Answers
Step-by-step explanation:
[tex]a^n={\underbrace{a\cdot a\cdot a\cdot...\cdot a}_{n}[/tex]
METHOD 1.[tex]\left(b^3\right)^2=\underbrace{b^3\cdot b^3}_{2}=\underbrace{b\cdot b\cdot b}_{3}\cdot\underbrace{b\cdot b\cdot b}_{3}=\underbrace{b\cdot b\cdot b\cdot b\cdot b\cdot b}_{6}=b^6[/tex]
METHOD 2.[tex]\left(b^3\right)^2=\underbrace{b^3\cdot b^3}_{2}=b^{3+3}=b^6\qquad\text{used}\ a^n\cdot a^m=a^{n+m}[/tex]
METHOD 3.[tex]\left(b^3\right)^2=\left(\underbrace{b\cdot b\cdot b}_{3}\right)^2=b^2\cdot b^2\cdot b^2=b^{2+2+2}=b^6\\\text{used}\ (ab)^n=a^nb^n,\ a^n\cdot a^m=a^{n+m}[/tex]
METHOD 4.[tex]\left(b^3\right)^2=b^{3\cdot2}=b^6\qquad\text{used}\ \left(a^n\right)^m=a^{nm}[/tex]
Related Questions
Imagine a player getting ready for a tournament. He has 4 games to play during the day: 9:00 a.M., 11:00 a.M., 1:00 p.M., and 3:30 p.M. He refuses to wear shorts until temperature rises to at least +5 degrees. Based on a starting temperature of -9 degrees at 6am and an increase in temperature of 2 degrees an hour, when might he be able to change from his pants to shorts? Provide explanations why he can/can't put his shorts on for Game 1, Game 2, Game 3 and Game 4.
Answers
Answer:
by game 3(at 1:00 p.m.)
temperature increases to 5 degrees at 1:00 p.m
Pleaseeeeeee. Helpppppppppppp meeeeeeeeeeee
Answers
Answer:
first tower needs 4
second needs 3
third needs 2
and the fourth needs 1
Total needed triangles for all is 10
Step-by-step explanation:
Find the area of the shaded triangle.
Answers
Answer:
7.5
Step-by-step explanation:
The area of a triangle is found by the formula A=1/2bh, where b is the base length, and h is the height. If we count the squares, we can find that the base length of the triangle is 3 units, and the height is 5 units. If we plug those numbers into the equation to get A=1/2*3*5, we can solve to get A=7.5
What is the appropriate symbol? 1.42 _____ 1.420 = < >
Answers
Answer:
=
Step-by-step explanation:
1.42 is equal to 1.420. The 0 adds no value since it is after the decimal point so 1.420 is just 1.42, which is equal to itself, 1.42.
Answer:
=
Step-by-step explanation:
When you are looking at decimals, specifically on the right side of the decimal point, the amount of 0's after the last given non-0 digit can be disregarded.
1.420 is the same as 1.42
With this given information:
1.42 ____ 1.420
1.42 ____ 1.42
1.42 = 1.42
= would be your sign.
~
Help please thank you so much
Answers
Answer:
it is a function because it doesn't have two x coordinates at the same y coordinate.
Explain the significance of the equation 100x -2y+ 400 = 0 which represents the hourly cost of a car repair.
Answers
Answer: The significance is that it is how much you will pay for the total repair which will help you know how much money you will spend.
Step-by-step explanation:
Which of the following equations is graphed below?
Answers
Answer: 3rd answer choice
Step-by-step explanation:
Answer: 4th answer choice
Step-by-step explanation:
WHAT IS THE TRUE SIMILARITY STATEMENT
Answers
Answer:
Option 2
Step-by-step explanation:
ΔPQR - ΔSTR
Because
∠S ≅ ∠P
∠T ≅ ∠Q
∠R ≅ ∠R
I hope this helps you
look at image and help me please.
Answers
Answer:
-5
Step-by-step explanation:
the slope is -5
Answer:
-5
Step-by-step explanation:
The slope formula used is y=mx+b where m is the slope and b is the y-intercept.
In this case, -2/3 is the y-intercept and -5 is the slope.
Which represents the reflection of f(x) = x over the y-axis?
х
-1
0
1
4
f(x)
undefined
0
1
2
f(x)
х
-1
0
1
1
0
-1
-2
4
Answers
Answer:
Graph having x ≤ 0
Step-by-step explanation:
f(x) = [tex]\sqrt{(-x)}[/tex]
Given function 'f' when reflected across the y--axis,
Translated form of the parent function will be,
g(x) = [tex]\sqrt{(-x)}[/tex]
Table for the input-output values for this function will be,
x g(x)
-1 1
0 0
1 undefined
4 undefined
Table shows that the given function is undefined for x > 0
Domain of g(x) will be (-∞, 0],
Therefore, graph having values of x ≤ 0 will be the answer.
Answer:
I think its D on edge!
Step-by-step explanation:
The nth term of a sequence is n(n - 1).
What are the first four terms?
What is the 50th term?
Is 59 a term in the sequence?
Which term is 182?
The ______ th term
Answers
Answer:
T1=0
T2=2
T3=6
T4=12
T50=2450
59 is not a term in the sequence
Step-by-step explanation:
Tn=n(n-1)
182=n2 - n
0=n2 - n - 182
0=n2-14n+13n-182
0=n(n-14)+13(n-14)
0=(n-14) (n+13)
Since n cannot be negative n is not equal to -13
Therefore,
n=14
. Una persona desea realizar una pintura para su próxima exposición en donde esta tenga tres colores fluorescentes y dos colores pastel, al realizar la revisión de su paleta de pintura, este artista cuenta con siete colores fluorescentes y cinco colores pastel. De lo anterior se puede indicar que la cantidad de maneras en que puede realizar la pintura como lo desea es *
A. 305.
B. 350.
C. 405.
D. 450
Answers
Answer: B. 350.
Step-by-step explanation:
Given: Total number of fluorescent colors = 7
Total number of pastel colors = 5
Since , he want three fluorescent colors and two pastel colors.
Number of ways to select r things out of n things = [tex]^nC_r=\dfrac{n!}{r!(n-r)!}[/tex]
Number of ways to choose colors = [tex]^7C_3\times\ ^5C_2[/tex]
[tex]=\dfrac{7!}{3!4!}\times\dfrac{5!}{2!3!}\\\\=\dfrac{7\times6\times5\times4!}{3\times2\times1\times4!}\times\dfrac{5\times4\times3!}{2\times3!}\\\\=350[/tex]
Hence, the correct option is B. 350.
Can someone help fast please
Answers
Answer:
[tex] \frac{3a}{a-2} [/tex]
Step-by-step explanation:
[tex] \frac{2a - 7}{a}*\frac{3a^2}{2a^2 - 11a + 14} [/tex]
Factorise [tex] 2a^2 - 11a + 14} [/tex]
[tex]\frac{2a - 7}{a}*\frac{3a^2}{(2a - 7)(a - 2)}[/tex]
[tex] 2a - 7 [/tex] cancels 2a - 7
[tex] \frac{1}{a}*\frac{3a^2}{(1))(a - 2)} [/tex]
[tex] \frac{1(3a^2)}{a(a-2)} [/tex]
[tex] \frac{a(3a)}{a(a-2)} [/tex]
"a" cancels "a"
[tex] \frac{3a}{a-2} [/tex]
Thus,
[tex] \frac{2a - 7}{a}*\frac{3a^2}{2a^2 - 11a + 14} [/tex] = [tex] \frac{3a}{a-2} [/tex]
i will give best answer a right rectangular prism is shown What shape best describes the cross section cut at an angle to the base of a right rectangular prism? Trapezoid Parallelogram Square Rectangle
Answers
Answer:
parallelogram
Step-by-step explanation:
Answer:
parallelogram
Step-by-step explanation:
did the test
The probability that Paul wins a raffle is given by the expression n/n + 6 . What is the expression, in the form of a combined single fraction, for the probability that Paul does not win.
Answers
Answer:
The probability that he doesn’t win is 6/(n + 6)
Step-by-step explanation:
Mathematically, the probability that an event occur is 1 minus the probability that the event doe not occur.
Thus, what we are saying here is that the sum of the probabilities that Paul wins the raffle draw and he doesn’t win the raffle draw is 1
This can be mathematically expressed as;
probability that he doesn’t win = 1 - probability that he wins
Thus we have;
1- n/(n+ 6)
= [(n+ 6) -(n)]/(n+6) = 6/n+ 6
What is the measure of Angle c? 3 lines intersect to form 5 angles. Clockwise, from top left, the angles are b, 90 degrees, c, 124 degrees, a.
Answers
Answer:
c
Step-by-step explanation:
Answer:the answer is 90
Step-by-step explanation:
If two lines meet at a right angle they are said to be _________ to each other.
Answers
Answer: perpendicular
Answer:
perpendicular
Step-by-step explanation:
If two lines meet at a right angle they are said to be perpendicular to each other.
Two lines are perpendicular when they intersect at a right angle.
Find the slope of the line that passes
through these two points.
Point 1(3,5) Point 2(4,2)
Answers
Answer:
Slope = -3
Step-by-step explanation:
(3 , 5) ; (4, 2)
[tex]Slope=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}\\\\=\frac{2-5}{4-3}\\\\=\frac{-3}{1}\\\\=-3[/tex]
The volume of a cone with a height of 6 cm is 8 pi cubic centimeters. Which expression can be used to find r, the radius of the base of the cone? 6 = one-third pi (r squared) (8 pi) 8 pi = one-third pi (r) (6 squared) 6 = one-third (pi r)(8 pi) 8 pi = one-third pi (r squared) (6)
Answers
Answer:
last option is correct
Step-by-step explanation:
Mathematically, we can write the volume of a cone as;
V = 1/3 * pi * r^2 * h
From the question, V is 8 pi cm^3 while h is 6cm
Thus, substituting these values into the equation, we have;
8pi = 1/3 * pi * r^2 * 6
The last option is the correct answer that tallies with the above
Answer:
8 pi = one-third pi (r squared) (6)
its d
Step-by-step explanation:
Plzzz helpppp urgenly❤️
Answers
Answer:
[tex]\mathrm{D.} \: (\frac{5}{4} )^{\frac{7}{2}[/tex]
Step-by-step explanation:
[tex]\sqrt{(\frac{5}{4})^7 }[/tex]
Apply rule : [tex]\sqrt{a} =a^{\frac{1}{2} }[/tex]
[tex]((\frac{5}{4})^7 )^{\frac{1}{2} }[/tex]
Apply rule : [tex](a^b)^c=a^{bc}[/tex]
[tex](\frac{5}{4} )^{7 \times \frac{1}{2} }[/tex]
[tex](\frac{5}{4} )^{\frac{7}{2}[/tex]
I need help with this question please help
Answers
Explanation:
Congruent means that they are the same size and shape.
Suppose you invest $2250 in a D that earns 3% APR and is compounded monthly. The Cd matures in 2 years. How much will this CD be worth at maturity?
Answers
Answer:
$2388.95
Step-by-step explanation:
Principal, P= $2250Annual Interest Rate, r= 3% =0.03Time, n= 2 yearsSince it is compounded monthly, Period, k= 12 MonthsThe worth of a compound deposit after a period of n years is calculated using the formula:
[tex]A(n)=P(1+\frac{r}{k})^{nk}[/tex]
[tex]A(2)=2250(1+\frac{0.03}{12})^{12 \times 2}\\\\=2250(1+0.0025)^{24}\\=2250(1.0025)^{24}\\=\$2388.95[/tex]
At maturity, the deposit will be worth $2388.95.
solve (-t-5)/3= (t-3)/5
Answers
Answer & Step-by-step explanation:
[tex]\frac{-t-5}{3}=\frac{t-3}{5}[/tex]
Cross multiply.
[tex]-5t-25=3t-9[/tex]
Subtract -3 on both sides.
[tex]-8t-25=-9[/tex]
Add 25 on both sides.
[tex]-8t=16[/tex]
Divide -8 on both sides.
[tex]t=-2[/tex]
Five thousand tickets are sold atâ $1 each for a charity raffle. tickets are to be drawn at random and monetary prizes awarded asâ follows: 1 prize of â$500â, 3 prizes of â$300â, 5 prizes of â$30â, and 20 prizes ofâ $5. what is the expected value of this raffle if you buy 1â ticket?
Answers
Answer:
-$0.67
Step-by-step explanation:
If you buy one ticket, the possible outcomes are:
100% chance of spending $1 (buying the ticket)
1 in 5,000 chance of winning $500
3 in 5,000 chance of winning $300
5 in 5,000 chance of winning $30
20 in 5,000 chance of winning $5.
The expected value of the raffle is determined by:
[tex]E(X)=-1+\frac{1}{5,000}*500+\frac{3}{5,000}*300+\frac{5}{5,000}*30+\frac{20}{5,000}*5\\E(X)=-\$0.67[/tex]
The expected value of this raffle if you buy 1 ticket is -$0.67.
The admission fee at an amusement park is $20 for children and $35 for adults. On a certain day, 390 people entered the park, and the admission fees collected totaled $10650. How many children and how many adults were admitted? NUMBER OF CHILDREN= ? NUMBER OF ADULTS= ?
Answers
Answer:
Children = 200
Adults = 190
Step-by-step explanation:
Children = x
Adults = y
x + y = 390
x = 390 - y..............(1)
20x + 35y = 10650
Substituting
20(390-y) + 35y = 10650
y = 190
x = 390 - 190 = 200
Answer:
Step-by-step explanation:
Number of children = c
Number of adults = a
Total people = 390
a + c = 390 ------------------ (I)
Admission fee for 'c' children = 20 * c = 20c
Admission fee for 'a' adult = 35 * a = 35a
Total amount = $ 10650
35a + 20c = 10650 -------------(II)
Multiply equation (I) by (-20)
(I)*(-20) -20a - 20c = - 7800
(II) 35a + 20c = 10650 { Now add and so 'c' will be eliminated}
15a = 2850
a = 2850/15
a = 190
Plug in a = 190 in equation (I)
190 + c = 390
c = 390 - 190
c = 200
Number of children = 200
Number of adults = 190
Please answer this question fast in 2 minutes
Answers
Answer:
<5solution,
<3+<4=180°( linear pair)----> equation (i)
<4+<5=180°( linear pair)------>equation (ii)
From equation (i) and (ii)
<3+<4=<4+<5
<3=<5 (vertically opposite angles)
hope this helps...
Good luck on your assignment
NEED ANSWER IN 2 MINUTES!
Answers
Answer: 11
Step-by-step explanation:
The stem is the 10s place and leaf is the ones
A cylinder has a diameter of 18 inches and a volume of 405/2π cubic inches. What is the height, in inches, of the cylinder? Enter the height in decimal form rounded to the nearest tenth.
Answers
Answer:
Step-by-step explanation:
diameter = 18 inches
radius = r = 18/2 = 9 in
Volume of cylinder = 405π/2
[tex]\pi r^{2}h = \frac{405}{2}\pi \\\\\\\pi * 9 * 9* h =\frac{405}{2}\pi \\\\\\h =\frac{405}{2*9*9*\pi }*\pi \\\\\\h=\frac{5}{2}[/tex]
h = 2.5 inches
Lara's living room is 9 meters wide and 9 meters long. She wants to install purple carpet that costs $8.00 per square meter. How much will it cost to buy enough carpet for the living room?
Answers
Answer:
$648.00
Step-by-step explanation:
==>Given:
Squared living room of 9m by 9m
Cost of purple carpet per m² = $8.00
==>Required:
Cost of buying carpet to cover the squared living room
==>Solution:
Find the area of the room:
Area of squared room = 9m × 9m = 81m²
Find cost of purple carpet that would cover 81m²:
Let x be the cost of carpet required to cover the room.
Thus,
1m² = $8.00
81m² = x
cross multiply
1*x = 8.00*81
x = 648
Cost of purple carpet to cover the living room = x = $648.00
How is the graph of the cosine function different from the graph of the sine function? How is it the same?
Answers
Answer:
Similarity:
In Both cosine and sine graphs, a positive and negative number vertically flips the graph and tells whether the graph starts at maximum (positive) or minimum (negative).
Difference:
The difference between the sine and the cosine graph is the point where they start.
The graph of positive cosine starts at the maximum while that of the negative cosine starts at the minimum.
The graph of a positive sine starts at the middle, goes up and then down while that of the negative sine starts at the middle goes down and then up.