For the inequality root(2x + 5) ≤ 7, the solution is x ≤ 24/2 or x ≤ 12.
To solve the inequality root(2x + 5) ≤ 7, we can square both sides of the inequality to eliminate the square root. However, we need to be careful because squaring can introduce extraneous solutions.
Squaring both sides, we have:
2x + 5 ≤ 49
Subtracting 5 from both sides, we get:
2x ≤ 44
Dividing both sides by 2, we find:
x ≤ 22
However, we also need to consider the restriction of the square root function, which states that the radicand (2x + 5) must be non-negative. Setting 2x + 5 ≥ 0, we find x ≥ -2.5.
Combining these conditions, the solution to the inequality is x ≤ 12.
3] For the inequality root(2x - 1) > root(3 - x), there is no solution.
To solve the inequality root(2x - 1) > root(3 - x), we can square both sides of the inequality. However, we need to be cautious because squaring can introduce extraneous solutions.
Squaring both sides, we have:
2x - 1 > 3 - x
Combining like terms, we get:
3x > 4
Dividing both sides by 3, we find:
x > 4/3
However, we also need to consider the restriction of the square root function, which states that the radicand (2x - 1) and (3 - x) must be non-negative. Setting 2x - 1 ≥ 0 and 3 - x ≥ 0, we find x ≥ 1/2 and x ≤ 3.
Combining these conditions, we see that there is no solution that satisfies both the inequality and the restrictions.
4] For the inequality root(3x - 2) < x, the solution is x > 2.
To solve the inequality root(3x - 2) < x, we can square both sides of the inequality. However, we need to be cautious because squaring can introduce extraneous solutions.
Squaring both sides, we have:
3x - 2 < x^2
Rearranging the terms, we get:
x^2 - 3x + 2 > 0
Factoring the quadratic equation, we have:
(x - 1)(x - 2) > 0
To determine the sign of the expression, we can use the concept of intervals. We analyze the sign changes and find that the solution is x > 2.
5] For the inequality root(5x + 6) > x, the solution is x < 6.
To solve the inequality root(5x + 6) > x, we can square both sides of the inequality. However, we need to be cautious because squaring can introduce extraneous solutions.
Squaring both sides, we have:
5x + 6 > x^2
Rearranging the terms, we get:
x^2 - 5x - 6 < 0
Factoring the quadratic equation, we have:
(x - 6)(x + 1) < 0
To determine the sign of the expression, we can use the concept of intervals. We analyze the sign changes and find that the solution is x < 6.
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Find the distance between the points (–7,–9) and (–2,4).
Answer:
√194 or 13.9
Step-by-step explanation:
√(x2 - x1)² + (y2 - y1)²
√[-2 - (-7)² + [4 - (-9)]
√(5)² + (13)²
√25 + 169
√194
= 13.9
approximately what interest rate to the nearest whole percentage would you need to earn in order to turn $3,500 into $7,000 over 10 years?
a. 5%
b. 7%
c. 9%
d. 10%
The approximate interest rate needed to turn $3,500 into $7,000 over 10 years is 9%. Correct answer is C.
The value of money increases over time with the help of compounding interest. If one puts in a principal amount in an account, the amount will increase over time as interest accrues. Let's use the future value formula for the calculation. Let’s assume that the interest rate needed to turn $3,500 into $7,000 over 10 years is x percent. P = $3,500 (principal)FV = $7,000 (future value)
N = 10 years (duration of the investment)Using the future value formula:
FV = P(1 + r/n)^(nt)where, r is the annual interest rate, n is the number of times the interest is compounded in a year, and t is the duration of the investment in years.
Substituting the given values, we have: $7,000 = $3,500(1 + x/n)^(n × 10)We can solve for x by approximating the interest rate using each of the answer options given in the question until we find an answer that is close to $7,000. A calculator can also be used to calculate the compound interest for each option. If the interest rate is 7%, then the interest is compounded annually. Therefore, n = 1$7,000
= $3,500(1 + 0.07/1)^(1 × 10) If the interest rate is 10%, then the interest is compounded annually.
Therefore, n = 1$7,000 = $3,500(1 + 0.1/1)^(1 × 10)Thus, x ≈ 9.57%, greater than the required amount.
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Rationalise √2+√3/3√2-2√3=a-b√6
Answer: 3√6-6/6 + √2=a-b√6
Step-by-step explanation: multiply radicals in the denominator by conjugate to get (a+b)(a-b)=a^2-B^2 pattern.
MSL7
Dificuit Dimensions
A tool box has the dimensions of 8 in by 7 in by 4 in. If Jacob plans to double all three
dimensions to build a larger tool box, he believes he would double the volume of the tool box,
Is he correct?
A drawbridge has the shape of an isosceles trapezoid. The entire length of the bridge is 100 feet while the height is 25 feet. If the angle at which the bridge meets the land is approximately 60 degrees, how long is the part of the bridge that opens?
Answer:
The part of the bridge that opens is 50 ft.
Step-by-step explanation:
The given parameters of the drawbridge are;
The entire length of the bridge = 100 feet
The height of the isosceles trapezoid formed = 25 feet
The angle at which the drawbridge meets the land ≈ 60°
Therefore, the part of the bridge that opens = The top narrow parallel side of the isosceles trapezoid
The length of each half of the bridge = (The entire length)/2 = 100 ft./2 = 50 ft.
Let 'x' represent the path of the waterway still partly blocked by each half of the bridge inclined
∴ x = 50 × cos(60°) = 25
x = 25 ft.
The path covered by both sides of the drawbridge = 2·x = 2 × 25 ft. = 50 ft.
The part of the bridge that opens = The entire length - 2·x
∴ The part of the bridge that opens = 100 ft. - 50 ft. = 50 ft.
The part of the bridge that opens = 50 ft.
Jenica bowls three games and scores an average of 116 points per game. She scores 105 on her first game and 128 on her second game. What does she need to score on her third game to get a mean score of ?
Answer:
230
Step-by-step explanation:230
A car drove 5 miles in 30 minutes. How far will the car go in 1 hour?
Answer: 10 miles
Step-by-step explanation:
Practically, just look at it. 30 minutes = 5 miles, 60 minutes = 10 miles
Mathmatically, find the constant of proportionality.
30 minutes divided by 5 miles = 6 minutes per 1 mile. 60 minutes = 10 miles
What does the C equal to in -1/6 +7/6 = c
Answer:
c = 1
Step-by-step explanation:
we have -1/6 + 7/6
since 6 is a common denominator we can do
[tex]\frac{-1}{6} +\frac{7}{6} = c\\\frac{-1+7}{6} = c\\\frac{6}{6} = c\\1 = c\\c = 1[/tex]
Helppppp it’s due today
What is the perimeter of thjs
Answer:73 ft
Step-by-step explanation:
Answer:
(120 + 12.5pi) ft^2
Step-by-step explanation:
10ft x 12 ft = 120ft^2
10ft/2 = 5 ft (Radius)
Area of semi circle:
[tex]\frac{\pi r^{2} }{2} = \frac{\pi 5^{2} }{2} = 12.5\pi ft^{2}[/tex]
Area = (120 + 12.5pi) ft^2
Which expression represents the length of the spring after Gerard removes some weight? Gerard adds weight to the end of the hanging spring D-- The song stretches to a length of p centimeters. Gerard removes some weight and the song moves up by a 8 E-p) - 9 D-9--
Answer: p+(-q)
Step-by-step explanation:
You roll a single 6 sided die. What are the odds of rolling a 9?
A. 1/6
B. 0
C. 1/9
D. 9
Answer:
B. 0
Step-by-step explanation:
There aren't enough sides for you to roll a nine
what is the inverses operation needed to solve for P?
800=p-275
A subtraction
B addition
C multiplication
D division ill mark brainlist
Just give me some ideas for this please.
Using what you know about fair and unfair games, as well as expected value, design a game that will be fair to both you and the player. Be creative in your design, trying not to mimic anything that you have already seen in this course or in searching the internet. Include a thorough description as well as a visual representation of the game that includes evidence of fairness.
Answer:
For game ideas, try to make a game that everyone will want to play. Make it fun, challenging, but still beatable, but not too easy. One thing you could do is a trivia game! With lots of different subjects so people can choose what they get questions about. Also, do a lot of research to get the questions! Hope this helped :)
Step-by-step explanation:
Answer:
KING OF QUESTIONS!!!
Step-by-step explanation:
Each player starts out with 10 tokens ( tokens can be anything I recommend spare change or coins. ) the tokens will be used as point tallies at the end of the game. But to determine who goes first the question master asks a question from the starting deck( The easiest questions) and starting with player one the players answer and whoever answers with the correct answer will go first, the other players will form an orderly line from closest to the correct answer to farthest. ( If there are more than 1 successful answers you pull another card from the next deck. This is an increase in difficulty. And it will keep increasing until there is one person with the correct or closest answer or until they reach the end of the final deck. Remember that this event is highly unlikely) After this is done the game begins. The question master asks a question the players will answer. The players that get it correct will receive 2 token. The players that do not but are close get 1 and the player to get the farthest from the correct answer loses 1 token. ( Tokens are worth 1 point.)
Roles:
Player 1 ( Answers the questions.)
Player 2 ( Answers the questions.)
Player 3 ( Answers the questions.)
Player 4 ( Answers the questions.)
Question Master & Token Master ( Asks the questions and gives the token to the correct answer. )
How to Win:
Quick Match- Play until a player reaches 30 tokens.
Long Match- Play until all but one player is eliminated.
Ways to Lose- If a player loses all of there tokens or is cheating they are eliminated, this happens only when the player is caught cheating or stealing tokens from other players or when the player loses all of these tokens due to incorrect answers.
Somebody know this? thanks
Answer:
4 right angles
Step-by-step explanation:
a straight light intersects another straight line= creating 4 right angles
please help 6th grade math please please help
i: 1
ii: 6
iii: 3
iv: 2
v: 4.5
vi: 2.5
The diameter of a circle is 6 kilometers. What is the area?
d=6 km
Give the exact answer in simplest form.
_____ square kilometers
Answer:
28.26
Step-by-step explanation:
6 divided by 2 = 3^2 = 9 x 3.14 = 28.26
A radius is
the diameter
Answer:
Radius is the diameter divided by 2
I dont know how to do this
Answer:
a) 55°
b) 125°
c) 55°
d) 55°
Step-by-step explanation:
a) 180-(90+35) = 55
b) this angle forms a straight angle with ∡a
c) this angle is vertical, and congruent, with ∡a
d) 180-(70+55) = 55
Use The Figure Below to Solve For x.
Answer:
x=-1
Step-by-step explanation:
Hello there!
The information we are given:
We are told that the distance from point a to c is x + 10
We are told that the distance from a to b is 5
we are also told that the distance from b to c is 2x+6
Because from point A to B and B to C is inside the total of A to C we can add the two together and create a equation to solve for x
so the sum of the two parts 5 + 2x + 6
*combine like terms*
11 + 2x
is equal to the total distance (x+10)
now we solve for x
11 + 2x = x + 10
step 1 subtract x from each side by
2x - x = x
x -x cancels out
now we have 11 + x = 10
step 2 subtract 11 from each side
11-11 cancels out
10 - 11 = -1
we're left with x = -1
Now lets plug in x and see if A to C is equal to A to B + B to C
(-1) + 10 = 5 + 2(-1) + 6
10 - 1= 9
2*-1=-2
6-2=4
4+5=9
9=9
which is true so we can conclude that x = -1
Draw a two-dimensional representation of each prism. Then find the area of the entire surface of each prism
Answer:
Surface area of cuboid = 78 unit²
Step-by-step explanation:
Given diagram is a cuboid prism
Given:
Length of cuboid = 5 unit
Width of cuboid = 3 unit
Height of cuboid = 3 unit
Find:
Surface area of cuboid
Computation:
Surface area of cuboid = 2[lb + bh + hl]
Surface area of cuboid = 2[(5)(3) + (3)(3) + (3)(5)]
Surface area of cuboid = 2[15 + 9 + 15]
Surface area of cuboid = 2[39]
Surface area of cuboid = 78 unit²
I really need help!!!!!!
Answer:
y = 1.50x + 4 ;
Step-by-step explanation:
Given that bike rental cost $4 plus $1.50 per hour
From the information given, the change in y per unit change in x is the value of the slope ;
Therefore, Given that total cost = y and x) number of hours
Change in cost per change in number of hours) 1.50 = slope ; intercept = constant = $4
The equation, in slope intercept form :
y = mx + c
y = 1.50x + 4
Calculate the 90% confidence interval for the following sample Sample: 7.9, 8.3, 8.4, 9.6, 7.7, 8.1, 6.8, 7.5, 8.6, 8, 7.8,7.4, 8.4, 8.9, 8.5, 9.4, 6.9,7.7. Assume normality of the data.
The 90% confidence interval for the given sample is (7.58, 8.60).
To calculate the 90% confidence interval for the given sample assuming normality of the data, we need to use the formula as follows;Confidence interval = X ± Z α/2(σ/√n)Where, X is the sample meanZ α/2 is the Z-score for the desired level of confidenceσ is the population standard deviationn is the sample sizeFirst, we need to calculate the sample mean and standard deviation.Sample mean,
X= (7.9 + 8.3 + 8.4 + 9.6 + 7.7 + 8.1 + 6.8 + 7.5 + 8.6 + 8 + 7.8 + 7.4 + 8.4 + 8.9 + 8.5 + 9.4 + 6.9 + 7.7) / 18
= 8.09
Sample standard deviation,
σ = √[Σ(xi - X)² / (n - 1)]σ = √[(7.9 - 8.09)² + (8.3 - 8.09)² + (8.4 - 8.09)² + (9.6 - 8.09)² + (7.7 - 8.09)² + (8.1 - 8.09)² + (6.8 - 8.09)² + (7.5 - 8.09)² + (8.6 - 8.09)² + (8 - 8.09)² + (7.8 - 8.09)² + (7.4 - 8.09)² + (8.4 - 8.09)² + (8.9 - 8.09)² + (8.5 - 8.09)² + (9.4 - 8.09)² + (6.9 - 8.09)² + (7.7 - 8.09)² / (18 - 1)]σ = 0.761
Now, we need to find the Z α/2 value from the standard normal distribution table.
Z α/2 = 1.645 (for 90% confidence level)Putting the values in the formula,Confidence interval =
X ± Z α/2(σ/√n)
= 8.09 ± 1.645(0.761/√18)
= 8.09 ± 0.511
= (8.09 - 0.511, 8.09 + 0.511)
= (7.58, 8.60).
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Solve the following ordinary differential equations using Laplace trans- forms: (a) y(t) + y(t) +3y(t) = 0; y(0) = 1, y(0) = 2 (b) y(t) - 2y(t) + 4y(t) = 0; y(0) = 1, y(0) = 2 (c) y(t) + y(t) = sint; y(0) = 1, y(0) = 2 (d) y(t) +3y(t) = sint; y(0) = 1, y(0) = 2 (e) y(t) + 2y(t) = e';y(0) = 1, y(0) = 2
(a) The ordinary differential equation is given by y(t) + y(t) + 3y(t) = 0. Using Laplace transform, we have(L [y(t)] + L [y(t)] + 3L [y(t)]) = 0L [y(t)] (s + 1) + L [y(t)] (s + 1) + 3L [y(t)] = 0L [y(t)] (s + 1) = - 3L [y(t)]L [y(t)] = - 3L [y(t)] /(s + 1)Taking the inverse Laplace of both sides, we have y(t) = L -1 [- 3L [y(t)] /(s + 1)]y(t) = - 3L -1 [L [y(t)] /(s + 1)]
On comparison, we get y(t) = 3e^{-t} - 2e^{-3t}.The initial conditions are y(0) = 1 and y(0) = 2 respectively.(b) The ordinary differential equation is given by y(t) - 2y(t) + 4y(t) = 0. Using Laplace transform, we have L [y(t)] - 2L [y(t)] + 4L [y(t)] = 0L [y(t)] = 0/(s - 2) + (- 4)/(s - 2)
Taking the inverse Laplace of both sides, we have y(t) = L -1 [0/(s - 2) - 4/(s - 2)]y(t) = 4e^{2t}.The initial conditions are y(0) = 1 and y(0) = 2 respectively.(c) The ordinary differential equation is given by y(t) + y(t) = sint. Using Laplace transform, we have L [y(t)] + L [y(t)] = L [sint]L [y(t)] = L [sint]/(s + 1)
Taking the inverse Laplace of both sides, we have y(t) = L -1 [L [sint]/(s + 1)]y(t) = sin(t) - e^{-t}.The initial conditions are y(0) = 1 and y(0) = 2 respectively.(d) The ordinary differential equation is given by y(t) + 3y(t) = sint. Using Laplace transform, we have L [y(t)] + 3L [y(t)] = L [sint]L [y(t)] = L [sint]/(s + 3)Taking the inverse Laplace of both sides, we have y(t) = L -1 [L [sint]/(s + 3)]y(t) = (1/10)(sin(t) - 3cos(t)) - (1/10)e^{-3t}.
The initial conditions are y(0) = 1 and y(0) = 2 respectively.(e) The ordinary differential equation is given by y(t) + 2y(t) = e^{t}. Using Laplace transform, we have L [y(t)] + 2L [y(t)] = L [e^{t}]L [y(t)] = 1/(s + 2)Taking the inverse Laplace of both sides, we havey(t) = L -1 [1/(s + 2)]y(t) = e^{-2t}The initial conditions are y(0) = 1 and y(0) = 2 respectively.
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Find the area of the parallelogram
Height=4cm
Base=5cm
Answer:
The area of the parallelogram is 20cm²
Answer:
A = 20 cm²
Step-by-step explanation:
The area (A) of a parallelogram is calculated as
A = bh ( b is the base and h the height ) , then
A = 5 × 4 = 20 cm²
1. Find the solution to the recurrence relation an = 3an-1 + 4an-2 with initial values ao = 2 and a₁ = 3.
The solution to the recurrence relation an = 3an-1 + 4an-2 with initial values ao = 2 and a₁ = 3 is given byan = (-1)4ⁿ - 4(4)ⁿ-¹/16
Given recurrence relation is an = 3an-1 + 4an-2, with initial values ao = 2 and a₁ = 3.
The characteristic equation of the recurrence relation is given byr² - 3r - 4 = 0
Solving the characteristic equation, we get
r² - 4r + r - 4 = 0
r(r - 4) + 1(r - 4) = 0
(r - 4)(r + 1) = 0
r1 = 4, r2 = -1
So, the general solution of the recurrence relation is given by
an = Ar¹ + Br²
For r1 = 4, a4 = 3
a3 + 4a2a4 = 3a3 + 4a2 = 3(4a2 + 4a1) + 4a2= 16a2 + 12a1 ....(1)
For r2 = -1, aₙ₊₁ = 3an + 4an-1aₙ₊₁ = 3an + 4an-1 = 3(A(-1)^n + B(4)^n) + 4(A(-1)^(n-1) + B(4)^(n-1))= 3A(-1)^n - 4A(-1)^(n-1) + 12B(4)^n + 4B(4)^(n-1)= A(-1)^n + 4B(4)^n ....(2)
Putting n = 0 in (2), we get
a1 = A - 4A = -3A = 3 => A = -1
Substituting A = -1 in (1), we get
a4 = 16a2 + 12a1=> a4 = 16a2 + 12(2) => a4 = 16a2 + 24a4 = 16a2 + 24 => a2 = (a4 - 24)/16
Thus the solution to the recurrence relation an = 3an-1 + 4an-2 with initial values ao = 2 and a₁ = 3 is given by
an = (-1)4ⁿ - 4(4)ⁿ-¹/16
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Verify the following properties of the Fourier transform = 1. (Fu)(E) = 27 (F-1u)(-5) 2. (F (eiat u)) (E) = (Fu)(8 + a)
The first property states that the Fourier transform of a function evaluated at a certain frequency is equal to 2π times the inverse Fourier transform of the function evaluated at the negative of that frequency.
The second property states that the Fourier transform of a modulated function is equal to the Fourier transform of the original function shifted by the modulation frequency.
To verify the given properties of the Fourier transform, we can use the definitions and properties of the Fourier transform. Here's how we can verify each property:
1. Property: (Fu)(ω) = 2π (F^-1u)(-ω)
To verify this property, we need to use the definitions of the Fourier transform and its inverse. Let's denote the Fourier transform operator as F and its inverse as F^-1.
According to the definition of the Fourier transform, for a function u(t), its Fourier transform is given by:
(Fu)(ω) = ∫[from -∞ to ∞] u(t) e^(-iωt) dt
Similarly, the inverse Fourier transform of a function U(ω) is given by:
(F^-1U)(t) = (1/2π) ∫[from -∞ to ∞] U(ω) e^(iωt) dω
Now, let's substitute -ω for ω in the inverse Fourier transform:
(F^-1u)(-ω) = (1/2π) ∫[from -∞ to ∞] u(t) e^(i(-ω)t) dt
= (1/2π) ∫[from -∞ to ∞] u(t) e^(iωt) dt
Comparing this with the Fourier transform, we see that (F^-1u)(-ω) is equal to (Fu)(ω) multiplied by 2π, which verifies the first property.
2. Property: (F(e^(iat)u))(ω) = (Fu)(ω + a)
To verify this property, we use the modulation property of the Fourier transform. According to this property, if u(t) has a Fourier transform U(ω), then the Fourier transform of e^(iat)u(t) is given by:
(F(e^(iat)u))(ω) = (Fu)(ω + a)
Applying this property to the given expression, we have:
(F(e^(iat)u))(ω) = (Fu)(ω + a)
This verifies the second property.
In summary, we have verified both properties of the Fourier transform as stated.
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the circumference of a circle is 64π. what is the radius of the circle?
The radius of the circle can be found by dividing the circumference by 2π. In this case, the radius is 32.
The formula for the circumference of a circle is given by C = 2πr, where C is the circumference and r is the radius. We are given that the circumference is 64π.
To find the radius, we can rearrange the formula as r = C / (2π). Substituting the given value of the circumference, we have r = 64π / (2π) = 32.
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Two ordinary dice are thrown simultaneously. Determine the n
of throws necessary to obtain at least once with probability 0.49.
at least once the pair (6;6)
Two ordinary dice are thrown simultaneously. Determine the number of throws necessary to obtain at least once with probability 0.49 at least once the pair (6,6).
Solution: The probability of getting a pair of 6s in a single throw is 1/36.The probability of not getting a pair of 6s in a single throw is 1 - 1/36 = 35/36.
The probability of not getting a pair of 6s in n throws is (35/36)^n.
The probability of getting a pair of 6s in n throws is 1 - (35/36)^n.
So, for at least one pair of 6s with probability 0.49 in n throws, we have:
1 - (35/36)^n = 0.49⇒ (35/36)^n = 0.51⇒ n ln (35/36) = ln 0.51⇒ n = ln 0.51/ln (35/36) = 72.5 ~ 73So, at least 73 throws are necessary to obtain at least once with probability 0.49 at least once the pair (6,6).
Answer: At least 73 throws are necessary to obtain at least once with probability 0.49 at least once the pair (6,6).
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The perimeter of a piece of paper is 38 inches. Its length is 11 inches.
Find the area of the piece of paper.
Answer:
Buddy this might not be the correct answer but I got either 98 or 418 inches. Don't quote me on it though.
Step-by-step explanation: