The exact solutions are x ≈ 0.590, x ≈ 2.552, and x ≈ 5.103.
The equation we are solving for exact solutions in the interval (0,2π) is Cos (2x) cos(x) - sin(2x)sin(x) = - √3 / 2.
First, let's use the double angle formula for cosine to simplify the equation:
cos(2x) = 1 - 2sin^2(x)
Substituting this into the equation, we get:
(1 - 2sin^2(x))cos(x) - sin(2x)sin(x) = - √3 / 2
Next, let's use the double angle formula for sine to simplify the equation further:
sin(2x) = 2sin(x)cos(x)
Substituting this into the equation, we get:
(1 - 2sin^2(x))cos(x) - 2sin^2(x)cos(x) = - √3 / 2
Combining like terms and rearranging, we get:
4sin^2(x)cos(x) - cos(x) = √3 / 2
Factoring out cos(x), we get:
cos(x)(4sin^2(x) - 1) = √3 / 2
Dividing both sides by (4sin^2(x) - 1), we get:
cos(x) = (√3 / 2) / (4sin^2(x) - 1)
Using the Pythagorean identity, sin^2(x) + cos^2(x) = 1, we can substitute for sin^2(x):
cos(x) = (√3 / 2) / (4(1 - cos^2(x)) - 1)
Multiplying both sides by (4(1 - cos^2(x)) - 1), we get:
cos(x)(4(1 - cos^2(x)) - 1) = √3 / 2
Expanding and rearranging, we get:
4cos^3(x) - 5cos(x) + √3 / 2 = 0
This is a cubic equation, which is difficult to solve algebraically. However, we can use a graphing calculator to find the approximate solutions. The solutions are x ≈ 0.590, x ≈ 2.552, and x ≈ 5.103.
Since all of these solutions are in the interval (0,2π), the exact solutions are x ≈ 0.590, x ≈ 2.552, and x ≈ 5.103.
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what is the 20th term of the sequence 1,3,9,27
Answer:
1162261467
Step-by-step explanation:
Note that this is a geometric sequence.
1,3,9,27
The pattern is to multiply the number by 3 to get to the next term.
a = 1
r = 3
n=20
arⁿ⁻¹ = nth term
You then substitute the values of a,r and n into the nth term:
arⁿ⁻¹=3¹⁹
3¹⁹=1162261467 which is the 20th term of the sequence
Hoped this helped
Answer:
To find the 20th term of the sequence 1, 3, 9, 27, we need to first identify the pattern of the sequence. It appears that each term of the sequence is obtained by multiplying the previous term by 3. This means that the sequence is a geometric sequence with first term (a) = 1 and common ratio (r) = 3.
Using the formula for the nth term of a geometric sequence:
an = a * r^(n-1)
where an is the nth term of the sequence, a is the first term, r is the common ratio, and n is the term number.
Substituting the values we have:
a = 1, r = 3, and n = 20
an = 1 * 3^(20-1) = 1 * 3^19 = 1162261467
Therefore, the 20th term of the sequence 1, 3, 9, 27 is 1162261467.
Step-by-step explanation:
brainliest pls
Answer this easy geometry question. And no links, please.
Answer:
x = 10
Step-by-step explanation:
Since KL is parallel to HI
m∠JKL = m∠JHI
m∠JLK = m∠LIH
For the two triangles JKL and JHI, we have the common angle J and two angles equal to the corresponding two angles
Therefore the triangles are similar
Ratio of the sides to the corresponding sides must be equal
Hence
[tex]\dfrac{JH}{JK} = \dfrac{JI}{JL}\\[/tex]
JH = JK + KH = 28 + 20 = 48
JI = JL + JL = 14 + x
Therefore
[tex]\dfrac{JH}{JK} = \dfrac{JI}{JL}\\\\= > \dfrac{48}{28} = \dfrac{14 + x}{14}[/tex]
[tex]\dfrac{48}{28} = \dfrac{12}{7}[/tex] by dividing numerator and denominator by 4
Hence
[tex]\dfrac{48}{28} = \dfrac{14 + x}{14}\\\\\rightarrow \quad \dfrac{12}{7} = \dfrac{14 + x}{14}\\\\[/tex]
Multiply both sides by 14:
[tex]14 \cdot \dfrac{12}{7} = 14 \cdot \dfrac{14 + x}{14}\\\\2 \cdot 12 = 14 + x\\\\24 = 14 + x\\\\\text{Subtract 14 both sides:}\\\\24 - 14 = x\\\\or\\\\x = 10\\\\[/tex]
HELP ME PLEASE!!!!!!!!!!!!!!!
Answer: 480
Step-by-step explanation: Since this is a triangle, we are using 1/2 * base * height. So since the height is 15, and the base is 64, that would equal 960. Then we are going to divide it by 2, which equals 480.
Calculate the present value. (Round your answer to two decimal
places.)
A = $35,000, r = 7% compounded monthly, t = 6 years
The present value of A = $35,000, r = 7% compounded monthly, t = 6 years is $24,036.89.
The present value is the amount of money that is needed today in order to produce a specified future value at a specified interest rate and time period. It is calculated using the formula: PV = A / (1 + r/n)^(n*t), where A is the future value, r is the interest rate, n is the number of compounding periods per year, and t is the time period in years.
Given that A = $35,000, r = 7%, n = 12 (since the interest is compounded monthly), and t = 6 years, we can plug these values into the formula to calculate the present value:
PV = $35,000 / (1 + 0.07/12)⁷²
PV = $35,000 / (1.00583)⁷²
PV = $35,000 / 1.45558
PV = $24,036.89
Therefore, the present value is $24,036.89.
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Find the gradients of lines A and B.
B
-2
6
O
-21
Fet
A
4
72%
X
The gradient of line A is 4 and the gradient of line B is -2.
What is graph?Graph is a data structure that consists of nodes (or vertices) connected by edges. It is a way of representing data in a structured form and can be used to represent any type of real-world relationship. It can be used to represent geographical relationships between cities, social networks, and even computer networks. Graphs are often used in computer science, mathematics, and engineering to represent relationships between data points.
To calculate the gradient of a line, the formula is rise/run. Thus, the gradient of line A can be calculated as rise/run = 72/4 = 18. On the other hand, the gradient of line B can be calculated as rise/run = 6/-2 = -3
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following exercises, perform the indicated operations. 7. (7)/(10x^(2)y)+(4)/(15xy^(2))
After performing the indicated operation, the sum of (7)/(10x²y) + (4)/(15xy²) is (21y + 8x)/(30x²y²).
To perform the indicated operations, we need to find a common denominator for the two fractions. The common denominator for 10x²y and 15xy² is 30x²y². We can then rewrite the fractions with the common denominator and add them together:
(7)/(10x²y) + (4)/(15xy²)
To do this, multiply both fractions by 30x²y²/30x²y² and simplify as a fraction with denominator 30x²y².
= (7)/(10x²y)(30x²y²/30x²y²) + (4)/(15xy²)(30x²y²/30x²y²)
= (21y)/(30x²y²) + (8x)/(30x²y²)
Finally, since the denominators of the two fractions are the same, add the two fractions by adding their numerators.
= (21y + 8x)/(30x²y²)
Therefore, the answer is (21y + 8x)/(30x²y²).
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URGENT PLEASE HELP!! 50 POINTS
The value of x of the triangle is given by the trigonometric relation x = 30°
What are trigonometric relations?Trigonometry is the study of the relationships between the angles and the lengths of the sides of triangles
The six trigonometric functions are sin , cos , tan , cosec , sec and cot
Let the angle be θ , such that
sin θ = opposite / hypotenuse
cos θ = adjacent / hypotenuse
tan θ = opposite / adjacent
tan θ = sin θ / cos θ
cosec θ = 1/sin θ
sec θ = 1/cos θ
cot θ = 1/tan θ
Given data ,
Let the triangle be represented as ΔPQR
Now , the measure of side PQ = 48 cm
The measure of side PQ = 96 cm
The measure of ∠x is calculated by
From the trigonometric relations ,
sin x = opposite side / hypotenuse
On simplifying , we get
sin x = 48 / 96
sin x = 1/2
Taking inverse on both sides , we get
x = sin ⁻¹ ( 1/2 )
x = π/6
x = 30°
Therefore , the value of x is 30°
Hence , the angle of the triangle is 30°
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please help me out with anybody this if u can and answer it right i will give brainy
Question 12
Find the five-number summary of the data set:
135, 149, 156, 112, 134, 141, 154, 116, 134, 156
Minimum: 112
Quartile Q1: 129.5
Median: 138
Quartile Q3: 154.5
Maximum: 156
Leveled Practice In 8-11, complete each statement.
8. A die has 12 sides shown as follows: 6 triangles,
3 circles, and 3 squares.
The probability rolling a triangle is
Q
2
out of 12, or
or
%.
(s
The probability of rolling a triangle is 50%
How to determine the probability of rolling a triangleFrom the question, we have the following parameters that can be used in our computation:
Sides = 12
triangles = 6
Circles = 3
Squares = 3
The die has a total of 6 + 3 + 3 = 12 sides.
Since there are 6 triangles on the die, the probability of rolling a triangle is:
P(triangle) = number of favorable outcomes / total number of outcomes
Substitute the known values in the above equation, so, we have the following representation
P(triangle) = 6 / 12
Evaluate
P(triangle) = 50%
Hence, the probability of rolling a triangle on the die is 1/2 or 0.5.
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An electric utility company charges $24 per month maintenance fee to customers generating their own solar power, but refunds them $0.08{ per kilowatt-hour of net electricity returned to the grid.
How many kilowatt-hours per month does one have to return to the grid to break even (do not pay nor receive any money)? Round your answer to the nearest kilowatt-hour. Do not include units in your answer
300 kilowatt-hours per month does one have to return to the grid to break even.
To find out how many kilowatt-hours per month one has to return to the grid to break even, we need to set up an equation and solve for x, where x is the number of kilowatt-hours returned to the grid.
The equation would be:
24 = 0.08x
To solve for x, we need to isolate the variable on one side of the equation. We can do this by dividing both sides of the equation by 0.08:
24/0.08 = x
x = 300
Therefore, one would have to return 300 kilowatt-hours per month to the grid to break even.
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True or False with explanation (e.g. a piece of the Invertible Matrix Theorem) or a counterexample. All matrices aren×n. - (a) If the equationAx=0has only the trivial solution, thenAis row equivalent to the identity matrix. - (b) If the columns ofAspanRn, then they are linearly independent. - (c) IfATis not invertible, then neither isA. - (d) If there is a matrixDwithAD=I, thenDA=Ialso.
(a) If the equation Ax=0has only the trivial solution, then A is row equivalent to the identity matrix is True.
(b) If the columns of Aspan Rn, then they are linearly independent is True.
(c) If AT is not invertible, then neither is A is True.
(d) If there is a matrix D with AD=I, then DA=I also is True.
If the equation Ax=0 has only the trivial solution, then the matrix A has a pivot in every column and is therefore row equivalent to the identity matrix.
If the columns of A span Rn, then they are linearly independent because if they were not, there would be a nontrivial linear combination of the columns that equals the zero vector, which would contradict the fact that they span Rn.
If AT is not invertible, then it has a nontrivial null space, which means that there is a nonzero vector x such that ATx=0. This implies that xTA=0, which means that x is in the null space of A. Since A has a nontrivial null space, it is not invertible.
If there is a matrix D with AD=I, then DA=I also because the inverse of a matrix is unique and both AD and DA must be equal to the inverse of A.
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Jacques needs 5/8 kg of flour to make a loaf of bread
he tips 2/5 Kg of white flour onto a weighing scale
how much more flour does he need to add?
9/40 more flour does he need to add.
What is Fraction?A fraction represents a part of a whole.
Given that Jacques needs 5/8 kg of flour to make a loaf of bread, he tips 2/5 Kg of white flour onto a weighing scale.
We need to find amount of flour he still need to make a loaf of bread.
2/5 + x =5/8
Subtract 2/5 from both sides
x = 5/8 -2/5
LCM of 8 and 5 is 40.
=25-16/40
=9/40
Hence, 9/40 more flour does he need to add.
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Un recipiente de aluminio tiene una capacidad de 6 litros a 28 grados celcius.
Determina el volumen del recipiente cuando este se caliento a 100 grados celcius
Answer: I don't speak Spanish but the answer might be 21.4285714286 liters
Step-by-step explanation:
"An aluminum container has a capacity of 6 liters at 28 degrees Celcius. Determine the volume of the container when it is heated to 100 degrees Celsius."
19. The co-ordinates (α, ß) of a moving point are given by,
(iv)
α = 1/2a(t+1/t), β = 1/2a(t-1/t), where a is a constant;
in each case, obtain the relation between α and β, and hence write down the locus of the point as t varies.
Answer: To obtain the relation between α and β, we can eliminate t from the given equations.
(iv)
α = 1/2a(t+1/t)
β = 1/2a(t-1/t)
We can multiply these two equations to eliminate t^2:
αβ = (1/2a(t+1/t))(1/2a(t-1/t))
αβ = (1/4a^2)(t^2 - 1/t^2)
Multiplying both sides by 4a^2 gives:
4a^2αβ = t^2 - 1/t^2
Adding 1/t^2 to both sides gives:
4a^2αβ + 1/t^2 = t^2 + 1/t^2
Multiplying both sides by t^2 gives:
4a^2αβt^2 + 1 = t^4 + 1
Rearranging and simplifying gives the relation between α and β:
4a^2αβ = t^4 - 4a^2t^2 + 1
Now we can write the locus of the point as t varies:
4a^2αβ = t^4 - 4a^2t^2 + 1
This is a fourth degree equation in t, which represents a curve in the (α, β) plane. However, we can simplify it by noting that t^2 is always non-negative. Therefore, we can treat 4a^2t^2 as a constant and write:
4a^2αβ = (t^2 - 2a^2)^2 + 1 - 4a^4
This is the equation of a conic section called a hyperbola. Its center is at (0,0), its asymptotes are the lines α = ±β, and its foci are at (a√2,0) and (-a√2,0).
Step-by-step explanation:
Which of these statements describe properties of parallelograms? Check all
that apply.
Answer: The ones you have selected are correct
Step-by-step explanation:
Answer:
the ones you selected are all correct
Step-by-step explanation:
Question 1 1.1. Given: √9+25; π-4; √-27 ::: √-27 3 3 ; 2 From the list given above, write down: Question 2 1.1.1. A natural number. 1.1.2. A negative irrational number. 1.1.3. A non-real number. 1.1.4. A rational number which is not an integer. 1.2. Between which two consecutive integers does √138 lie? 1.3. Rewrite 0,26 as a proper fraction (in the form of), show all steps.
√(9 + 25) is real; π - 4 is negative irrational ; √-27 is a non-real ; 3 3/2 is a rational that is not an integer.
√138 lies between 11 and 12; 0.26 as fraction = 13/50
What are types of numbers?A number is an arithmetic value which is used to represent the quantity of an object. There are different types of numbers as natural numbers, whole numbers, integers, real numbers, rational numbers, irrational numbers, complex numbers and imaginary numbers.
Given numbers,
a) √(9 + 25)
= √34
square root of a real number is real number.
b) π - 4
∵π is irrational and less than four,
∴π - 4 is negative irrational number
c) √-27
Square root of -27 is not possible,
√-27 is a non-real number
d) 3 3/2
= 9/2
= 4.5
3 3/2 is a rational number that is not an integer.
e) √138 = 11.747
∴ two consecutive integers between which √138 lies are 11 and 12
f) 0.26
multiplying and dividing with 100
= 26/100
Simplifying
= 13/50
Hence,
√(9 + 25) is real number; π - 4 is negative irrational number;
√-27 is a non-real number; 3 3/2 is a rational number that is not an integer.
Two consecutive integers between which √138 lies are 11 and 12
0.26 as fraction = 13/50
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4. An ant leaves the origin at time zero, travelling along the positive x-axis at a speed of two Poincare units of length per second.
(a) Find the (Euclidean) coordinates of the ant’s position after 2 seconds.
(b) How long will it take the ant to pass the point (0.999, 0)?
(a) After 2 seconds, the ant's position in the (Euclidean) coordinates is (4,0)
(b) To pass the point (0.999, 0), the ant needs 0.4995 seconds.
The ant is traveling along the positive x-axis at a speed of 2 Poincare units of length per second. This means that its position at any given time can be determined using the equation:
x = 2t
where x is the ant's position along the x-axis, and t is the time in seconds.
(a) To find the ant's position after 2 seconds, we can simply plug in t = 2 into the equation:
x = 2(2) = 4
So the ant's position after 2 seconds is (4, 0).
(b) To find how long it will take the ant to pass the point (0.999, 0), we can set x = 0.999 and solve for t:
0.999 = 2t
t = 0.999/2 = 0.4995
So it will take the ant 0.4995 seconds to pass the point (0.999, 0).
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Choose two ratios that describe the collection of baseballs to gloves.
8:4
06:4
02:1
02:4
10
4 of 15 answered
need help?
->>
Two ratios that describe the collection of baseballs to gloves are
8:4 and 2:1 .
What is ratio?The ratio is defined as the comparison of two quantities of the same units that indicates how much of one quantity is present in the other quantity. Ratios can be classified into two types. One is part to part ratio and the other is part to whole ratio.
Given,
Number of gloves = 16
Number of baseballs = 8
Ratio of gloves to baseballs
= 16/8
= 8/4 = 8:4
= 2/1 = 2:1
Hence, 8:4 and 2:1 are two ratios that describe the collection of baseballs to gloves.
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Complete question is:
There are 16 baseballs and 8 gloves,
Choose two ratios that describe the collection of baseballs to gloves.
8:4, 6:4, 2:1, 2:4, 10:4
A cylinder has a volume of 1 and one sixteenth in3 and a radius of one fourth in. What is the height of a cylinder? Approximate using pi equals 22 over 7.
119 twelfths inches
119 over 22 inches
119 over 44 inches
119 over 56 inches
The height of the cylinder is approximately 2.45 inches.
What is Volume?Volume is the measure of the space occupied by a three-dimensional object. It is typically expressed in cubic units.
The volume of a cylinder is given by the formula V = πr²h, where V is the volume, r is the radius, and h is the height.
Substituting the given values, we get:
1 and 1/16 = π(1/4)²h
Simplifying and solving for h, we get:
h = (1 and 1/16) / (π(1/4)²)
h = (17/16) / (π/16)
h = 17/π
Approximating using π = 22/7, we get:
h ≈ 17 / (22/7)
h ≈ 2.45 inches (rounded to two decimal places)
Therefore, the height of the cylinder is approximately 2.45 inches
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Determine if the relation defines y as a function of x. y 4+ 3+ 3 2 . 1 2 1+ 2+ -3+ 4+ Yes, this relation defines y as a function of x. Х 5 No, this relation does not define y as a function of x.
No, this relation does not define y as a function of x.
A function is a relation in which each input (x-value) is paired with exactly one output (y-value). In this relation, the x-value of 2 is paired with two different y-values (3 and -3), which violates the definition of a function.
Therefore, this relation does not define y as a function of x.
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Suppose x > y > 0 and a > b > 0. Is it true that x/b > y/a? if so
For the inequality x > y > 0 and a > b > 0 the expression ( x /y)> (x +b)/ (y+ a) > b/a is true if x/b > y/a.
For x > y > 0 and a > b > 0
The inequality x/b > y/a
Simplify by cross-multiplication we get,
⇒xa > yb
Adding xy to both sides,
⇒xy + xa > xy + yb
Factoring the left-hand side,
⇒ x(y + a) > y(x + b)
Dividing both sides by (y + a)(x + b), as x > y > 0 and a > b > 0,
⇒ x/(x + b) > y/(y + a)
Multiplying both sides by x/y we get the expression,
⇒x/y > (x + b)/(y + a) __(1)
It proves the half part of the expression, x/y > (x + b)/(y + a)
Now second part x/y > (x + b)/(y + a) > b/a.
Using inequality x/b > y/a to get:
a/b > y/x
Multiplying both sides by (x + b)/(y + a),
⇒(a/b) × (x + b)/(y + a) >(y/x) × (x + b)/(y + a)
Expand both sides and simplifying,
⇒ ( ax + ab ) / (by + ab ) > ( xy + by ) / ( xy + ax )
⇒( ax + ab )( xy + ax ) > ( xy + by ) (by + ab )
⇒ ax²y + a²x² + abxy + a²bx > by²x + abxy + b²y² + ab²y
⇒ (ax -by )( x + b )( y + z) > 0
⇒ax - by > 0 or ( x + b )> 0 or ( y + z) > 0
⇒ ax > by
⇒ x /y > b /a
As a > b > 0
⇒ (x +b)/ (y+ a) > b/a __(2)
From (1) and (2) we have,
( x /y)> (x +b)/ (y+ a) > b/a
Therefore , the expression ( x /y)> (x +b)/ (y+ a) > b/a is true for the given condition.
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The above question is incomplete, the complete question is:
Suppose x > y > 0 and a > b > 0. Is it true that x/b > y/a then expression
( x /y)> (x +b)/ (y+ a) > b/a.
Solve The Equation 6x^4 + 8x^2 = 26x^2
Answer: [tex]\sqrt{3}[/tex]
Step-by-step explanation:
take,
x^2 = Y
6Y^2 + 8Y = 26Y
6Y^2 + 8Y - 26Y = 0
6Y^2 - 18Y = 0
6Y (Y - 3) = 0
(Y - 3) = 0
Y = 3
x^2 = y
x^2 = 3
x = [tex]\sqrt{3}[/tex]
quired
1) Coordinate point B is at (4,3). What will the coordinates be for B' after a
translation of (x-2y+3)?
OB' (5,4)
OB' (2,6)
OB' (6,2)
OB' (-2,3)
The coordinates after the translation are (2, 6).
Which will be the coordinates after the translation?Here we start with the point (4, 3) and we want to apply the translation defined by (x - 2, y + 3)
This would be a translation of 2 units to the left and 3 units up, using a "coordinate-axis" notation.
So we just need to subtract 2 from the x-value and add 3 to the y-value, we will get the new coordinates:
(4 - 2, 3 + 3) = (2, 6)
These are the coordinates of point B after the translation, the correct option is the second one.
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Answer:
OB' (2,
Step-by-step explanation:
take your first point (B) (4,3) and plug it into the x and y in (x-2, y+3) so you get (4-2, 3+3) which will give you (2,
alice recipe for jam requires 4.8 of sugar. her kitchen weighing only gives measurements in pounds. taking 1kg = 2.205 lb, convert 4.8 kg to pounds
Alice needs to use 10.584 pounds of sugar for her jam recipe. This can be calculated using the conversion factor.
To convert 4.8 kg to pounds, we need to use the conversion factor of 1 kg = 2.205 pounds. This means that for every 1 kg, there are 2.205 pounds. To find out how many pounds are in 4.8 kg, we simply multiply 4.8 by 2.205.
The equation for this conversion is:
4.8 kg × 2.205 pounds/kg = 10.584 pounds
So, 4.8 kg is equivalent to 10.584 pounds.
Therefore, the correct answer is 10.584 pounds.
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Concepts to make sure are (re)-discussed: Isolating the radical Checking for extraneous solutions Solving rational exponents in equations- more than one solution Sample problems: 1. V4x + 1 - Vx+ 10 = 2. V2x+30 = (x+3)
To solve the given equations, we need to follow these steps:
1. Isolate the radical on one side of the equation.
2. Square both sides of the equation to eliminate the radical.
3. Solve the resulting equation for the variable.
4. Check for extraneous solutions by plugging the solution back into the original equation.
5. If there are rational exponents, use the same steps but raise both sides of the equation to the reciprocal of the exponent.
Let's apply these steps to the sample problems:
1. V4x + 1 - Vx+ 10 = 2
First, isolate the radical on one side:
V4x + 1 = Vx+ 10 + 2
V4x + 1 = Vx+ 12
Next, square both sides to eliminate the radical:
(4x + 1) = (x+ 12)^2
4x + 1 = x^2 + 24x + 144
Solve for x:
0 = x^2 + 20x + 143
Using the quadratic formula:
x = (-20 ± √(20^2 - 4(1)(143)))/(2(1))
x = (-20 ± √(400 - 572))/2
x = (-20 ± √(-172))/2
x = (-20 ± √172i)/2
There are no real solutions for this equation.
2. V2x+30 = (x+3)
Isolate the radical:
V2x+30 = x+3
Square both sides:
2x + 30 = (x+3)^2
2x + 30 = x^2 + 6x + 9
Solve for x:
0 = x^2 + 4x - 21
Using the quadratic formula:
x = (-4 ± √(4^2 - 4(1)(-21)))/(2(1))
x = (-4 ± √(16 + 84))/2
x = (-4 ± √100)/2
x = (-4 ± 10)/2
x = 3 or x = -7
Check for extraneous solutions by plugging the solutions back into the original equation:
V2(3)+30 = (3+3)
V36 = 6
6 = 6 (True)
V2(-7)+30 = (-7+3)
V16 = -4
4 = -4 (False)
Therefore, the only solution is x = 3.
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At the football team banquet, 60 out of the 80 people attending had dessert with their dinner. What percent of the attendees had dessert?
The percentage of the attendees that had dessert at the football team banquet is 75%.
What percent of the attendees had dessert?Percentage is simply number or ratio expressed as a fraction of 100.
It is expressed as;
Percentage = ( Part / Whole ) × 100%
To find the percentage of attendees who had dessert, we can use the formula:
Percentage = (part/whole) x 100%
where:
part = the number of attendees who had dessert = 60whole = the total number of attendees = 80Substituting the given values, we get:
percentage = (60/80) x 100%
percentage = 0.75 x 100%
percentage = 75%
Therefore, 75 perecent of the attendees had dessert.
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What is the remainder when f(x)=x^3+7x^2+9x-5 is divided by (x+4)
On dividing (x³ + 7x² + 9x - 5) by (x + 4), we get -
h(x) = x² + 3x - 3 + 7/(x + 4).
What is Division algorithm?Division algorithm states that -
Dividend = (Divisor x Quotient) + Remainder
Given is to find the remainder when -
(x³ + 7x² + 9x - 5) ÷ (x + 4)
We can write -
f(x) = (x³ + 7x² + 9x - 5)
g(x) = (x + 4)
So -
h(x) = f(x) ÷ g(x)
h(x) = (x³ + 7x² + 9x - 5) ÷ (x + 4)
h(x) = (x³ + 4x² + 3x² + 9x - 5)/(x + 4)
h(x) = x² + (3x² + 9x - 5)/(x + 4)
h(x) = x² + 3x + (-3x - 5)/(x + 4)
h(x) = x² + 3x - 3 + 7/(x + 4)
Therefore, on dividing (x³ + 7x² + 9x - 5) by (x + 4), we get -
h(x) = x² + 3x - 3 + 7/(x + 4).
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What is the solution to this equation?
9 ^x- 1 = 2
O A. 1
O B. 2
O C.
1/2
OD. -1/2
How do you find the scale factors with fractions
To find the scale factors with fractions, you first need to understand what scale factors are. Scale factors are the ratios of corresponding lengths in two similar figures. They tell you how much larger or smaller one figure is compared to another.
To simplify fractions, you need to find the greatest common factor (GCF) of the numerator and denominator and divide them by it.
For example, if we have the fraction 6/12, we can simplify it by finding the GCF of 6 and 12, which is 6. Then, we divide both the numerator and denominator by 6:
6/12 = (6 ÷ 6) / (12 ÷ 6) = 1/2
So, 6/12 simplifies to 1/2.
If the fraction is already in its simplest form, then there is no need to simplify it further.
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The complete question i:
How do you find the scale factors with fractions? Give example.
a set of eight cards was labled m, u, t, i, p, l, y. what is the sample space for choosing one card
The sample space for choosing one card from the set of eight cards labeled m, u, t, i, p, l, y is 8.
What is sample space?An assortment or set of potential results from a random experiment make up a sample space. With the letter "S," the sample space is denoted. Events are a subset of the possible results of an experiment. Depending on the experiment, a sample space could have several different outcomes. Discrete sample spaces, often known as finite sample spaces, are those that have a finite number of outcomes.
The sample space for choosing 1 card is given as:
Sample space = 8C1 = 8! / (1!)(8 - 1)!
Sample space = 8.
Hence, the sample space for choosing one card from the set of eight cards labeled m, u, t, i, p, l, y is 8.
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