Which expressions are equivalent to ? Choose all the correct answers. Show your work.
Answers
Answer:
C, D, F
Step-by-step explanation:
Exponent rules:
[tex]\dfrac{a^b}{a^c}=a^{b-c}[/tex]
[tex]a^{-n}=\dfrac{1}{a^n}[/tex]
[tex]\dfrac{1}{a^{-n}}=a^n[/tex]
[tex]a^n \cdot b^n=(ab)^n[/tex]
[tex]a^0=1[/tex]
[tex](a^b)^c=a^{bc}[/tex]
[tex]\textsf{A}\quad\dfrac{24^{-3}}{24^{-4}}=24^{-3-(-4)}=24^1=24[/tex]
[tex]\textsf{B}\quad3^{-2} \cdot 8^{-5}=\dfrac{1}{3^2} \cdot \dfrac{1}{8^5}=\dfrac{1}{9} \cdot \dfrac{1}{32768}=\dfrac{1}{294912}[/tex]
[tex]\textsf{C}\quad\left(\dfrac{1}{24^{-7}}\right)^{-1}=\left(24^7\right)^{-1}=24^{-7}[/tex]
[tex]\textsf{D}\quad\dfrac{8^{-7}}{3^7}=\dfrac{1}{8^7 \cdot 3^7}=\dfrac{1}{(8 \cdot 3)^7}=\dfrac{1}{24^7}=24^{-7}[/tex]
[tex]\textsf{E}\quad24^7 \cdot 24^0=24^7 \cdot 1=24^7[/tex]
[tex]\textsf{F}\quad(24^3 \cdot 24^4)^{-1}=\left(24^{3+4}\right)^{-1}=(24^7)^{-1}=24^{-7}[/tex]
Related Questions
PLS HELP I CANT FAIL
No links pls and Ty <3333!!!!!
Answers
Answer:
Option 1: 43π feet
Step-by-step explanation:
We are given that:
encloses garden with circular fence
garden measures 43 feet across = diameter
To find how much fencing is needed, we have to find the cicumference of the circular fence using the formula:
C = 2πr
C = Circumference
r = radius = half the diameter
We are given the diameter, so we just do half of it to get the radius
43 ÷ 2 = 21.5
r = 21.5
Now we substitute this into the formual:
C = 2πr
Substitute radius into formula
C = 2π(21.5)
Multiply 2 and 21.5
C = 43π
HELLLLLLLLLLLLLLLLLLPPPPPPPPPPPPPPPPPPPPPPPPP
Answers
Answer:
(a) 10.3
(b) 11
Step-by-step explanation:
(a) Step 1: mean is the average of a set of numbers. Add them all together and then divide by how many numbers you were given
11+12+5+11+8+13+12 = 72
Step 2: There are 7 numbers so you divide 72 by 7
72/7 = 10.28
(a) The mean equals 10.3
(b) Step 1: Median is the middle number in a list of numbers. Line the numbers up in order and find the middle one.
5, 8, 11, 11, 12, 12, 13
(b) the median equal 11
As an estimation we are told £3 is €4. Convert £7. 50 to euros
Answers
3/4=7/x
Solve for x
7.5*4=3*x
30=3x
X=10
Melissa and tomas are playing a game with complex numbers. if melissa has a score of 5 – 4i and tomas has a score of 3 2i, what is their total score? 8 – 6i 8 6i 8 – 2i 8 2i
Answers
The total score of Melissa and Tomas who are playing a game with complex numbers is 8-2i.
What is complex number?A complex number is the combination of real and imaginary number. It can be written as,
[tex]a+bi[/tex]
Here, (a) is a real number and (b) is an imaginary number.
Melissa and Tomas are playing a game with complex numbers. Melissa has a score of 5 – 4i and Tomas has a score of 3 2i. The sum of their score is,
[tex]S=5 -4i +(3+2i)\\S=5+3-4i+2i\\S=8-2i[/tex]
Hence, the total score of Melissa and Tomas who are playing a game with complex numbers is 8-2i.
Learn more about the complex number here;
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Answer:
8-2i
Step-by-step explanation:
c
In the triangle ABC, angle C is a right angle. Find the value of the trig function indicated. Find sin A if a = 3013, b = 2
Answers
[tex]Given: Statement\\ To\ find: Correct\ optician\\ tan\theta=\frac{2}{30\sqrt{13}}[/tex]
[tex]sin\ B=\frac{2}{33}[/tex]
[tex]sin A=\frac{1}{7}=\frac{30\sqrt{13}}{3311}=\frac{3\sqrt{13}}{11}[/tex]
I hope this helps you
:)
PLEASE HELP ME WITH MY MATH WHO EVER GETS IT GETS BRAINLIEST
Answers
Answer:
don't use this this is just a guess but I think that it is the lowest possible one so A It coulld be wrong
Step-by-step explanation:
E
Step-by-step explanation:
The potential energy of an object varies jointly with the mass of the object and the height of the object off the ground. a 25-kg object has 980 joules of potential energy when it is 4 meters off the ground. another object has 150 joules of potential energy at 3 meters off the ground. what is the mass of the second object? round to two decimal places. 0.32 kilogram 2.88 kilograms 5.10 kilograms 45.90 kilograms
Answers
The mass of the object which is at 3 meters off the ground (earth assumingly), with the potential energy of 150 joules is given by: Option C: 5.10 kg
What is gravitational potential energy?Gravitational potential energy is the energy which a body posses because of its position.
The gravitational potential energy of a body is given as,
[tex]U=mgh[/tex]
Here, (m) is the mass of the body, (g) is the gravitational accelaration and (h) is the height of the body.
Here, for the second object, we have:
Potential energy = 150 joulesDistance from the ground = 3 mg = gravitational acceleration = [tex]9.8 \: \rm m/s^2[/tex]Let its mass be m kg, then:
[tex]U=mgh\\\\150 = m(9.8)(3)\\\\m = 50/9.8 \approx 5.10 \: \rm kg[/tex]
Thus, the mass of the object which is at 3 meters off the ground (earth assumingly), with the potential energy of 150 joules is given by: Option C: 5.10 kg
Learn more about the gravitational potential energy here;
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2. You are making wooden picture
frames of different sizes but you
have limited supplies, so you are
restricting the perimeter of each
frame to 4 feet or less and the length
to exactly 1.5 feet. Find the range of
the frame width. Show your work.
Answers
The range of the frame width for the considered case is 0.5 (feet), because for this case, it can be at max of 0.5 feet, and at minimum of 0 feet.
What is the range of a particular data set?For a set of data, the range is the difference between the maximum and minimum value. It sort of gives an idea of spread of the data.
For this case, we're given that:
Frame is rectangular (assumingly).The perimeter of the frame ≤ 4 feetThe length of the frame = 1.5 feetPerimeter of a rectangle = 2(length + width)
Let 'l' denotes length, and 'w' denotes width, then we get:
[tex]Perimeter \leq 4\\2(l+w) \leq 4\\2(1.5 + w) \leq 4\\\\\text{Dividing both the sides by 2}\\\\1.5 + w \leq 2\\\\\text{Subtracting 1.5 from both the sides so as to get 'w' on one side}\\\\w \leq 0.5[/tex]
Now since the lowest value of width of a frame can be zero only, therefore, we get:
[tex]0 \leq w \leq 0.5[/tex]
Thus, the range of values 'w' can assume is: 0.5 - 0 = 0.5
Thus, the range of the frame width for the considered case is 0.5 (feet), because for this case, it can be at max of 0.5 feet, and at minimum of 0 feet.
Learn more about range here:
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HELP HELP HELP HELP HELP HELP HELP HELP HELP HELP HELP HELP HELPPPPPPPPPPPPPPPPPPPPPPPPPPP
Answers
Answer:
The answer is (A) or 3/4.
Step-by-step explanation:
By plugging in a through d, the only one that gave an acurate answer was A.
2(6-2x) - 2x = 2(5+x)-4
turns into
2(6-2[3/4]) - 2[3/4] = 2(5+[3/4]) -4
Hope this helps!
Answer:
x = 3/4Therefore , option A is correct .Step-by-step explanation:
In the question we're given with an equation i.e.,
2 ( 6 - 2x ) - 2x = 2 ( 5 + x ) - 4And we are asked to find the value of x .
Solution :
[tex] \longmapsto \: 2 ( 6 - 2x ) - 2x = 2 ( 5 + x ) - 4 [/tex]
Step 1 : Solving parenthesis by multiplying it with 2 on both the sides :
[tex] \longmapsto \: 12 - \bold{4x} - \bold{2x} = \bold{10} + 2x - \bold{4}[/tex]
Step 2 : Adding like terms on left hand side and subtracting like terms on right hand side :
[tex] \longmapsto \: 12 - 6x = 2x + 6[/tex]
Step 3 : Transposing 12 to right hand side and 2x to left hand side :
[tex] \longmapsto \: -2x - 6x = 6 - 12[/tex]
On further calculations we get :
[tex] \longmapsto \: \cancel{ - }8x = \cancel{- }6[/tex]
Step 4 : Transposing 8 to right hand side :
[tex] \longmapsto \: x = \frac{\cancel{6}}{\cancel{8}} [/tex]
Step 5 : Cancelling 6/8 to their simplest form :
[tex] \longmapsto \: \pink{\boxed{x = \frac{3}{4} }}[/tex]
Therefore , value of x is 3/4 and it will make the equation true .#Keep LearningSpecial Triangle: Solve for x and y.
Answers
Answer:
x = 8.67 and y = 10
Step-by-step explanation:
In right angled triangle
cos 60⁰ = 5/y
1/2 = 5/y
y = 10
in right angled triangle,
tan 60⁰ = x/5
√3 = x/5
x = 5√3 = 5 × 1.73 = 8.65
x = 8.67
Someone help me please
Answers
Answer:
Step-by-step explanation:
Angle A= ___? degrees
Angle B= ___ ?degrees
Angle C= ___? degrees
Answers
Answer:
Angle A = 45 degrees
Angle B = 64 degrees
Angle C = 60 degrees
Hope this helps!
There are 23 pennies on one side of a balance and 17 pennies on the other
side. Levi thinks 3 pennies should be added to the higher pan, Arjan thinks 4
Pennies should be added, and Charlotte thinks 6 pennies should be added. Who Is correct and why?
Answers
To have the same number of pennies in both sides, we should add 6 pennies, so Charlotte is correct.
How many pennies should we add?We want to have the same number of pennies on both sides, on one side we have 23 pennies, and in the other 17. So we will add x pennies to the last side, such that we get:
23 = 17 + x
This is a linear equation. To solve it, we need to isolate the variable x, we can do that by subtracting 17 in both sides:
23 - 17 = 17 + x - 17
6 = x
This means that the solution is 6, so we should add 6 pennies, meaning that Charlotte is correct.
If you want to learn more about linear equations, you can read:
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Write in slope intercept form an equation of the line that passes through (-2,5),(-1,1)
Answers
Answer:
y=-4x-3
Step-by-step explanation:
Hi there!
We are given the following two points: (-2,5) and (-1,1)
We want to write the equation of the line that passes through these two lines in slope-intercept form
Slope-intercept form is given as y=mx+b, where m is the slope and b is the y intercept
First, let's find the slope
The formula for the slope (m) calculated from 2 points is [tex]\frac{y_2-y_1}{x_2-x_1}[/tex], where [tex](x_1, y_1)[/tex] and [tex](x_2, y_2)[/tex] are points
We have everything we need to calculate the slope, but let's label the value of the points to avoid any confusion
[tex]x_1=-2\\y_1=5\\x_2=-1\\y_2=1[/tex]
Now substitute into the formula
m=[tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
m=[tex]\frac{1-5}{-1--2}[/tex]
Simplify
m=[tex]\frac{1-5}{-1+2}[/tex]
Subtract
m=[tex]\frac{-4}{1}[/tex]
Divide
m=-4
Now substitute -4 as m into the equation:
y=-4x+b
Now we need to find b
As the equation passes through both (-2, 5) and (-1, 1), we can use either point to help solve for b.
Taking (-2,5) for example:
Substitute -2 as x and 5 as y:
5=-4(-2)+b
Multiply
5=8+b
Subtract 8 from both sides
-3=b
Substitute -3 as b.
y=-4x-3
Hope this helps!
See more on this topic here: https://brainly.com/question/27304092
what is 7/-13 + 4/-13
Answers
Answer:
7/-13 + 4/-13 = -7/13 - 4/13 = - 11/13
The radius of a circle is 20 centimeters.
What is the circumference, in centimeters, of the circle? Round your answer to
the nearest tenth.
Response:
Answers
Answer:
The circumference is 125.7cm
substituting in the radius makes the equation 3/4(pi)20^3
which equals 33,493.333333..
to the nearest tenth the answer is 33,493.3 :)
Help ulitt ihihihihi
Answers
Answer:
1.A , 2.B , 3.D , 4.B , 5.C
Step-by-step explanation:
hope this helped! :)
this has to be one of the most random question i seen
Answers
144 Inches or 12 Feet
Step-by-step explanation
7 feet converted to inches is 84 So 84+60=144
And if you convert 60 inches into feet it would be 5
Answer:
144 inches
Step-by-step explanation:
1 ft = 12 inches
7 ft = 12 x 7 inches
7ft = 84 inches
Ice path you are floating on = 84 inches
other ice path = 60 inches
all together = 84 + 60
=> 144 inches
Hope this helps!
If 10 lemons are required to make 15 cups of lemonade at what rate are lemon being used per cup of lemonade
Answers
Answer:
2/3 lemon's per cup.
Step-by-step explanation:
10÷15=2÷3 .
Please give me brainliest.Thank you. :-):-)
Anybody knows this?? 3x^2+6x-10 + 3x+5
Answers
Answer:
3x2+9x−5
Step-by-step explanation:
You just have to add the like terms
Answer:
3x² + 9x - 5
Step-by-step explanation:
Group like terms:
3x² + 6x - 10 + 3x + 5
3x² + 9x -5
hope this helps :)
Write an equation in slope-intercept form for the line that passes through (-1, -2) and (3, 4).
Answers
Answer:
y = 3/2x - 1/2
all steps explained in pic attached below :)
50 PTS 2. Consider the following line plot.
(a) What is the general trend of the graph?
(b) What is the median of the data? Explain.
(c) What is the mean of the data? Explain.
(d) Would the mean or median be affected more with a data point of 20? Explain.
Answers
Answer:
Picture so I can solve it
Point A is an element of a direct variation. Select two points, other than A, that are elements of this direct
A
variation.
No links please
Answers
Answer:
Step-by-step explanation:
B and C is crorect answer tha ks
A carnival has a duck-pond booth. You choose a rubber duck at random. The mark on the bottom of the duck tells you whether you won a small, medium, or large prize, or no prize at all. There are 56 ducks floating in the pond. There are 5 ducks marked as large-prize winners, 10 ducks marked as medium-prize winners, and 20 ducks marked as small-prize winners. Find the theoretical probability of winning a small prize at the duck pond. Express your answer as a percent. If necessary, round your answer to the nearest thousandth.
35.714%
62.5%
280%
64.286%
Answers
The probability helps us to know the chances of an event occurring. The probability of winning a small prize in the carnival is 35.714%.
What is Probability?The probability helps us to know the chances of an event occurring.
[tex]\rm Probability=\dfrac{Desired\ Outcomes}{Total\ Number\ of\ outcomes\ possible}[/tex]
Given that there is a total of 56 ducks floating in the pond, out of which 20 ducks are marked as small-prize winners. Therefore, the probability of winning a small price can be written as:
[tex]\rm Probability=\dfrac{Desired\ Outcomes}{Total\ Number\ of\ outcomes\ possible}\\\\\\\rm Probability=\dfrac{\text{Nnmber of small price ducks}}{\text{Total number of ducks}}\\\\\\Probability = \dfrac{20}{56} = 0.35714 = 35.714\%[/tex]
Hence, the probability of winning a small prize in the carnival is 35.714%.
Learn more about Probability:
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PLEASE HELP ME ASAP!!!!! I WILL GIVE YOU 30 POINTS!
For each equation, draw a tape diagram and find the unknown value.
Part A:x+9=16
Part B:4⋅x=28
Answers
Answer:
Part A=7
Part B=7
Step-by-step explanation:
Part A = 7+9=16
Part B = 4 times 7= 28
Sunny is a volunteer at the animal shelter. The animal shelter has only dogs and cats. 3
10
of the animals are dogs. There are 8 fewer dogs than cats. How many animals are there in the animal shelter?
Answers
Answer: 14 Animals
Step-by-step explanation: Made of 3 dogs and 11 Cats
Dogs( 11-8)
PLEASE HELPPP!!! I will give brainly points
Answers
Answer:
should be a. took the test and It was horrible. I remember trying and forgot how to do everything beother
Step-by-step explanation:
no balls
From the observation deck of a skyscraper, Meena measures a 48∘ angle of depression to a ship in the harbor below. If the observation deck is 1068 feet high, what is the horizontal distance from the base of the skyscraper out to the ship? Round your answer to the nearest tenth of a foot if necessary.
Answers
Using the slope concept, it is found that the horizontal distance from the base of the skyscraper out to the ship is of 961.6 feet.
What is a slope?The slope is given by the vertical change divided by the horizontal change, and it's also the tangent of the angle of depression.
In this problem:
The angle is of 48º.The vertical change is of 1068 ft.The horizontal change is of x.Hence:
[tex]\tan{48^\circ} = \frac{1068}{x}[/tex]
[tex]x = \frac{1068}{\tan{48^\circ}}[/tex]
x = 961.6
The horizontal distance from the base of the skyscraper out to the ship is of 961.6 feet.
More can be learned about the slope concept at https://brainly.com/question/18090623
Rebbeca needs a box with a rectangular base of 36 cm^2 and a volume of 180 cm^3. What would be the height
of the box?
Answers
Answer:5cm
Step-by-step explanation: Area =length × breadth
Volume = length ×breadth ×height
180= Area ×height
180 = 36×h
180÷36=h
Ans 5
Martha's class is making banners to fly outside of the school. Each banner will be in the shape of a triangle with a base of 12 inches and a height of 20 inches The class needs 12 banners. How much material will they need?
Answers
Answer:
1440 square inches of fabric
Step-by-step explanation:
Answer:
1440 square inches of fabric
Step-by-step explanation:
Solve for 1 banner
Area of 1 banner:
12*20/2
12*10
120.
12 banners,
12*120
= 1440 square inches of fabric
(or other types of material)