(2/√3) can be rationalized by multiplying both the numerator and the denominator by √3 to get (2√3/3) .
What is mean by Square root and how to find it ?The square root is the value that gives a prime number multiplied by itself. Four methods can be used to find the square root: prime factorization, repeated subtraction, long division, and the evaluation method.
In geometry, we often encounter the square root when calculating the size of shapes, such as the length, area or volume of certain geometric shapes. Simplifying square roots can make calculations much easier and more efficient.
Here are some rules for simplifying square roots:
Simplify perfect squares under the radical sign: For example, √9 = 3 and √25 = 5. Multiplying or dividing a number outside the radical sign: For example, 2√3 can be simplified to √12. Adding or subtracting like terms: For example, 3√2 2√2 = 5√2.
You can rationalize the denominator by multiplying the numerator and denominator by the conjugate of the denominator: For example, (2/√3) can be rationalized by multiplying both the numerator and the denominator by √3 to get (2√3/3) .
Applying these rules, we can simplify the square root and make calculations easier and more accurate in geometric problems..
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A soccer ball is kicked in the air off a 27.0-meter high hill. The equation h(t) = -2t^2 + 4t + 27 gives the approximate height h, in meters, of the ball t in seconds after it is kicked. Does the ball reach a height of 40 m?
The ball reaches a height of 40 meters at approximately 3.38 seconds after it is kicked.
To determine if the ball reaches a height of 40 meters, we can substitute h(t) = 40 into the equation and solve for t.
40 = -2t² + 4t + 27
Rearranging the terms, we get:
2t² - 4t - 13 = 0
We can solve for t using the quadratic formula:
t = [4 ± √(4² - 4(2)(-13))]/(2(2))
t = [4 ± √(176)]/4
t ≈ 3.38 or t ≈ -0.88
Since time cannot be negative, we can discard the negative solution. Therefore, the ball reaches a height of 40 meters at approximately 3.38 seconds after it is kicked.
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(A) 0
(B) 1
2
(D) 3
Si un garçon peut courir une distance de 10 mètres pendant qu'une voiture en parcourt
0, combien de mètres le garçon pourra-t-il courir pendant que la voiture parcourt 66 mètres?
(A) 12
(B) 90
(C) 22
(D) 25
10 x = 30
Une équipe d'ouvriers fabriquaient 1,000 uniformes par semaine. La production ayar
té augmentée de 20%, chaque ouvrier se vit obligé de confectionner 50 uniformes de plus
Combien y avait-il d'ouvriers dans cette équipe?
(A) 4
(B) 15
(C) 20
110
(D) 24
2x+15-8=14
find the value of x
Answer:
x = 3.5
Step-by-step explanation:
Isolate the variable, x. Note the equal sign, what you do to one side, you do to the other. Do the opposite of PEMDAS. PEMDAS is the order of operations, and stands for:
Parenthesis
Exponents (& Roots)
Multiplications
Divisions
Additions
Subtractions
~
First, simplify. Combine like terms. Like terms are terms that share the same amount of the same variables:
[tex]2x + 15 - 8 = 14\\2x + (15 - 8) = 14\\2x + (7) = 14[/tex]
Next, isolate the variable, x. First, subtract 7 from both sides of the equation:
[tex]2x + 7 = 14\\2x + 7 (-7) = 14 (-7)\\2x = 14 - 7\\2x = 7[/tex]
Finally, divide 2 from both sides of the equation:
[tex]2x = 7\\\frac{(2x)}{2} = \frac{(7)}{2}\\ x = \frac{7}{2}\\ x = 3.5[/tex]
x = 3.5 is your answer.
~
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Answer:
[tex]\bold{\Large \boxed{x=\frac{7}{2}}}[/tex]
Step-by-step explanation:
To solve the equation [tex] 2x+15-8=14 [/tex] for x, we need to isolate x on one side of the equation.
We can do this by first combining the constants on the right-hand side of the equation:
[tex]2x+15-8=14[/tex]
[tex]2x+7=14[/tex]
Next, we can isolate x by subtracting 7 from both sides of the equation:
[tex]2x=7[/tex]
Finally, we can solve for x by dividing both sides of the equation by 2:
[tex]x=\frac{7}{2}[/tex]
Therefore, the solution to the equation [tex]2x+15-8=14[/tex] is [tex]\bold{x=\frac{7}{2}}[/tex].
The sound wave of two music notes can be represented by the function y = 2sin2x and y = sin x, where x represents the time since the note is played. At what times will the frequencies of the sound waves be the same in the interval [0°, 360°)?
Group of answer choices
x = 0°, 30°, 150°, 180°
x = 0°, 180°, 210°, 330°
x = 30°, 90°, 150°, 270°
x = 90°, 210°, 270°, 330°
The correct answer is:
x = 0°, 30°, 150°, 180°
This is because the sine function equals 0 at 0° and 180° and equals 1/2 at 30° and 150°.
How to solveFor the frequencies to be the same, we need to find values of n and m such that:
n = m
Solving for n and m, we get:
n = m = 2
So both functions complete two cycles in the interval [0, 2π).
We can find the times when this occurs by setting the angles in radians equal to multiples of 2π/2, or π:
2sin2x = sin x
2sin2x - sin x = 0
sin x (2sin x - 1) = 0
sin x = 0 or 2sin x - 1 = 0
sin x = 0 when x is an integer multiple of π.
2sin x - 1 = 0 when sin x = 1/2, which occurs when x = π/6 or x = 5π/6.
Therefore, the frequencies of the sound waves are the same at x = π/6, x = π/2, x = 5π/6, and x = 3π/2.
The correct answer is:
x = 0°, 30°, 150°, 180°
This is because the sine function equals 0 at 0° and 180° and equals 1/2 at 30° and 150°.
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NEED HELP FOR MATH HW! I need some help number 3 WITHOUT the use of a t1-83
Step-by-step explanation:
Here is a graph from Desmos....you should be able to see where the function is > 0
Help me please, this assignment is alr past due
Answer:
Step-by-step explanation:
However many decimals you move to get 1 after the first number that is not 0 is what goes in the exponent. Negative version because to get to a decimal you move in the negative direction.
.1 = 1.0 x [tex]10^{-1}[/tex]
.01 = 1.0 x [tex]10^{-2}[/tex]
.001 = 1.0 x [tex]10^{-3}[/tex]
.000001 =,1.0 x [tex]10^{-6}[/tex]
Find the equation of the quadratic function g whose graph is shown below.
The equation of the quadratic function g whose graph is shown above is g(x) = -(x + 4)² - 4
How to determine the factored form of a quadratic equation?In Mathematics, the vertex form of a quadratic function is represented by the following mathematical equation:
f(x) = a(x - h)² + k
Where:
h and k represents the vertex of the graph.a represents the leading coefficient.Based on the information provided about the vertex and other points, we can determine the value of a as follows:
g(x) = a(x - h)² + k
-13 = a(-7 + 4)² - 4
-13 = a(-3)² - 4
-13 + 4 = 9a
-9 = 9a
a = -1.
Therefore, the required quadratic function is given by:
g(x) = a(x - h)² + k
g(x) = y = -(x + 4)² - 4
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The company performed another experiment in which they tested three website designs to see which one would lead to the highest probability of a purchase. The first (design A) used enhanced product information, the second (design B) used extensive iconography, and the third (design C) allowed the customer to submit their own product ratings. After 6 weeks of testing, the designs delivered probabilities of purchase of 4.5%, 5.2%, and 3.8% respectively. Equal numbers of customers were sent randomly to each website design. what is the probability that a customer who visited made a purchase?
The probability that a customer who visited any of the three website designs made a purchase is 4.5%.
To find the probability that a customer who visited any of the three website designs made a purchase, we need to find the average probability of purchase across all three designs.
We can do this by taking the mean of the three probabilities:
Mean probability = (4.5% + 5.2% + 3.8%) / 3
= 13.5% / 3
= 4.5%
This assumes that the customers were randomly assigned to each design and that there were no other factors that may have influenced their purchasing behavior. Additionally, the sample size and duration of the experiment may also affect the accuracy of the results.
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A surfer recorded the following values for how far the tide rose, in feet, up the beach over a 15-day period. 5, 6, 7, 8, 9, 11, 12, 13, 14, 15, 16, 21, 22, 23, 24 Which of the following histograms best represents the data collected?
Jeff is buying tickets for a group of concerts. He wants tickets for at least 8 concerts. Each ticket for an afternoon concert costs $15 and each ticket for an evening concert costs $30. Jeff wants to spend no more than $300.
Which system of inequalities can Jeff use to find the number of tickets he can buy?
A. x + y ≥ 8 and 300 ≥ 15x + 30y
B. x + y ≤ 8 and 300 ≥ 15x + 30y
C. x + y ≥ 300 and 8 ≥ 15x + 30y
D. x + y ≤ 300 and 8 ≤ 15x + 30y
Answer:
(A.)
Step-by-step explanation:
you just have to follow the order that there going in so when they say less than you use the less than sign
A container built for transatlantic shipping is constructed in the shape of a right rectangular prism. Its dimensions are 4.5 ft by 11.5 ft by 10.5 ft. The container is entirely full. If, on average, its contents weigh 0.4 pounds per cubic foot, and, on average, the contents are worth $4.60 per pound, find the value of the container’s contents. Round your answer to the nearest cent.
The value of the container's contents is approximately $983.25
What is the value of the container's contents?To find value of the contents, we must calculate its volume first.
Volume = length x width x height
Volume = 4.5 ft x 11.5 ft x 10.5 ft
Volume = 534.375 cubic feet
The container is full and its contents have a volume of 534.375 cubic feet. If its contents weigh 0.4 pounds per cubic, then, total weight of the contents is:
= Volume x Weight per cubic foot
= 534.375 cubic feet x 0.4 pounds per cubic foot
= 213.75 pounds
If the contents are worth $4.60 per pound on average, then the total value of the contents is:
= Weight x Value per pound
= 213.75 pounds x $4.60 per pound
= $983.25.
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The electrical signal created by a piece of test equipment at a specific point in time is described by the function v inst(t)=12xsin(360x60x6.3+79). What is the maximum voltage produced by the system?
The maximum voltage produced by the system is 12 volts.
The function given is:
[tex]v_{inst}(t) = 12 * sin(360 * 60 * 6.3 + 79)[/tex]
To find the maximum voltage produced by the system, we need to determine the maximum value of the sine function within the given range.
Let's focus on the argument of the sine function: 360 * 60 * 6.3 + 79.
First, calculate the value of the argument:
360 * 60 * 6.3 + 79 = 136080 + 79 = 136159
Now, substitute this value back into the sine function:
sin(136159)
The sine function has a periodicity of 360 degrees or [tex]2\pi[/tex] radians. Therefore, we can subtract multiples of 360 degrees from the argument without changing the value of the sine function. Let's find the nearest multiple of 360 degrees to 136159:
136159 ÷ 360 [tex]^\sim_\sim[/tex] 378.22
Since the quotient is not an integer, we can conclude that subtracting multiples of 360 degrees will not bring us closer to a maximum or minimum value of the sine function.
Therefore, to find the maximum voltage, we need to evaluate sin(136159) directly. However, calculating the sine function of such a large number is not practical or necessary. The sine function oscillates between -1 and 1, and the maximum value it can reach is 1.
So, regardless of the specific value of sin(136159), the maximum voltage produced by the system will be:
Maximum voltage = 12 * 1 = 12 volts.
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There are 15 tables at a wedding reception,
5 of which have purple centerpieces.
1) What is the probability that a randomly
selected table will have a purple centerpiece?
◄) Write your answer as a fraction or whole
number.
Answer:
1/3
Step-by-step explanation:
There are 15 tables and 5 have a purple centerpiece. Divide 15 by 5 to get the probability of a randomly selected table being purple.
5/15 is 5 out of 15. 5/15 simplifies to 1/3.
Riley runs a stable that boards a range of horses.
white 3
bay 2
palomino 9
black 1
Considering this data, how many of the next 20 horses that come to board should you expect to be white horses?
_____ white horses
Since there are 3 white horses in a total of 15 horses, the ratio of white horses, to the total number of horses are 1 : 5 So for 20 total number of horses, the number of white horses should be 4. The ratio of white horses to the total number of horses is 4 : 20 which is 1: 5
Therefore, 4 of the next 20 horses that come to board should you expect to be white horses
What are the values of x and y?
X=
Y=
Answer:
X = 6
Y = 17
Step-by-step explanation:
The points GHIJ for a cyclic quadrilateral.
The sum of opposite angles of a cyclic quadrilateral is 180°
So
∠J + ∠H = 180°
⇒ 6y + 78° = 180°
⇒ 6y = 180° - 78°
⇒ 6y = 102°
⇒ y = 102°/6
⇒ y = 17°
Similarly for angle x
∠I + ∠G = 180°
⇒ 16x + 14x = 180°
⇒ 30x = 180°
⇒ x = 180°/30
⇒ x = 6°
A clock pendulum swings back and forth once every two seconds. If its length is one meter and the greatest
angle that it makes with the vertical is 12 degrees, how many kilometers does the bottom end of the pendulum travel in
one day?
The bottom end of the pendulum travels 18,115.2 meters/day, which is approximately 18.12 kilometers/day (since 1 kilometer = 1000 meters).
The motion of the pendulum is a simple harmonic motion and the period of oscillation can be calculated as follows:
T = 2π√(l/g)
where l is the length of the pendulum and g is the acceleration due to gravity (approx. 9.81 m/s²).
Substituting l = 1 m, we get
T = 2π√(1/9.81)
T ≈ 2.006 s.
In one day, there are
24 hours x 60 minutes/hour x 60 seconds/minute
= 86,400 seconds.
The pendulum makes half a period (i.e., one back-and-forth swing) in 2/2 = 1 second. Therefore, it makes
86,400/2
= 43,200 back-and-forth swings in one day.
The distance traveled by the bottom end of the pendulum in one complete swing is equal to the length of the pendulum times twice the maximum angle it makes with the vertical, which is
2 x 12 degrees
= 24 degrees
= 0.419 radians.
Therefore, the distance traveled by the bottom end of the pendulum in one complete swing is
1 meter x 0.419
= 0.419 meters.
Multiplying by the number of swings in one day, we get:
0.419 meters/swing x 43,200 swings/day
= 18,115.2 meters/day.
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need help asap
How many square feet of outdoor carpet will
we need for this hole?
3 ft
2 ft
12 ft
,1 ft
2 ft
ft²
The area needed for the green region is 40 square feet.
How to find the area?To do so, we can take the area of the whole green area, and then remove the areas of the two holes.
Remember that the area of any rectangle is the product of the two dimensions.
For the green one:
A = 4ft*12ft = 48 ft²
Removing the two areas for the holes we have:
a1 = 3ft*2ft = 6ft²
a2 = 1ft*2ft = 2ft²
Remove that:
green area= 48 ft² - 6ft² - 2t² = 40ft²
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1. The rectangle shown is dilated by a scale factor of 3. (a) Calculate the length of each side of the dilated image. (b) Draw the new image and label it .
According to the information, the dilated rectangle would have the dimensions of 2.66cm on the side and 5cm on the base.
How to calculate the length of each side of the dilated image?To calculate the dimensions of each side of the dilated figure we must identify the dilation factor. In this case it is 3, so we must divide the length of each side into the number of the expansion factor as shown below:
8 / 3 = 2.6615 / 3 = 5According to the above, the dilated rectangle would remain with the dimensions of 2.66cm on the side and 5cm on the base.
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i need answer please
The surface area of the rectangular prism is 210 in²
What is an equation?An equation is an expression that shows the relationship between numbers and variables using mathematical operators.
The surface area of a rectangular prism is the sum of each area for the surface.
Hence:
Surface area = 2(8 in * 5 in) + 2(5 in * 5 in) + 2(8 in * 5 in) = 210 in²
The surface area of the prism is 210 in²
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State whether the decay is linear or exponential, and answer the associated question.
The value of a car is decreasing by 12% per year. If the car is worth $9,000 today, what will it be worth in two years?
_________________________________
= 12 × 9,000 ÷ 100= 1,080= 1,080 × 2= 2,160= 9,000 - 2,160= $6,840The Car Will Be Worth $6,840 After 2 Years_________________________________
Answer:
$6,840
Step-by-step explanation:
find the value of x in the cube
Answer:
3√3 ft or 5.20 ft
Step-by-step explanation:
The main diagonal of any cube can be found by multiplying the length of one side by the square root of 3. Where “x” is the cube side.
x = L × √3
x = 3 × √3
x = 3 × 1.7
x = 5.20 ft
7) If a professor can grade 5 essays in 40 minutes, the professor can grade 32 essays in 256 minutes. (10pts)
O True
O False
Answer:
O True
Step-by-step explanation:
Unit rate of essays/minute:
40 minutes / 5 essays = 8 essays/minute
256 essays / 32 minutes = 8 essays/minute
The unit rates are equal.
Answer: O True
(-6,-4), (0, -4), and (2,-4)
What is the equation of this line?
Answer: y = -4
Step-by-step explanation:
Based on these three given points, we can tell that this line is a horizontal line because there is no slope. All of the points have the same y-value, -4.
This means the equation of the line is:
y = -4
See attached for a visual representation. I have graphed the given points over the top of the equation we wrote for the line.
Please help solve graphs
The graphs are:
1) not one-to-one
2) one-to-one
3) not one-to-one
Are the graphs one-to-one?A graph represents an one-to-one function only if.
We can't draw a vertical line that touches the graph twice or more.
We can't draw an horizontal line that touches the graph twice or more.
For example, for the first graph, we can see that there are horizontal lines like y = -5 that touch the graph two times.
Similarly forthe third graph, the line y = 0 touches two points-
So these two are not one-to-one.,
For the remaining graph, the middle one, no line touches the graph more than once, so it is one-to-one.
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Need help. What is the x value pic attached below
The value of x in the function f(x) = (1/3)^x - 2 such that f(x) = 7 is -2
Calculating the value of xFrom the question, we have the following equation that can be used in our computation:
f(x) = (1/3)^x - 2
When the value of f(x) is 7, we have
(1/3)^x - 2 = 7
So, we have
(1/3)^x = 9
Take the log of both sides
x = log(9)/log(1/3)
Evaluate
x = -2
Hence, the value of x is -2
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a grocery store sells a 7 oz bag of raisins for $1.10 and a 9oz bag of raisins for $1.46. Which size bag has the lower price per ounce?
To determine which size bag has the lower price per ounce, we need to calculate the price per ounce for each bag.
For the 7 oz bag, the price per ounce is:
1.10 / 7 = 0.1571
For the 9 oz bag, the price per ounce is:
1.46 / 9 = 0.1622
Therefore, the 7 oz bag has the lower price per ounce, at approximately $0.16 per ounce, compared to the 9 oz bag at approximately $0.16 per ounce. So, if the goal is to get the most value for your money, it would be better to purchase the 7 oz bag of raisins.
Find the endpoints of the latus rectum of the parabola below.
(y - 1)? = 16(x + 1)
Answer:
(3, 9) and (3, -7)
Step-by-step explanation:
You want the end points of the latus rectum for the parabola defined by ...
(y -1)² = 16(x +1)
Vertex and scale factorCompare the given equation to the form ...
(y -k)² = 4p(x -h)
we see that (h, k) = (-1, 1) and p = 16/4 = 4. The ordered pair (h, k) is the vertex of the parabola. The scale factor 'p' gives the distance from the vertex to the focus (and from the directrix to the focus). Larger 'p' values result in a "flatter" parabola.
Latus rectumSince the squared term is a y-term, and the value of 'p' is positive, we know the parabola opens to the right. The end points of the latus rectum are ...
(h+p, k±2p) = (-1+4, 1±2·4) = (3, 9) and (3, -7)
__
Additional comment
If the roles of x and y are interchanged (the parabola opens up or down), then the end points of the latus rectum are (h±2p, k+p).
On a graph of the parabola, the end points of the latus rectum lie on lines through the vertex with slope ±2 (parabola opens in x-direction), or with slope ±1/2 (parabola opens in y-direction).
Suppose in an orchard the number of apples in a tress is normally distributed with a mean of 300 and a standard deviation of 30 apples. Find the probability that a given tree has between 300 and 390 apples.
Using a normal distribution calculator and entering the mean as 300, the standard deviation as 30 and the range (300 to 390), the probability that a given tree has between 300 and 390 apples is 0.4987 or 49.87%.
How the probability is determined:Probability refers to the chance or likelihood that an expected event occurs out of many possible events.
Probability lies between 0 and 1, depending on the degree of certainty.
Mean = 300
Standard deviation = 30
Range = 300 to 390
Thus, the probability that a given tree has between 300 and 390 apples is 0.4987 or 49.87%.
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Can someone help me with this
Answer:
x = 23°
Step-by-step explanation:
We Know
The 67° angle + the x must be equal to 90°
Find the x.
Let's solve
67° + x = 90°
x = 23°
m ∠ � = ( � + 21 ) ∘ ∠A=(x+21) ∘ and m ∠ � = ( 4 � − 30 ) ∘ ∠B=(4x−30) ∘ , then find the measure of ∠ � ∠B.
The measure of angle B is given as follows:
m < B = 49.2º.
What are complementary angles?Two angles are said to be complementary angles when the sum of their measures is of 90º.
The measures are given as follows:
m < A = (x + 21)ºm < B = (4x - 30)º.As the angles are complementary, the value of x is obtained as follows:
x + 21 + 4x - 30 = 90
5x - 9 = 90
5x = 99
x = 19.8.
Hence the measure of angle B is obtained as follows:
m < B = 4 x 19.8 - 30
m < B = 49.2º.
Missing InformationThe measures are given as follows:
m < A = (x + 21)ºm < B = (4x - 30)º.The angles are complementary, and it asks for the measure of angle B.
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