Using the Laplace transform, the value o y' − 2y = (t − 4), y(0) = 0 is⇒y(t) = 0 e^-t + u(t -1)e^1-t
Laplace rework is an critical rework approach that is in particular useful in fixing linear normal equations. It unearths very huge applications in regions of physics, electrical engineering, control optics, arithmetic and sign processing.
y' − 2y = (t − 4),
y(0) = 0
Taking the Laplace transformation of the differential equation
⇒sY(s) - y (0) + Y(s) = e-s
⇒(s + 1)Y(s) = (0+ e^-s)/s + 1
⇒y(t) = L^-1{0/s+1} + {e ^-s/s + 1}
⇒y(t) = 0 e^-t + u(t -1)e^1-t
The Laplace remodel method, the feature within the time area is transformed to a Laplace characteristic within the frequency domain. This Laplace feature will be inside the shape of an algebraic equation and it can be solved easily.
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HELPPPP WITH ALL OF THE 3 PLSSS
Answer:
See picture.
C is the point that does not move because it is on the line of reflection
Yes, a reflection is a rigid motion. It does not change size. A dilation changes the size.
Step-by-step explanation:
In the picture, you will see that I traced the triangle on tracing paper and then folded (flipped) the drawing over the line of reflection.
In 4 weeks, Mark earns an average of $400 per
week. If, after working another 2 weeks at a
constalat salary, his average carnings per week
are $500, how much did he earn in the last 3
weeks?
rounding to 1 significant figure, estimate the
answers to these questions:
a)
78 × 92
b)
615 × 38
C)
423 × 764
Answer:
a) 7000
b) 20000
c) 300000
Rounding is the act of replacing a number with values that are an approximation.
can be used to create simpler, or more explicit answersBasic rounding rules:
1. If the number you are rounding is followed by 5, 6, 7, 8, or 9, round the number up. Example: 68 rounded to 1 significant figure would be 70.
2. If the number you are rounding is followed by 0, 1, 2, 3, or 4, round the number down. Example: 13 rounded to 1 significant fugue is 10.
3. Zero digits that come after a non zero digit are non significant. Example: 10000 only has 1 significant figure
Calculations:
A) 78 x 92 = 7176
to round to 1 sig fig we must make all digits after 7 insignificantwe must also take note of whether the 7 will remain the same or be rounded upthe digit that comes after is a 1, following the rules of rounding it will remain a 7The answer for A is 7000
B) 615 x 38 = 23370
all digits after 2 must be insignificant the digit that comes after is a 3, following the rules of rounding the 2 will remain a 2Answer for B is 20000
C) 423 x 764 = 323172
all digits after 3 must be insignificantthe digit that comes after is a 2, following the rules of rounding the 3 will remain a 3Answer for C is 300000
Find the maximum and minimum values attained by f(x, y, z) = 2xyz on the unit ball x2 y2 z2 ≤ 1
The maximum and minimum values of f(x,y,z) = 2xyz are [tex]\frac{2}{\sqrt{3} } and \frac{-2}{\sqrt{3} }[/tex]
The value of the function at a maximum point is called the maximum value of the function and the value of the function at a minimum point is called the minimum value of the function. Differentiate the given function.
f(x,y,z)=2xyz
Computation:
Differentiating the given equation up to second order
[tex]\begin{gathered}f_x=2yz\Rightarrow 2yz=0 either y=0 or z=0\\f_y=0\Rightarrow 2xz=0 either x=0 or z=0\\f_z=0\Rightarrow 2xy=0 either x=0 or y=0\end{gathered}[/tex]
So, the critical point is (0,0,0)
Now, using the Lagrange's on the boundary,
[tex]\begin{gathered}g(x,y,z)=x^2+y^2+z^2-1=0\\g_x=2x\\g_y=2y\\g_z=2z\end{gathered}[/tex]
[tex]So, \bigtriangledown f=\lambda \bigtriangledown g\left < 5yz,5xz,5xy \right > =\lambda \left < 2x,2y,2z )[/tex]
By solving we get,
[tex]x^2=y^2=z^2[/tex] then,
[tex]\begin{gathered}x^2+y^2+z^2=1\\3z^2=1\\z=\pm \frac{1}{\sqrt{3} } \\y=\pm \frac{1}{\sqrt{3} } \\\\x=\pm \frac{1}{\sqrt{3} } \\\end{gathered} x 2+y 2+z 2=13z 2=1z=± 31[/tex]
[tex]So, the critical points are (0,0,0),(\frac{1}{\sqrt{3} } ,\frac{1}{\sqrt{3} } ,\frac{1}{\sqrt{3} } )and (\frac{-1}{\sqrt{3} }, \frac{-1}{\sqrt{3} },\frac{-1}{\sqrt{3} })[/tex]
So, by substituting the critical points we get,
[tex]\begin{gathered}f(0,0,0)=0\\f(\frac{1}{\sqrt{3} }, \frac{1}{\sqrt{3} },\frac{1}{\sqrt{3} })=2(\frac{1}{\sqrt{3} })(\frac{1}{\sqrt{3} })(\frac{1}{\sqrt{3} })\\=\frac{2}{3\sqrt{3} } \\f(-\frac{1}{\sqrt{3} },-\frac{1}{\sqrt{3} },-\frac{1}{\sqrt{3} })=2(-\frac{1}{\sqrt{3} })(-\frac{1}{\sqrt{3} })(-\frac{1}{\sqrt{3} })\\=-\frac{2}{3\sqrt{3} }\end{gathered}[/tex]
Hence the maximum and minimum values of f(x,y,z) are [tex]\frac{2}{\sqrt{3} } and \frac{-2}{\sqrt{3} }[/tex]
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20 points and I will mark brainlyist to the first right answer.
Answer:
Step-by-step explanation:
Movie A: 267 students
Movie B: 217 students
Movie C: 233 students
Movie D: 183 students
pls help solve math problem!!! lots of points
4|a|+8-a if a=-2
ASAP GIVING BRAINLIEST PLEASE HELP!!
Answer: 18
Step-by-step explanation:
4 I-2I + (8+2)=
4(2) + 8+2=
8+8+2=
18
In the year 2000, there were 200,000 cell phone subscribers in a city in new york. the number of subscribers increased by 60 percent per year after 2000. which equation can be used to model the number of subscribers, y, in the city t years after 2000?
The equation can be used to model the number of subscribers, y, in the city t years after 2000 is y = 200,000(1+60)t.
What is an equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign. For example, 3x – 5 = 16 is an equation. Solving this equation, we get the value of the variable x as x = 7.
The first step is to calculate the percentage increase for each year.
If the subscribers increase by 60%, it means that the subscribers will be (100+60)% of the previous year.
(100+60)% = (100/100 + 60/100)
= (1 + 0.6)
After 2,000, the subscribers will be 200,000×(1+0.6).
For the following years the 200,000×(1+0.6)t
So, the value of y will be given by,
Y=200,000(1+0.6)t
Hence,The equation Y=200,000(1+0.6)t .
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Does the graph represent a function? Why or why not?
A. No, because it fails the horizontal line test
B. Yes, because it passes the horizontal line test
C. No, because it fails the vertical line test.
•
D. Yes, because it passes the vertical line test.
Answer:
D.
Step-by-step explanation:
Yes, because it passes the vertical line test.
A bird (B) is spotted flying 6,000 feet from a tower (). An observer (0) spots the top of tower (T) at a distance of 9,000 feet. What is the angle of depression from the bird (B) to the
observer (0)?
Using relations in a right triangle, it is found that the angle of depression is of θ = 56.31º.
What are the relations in a right triangle?The relations in a right triangle are given as follows:
The sine of an angle is given by the length of the opposite side to the angle divided by the length of the hypotenuse.The cosine of an angle is given by the length of the adjacent side to the angle divided by the length of the hypotenuse.The tangent of an angle is given by the length of the opposite side to the angle divided by the length of the adjacent side to the angle.For this problem, we have that:
The opposite side to the angle of depression is the top of tower, at a height of 9000 feet.The adjacent side to the angle is the distance to the bird, of 6000 feet.Hence, considering θ as the depression angle, we have that:
tan(θ) = 9000/6000
tan(θ) = 1.5
θ = arctan(1.5)
θ = 56.31º.
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Use the method of undetermined coefficients to find the general solution to the de y′′−3y′ 2y=ex e2x e−x
I'll assume the ODE is
[tex]y'' - 3y' + 2y = e^x + e^{2x} + e^{-x}[/tex]
Solve the homogeneous ODE,
[tex]y'' - 3y' + 2y = 0[/tex]
The characteristic equation
[tex]r^2 - 3r + 2 = (r - 1) (r - 2) = 0[/tex]
has roots at [tex]r=1[/tex] and [tex]r=2[/tex]. Then the characteristic solution is
[tex]y = C_1 e^x + C_2 e^{2x}[/tex]
For nonhomogeneous ODE (1),
[tex]y'' - 3y' + 2y = e^x[/tex]
consider the ansatz particular solution
[tex]y = axe^x \implies y' = a(x+1) e^x \implies y'' = a(x+2) e^x[/tex]
Substituting this into (1) gives
[tex]a(x+2) e^x - 3 a (x+1) e^x + 2ax e^x = e^x \implies a = -1[/tex]
For the nonhomogeneous ODE (2),
[tex]y'' - 3y' + 2y = e^{2x}[/tex]
take the ansatz
[tex]y = bxe^{2x} \implies y' = b(2x+1) e^{2x} \implies y'' = b(4x+4) e^{2x}[/tex]
Substitute (2) into the ODE to get
[tex]b(4x+4) e^{2x} - 3b(2x+1)e^{2x} + 2bxe^{2x} = e^{2x} \implies b=1[/tex]
Lastly, for the nonhomogeneous ODE (3)
[tex]y'' - 3y' + 2y = e^{-x}[/tex]
take the ansatz
[tex]y = ce^{-x} \implies y' = -ce^{-x} \implies y'' = ce^{-x}[/tex]
and solve for [tex]c[/tex].
[tex]ce^{-x} + 3ce^{-x} + 2ce^{-x} = e^{-x} \implies c = \dfrac16[/tex]
Then the general solution to the ODE is
[tex]\boxed{y = C_1 e^x + C_2 e^{2x} - xe^x + xe^{2x} + \dfrac16 e^{-x}}[/tex]
Jaxon is training for a climbing competition.
He breaks his training up into strength and
endurance training in the ratio 5:3.
If he spends 4 hours on endurance training,
how long should he spend on strength training?
======================================================
Work Shown:
(x hours strength)/(4 hours endurance) = 5/3
x/4 = 5/3
3x = 4*5
3x = 20
x = 20/3
x = (18+2)/3
x = 18/3 + 2/3
x = 6 + 2/3
x = 6 & 2/3
He needs to spend 6 full hours, plus an additional 2/3 of an hour, on strength training.
1 hr = 60 min
2/3 hr = (2/3)*60 min
2/3 hr = 40 min
6 hr + 2/3 hr = 6 hr + 40 min
Therefore, he needs to spend 6 hours, 40 minutes on strength training.
This is equivalent to 6*60+40 = 360+40 = 400 minutes.
Lamar is taking a stunt man training course. he scored a 99 on his first test, but he only scored an 85 on his second test. what is the lowest score that lamar can make on his third and final test in order to have an overal average of 90?
Answer:
86.
Step-by-step explanation:
His total score is 99 + 85 + x where x is score on third test,
99 + 85 + x = 3 *90 (as his average must be 90, so:
184 + x = 270
x = 270 - 184
= 86.
Answer:
86
Step-by-step explanation:
Let x be the required score for Lamar's third test in order to get an average of 90 or higher.
Start with the initial equation:
[tex]\frac{99+85+x}{3}\geq 90[/tex]
Simplify the numerator in the fraction:
[tex]\frac{184+x}{3}\geq90[/tex]
Multiply both sides by 3 to cancel out division on left side of equation:
[tex]184+x\geq 270[/tex]
Subtract 184 from both sides to isolate the x variable:
[tex]x\geq86[/tex]
Leaving us with x must be greater than or equal to 86.
One day, thirteen babies are born at a hospital. assuming each baby has an equal chance of being a boy or girl, what is the probability that at most eleven of the thirteen babies are girls?
Using the binomial distribution, there is a 0.9983 = 99.83% probability that at most eleven of the thirteen babies are girls.
What is the binomial distribution formula?The formula is:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
The parameters are:
x is the number of successes.n is the number of trials.p is the probability of a success on a single trial.For this problem, the values of the parameters are:
p = 0.5, n = 13
The probability that at most eleven of the thirteen babies are girls is:
[tex]P(X \leq 11) = 1 - P(X > 11)[/tex]
In which
P(X > 11) = P(X = 12) + P(X = 13)
Then:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 12) = C_{13,12}.(0.5)^{12}.(0.5)^{1} = 0.0016[/tex]
[tex]P(X = 13) = C_{13,13}.(0.5)^{13}.(0.5)^{0} = 0.0001[/tex]
So:
P(X > 11) = P(X = 12) + P(X = 13) = 0.0016 + 0.0001 = 0.0017
[tex]P(X \leq 11) = 1 - P(X > 11) = 1 - 0.0017 = 0.9983[/tex]
0.9983 = 99.83% probability that at most eleven of the thirteen babies are girls.
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1. Use the figure to determine the value of x and y.
Answer:
Step-by-step explanation:
x=100 bc like 180-80=100
y=80 bc vertical angles
Answer:
y = 80*
x = 100*
Step-by-step explanation:
y is the same to the 80* angle and therefore x is 100*
180* - 80 = 100*
Hundred chart: I am thinking of a number that is greater than 70 but less than 100.
It is not divisible by 10. It is not divisible by 4. It is not an odd number. What can I be
The numbers which is greater than 70 but less than 100, not divisible by 10, not divisible by 4, not an odd number are 74, 78, 82, 86, 94, 98
Even and odd numbersA number greater than 70 but less than 100Not divisible by 10Not divisible by 4Not odd numberA number greater than 70 but less than 100
71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 98
Not odd number
72, 74, 76, 78, 80, 82, 84, 86, 88, 90, 92, 94, 96, 98
Not divisible by 10
72, 74, 76, 78, 82, 84, 86, 88, 92, 94, 96, 98
Not divisible by 4
74, 78, 82, 86, 94, 98
Therefore, the numbers which is greater than 70 but less than 100, not divisible by 10, not divisible by 4, not an odd number are 74, 78, 82, 86, 94, 98.
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-5 ____ =2
please help me lol.
[tex] - 5 + x = 2 \\ add \: 5 \: to \: both \: sides \\ x = 2 + 5 = 7[/tex]
7 is your answer[tex] - 5 x =2 \\ x = -2/5[/tex]
Assuming you're multiplying:
Answer:
Step-by-step explanation:
Comment
The simple answer is you should put something equivalent to -2/5 in the blank. This is what will happen,
-5 * - 2/5
The 5's will cancel out. The minus sign that was in front of the 5 will become positive because 2 minuses make a plus.
Another way to do the problem is to call the ___ = x
-5 x = 2 Divide both sides by - 5
-5x/ -5 = 2/-5
x = - 2/5
It comes to the same thing.
A third way is just to multiply by - 0.4
-5 * -0.4 = 2
add and subtract function PLS HELP!!!!
Answer:
The first option:
[tex]6x^{2} -4x+6[/tex]
Step-by-step explanation:
Trust me I am right.
If you need work please ask!
Have a nice day!
Sandy used a virtual coin toss app to show the results of flipping a coin 80 times, 800 times, and 3,000 times. Explain what most likely happened in Sandy's experiment.
Sandy's experimental probability was exactly the same as the theoretical probability for all three experiments.
Sandy's experimental probability was closest to the theoretical probability in the experiment with 80 flips.
Sandy's experimental probability was closest to the theoretical probability in the experiment with 800 flips.
Sandy's experimental probability was closest to the theoretical probability in the experiment with 3,000 flips.
Question 2(Multiple Choice Worth 2 points)
(Experimental Probability MC)
A spinner with 4 equal sections is spun 20 times. The frequency of spinning each color is recorded in the table below.
Outcome Frequency
Pink 6
White 3
Blue 7
Orange 4
What statement best compares the theoretical and experimental probability of landing on orange?
The theoretical probability of landing on orange is one fifth, and the experimental probability is 20%.
The theoretical probability of landing on orange is one fourth, and the experimental probability is 20%.
The theoretical probability of landing on orange is one fifth, and the experimental probability is 30%.
The theoretical probability of landing on orange is one fourth, and the experimental probability is 50%.
Question 3(Multiple Choice Worth 2 points)
(Experimental Probability MC)
Michael has a bag of marbles. The frequency of selecting each color is recorded in the table below.
Outcome Frequency
Green 4
Black 6
Orange 5
Based on the given frequency, determine the experimental probability of selecting an orange marble.
0.27
0.33
0.40
0.67
Question 4(Multiple Choice Worth 2 points)
(Experimental Probability LC)
A number cube is tossed 60 times.
Outcome Frequency
1 12
2 13
3 11
4 6
5 10
6 8
Determine the experimental probability of landing on a number less than 2.
35 over 60
25 over 60
13 over 60
12 over 60
Question 5(Multiple Choice Worth 2 points)
(Experimental Probability MC)
A coin is flipped 200 times. The table shows the frequency of each event.
Outcome Frequency
Heads 98
Tails 102
Determine the experimental probability of landing on heads.
102%
98%
50%
49%
Question 6 (Essay Worth 4 points)
(Experimental Probability HC)
A coin is flipped at the start of every game to determine if Team A (heads) or Team B (tails) will get the ball first.
Part A: Find the theoretical probability of a fair coin landing on heads. (1 point)
Part B: Flip a coin 14 times and record the frequency of each outcome. Be sure to include the frequency of each outcome in your answer. Then, determine the experimental probability of landing on heads and compare it to the theoretical probability. (3 points)
Sandy's experimental probability was exactly the same as the theoretical probability for all three experiments.
The theoretical probability of landing on orange is one fourth, and the experimental probability is 20%.
The experimental probability of selecting an orange marble is 0.33.
The experimental probability of landing on a number less than 2 is 12 over 60.
The experimental probability of landing on heads is 49%.
The theoretical probability of a fair coin landing on heads is 0.5.
How to calculate the probability?It should be noted that a coin has a head and tail. Therefore, the probability of getting either will be:
= 1/2 = 0.5
Therefore, Sandy's experimental probability was exactly the same as the theoretical probability for all three experiments.
The statement that compares the theoretical and experimental probability of landing on orange is that the theoretical probability of landing on orange is one fourth, and the experimental probability is 20%.
The experimental probability will be:
= 4/(6+3+7+4)
= 4/20 = 1/5
Based on the given frequency, the experimental probability of selecting an orange marble will be:
= 5/(4+6+5)
= 5/15
= 0.33
The experimental probability of landing on a number less than 2 is 12 over 60.
The experimental probability of landing on heads will be:
= 98/(98 + 102)
= 98/200
= 49%
The theoretical probability of a fair coin landing on heads will be:
= 1/2 = 0.5
Flip a coin 14 times and record the frequency of each outcome gives:
Head, Tail, Head, Head, Head, Tail, Tail, Head, Tail, Tail, Tail, Tail, Head, Head. The theoretical and experimental probability are 0.5.
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help fast pls!
it doesn't have to be a long explanation i just need the answer and a lil blurb to know ur not lying tysm!!!
Answer:
c 0.5⁻ˣ
Step-by-step explanation:
The slowest rate is:
0.5⁻ˣ
PLEASE PLEASE PLEASE HELP ME ITS A MATH PROBLEM!!! EXPLANATIONS WELCOMED
Answer:
8
Step-by-step explanation:
The given ratios can be combined to a composite ratio using least common multiples.
Given ratiosWe can identify each of the entities with a 2-letter designation:
TT - Tumtum tree; TW - tulgey wood; BS - frumious Bandersnatch;
ST - slithy tove; BG - borogoves; MR - mome raths; JW - Jabberwocky;
JB - Jubjub birds.
Then the given ratios are ...
20 TT : 1 TW1 TW : 1 BS5 ST : 2 BG2 MR : 1 JW2 JB : 200 TT . . . . (reduces to 1 : 100)200 MR : 1 BG5 JB : 1 STComposite ratiosThe path from BS to JW is unique, so we can work our way there one ratio at a time. Having done this once, we can go back and do it again with the least possible multiplier.
Here, that turns out to be 125 Bandersnatches. We can combine these to the composite ratio ...
125 BS : 125 TW : 2500 TT : 25 JB : 5 ST : 2 BG : 400 MR : 200 JW
Then the ratio of Bandersnatches to Jabberwocks is 125 : 200 = 5 : 8.
If there are 5 frumious Bandersnatches, there should be 8 Jabberwocks.
__
Additional comment
We know 1 JW : 2 MR and 200 MR : 1 BG. In order to get a common value of 200 MR in these ratios, we need to multiply the first by 100:
100 JW : 200 MR : 1 BG
Next, we notice the other ratio involving BG is 2 BG : 5 ST, which means we need to multiply by 2 again:
200 JW : 400 MR : 2 BG : 5 ST
The number of JB is 5 times the number of ST, so this extends to ...
... 5 ST : 25 JB
The number of TT is 100 times the number of JB, so we have ...
... 5 ST : 25 JB : 2500 TT
Continuing in like fashion, we get the composite ratio shown above. We originally worked this starting from BS. Reducing the JB/TT ratio from 2/200 to 1/100 helped eliminate an extra factor of 2.
Step-by-step explanation:
it's not really a math problem per se, it is more like a regular riddle with numbers.
true, everything involving numbers is essentially math, but then what will you do in life with things like earning a salary, going shopping, checking a calendar and schedules for bus, train and flights or business meetings, sharing a pizza with friends, playing computer games, ...
life is for a big part numbers and therefore math.
so, don't be afraid, just use your brain and common sense !
let's think this through (just be strict, concentrated, and follow each line literally) :
5 fr. Band. means 5 tulgey woods.
which means 20×5 = 100 tumtum trees.
as there are 2 jubjub birds in 200 tumtum trees, that means that there is 1 jubjub bird in the given 100 tumtum trees.
as there are 5 jubjub birds in 1 slithy toves, but we have only 1 bird, that means we have only 1/5 slithy toves.
there are 5 slithy toves in 2 borogoves. that means 1 slithy toves in 2/5 borogoves. and 1/5 slithy toves in 2/5 / 5 = 2/25 borogoves.
there are 200 mome raths in each borogove. and we have 2/25 borogoves. that means we have
200 × 2/25 = 400/25 = 16 mome raths.
and there are 2 mome raths per jabberwocky. we have 16 raths. how many pairs of raths does that make ?
16/2 = 8 pairs of raths = jabberwocks.
so, there should be 8 jabberwocks.
you see ? that's all that was needed. this was like a labyrinth riddle, where you need to find the way from an inside starting point to the exit without crossing a line (or wall).
On a number line, the directed line segment from q to s has endpoints q at –14 and s at 2. point r partitions the directed line segment from q to s in a 3:5 ratio. which expression correctly uses the formula (startfraction m over m n endfraction) (x 2 minus x 1) x 1 to find the location of point r?
The coordinates of point r(-8,0).
What is midpoint formula in coordinate geometry?The coordinates of the point r(x,y) which divides the line segment joining the points p([tex]x_{1}[/tex],[tex]y_{1}[/tex]) and q([tex]x_{2}[/tex],[tex]y_{2}[/tex]) internally in the ratio :[tex]m_{1}[/tex][tex]m_{2}[/tex] are
[tex]\left(\frac{m_{1}x_{2}+ m_{2}x_{1} }{m_{1}+m_{2} } ,\frac{m_{1}y_{2}+ m_{2}y_{1} }{m_{1}+m_{2} }\Rifgt)[/tex]
Given that,
Two end points on the line q(-14,0) and s(2,0). point r(x,y) is the partition of the line segment from q to s in a ratio 3:5
[tex]m_{1}[/tex] = 3 and [tex]m_{2}[/tex] = 5
By using the midpoint formula
[tex]\left(\frac{m_{1}x_{2}+ m_{2}x_{1} }{m_{1}+m_{2} } ,\frac{m_{1}y_{2}+ m_{2}y_{1} }{m_{1}+m_{2} }\Rifgt)[/tex]
[tex]\left(\frac{3(2)+ 5(-14) }{3+5 } ,\frac{3(0)+ 5(0) }{3+5 }\Rifgt)[/tex]
[tex]\left(\frac{-64}{8 } ,\frac{0 }{8 }\Rifgt)[/tex]
[tex]\left(-8 ,0\Rifgt)[/tex]
Hence, The coordinates of point r(-8,0).
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Kaitlin, Joe, and Miguel have a total 96 of in their wallets. Kaitlin has 6 less than Joe. Miguel has 4 times what Joe has. How much does each have?
Answer:
15, 11, 60
Step-by-step explanation:
Let Joe's amount be x
x + x - 6 + 4x = 96
6x - 6 = 96
6x = 90
x = 15
Joe has 15
Kaitlin has 11
Miguel has 60
Write an equation for the nth term of the arithmetic sequence.
Step-by-step explanation:
Given [tex] \sf \: first \: term \: (a) = \dfrac{1}{4} \\ [/tex][tex] \small{\sf \: Common \: difference \: (d) = \dfrac{1}{2} - \dfrac{1}{4} = \bold{\dfrac{1}{4}}}[/tex]To findnth termSolution[tex] \sf \: T_n = a+(n-1)d[/tex]
[tex] \sf \: T_n = \frac{1}{4} +(n-1) \frac{1}{4} [/tex]
[tex]\sf \: T_n = \frac{1}{4} + \frac{n}{4} - \frac{1}{4} [/tex]
[tex]\sf \: T_n = \frac{n}{4}[/tex]
an equation for the nth term of the arithmetic sequence. is n/4
Step-by-step explanation:
TN=n/4 is the nth term of arithmetic sequence.
Solve for x.
°x = 196
Enter your answers in the boxes. Enter the smallest answer first.
x= ____ and x= ____
4 andfirst find x by finding its smallest factor
The solution to the given system of equation is -7 and 7
What is linear equation?A linear equation is an algebraic equation of the form y=mx+b. involving only a constant and a first-order (linear) term, where m is the slope and b is the y-intercept. Occasionally, the above is called a "linear equation of two variables," where y and x are the variables.
Given:
4x² = 196
4x²/4= 196/4
x² = 49
x=√49
x= ±7
Hence, the solution to the given system of equation is -7 and 7
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Aisha wants to paint the four walls of her living room.
Each wall is 2.4 m high and 5.2 m long.
One wall has a door of 2 m by 0.8 m.
Tins of paint cost £12 per 2 litre tin.
Each litre of paint can cover 12 m2 of wall.
There is an offer of: Buy 2 tins get the 3rd at half price.
How much will Aisha pay to paint her living room?
The total amount Aisha would pay to paint her room is $54.
What is the cost of painting the rooms?The first step is to determine the area of the walls. The walls have the shape of a rectangle. Thus, the formula for the area of a rectangle would be used to determine the area of the wall.
Area of the three walls without a door : 3 x (length x width)
3 x (2.4 x 5.2) = 37.44 m²
Area of the fourth wall with a door : area of the wall - area of the door
(2.4 x 5.2) - (2 x 0.8) = 10.88m²
Total area of the walls : area of the three walls + area of the wall with the door
10.88m² + 37.44 m² = 48.32 m²
The next step is to determine the number of tins that would be needed:
48.32 /12 = 4.03
5 tins would needed
Cost of the 5 tins: (4 x 12) + (0.5 x 12) = $54
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It is October and that means it is State Fair time again! Your uncle took you and 2 of your friends to the
fair. Admission for everyone to get into the fair was $20.00. You then went to the Midway, where they
have all of the rides, and he bout all-day ride passes for you and your friends. If your uncle spent a total
of $65.00 at the fair, how much did each of the all-day ride passes cost?
Answer: All-day ride passes cost $15 each
Step-by-step explanation:
It was $20 in total for everyone to get in, so subtract that from $65 to just focus on the all day passes
65-20=45
So the all day passes all together cost $45
Since your uncle bought it for you and 2 friends that's 3 people in total so divide 45 by 3
45 divided by 3 = 15
So each of the all day passes cost $15
Hope this helped :)
By which number -7÷25 should be divided to get -1÷15
Answer:
Step-by-step explanation:
Set it up like an equation first:
[tex]\frac{\frac{-7}{25} }{x}=-\frac{1}{15}[/tex] and then bring up the lower fraction, flip it, and multiply:
[tex]-\frac{7}{25}*\frac{1}{x}=-\frac{1}{15}[/tex]
Simplify to
[tex]-\frac{7}{25x}=-\frac{1}{15}[/tex] and cross multiply to get
-25x = -105 and divide both sides by -25 to get that
[tex]x=\frac{105}{25}=\frac{21}{5}[/tex]
Point R divides PQin the ratio 1:3. If the x-coordinate of Ris -1 and the x-coordinate of Pis -3, what is the x-coordinate of Q?
Since Point R divides PQ in the ratio 1:3. the x-coordinate of Q is 3
The question has to do with line division
What is line division?This is the division of a line into a given ratio.
How to find the coordinate of Q?
Since Point R divides PQ in the ratio 1:3. If the x-coordinate of R is -1 and the x-coordinate of P is -3.
Let
x₁ = coordinate of P = -3, x₂ = coordinate of R = -3 and x₃= coordinate of Q.Since R divides PQ in the ratio, 1:3, we have that
PR/RQ = 1/3
(x₂ - x₁)/(x₃ - x₂) = 1/3
Substituting the values of the variables into the equation, we have
(x₂ - x₁)/(x₃ - x₂) = 1/3
(-1 - (-3))/(x₃ - (-3)) = 1/3
(-1 + 3)/(x₃ + 3) = 1/3
2/(x₃ + 3) = 1/3
x₃ + 3 = 2 × 3
x₃ + 3 = 6
x₃ = 6 - 3
x₃ = 3
So, the x-coordinate of Q is 3
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A solid right pyramid has a regular hexagonal base with an area of 5.2 cm2 and a height of h cm. a solid right pyramid has a regular hexagonal base with an area of 5.2 centimeters squared and a height of h centimeters. which expression represents the volume of the pyramid?
The calculations show that this pyramid's volume is equivalent to:
5.2h/3 cm3.
What is a pyramid?A polyhedron constructed by joining a polygonal base and a point, is called a pyramid. A lateral face is a triangle formed by the base edge and vertex of each base. Conic solid with a polygonal basis describes it. The number of vertices, faces, and edges on a pyramid with an n-sided base is n + 1.
Given information:Base area = 5.2 [tex]cm^2[/tex].
Height in centimeters is equal to h.
How can the volume of a pyramid be calculated?The following formula is used to determine a pyramid's volume mathematically:
Base area divided by height equals one-third of the volume.
When we enter the parameters into the formula, we get;
Volume = 1/3 *5.2* h
Volume = 5.2h/3 [tex]cm^3.[/tex]
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I understand that the question you are looking for is :
A solid right pyramid has a regular hexagonal base with an area of 5. 2 cm2 and a height of h cm. a solid right pyramid has a regular hexagonal base with an area of 5. 2 centimeters squared and a height of h centimeters. which expression represents the volume of the pyramid? one-fifth(5. 2)h cm3 start fraction 1 over 5 h infraction(5. 2)h cm3 one-third(5. 2)h cm3 start fraction 1 over 3 h infraction(5. 2)h cm3
