Therefore, the general solution of the given system is: x(t) = c1 (7/4)e^(10t) [1; -4/5; 1] + c2 (7/10)e^(2t) [1; -2/5; 1] + c3 (7/6)e^(7t) [1; 1/2; 1]
To find the general solution of the given system, we first need to find the matrix A and the vector f such that:
d/dt [x(t); y(t); z(t)] = A [x(t); y(t); z(t)] + f
where A is the coefficient matrix and f is the constant vector.
Using the given system, we have:
A = [2 -7 0; 5 10 4; 0 5 2]
f = [0; 0; 0]
To solve the system, we need to find the eigenvalues and eigenvectors of the matrix A. The characteristic equation is:
det(A - λI) = 0
where I is the identity matrix and λ is the eigenvalue.
Solving for λ, we get:
λ^3 - 14λ^2 - 5λ + 140 = 0
Using synthetic division or a numerical method, we find that the eigenvalues are:
λ1 = 10, λ2 = 2, λ3 = 7
To find the eigenvectors, we solve the system (A - λI)x = 0 for each eigenvalue.
For λ1 = 10, we have:
(A - λ1I)x1 = 0
[ -8 -7 0 ][x1] = [0]
[ 5 0 4 ][y1] = [0]
[ 0 5 -8 ][z1] = [0]
Solving this system, we get the eigenvector:
x1 = [7/4; -4/5; 1]
For λ2 = 2, we have:
(A - λ2I)x2 = 0
[ 0 -7 0 ][x2] = [0]
[ 5 8 4 ][y2] = [0]
[ 0 5 0 ][z2] = [0]
Solving this system, we get the eigenvector:
x2 = [7/10; -2/5; 1]
For λ3 = 7, we have:
(A - λ3I)x3 = 0
[ -5 -7 0 ][x3] = [0]
[ 5 3 4 ][y3] = [0]
[ 0 5 -5 ][z3] = [0]
Solving this system, we get the eigenvector:
x3 = [7/6; 1/2; 1]
The general solution of the system is:
x(t) = c1 e^(λ1t) x1 + c2 e^(λ2t) x2 + c3 e^(λ3t) x3
where c1, c2, and c3 are constants determined by the initial conditions.
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Mr. Daniels is organizing a class trip. He wants to spend less than $300. Which inequality represents the cost, c, that Mr. Daniels can spend on the class trip?
c < 300
The inequality that represents the cost, c, that Mr. Daniels can spend on the class trip is; c < 300
How to solve Inequality word problems?
We are told that;
Mr. Daniels is organizing a class trip.
Mr. Daniels wants to spend less than $300
Thus, if the cost that Mr. Daniels can spend on the class trip is given as c, then it means that c has to be less than the amount which he wants to spend which is $300.
Thus, since c has to be less than $300, then it means that the inequality to be used would be a less than sign which can be expressed as;
c < 300
Thus, we conclude that it is the required inequality.
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Answer This CORRECTLY. I really need help, the question will be placed first, and then the answer choices will be in order from A - D as graphs.
Answer:
C is the correct oneStep-by-step explanation:
GivenFunction
y = -3/2x - 2To find The correct graphSolutionWe can see all 3 graphs have y-intercept of -2
Since the slope is negative, it is decreasing function, therefore possible options are A or C
Checking x-intercept and comparing with same of A and C
y = 0-3/2x - 2 = 0-3/2x = 2x = -4/3 = -1.33As we see it matches Option C, which is the answer
Answer:
4
Step-by-step explanation:
Determine the intervals of concavity for the function f(x)=xe
x
.
The function f(x) = x * e^x is concave up on the interval (-∞, -1) and concave down on the interval (-1, ∞).
To determine the intervals of concavity for a function, we need to analyze the sign of its second derivative. Let's start by finding the second derivative of f(x).
First, we find the first derivative:
f'(x) = (x * e^x)' = e^x + x * e^x = e^x(1 + x).
Next, we find the second derivative:
f''(x) = (e^x(1 + x))' = e^x + (e^x)'(1 + x) = e^x + e^x(1 + x) = e^x(2 + x).
Now, we can analyze the sign of f''(x) to determine the intervals of concavity.
For x < -1, both e^x and (2 + x) are positive, so f''(x) = e^x(2 + x) > 0. This indicates that the function is concave up in this interval.
For x > -1, e^x remains positive, but (2 + x) becomes negative. Therefore, f''(x) = e^x(2 + x) < 0, indicating that the function is concave down in this interval.
In summary, the function f(x) = x * e^x is concave up on the interval (-∞, -1) and concave down on the interval (-1, ∞). The point x = -1 acts as an inflection point where the concavity changes from up to down.
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need help to solve please
Answer:
\(\displaystyle m\angle RTU=73^\circ\)
Step-by-step explanation:
Interior Angle of a Circle
An interior angle of a circle is formed at the intersection of two lines that intersect inside a circle.
Lines AC and BD of the figure attached below intersect forming arcs p and q. The measure of the interior angle x is:
\(\displaystyle x=\frac{p+q}{2}\)
The question includes the drawing of a circle with lines US and RV intersecting at point T. The measure of the interior angle RTU is:
\(\displaystyle m\angle RTU=\frac{68^\circ+78^\circ}{2}\)
\(\displaystyle m\angle RTU=\frac{146^\circ}{2}\)
\(\boxed{\displaystyle m\angle RTU=73^\circ}\)
Candice leaves on a trip driving at 25 miles per hour.four hours later,her sister liz starts from the same location driving at 50 miles per hour.how long after liz leaves home will she catch up to candie
Answer:
Step-by-step explanation:
Candice = 25mph for 4 hours.
Candice has driven= 25 * 4= 100miles.
Liz =50mph
Liz time to catch up to candice= 50 * 2= 100miles.
Therefore, It would have taken Liz two hours to catch up with Candice
5. Based on the information provided in the diagram below, determine measure of side m, to one
decimal place accuracy. Be sure to label the diagram and show all work. (3 marks)
m
40°
10
Answer: please provide more information
Step-by-step explanation:
Find the determinant of the elementary matrix. (Assume k # 0.) 1 0 0 4k 1 0 0 0 1 I Find 141. Begin by finding 4, and then evaluate its determinant. Verify your result by finding (A) and then applying the formula 14-11- A [21] 14-¹1- Need Help? Readi
The given matrix is an elementary matrix that represents an elementary row operation of multiplying the second row by 4k. The determinant of this matrix is determinant of the original matrix, which is 4k.
Therefore, the determinant of the given elementary matrix is 4k.
To verify this result, we can also compute the determinant using the formula for a 3x3 matrix. The matrix obtained by applying the elementary row operation to the identity matrix is:
\(\left[\begin{array}{ccc}1&0&0\\0&4k&0\\0&0&1\end{array}\right]\)
The determinant of this matrix is calculated as: det(A) = 1 * (4k) * 1 - 0 * 0 * 0 - 0 * (4k) * 0 = 4k. So, the determinant of the given elementary matrix is indeed 4k, which matches our previous result.
In summary, the determinant of the elementary matrix is 4k, and this can be verified by calculating the determinant using the formula for a 3x3 matrix.
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helppppppppppppppppppppppppppppp
Answer:
1000
Step-by-step explanation:
For each digit you get 10 options: 0,1,2,3,4,5,6,7,8,9.
If you are able to use three digits then you multiply the amount of digits by 3 (10x10x10)
10x10=100
100x10=100
Therefore 1000 is your answer
Answer:
1000 because there are 10*10*10 ways to choose numbers
Hope this helps
With solving and it’s better to edit the photo and send it
Step-by-step explanation:
please mark me as brainlest
POPULATION In 2000, the world population was calculated to be 6,071,675,206. The world population increases at a rate of about 1.2% annually.
Write a function that represents the world population y after x years.
A) y = 6,071,675,205(1.012)^x
B) y = 6,071,675,206(1.012)^x
C) y = 6,071,605,205(1.012)^x
D) y = 6,071,675,215(1.012)^x
PLEASE HELP!!
Answer:
B) y = 6,071,675,206(1.012)^x
Step-by-step explanation:
It appears that this question asks for an exponential model that represents the population growth. I believe you could view the equation in the form y = (initial population)(rate)^x
Since the initial population is 6,071,675,206, you could substitute that in to get y = 6,071,675,206(rate)^x
Since your rate is increasing by 1.2% (0.012 in decimal form), just convert that to decimal form (knowing that 100% = 1.0, add 0.012 to get 1.012). Substitute that in to get y = 6,071,675,206(1.012)^x
Hope that helps. Feel free to let me know if it made sense.
g a biker is riding along a trail at 13ft/s . she spots an aspen tree that is 15 feet away from a traffic cone located along the trail at the shortest distance from the trail to the aspen tree (see diagram). how fast is the angle between her line of sight and the trail changing when she is 25 feet away from the tree?
Therefore, the angle between the biker's line of sight and the trail is changing at a rate of approximately 0.039 radians per second when she is 25 feet away from the tree.
To solve this problem, we need to use trigonometry and calculus. Let's call the angle between the biker's line of sight and the trail θ, and let's call the distance from the traffic cone to the aspen tree x. Then we can use the tangent function to relate θ and x:
tan(θ) = x/15
We can also use the Pythagorean theorem to relate x and the distance d between the biker and the tree:
d^2 = x^2 + 25^2
Taking the derivative of both sides with respect to time t, we get:
2d (dd/dt) = 2x (dx/dt)
Now we can substitute the equation for x in terms of θ and solve for (dθ/dt):
tan(θ) = x/15
sec^2(θ) (dθ/dt) = (1/15) (dx/dt)
(dθ/dt) = (1/15) (dx/dt) sec^2(θ)
We can use the equation for d to solve for x:
x^2 = d^2 - 25^2
2x (dx/dt) = 2d (dd/dt)
(dx/dt) = (d/dd) (sqrt(d^2 - 25^2)) (dd/dt)
(dx/dt) = (d/ sqrt(d^2 - 25^2)) (dd/dt)
Now we can substitute this expression for (dx/dt) into the previous equation and evaluate it when d = 25 and θ = arctan(15/25):
(dθ/dt) = (1/15) [(d/ sqrt(d^2 - 25^2)) (dd/dt)] sec^2(arctan(15/25))
(dθ/dt) = (1/15) [(25/ sqrt(25^2 - 25^2)) (13)] sec^2(arctan(15/25))
(dθ/dt) = (13/375) sec^2(arctan(15/25))
(dθ/dt) ≈ 0.039 radians per second
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John will toss a coin 3 times. What is the probability the coin lands on heads all three times? Write the probability as a fraction and a decimal
Answer:
It has to be either HEADS or TAILS (obviously). If it's a “Fair” coin the probability of getting either a Heads or Tails is (1/2) for each option.
Conclusion(so far):
Prob (Heads Coin 1) = (1/2) AND
Prob (Tails Coin 1) = (1/2)
To meet the requirements of the question, the second coin toss must have the same result as for the first coin toss.
So if the result for Coin 1 was Heads then the result for Coin 2 must also be Heads.
So
(Prob (Heads Coin 1 AND Heads Coin 2) = (Prob Heads Coin1) * (Prob Heads Coin 2) = (1/2)*(1/2) = (1/4)
Conclusion (so far) (2 coins tossed):
Prob of two coin tosses BOTH giving Heads is (1/2)*(1/2) = (1/4)
AND similarly
Prob of two coin tosses BOTH giving Tails is also (1/2)*(1/2) = (1/4)
To meet the requirements of the question, the third coin toss will, by definition be either HEADS or TAILS.
AND
Prob (Coin 3 Heads) = (1/2) AND
Prob (Coin 3 Tails) = (1/2)
The question is clear: We are asked to find the Probability that the (3 tosses) are the same.
That is, if the first toss (Coin 1) is Heads, then the results for Coin 2 and Coin 3 tosses must also be Heads.
Similarly if the the first toss (Coin 1) is Tails, then the results for Coin 2 and Coin 3 tosses must also be Tails.
So for the tosses for Coins 1, 2 and 3 to each be Heads, we have:
Prob (Coin 1 Heads, Coin 2 Heads, Coin 3 Heads) = (1/2)*(1/2)*(1/2) = (1/8)
AND
Prob (Coin 1 Tails, Coin 2 Tails, Coin 3 Tails) = (1/2)*(1/2)*(1/2) = (1/8)
There are NO OTHER NUMBER COMBINATIONS WHICH MEET THE REQUIREMENTS OF THE QUESTION other than 3 Heads AND 3 Tails.
It is important to note THAT THE SITUATIONS ABOVE (3 Heads AND 3 Tails) are BOTH VALID SOLUTIONS.
Therefore
The Probability for 3 Heads is (1/8)
AND
The Probability for 3 Tails is (1/8)
BUT BOTH THESE SOLUTIONS ARE VALID PROBABILITIES and BOTH meet the requirements of the question.
Therefore the overall probability is THE SUM OF BOTH PROBABILITIES, that is:
The probability that after 3 tosses, the tosses of each coin ALL give the same result is:
(1/8) + (1/8) = (2/8) = (1/4) or 0.25 or 25%
This means that after 3 coin tosses there is a 25% probability that we will get either 3 Heads or 3 Tails.
(A note of interest: It would be an error to ignore the fact that there are TWO valid number combinations which meet the requirements of the question, not one).
(In my analysis above I have identified ONLY the valid-number combination)
Step-by-step explanation:
An elevator has a placard stating that the maximum capacity is 1884 lb-12 passengers. So, 12 adult male passengers can have a mean weight of up to 1884/12=157 pounds. If the elevator is loaded with 12 adult male passengers, find the probability that it is overloaded because they have a mean weight greater than 157 lb. (Assume that weights of males are normally distributed with a mean of 165 lb and a standard deviation of 32 lb.) Does this elevator appear to be safe? BICICIE The probability the elevator is overloaded is (Round to four decimal places as needed) Does this elevator appear to be safe? OA. No, there is a good chance that 12 randomly selected adult male passengers will exceed the elevator capacity OB. No, 12 randomly selected people will never be under the weight limit. OC. Yes, there is a good chance that 12 randomly selected people will not exceed the elevator capacity OD. Yes, 12 randomly selected adult male passengers will always be under the weight limit. A bank's loan officer rates applicants for credit. The ratings are normally distributed with a mean of 200 and a standard deviation of 50. If an applicant is randomly selected, find the probability of a rating that is between 200 and 275. Round to four decimal places. www OA. 0.4332 OB. 0.9332 OC. 0.5000 OD. 0.0668 Find the value of the linear correlation coefficient r. The paired data below consist of the costs of advertising (in thousands of dollars) and the number of products sold (in thousands). Cost 9 2 3 5 9 10-> 4 2 68 67 Number 52 55 85 A. 0.235 OB. 0.708 OC. 0.246 OD. -0.071 86 83 73
The answer is option A. No, there is a good chance that 12 randomly selected adult male passengers will exceed the elevator capacity.
Probability that it is overloaded if 12 adult male passengers have a mean weight greater than 157 lb is 0.0229.Round to four decimal places as needed.Based on the calculations the elevator does not appear to be safe.The solution for the given problem is as follows:
Given that, the maximum capacity of the elevator is 1884 lb - 12 passengers.
We can write as below:
Maximum capacity per person=1884/12=157lb.
And, weights of males are normally distributed with a mean of 165 lb and a standard deviation of 32 lb.Thus, Z = (157-165) / (32 / √12) = -1.7321Then, P(Z > -1.7321) = 0.9586
Hence, the probability that it is overloaded if 12 adult male passengers have a mean weight greater than 157 lb is:P(Z > -1.7321) = 1 - P(Z < -1.7321) = 1 - 0.0229 = 0.9771 (rounded off to 4 decimal places).This probability is greater than 5% and therefore, the elevator does not appear to be safe.
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Write the equation of this line in slope-intercept form.
Answer:
Slope-Intercept Form: \(y = 2*x -3\)
or
Point-intercept form: \(y-(-3)=2(x-0)\)
Step-by-step explanation:
Method 1: Start from 1 point and then count the rise overrun.Slope-Intercept Form: \(y=mx+b\)
Start from the Y-axis where \(b=-3\) then rise/run to the next point. making that our slope.
Method 2: Using the point-intercept formPoint-intercept form: \(y-y_0=m(x-x_0)\)
Solve the slope using the two points.
\((0,-3)\) and \((2,1)\) plug those values into the formula. Make \((x,y)=(0,-3)\) and \((x_0,y_0)=(2,1)\)
\(-3-1=m(0-2)\)
\(-4=m(-2)\)
\(m=-2\)
\(y-(-3)=-2(x-0)\)
what is the answer? the two triangles below are similar. calculate the value of x
Step-by-step explanation:
If they are similar, then 10 is to 3 as x is to 15
10/3 = x/15 multiply both sides by 15
50 mm = x
verify that the vector xp is a particular solution of the given nonhomogeneous linear system.
x’ = (2 1 1 -1)x+(-5 2); x˅p = (1 3)
To verify that the vector xp is a particular solution of the given nonhomogeneous linear system, we need to substitute xp into the system and check if it satisfies the equation.
The given nonhomogeneous linear system can be written in the form x' = Ax + f, where A is the coefficient matrix (2 1 1 -1) and f is the constant vector (-5 2). The vector xp = (1 3) is a particular solution if it satisfies the equation x' = Ax + f.
Substituting xp into the equation, we get:
x' = (2 1 1 -1) (1 3) + (-5 2)
= (1 -1 2 -8)
Therefore, the left-hand side of the equation is:
x' = (1 -1 2 -8)
And the right-hand side is:
Ax + f = (2 1 1 -1) (1 3) + (-5 2)
= (1 -1 2 -8)
Since the left-hand side is equal to the right-hand side, we can conclude that the vector xp = (1 3) is indeed a particular solution of the given nonhomogeneous linear system.
We have verified that the vector xp = (1 3) is a particular solution of the given nonhomogeneous linear system by substituting it into the equation and checking if it satisfies the equation.
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What is the solution of equations 8x 3y 5 3x 2y 5 *?
The solution of the given system of equations 8x+3y=5 and 3x-2y=5 is x = 1 and y = -1
In this question we have been given a system of equations.
8x+3y=5 ..........(1)
and 3x-2y=5 ..........(2)
We need to find the solution of the given system of equations.
As right hane side of both equations is equal, we equate LHS of both equations.
so, we get,
8x + 3y = 3x - 2y
⇒ 8x - 3x = - 2y - 3y
⇒ 5x = - 5y
⇒ x = - y .............(3)
By substituting x = - y in equation (1), we get,
8 ( - y ) + 3y = 5
⇒ - 8y + 3y = 5
⇒ - 5y = 5
⇒ y = - 1
Substitute above value of y in equation (3)
⇒ x = - (- 1)
⇒ x = 1
Therefore, x = 1 and y = -1 is solution of given equations.
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Angles 3 and 5 are what type of angle pair?
Answer:
interior opposite angles
Step-by-step explanation:
they are inside of the shape but on opposite sides (and i did this freshman year)
Answer:
alternate interior angles
Step-by-step explanation:
∠ 3 and ∠ 5 are alternate interior angles.
These angles are on the opposite ( alternate ) sides of the transversal and are in between ( in the interior ) of the parallel lines.
PLS HELP FAST
At a hockey game, a vender sold a combined total of 232 sodas and hot dogs. The number of sodas sold was three times the number of hot dogs sold. Find the number of sodas and the number of hot dogs sold.
Number of sodas sold:
Number of hot dogs sold:
The vendor sold 172 sodas and 58 hotdogs at the hockey game.
What is a linear equation?An equation of degree one is known as a linear equation.
A linear equation of two variables can be represented by ax + by = c.
let, the number of soda cans be 'x' and the number of hot dogs be 'y'.
So, From the given information x = 3y and the vendor sold a total of 232.
Therefore, x + y = 232.
3y + y = 232.
4y = 232.
y = 232/4.
y = 58.
So, He sold 58 hot dogs and 3×58 = 172 soda cans.
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The diffusion equation can be written as R2=4Dt where R is the average displacement, D is the diffusion constant, and t is the time. What can you say about the relationship between average displacement squared (R2) and time (t)? (Is it linear, exponential, etc.?)
Question 10
For the analysis, we will include a trendline on our R2 vs. t graph. The trendline equation has the form y=mx+b. Which variable from the diffusion equation corresponds to y in the trendline equation? Which variable from the diffusion equation corresponds to x in the trendline equaton?
Question 11
Given your answer to question 10, how could you solve for the diffusion constant in terms of the slope and a constant?
Question 12
Suppose your trendline equation is y=1.24x+5.63 Solve for the diffusion constant.
The fοrmula D = m/4, we can calculate the diffusiοn cοnstant 'D' as:
D = 1.24/4 = 0.31
What is a Diffusiοn?Diffusiοn is the prοcess by which particles οf a substance mοve frοm an area οf high cοncentratiοn tο an area οf lοwer cοncentratiοn, resulting in a net mοvement οf particles dοwn their cοncentratiοn gradient.
This οccurs due tο the randοm mοtiοn οf individual particles, which leads tο a tendency fοr particles tο spread οut and becοme evenly distributed οver time.
Answer tο Questiοn 9:
The relatiοnship between average displacement squared (R²) and time (t) is linear.
Answer tο Questiοn 10:
The variable 'R2' in the diffusiοn equatiοn cοrrespοnds tο 'y' in the trendline equatiοn, and the variable 't' in the diffusiοn equatiοn cοrrespοnds tο 'x' in the trendline equatiοn.
Answer tο Questiοn 11:
We can sοlve fοr the diffusiοn cοnstant 'D' in terms οf the slοpe 'm' and a cοnstant 'c' by equating the diffusiοn equatiοn and the trendline equatiοn.
The diffusiοn equatiοn: R2 = 4Dt
The trendline equatiοn: y = mx + b
Substituting the cοrrespοnding variables, we get:
R2 = y, D = cοnstant, t = x, m = slοpe, b = cοnstant
Sο, we have:
R2 = 4Dt
y = mx + b
Equating the twο equatiοns, we get:
y = 4Dx + 0 (since b = 0)
Cοmparing this with the trendline equatiοn y = mx + b, we can see that:
m = 4D
Therefοre, we can sοlve fοr 'D' as:
D = m/4
Answer tο Questiοn 12:
Given the trendline equatiοn y = 1.24x + 5.63, we can see that the slοpe 'm' is 1.24.
Using the fοrmula D = m/4, we can calculate the diffusiοn cοnstant 'D' as:
D = 1.24/4 = 0.31
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Question 3 of 10 Which type of savings institution offers a range of services to its customers, including savings accounts, checking accounts, and money market accounts, and also makes loans and investments and buys government bonds? A. Credit union B. Savings and loan institution C. Savings bank D. Commercial bank
The type of savings institution that offers a range of services described in the question is commercial bank.
option D.
What is commercial bank?A commercial bank is a kind of financial institution that carries all the operations related to deposit and withdrawal of money for the general public, government and others.
commercial bank banks offers wide range of services including;
savings accountschecking accountsmoney market accountsloans and investmentsbuys government bonds, etcSo the type of savings institution that offers a range of services to its customers, including savings accounts, checking accounts, and money market accounts, and also makes loans and investments and buys government bonds is commercial bank.
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find the area of each figure in units squared and then match the figure with its area.
1)
the area of the given figure is,
base x height = 9.5 x 14 = 133
2)
the area of the given figure is ,
\(=\frac{1}{2}(30+19)\times16\)\(\begin{gathered} =\frac{1}{2}\times49\times16 \\ =392 \end{gathered}\)thus, the area is 392
3)
the area of the half circle is,
diameter d = 11
\(=\frac{1}{2}\times\pi\times\frac{d^2}{4}\)\(=\frac{1}{2}\times\frac{22}{7}\times\frac{11^2}{4}\)\(\begin{gathered} =\frac{11^3}{28} \\ =\frac{133}{28} \\ =47.52 \end{gathered}\)4)
the area of the trinagle is
1/2 x base x height
= 1/2 x 26.4 x 11
= 13.2 x 11
= 145.2
please help me subject math
i'll brainliest if you answer correctly
Step-by-step explanation:
1)
8 + (-4)
= 8 - 4
= 4
2)
-2/3 + (-5/6)
= -2/3 - 5/6
= -4-5/6
= -9/6
= -3/2
3)
(-9) (-12)
= 9 × 12
= 108
4)
-5 + (-5)
= -5 - 5
= - 10
5)
(8) (-4)
= 8 × -4
= -32
6)
(1/2) (2/5)
= 1/2 × 2/5
= 1/5
7)
12 + 14
= 26
8)
(13) (7)
= 13 × 7
= 91
9)
(-3/8) (3/4)
= -3/8 × 3/4
= -9/32
find the length of the third triangle of each triangle. the two sides listed are 20 and 29
Answer:
35.23
Step-by-step explanation:
I'm going to assume this is a right triangle so ill use the Pythagorean thm
Pythagorean Formula: a² + b² = c²
20² + 29² = c²
400 + 841 = c²
1241 = c²
\(\sqrt{1241} =\sqrt{c^2}\)
c = 35.23
SImplify the equation .. PLS HELP ME
Answer:
reeee
Step-by-step explanation:
Answer:
the answer would be: -27bk
10 goes on top of the b
4 goes on top of the k
Elena and Max used to rectangular wooden boards to make a set for the school play one board was 6 ft long and the other was 5 and 1/2 ft long the two boards had equal width the total area of the set was 60 and 3/8 square feet what was the width
Answer:the width is 5 1/4 ft
Step-by-step explanation:
Step 1
The area of a rectangle is given as Length x width
Therefore the area of the rectangular board = Length x width
The length of the first board =6ft
The length of the second board =5 1/2 ft (5.5ft) with both having a total area of 60 3/8 (60.375ft²). To find the width of the boards since both have equal width, we use the equation
Length x width of board A + Length x width of board B= area of board A and Board B
6w + 5.5w =60.375
Step 2---- Solving the equation
6w + 5.5w =60.375
11.5w = 60.375
w = 60.375/11.5
w= 5.25
Therefore the width of the two boards are 5.25 ft / 5 and 1/4 ft each
Antonio writes the equation 80.4÷d+0.0804
What value of d makes the equation true?
a. 10^2
b. 10^3
c. 10^4
d. 10^5
Answer
I think you meant to wtite
80.4/d = 0.0804
the answer is d = 1000 or 10^3
Step-by-step explanation:
Paul is 14 years old.
His sister is exactly 6 years younger, so this year she is 8 years old.
This year, the ratio of Paul’s age to his sister’s age is 14 : 8
14 : 8 written as simply as possible is 7 : 4
When Paul is 21, what will be the ratio of Paul’s age to his sister’s age?
Write the ratio as simply as possible.
Answer:
ratio = 21:15
Step-by-step explanation:
Paul's sister is 6 years younger than Paul so that means if Paul is 21, 21 - 6 = 15. Your new ratio would be 21:15
21:15 written as simply as possible is 10.5:7.5 or 11:8
I'm sorry if you get it wrong :(
Answer:
7:6 I believe is it's simplest form
How do I find the surface area of a composite figure? I've been struggling at this and it's been really hard on me and has also made me very upset. I use a schooling program called acellus and it doesn't really explain this stuff too well.
An easy way to find the surface area of a composite figure is to divide the composite figure up into smaller shapes whose area it is easier to find. It is best to divide a composite figure up into a figure composed of many triangles and rectangles. Then, one will find the area of each of these smaller figures and add the value up to find the total surface area of the composite figure.
solve the following equation
Hi,
x² + 8x + 12 = 0
a= 1 ; b= 8 c= 12
∆ = b² - 4ac
∆ = 8² - 4*1*12
∆ = 64 - 4*12
∆ = 64 - 48
∆ = 16
∆>0 :
x1 = (-b-√∆)/2a = (-8-4)/2 = -12/2 = -6
x2 = (-b+√∆)/2a = (-8+4)/2 = -4/2 = -2
S= { -6 ; -2 }
x = -6
or x = -2
✅(•‿•)
Answer:
x = -6 x = -2Step-by-step explanation:
x² + 8x + 12 = 0
➺ x² + 2x + 6x = 0
➺ x(x + 2) + 6(x + 2) =0
➺ (x + 6)(x + 2) = 0
Whether, x + 6 = 0
⠀⠀⠀⠀⠀➺ x = -6
⠀⠀or,⠀⠀⠀⠀ x + 2 = 0
⠀⠀⠀⠀⠀⠀➺ x = -2