6 then y=1/6x
Tom can do a job in 4 hours while Sam can do it in 6 hours. How many hours would it take to complete this job if they work together?
Answers
Answer:
12/5hours=2.4 hours
Step-by-step explanation:
Sam:6hours
Tom:4hours
This is a rate problem
Sam's rate is one job completed in 6 hours which is 1/6
Tom's rate is one job completed in 4 hours which is 1/4
Together, they could complete 1/4+1/6 of the job in y hours
We are trying to find the rate at which Sam and Tom could complete the job together, or one job in x days, for a rate of 1/y
1/4+1/6=1/y
The least common denominator is 12y
Multiplying through by the LCD which gives:
12y(1/4)+ 12y (1/6)= 12y (1/y)
3y + 2y=12
5y = 12
y=12/5 hours=2.4hours
Therefore it will take 12/5 hours or 2.4 hours to complete the job if they work together
Solve for s.
6 − 4s = –8 − 6s
s =
Answers
Step-by-step explanation:
6 - 4s = - 8 - 6s
Bringing like terms on one side
-4s + 6s = - 8 - 6
2s = - 14
S = - 14/2
S = - 7
2s=-2
S=2/-2
S=-1
Ans: s=-1
Another candle has a volume of 75 cubic inches and a height of 6 inches. What is the radius, in inches, of this candle? Round your answer to the nearest inch. Use 3.14 for π.
Answers
Answer: 3 inches
Step-by-step explanation:
Hi, to answer this question we have to apply the next formula:
Volume of a cone = 1/3 x π x radius^2 x height
Replacing with the values given:
75 = 1/3(3.14) r^2 (6)
Solving for r:
75 / (1/3 (3.14) 6) = r^2
75/ 6.28 = r^2
11.94 = r^2
√11.94 =r
3.45 inches = r
3 inches = r
Feel free to ask for more if needed or if you did not understand something.
there are 10 marbles, 2 yellow, three pink, and 5 black What is the probability of drawing two blue marbles if the first one is not placed back into the bag before the second draw?
Answers
Answer:
I think 15% im sorry if this is wrong
Round 3.44570830811 to the nearest hundred-thousandth,
Answers
Answer:
3.44571
Step-by-step explanation:
look at the number to the right of the decimal. if the number is higher than or is 5 round the number up, but if the number is less than 5 it will stay the same.
The number after rounding off to nearest hundred-thousandth or 5 decimal places will be -
3.44571
We have the following number - 3.44570830811
We have to round it of nearest hundred-thousandth or 5 decimal places.
What are Rounding numbers?Rounding means making a number simpler but keeping its value close to what it was. The result is less accurate, but easier to use. For example - 53 rounded to the nearest ten is 50.
According to the question, we have the following number -
3.44570830811
Rounding it off One by one until we get 5 digits after decimal -
R1 - 3.44570830811
R2 - 3.4457083081
R3 - 3.445708308
R4 - 3.44570831
R5 - 3.44570831
R6 - 3.4457083
R7 - 3.445708
R8 - 3.44571
Hence, the number after rounding off to nearest hundred-thousandth or 5 decimal places will be -
3.44571
To solve more questions on Rounding Numbers, visit the link below-
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The amount of money that Tom had in his pension fund n 2016 was E55 000. Dis plans involve him putting $8 200 in his fund every year for the next 15 years. How much will Tom have in the pension fund in 2031?
Answers
Answer:
$178,000
Check my explanation for further details
Step-by-step explanation:
$8200 in his pension fund for 15 years
=8200×15
=$123,000
By 2031
Tom will have a total of $55 000+$123,000
=$178,000
If by saying E55,000 you mean 55,000 Euro
Then,
$62,174.99=E55000
$62,174.99+$123,000
=$185,174.99
PLEASE HELP! Shalini found the sum of the measures of the interior angles of the triangle to be 175°. She knows the sum is supposed to be 180°. What was Shalini’s error? m∠A = 45° m∠B = 85° m∠C = 45° Shalini did not add the sum of the 3 angles correctly.
Answers
Answer:
its c
Step-by-step explanation:
because i said
Answer:
c is the correct option
Step-by-step explanation:
Wilson needs 9 pieces of wood that are each 1/3 ft long. He has one board that is 3 1/3 ft long. Will he be able to make all the pieces he needs from that one board?
Answers
Answer:
Yes, he will.
Step-by-step explanation:
Since he needs 9 pieces of 1/3 ft, yo would start by dividing 9 by 3 (9 x 1/3). This would give you 3, meaning that you would need 3 feet of would in all, and since he is given 3 and 1/3 feet, he has enough.
Hope this helps!
The low temperature during 4 days in September was 21°C, 21°C, 19°C and 19°C. What was the mean temperature?
Answers
Answer:
Step-by-step explanation:
The Answer is 20.
1: First, add up all the temperatures that has been provided, 21 + 21 + 19 + 19. It should give you 80.
2: Divide 80 by how many temperatures has been shown. There were 4 temperatures shown, so 80/4 = 20. Hope this helps you!
Which of the following is a secant on the circle below
Answers
Answer:
RT is more appropriate, though even SU could be called a secant.
Step-by-step explanation:
What is the final amount if 648 is decreased by 7% followed by a further 20% decrease?
Give your answer rounded to 2 DP.
Answers
Answer:
473 or excact is 473.04
Step-by-step explanation:
First,
100 - 23 = 73
Then take,
73% x 648 = 47,304
Finally,
47,304 / 100 = 473.04 or
rounded to 473.
Have a good day. :)
Hope this helps!
(brainliest would be appreciated)
what is the LCM of x^2+5 and x^2+10x+25?
Answers
Answer:
(x+5)²(x²+5)
Step-by-step explanation:
Given two functions x²+5 and x²+10x+25, to get their Lowest common factor, we need to to first factorize x²+10x+25
On factorising we have:
x²+5x+5x+25
= x(x+5) +5(x+5
= (x+5)(x+5)
= (x+5)²
The LCM can be calculated as thus
| x²+5, (x+5)²
x+5| x²+5, (x+5)
x+5| x²+5, 1
x²+5| 1, 1
The factors of both equation are x+5 × x+5 × x²+5
The LCM will be the product of the three functions i.e
(x+5)²(x²+5)
This hives the required expression.
Given the following exponential function, identify whether the change represents growth or decay , and determine the percentage rate of increase or decrease y =550(1.075)x
Answers
Answer:
It is growth and the percentage rate of increase is 7.5%
Step-by-step explanation:
The exponential equation is as follows;
y = 550(1.075)^x
Now, I can identify that the exponential equation is that of growth.
This is because what is in the bracket i.e can be represented as 1+ 0.075
The 0.075 represents the margin of increase as we move on from one value to another
The percentage rate can be gotten by expressing 0.075 as a percentage
That would be expressing is as a fraction
This is just 7.5/100 which means what we have is 7.5%
A bicycle has a listed price of $736.99 before tax. If the sales tax rate is 9.75%, find the total cost of the bicycle with sales tax included
Round your answer to the nearest cent, as necessary.
Please help me
Answers
Answer:
First, we need to calculate the tax. So we can multiply 736.99*0.0975 which will give us 71.856525 or about 71.86. So then we add them together and we get an answer of 808.85. Therefore the answer to this question is.
808.85
What is M and C for the line Y=X-6?
Answers
Answer:
Step-by-step explanation:
Equation of line: y = mx + c
y = x - 6
Slope m = 1
y-intercept c = -6
Answer:
m = 1
c = -6
Step-by-step explanation:
Formula for a line is y = mx+c
m = gradient
c = intercept.
Here:
m = 1
c = -6
Hope this helps
Good Luck
PLEASE HELP ASAP MATH
Answers
Answer:
3. 324+432=756 in cubed
4. 2100+7200=9300 yd cubed
At 7 p.m. the temperature was 5° F. At midnight the temperature was -7° F. What was the change in temperature?
Answers
Answer:
Change in temperature was 12 degrees
Step-by-step explanation:
If you start with five degrees and end into negative 7 degrees, you can find the result within two steps
5 degrees minus 5 = 0 degrees
then, 0 degrees minus 7 = -7 degrees
Because you subtracted 5 from five, and 7 from seven, you add those two values together
7 + 5 = 12 degrees
So the change in temperature was 12 degrees
Hope this helps!