laws exponents multiplication band power to a power simplifymake it small steps please the smallest you canbare minimum of steps
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Answer:
[tex](4r^4s^{-2})(-3rs^{-3})(rs)=-12r^6s^{-4}[/tex]Explanation:
Given the expression:
[tex](4r^4s^{-2})(-3rs^{-3})(rs)[/tex]This can be rearranged using law of multiplication (That multiplication is cummutative) to become:
[tex](4)(-3)(r^4rr)(s^{-2}s^{-3}s)[/tex]This becomes, using the law of exponents:
[tex]-12r^{4+1+1}s^{-2-3+1}[/tex]and finally, we have:
[tex]-12r^6s^{-4}[/tex]Related Questions
Find seco, coso, and coto, where is the angle shown in the figure.Give exact values, not decimal approximations.
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step 1
Find out the value of cosθ
cosθ=8/17 ------> by CAH
step 2
Find out the value of secθ
secθ=1/cosθ
secθ=17/8
step 3
Find out the length of the vertical leg in the given right triangle
Applying the Pythagorean Theorem
17^2=8^2+y^2
y^2=17^2-8^2
y^2=225
y=15
step 4
Find out the value f cotθ
cotθ=8/15 -----> adjacent side divided by the opposite side
therefore
secθ=17/8cosθ=8/17cotθ=8/15kName:ID:06/22/1973Time Remaining:00:55:49Teresa KundrataA car costs $14,000. The loan company hasasked for 1/10 of the cost of the car as adown payment what the down payment
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Given:
The cost of the car is $14,000.
Then 1/10 of the cost of the car is
[tex]\frac{1}{10}\times14000=1400[/tex]Hence, the down payment is $1400.
I need help with my math assignment thank you :)
Answers
Okay, here we have this:
Considering the provided information, we are going to match the situations to their corresponding functions, so we obtain the following:
1: The total pages a person reads in x days, if the person reads 6 pages a day: f(x)=6x.
2: The cost of x boxes of mangoes, if 1 box cost $6 and the shipping charge is $6 per order: f(x)=6x+6 -> f(x)=6(x+1)
3: The total cost of x notebooks, if one notebook cost $6 and students receive a discount of $1 off their bill: f(x)=6x-1
4: The total cost of x novels and a pocket dictionary if you buy a novels each at $6 and get a pocket dictionary at $1: f(x)=6x+1
Evaluate the function: g(x)=-x+4Find: g(b-3)
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The given function is:
[tex]g(x)=-x+4[/tex]Value of :
[tex]g(b-3)=?[/tex][tex]\begin{gathered} g(x)=-x+4 \\ x=b-3 \\ g(b-3)=-(b-3)+4 \\ g(b-3)=-b+3+4 \\ g(b-3)=7-b \end{gathered}[/tex]so the g(b-3) is 7-b.
Solve any quality express your answer in interval notation you decimal forms for numerical values
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Solution
[tex]\begin{gathered} 5z-11<-6.6+3z \\ Subtract\text{ 3z from both side} \\ 5z-3z-11<-6.6+3z-3z \\ 2z-11<-6.6 \\ Add\text{ 11 to both sides } \\ 2z-11+11<-6.6+11 \\ 2z<4.4 \\ \end{gathered}[/tex][tex]\begin{gathered} Divide\text{ both sides by 2} \\ \frac{2z}{2}<\frac{4.4}{2} \\ z<2.2 \\ z<2.2 \end{gathered}[/tex]In interval notation, we have
[tex]\left(-\infty \:,\:2.2\right)[/tex]The answer is
[tex]\left(-\infty \:,\:2.2\right)[/tex]During a Super Bowl day, 19 out of 50 students wear blue-colored jersey upon entering the campus. If there are 900 students present on campus that day, how many students could be expected to be wearing a blue-colored jersey? T T
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What is the equation of the line that passes through the origin and is perpendicular to the line 4x+3y=6
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The Equation of a Line
The slope-intercept form of a line can be written as:
y = mx + b
Where m is the slope of the graph of the line and b is the y-intercept.
In the specific case where the line passes through the origin (0,0), we can find the value of b by substituting x=0 and y=0:
0 = m(0) + b
Solving for b:
b = 0.
Thus, the equation of the line reduces to:
y = mx
We only need to find the value of the slope.
That is where we need the second data. Our line is perpendicular to the line of equation 4x + 3y = 6.
Solving for y:
[tex]y=-\frac{4}{3}x+2[/tex]The slope of the second line is -4/3.
We must recall that if two lines of slopes m1 and m2 are perpendicular, then:
[tex]m_1\cdot m_2=-1[/tex]Substituting the value of m1 and solving for m2:
[tex]\begin{gathered} -\frac{4}{3}\cdot m_2=-1 \\ m_2=\frac{3}{4} \end{gathered}[/tex]The slope of our line is 3/4 and the required equation is:
[tex]y=\frac{3}{4}x[/tex]From this last equation, we need to find the general form of the line.
Multiply both sides of the equation by 4:
4y = 3x
Subtract 3x on both sides:
4y - 3x = 0
Reorder:
-3x + 4y = 0
Escriba la razón del primer número al segundo: 32 a 44 simplifique si es posible.
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Write the ratio of the first number to the second.
[tex]\begin{gathered} 32\colon44 \\ \text{Ratio}=\frac{32}{44} \\ \text{Ratio}=\frac{8}{11} \\ \text{The ratio therefore is 8}\colon11 \end{gathered}[/tex]^3 sq root of 1+x+sq root of 1+2x =2
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The given equation is
[tex]\sqrt[3]{1+x+\sqrt{1+2x}}=2[/tex]First, we need to elevate each side to the third power.
[tex]\begin{gathered} (\sqrt[3]{1+x+\sqrt{1+2x}})^3=(2)^3 \\ 1+x+\sqrt{1+2x}=8 \end{gathered}[/tex]Second, subtract x and 1 on both sides.
[tex]\begin{gathered} 1+x+\sqrt{1+2x}-x-1=8-x-1 \\ \sqrt{1+2x}=7-x \end{gathered}[/tex]Third, we elevate the equation to the square power to eliminate the root
[tex]\begin{gathered} (\sqrt{1+2x})^2=(7-x)^2 \\ 1+2x=(7-x)^2 \end{gathered}[/tex]Now, we use the formula to solve the squared binomial.
[tex](a-b)=a^2-2ab+b^2[/tex][tex]\begin{gathered} 1+2x=7^2-2(7)(x)+x^2 \\ 1+2x=49-14x+x^2 \end{gathered}[/tex]Now, we solve this quadratic equation
[tex]\begin{gathered} 0=49-14x+x^2-2x-1 \\ x^2-16x-48=0 \end{gathered}[/tex]We need to find two number which product is 48 and which difference is 16. Those numbers are 12 and 4, we write them down as factors.
[tex]x^2-16x-48=(x-12)(x+4)[/tex]So, the possible solutions are
[tex]\begin{gathered} x-12=0\rightarrow x=12 \\ x+4=0\rightarrow x=-4 \end{gathered}[/tex]However, we need to verify each solution to ensure that each of them satisfies the given equation. We just need to evaluate it with those two solutions.
[tex]\begin{gathered} \sqrt[3]{1+x+\sqrt{1+2x}}=2\rightarrow\sqrt[3]{1+12+\sqrt{1+2(12)}}=2 \\ \sqrt[3]{13+\sqrt{1+24}}=2 \\ \sqrt[3]{13+\sqrt{25}}=2 \\ \sqrt[3]{13+5}=2 \\ \sqrt[3]{18}=2 \\ 2.62=2 \end{gathered}[/tex]As you can observe, the solution 12 doesn't satisfy the given equation.
Therefore, the only solution is -4.Find the equation for the line that passes through the points (-9, 8) and (-4,-4). Give youranswer in point-slope form. You do not need to simplify.
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Given:
The points are (-9,8) and (-4,-4).
Required:
We need to find the line equation in point-slope form.
Explanation:
Consider the slope equation.
[tex]slope,\text{ m=}\frac{y_2-y_1}{x_2-x_1}[/tex][tex]Substitute\text{ }y_2=-4,y_1=8,x_2=-4,\text{ and }x_1=-9\text{ in the formula to find the slope of the equation.}[/tex][tex]Slope,\text{ m=}\frac{-4-8}{-4-(-9)}[/tex][tex]Slope,\text{ m=}\frac{-12}{-4+9}[/tex][tex]Slope,\text{ m=}\frac{-12}{5}[/tex]Consider the point (-9,8).
Consider the point-slope form of the equation.
[tex](y-y_1)=m(x-x_1)[/tex][tex]Substitute\text{ }m=-\frac{12}{5},y_1=8,\text{ and }x_1=-9\text{ in the equation.}[/tex][tex](y-8)=-\frac{12}{5}(x-(-(-9))[/tex][tex](y-8)=-\frac{12}{5}(x+9)[/tex]Final answer:
[tex](y-8)=-\frac{12}{5}(x+9)[/tex]A buoy oscillates in simple harmonic motion as waves go past. At a given time it is noted that the buoy moves a total of 3.9 feet from its low point to its high point, and that it returns to its high point every 16 seconds
Answers
Concept
What is a simple harmonic motion ?Repetitive movement back and forth through an equilibrium, or central, position, so that the maximum displacement on one side of this position is equal to the maximum displacement on the other side. The time interval of each complete vibration is the same
a) y= 1.95ftcos(π/2)
b) v(t)= -0.76sin(π/5t)
Part aSince the buoy oscillates in simple harmonic motion the equation to model this is given by: y= A cos(ωt+θ)
For this case from the info given we know that:
2A= 3.9 , A= 3.9/2= 1.95ft
It returns to its high point every 16 seconds. That means period = 16 , and the angular frequency can be founded like this:
ω=2π/16
= π/8
Assuming that the value for the phase is (θ=0°) our model equation is given by
y= 1.95ftcos(π/2)
Part bFrom definition we can obtain the velocity with the derivate of the position function and if w calculate the derivate we got this,
dy/dt= v(t)= -1.95ft(π/8)sin(π/8t)
v(t)= -0.76sin(π/8t)
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K
Determine whether the statement is true or false, and explain why.
The derivative value f'(a) equals the slope of the tangent line to the graph of y=f(x) at x = a.
Choose the correct answer below.
OA. The statement is true because f'(x) is a function of x.
B. The statement is false because f(a) gives the instantaneous rate of change of f' at x = a.
OC. The statement is true because f'(a) gives the instantaneous rate of change of fat x = a.
OD. The statement is false because f'(a) gives the average rate of change of f from a to x.
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Answer: C. The statement is true because f'(a) gives the instantaneous rate of change of fat x = a.
A small regional carrier accepted 23 reservations for a particular flight with 2o seats. 14 reservations went to regular customers who will arrive for the flight. each of the remaining passengers will arrive for the flight with a 50 % chance ,independently of each other. (answers accurate to 4 decimal places.) Find the probability that overbooking occurs find the probability that the flight has empty seats
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Let's begin by identifying key information given to us:
Number of seats = 20
Number of reservation = 23
14 regular customers show up. So, we have:
[tex]23-14=9RemainingCustomers[/tex]The number of seats left is:
[tex]20-14=6seats[/tex]Overbooking means that more than 6 remaining customers show up (that could mean 7 or 8 or 9 of the remaining customers show up)
The probability of more than 6 customers arriving is given by:
Rewrite the expression in lowest terms.
4x²-12x +9
________
4x2-9
A. -12 x
B. 4x-3
2x-3
C. 2x+3
2x-3
D. 2x-3
2x+3
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answer is D
no real explanation its just math
What is the probability of rolling a 2 or a 3 when rolling a fair six-sided die?
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Answer:
It would be a 2/6 chance, or a 1/3 chance.
Step-by-step explanation:
Round 36,236 to the nearest ten thousand
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We have to round the number 36,236 to the nearest ten thousand (10,000).
Then, the number 36,236 is between 3 and 4 ten thousands. As 36,236 is over 35,000 we round it to 40,000.
Answer: 40,000
If there are 3 possible outcomes for event A, 5 possible outcomes for event B, and 2 possible outcomes for event C, how many possible outcomes are there for event A & event B & event C? Note that these three events are independent of each other. The outcome of one event does not impact the outcome of the other events.
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Possible outcomes for events A and events B and events C which are independent of each other is equal to 3/100.
As given in the question,
Total number of outcomes = 10
Possible outcomes of event A =3
P(A) =3/10
Possible outcome of event B =5
P(B) =5/10
Possible outcome of event C =2
P(C)=2/10
A, B, C are independent of each other
P(A∩B∩C) = P(A) × P(B) × P(C)
= (3/10) × (5/10) × (2/10)
= 3/100
Therefore, possible outcomes for events A and events B and events C which are independent of each other is equal to 3/100.
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Which of the following functions has an amplitude of 3 and a phase shift of pi over 2 question mark
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Remember that f(x) = A f(Bx-C) +D
Where |A| is the Amplitude and C/B is the phase Shift
Options
A, B C all have amplitudes of |3| so we have just eliminated D with the amplitude
We need a phase shift of C/B = pi/2
A has Pi/2
B has -Pi/2
C has pi/2 /2 = pi/4
Choice A -3 cos ( 2x-pi) +4 has a magnitude of 3 and and phase shift of pi/2
help meeeeeeeeee pleaseee !!!!!
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For the given functions, we can write the sum as:
(f + g)(x) = 9x + 1
How to find the sum between functions?Here we want to find the sum between functions f(x) and g(x), and in this case, we have:
f(x)= x - 8
g(x) = 8x + 9
The sum can be written as:
(f + g)(x) = f(x) + g(x)
Replacing the functions there we get:
(f + g)(x) = f(x) + g(x)
(f + g)(x) = (x - 8) + (8x + 9)
(f + g)(x) = x + 8x - 8 + 9
(f + g)(x) = 9x + 1
That is the sum of the functions.
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What is the sum of -15 + 182A. 33B. 3c. -3 D-33Your answer
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-15 + 18 is the same as 18 - 15, which is equal to 3.
Find any value of x that makes the equation x + 100 = x - 100 true.
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Since the sides are the same, this problem is unsolvable
The table gives a set of outcomes and their probabilities. Let A be the event "the outcome is less than 8". Find P(A). Outcome Probability 1 0.12 2 0.11 3 0.4 4 0.02 5 0.04 6 0.17 7 0.02 00 0.09 9 0.03
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We want to calculate the probability of this event A: "the outcome is less than 8". To calculate this probability, we should first note that we have a total of 9 outcomes. So, we will first identify out of this outcomes cause the event A to happen.
Since the event A is saying that the outcome is less than 8, then the outcomes that would make the event A to happen would be the numbers from 1 to 7. However, to calculate this probabilty, we will use this property of probability.
Given an event A, we have the
Solve Each System by Elimination:-12x-2y=30-4x+y=-5
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We solve as follows:
-12x - 2y = 30
2(-4x + y = -5)
---------------------
-12x -2y = 30
-8x + 2y = -10
--------------------
-20x = 20 => x = -1
Now we replace the value of x in one of the original equations to solve for y, that is:
-4(-1) + y = -5 => 4 + y = -5 => y = -9
So, the solution is the point (-1, -9).
A figure is made up of a triangle and a square. The square andthe triangle have the same base of 9 inches. The triangle has aheight of 7 inches, what is the total area of the figure?
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To solve the exercise, it is helpful first to draw the situation that the statement describes:
The total area of the figure will be
[tex]A_{\text{total}}=A_{\text{square}}+A_{\text{triangle}}[/tex]Then, we can calculate the area of the square using the following formula:
[tex]\begin{gathered} A_{\text{square}}=s\cdot s \\ \text{ Where s is one side of the square} \end{gathered}[/tex]So, we have:
[tex]\begin{gathered} s=9in \\ A_{\text{square}}=s\cdot s \\ A_{\text{square}}=9in\cdot9in \\ \boldsymbol{A}_{\boldsymbol{square}}\boldsymbol{=81in}^{\boldsymbol{2}} \end{gathered}[/tex]Now, we can calculate the area of the triangle using the following formula:
[tex]\begin{gathered} A_{\text{triangle}}=\frac{b\cdot h}{2} \\ \text{ Where b is the base and} \\ h\text{ is the height of the triangle} \end{gathered}[/tex]So, we have:
[tex]\begin{gathered} b=9in \\ h=7in \\ A_{\text{triangle}}=\frac{b\cdot h}{2} \\ A_{\text{triangle}}=\frac{9in\cdot7in}{2} \\ A_{\text{triangle}}=\frac{63in^2}{2} \\ \boldsymbol{A}_{\boldsymbol{triangle}}\boldsymbol{=31.5in}^{\boldsymbol{2}} \end{gathered}[/tex]Finally, we calculate the total area of the figure
[tex]\begin{gathered} A_{\text{total}}=A_{\text{square}}+A_{\text{triangle}} \\ A_{\text{total}}=81in^2+31.5in^2 \\ \boldsymbol{A}_{\boldsymbol{total}}\boldsymbol{=112.5in}^{\boldsymbol{2}} \end{gathered}[/tex]Therefore, the total area of the figure is 112.5 square inches, and the correct answer is option C.
Melanie has pears and papayas in a ratio of 13:25. How many pears does she have ifshe has 2500 papayas?On the double number line below, fill in the given values, then use multiplication ordivision to find the missing value.
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Given that the ratio of pears to papayas is 13:25,
[tex]\frac{\text{ Pears}}{\text{ Papayas}}=\frac{13}{25}[/tex]It means that Melanie has 13 pears, then the number of papayas must be 25.
It is asked to determine the number of pears corresponding to 2500 papayas.
First plot the values in the blank boxes on the double number line as below,
Let 'x' be the number of pears corresponding to 2500 papayas.
Now, cross multiply the terms,
[tex]25\cdot x=13\cdot2500[/tex]Divide both sides by 25,
[tex]\begin{gathered} 25\cdot x\cdot\frac{1}{25}=13\cdot2500\cdot\frac{1}{25} \\ x=13\cdot100 \\ x=1300 \end{gathered}[/tex]Thus, there should be 1300 pears corresponding to 2500 papayas.
What is an equation of the line that passes through the point (-4,-6)(−4,−6) and is perpendicular to the line 4x+5y=25?
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First you put the equation into y=mx+b form:
1. move the 4x to the other side
5y=-4x+25
2. divide by 5 on both sides
y=(-4/5)x+5
Next, since the line has to be perpendicular, you take the negative reciprocal of the slope (flip the fraction and put the opposite sign)
1. 5/4
Now, find the y intercept (the b)
1. set up the equation
-6=(5/4)(-4)+b
2. multiply the 5/4 and -4
-6=-5+b
3. move the -5 to the other side (add it)
-1=b
Now, put all the elements together
1. y=(5/4)x-1
1) A submarine is 84 feet below the surface of the water and descends 10 feet deeper every minute. How many minutes will it take for the submarine to be located 219 feet below the surface? Write and solve an equation.
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Answer
The equation for this question is
84 + 10x = 219
The number of minutes it'll take the submarine to reach 219 feet is 13.5 minutes
Explanation
Let the number of minutes it will take the submarine to reach 219 feet below the surface be x minutes.
The number of feet the submarine reaches in x minutes = (10x) feet
Since the submarine started from 84 feet, in x minutes, it would have reached a depth of
(84 + 10x) feet
This is equal to 219 feet
84 + 10x = 219
Subtract 84 from both sides
84 + 10x - 84 = 219 - 84
10x = 135
Divide both sides by 10
(10x/10) = (135/10)
x = 13.5 minutes
Hope this Helps!!!
given AD is congruent to AC and AB is congruent to AE, which could be used to prove?
Answers
Answer
Option B is correct.
SAS | 2 sides and the angle between them in one triangle are congruent to the 2 sides and the angle between them in the other triangle, then the triangles are congruent.
Explanation
We have been told that the two triangles have two sets of sides that are congruent to each other.
And we can see that the angle between those congruent sides for the two triangles is exactly the same for the two triangles.
So, it is easy to see that thes two triangles have 2 sides that are congruent and the angle between these two respective sides are also congruent.
Hope this Helps!!!
9 mVolume = 75 n mm3RadiusG
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we know that
The volume of a cone is equal to
[tex]V=\frac{1}{3}\cdot\pi\cdot r^2\cdot h[/tex]In this problem
we have
V=75pi mm^3
h=9 m------> convert to mm
h=9,000 mm
substitute in the given equation
[tex]\begin{gathered} 75\cdot\pi=\frac{1}{3}\cdot\pi\cdot r^2\cdot9,000 \\ \text{simplify} \\ 75=r^2\cdot3,000 \\ r^2=\frac{75}{3,000} \\ \\ r^2=\frac{1}{40} \\ \\ r=\frac{1}{\sqrt[\square]{40}} \\ \\ r=\frac{\sqrt[\square]{40}}{40} \\ \text{simplify} \\ r=\frac{2\sqrt[\square]{10}}{40} \\ \end{gathered}[/tex][tex]r=\frac{\sqrt[\square]{10}}{20}\text{ mm}[/tex]Consider the non-right triangle below.Suppose that m∠CAB=62∘, and that x=35 cm and y=17 cm. What is the area of this triangle? cm^2
Answers
Given that:
x=35 cm and y=17 cm
and angle CAB= 62 degree
[tex]\begin{gathered} A=\frac{1}{2}\times x\times y\times\sin (\angle CAB) \\ A=\frac{1}{2}(35)(17)\sin (62) \\ A=297.5\times\sin (62) \\ A=262.67cm^2 \end{gathered}[/tex]