The pair of functions f(x) and g(x) below that equals 0 as the limit as x goes to infinity of the quotient of f of x and g of x will be C. f(x) = ln(x); g(x) = ex
How to explain the informationFor the limit of the quotient of f(x) and g(x) to equal 0 as x approaches infinity, it is necessary for f(x) to grow more slowly than g(x).
Out of the options given, the only pair of functions where this is true is f(x) = ln(x) and g(x) = ex. As x approaches infinity, ex grows much faster than ln(x), so the limit of the quotient of these two functions as x approaches infinity is 0.
In conclusion, the correct option is C.
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what is - 3x > 15 equal to
Answer:
x < -5
Step-by-step explanation:
- 3x > 15 is equal to x < -5
Answer please! 50 Points!
Help please Hurry
What conclusion can be drawn about the number of trials and the probability of the coin landing on heads or tails? (1 point)
O a
О b
• c
O d
The experimental probability is closer to the theoretical probability for group Y than group X.
The experimental probability and the theoretical probability for group X is the same.
The experimental probability and the theoretical probability for group Y is the same.
The experimental probability is closer to the theoretical probability for group X than group Y.
The conclusion that can be drawn about the number of trials and the probability is A. The experimental probability is closer to the theoretical probability for group Y than X.
How to find the probability ?The theoretical probability for picking a heads or tails is 50 % as there are only two outcomes of heads and tails.
The experimental probability for heads is 53 % in Group Y and 47 % for tails. This is close enough to the 50 % theoretical probability.
For group X, the experimental probability for heads for Group x is :
= 33 / 50
= 66 %
This is too far from the theoretical probability.
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A stereo that regularly sells for $330 is on sale at 15% off. How much will a customer save on the stereo during the sale?
Answer: 49.5 dollars
Step-by-step explanation: the original price is 330, but the sale takes 15 percent off
so we turn 15% into a decimal so we can multiply 330 and 15%
we get 0.15 × 330 = 49.5
The proportion of twins born in a town is p = 0.12. Suppose we randomly select 100 women from this town who give birth in the next year. Which of the following is the mean of the sampling distribution of p hat ?
Mu Subscript p hat = p = 0.12
Mu Subscript p hat = n p = 100 (0.12) = 12
Mu Subscript p hat = 1 minus p = 1 minus 0.12 = 0.88
Mu Subscript p hat = n (1 minus p) = 100 (1 minus 0.12) = 88
The sampling distribution of p hat follows a normal distribution thus, the value of Mu Subscript p hat = p = 0.12. Option 1 is the correct answer.
What is normal distribution?A probability distribution that is symmetric about the mean is the normal distribution, sometimes referred to as the Gaussian distribution. It demonstrates that data that are close to the mean occur more frequently than data that are far from the mean.
The most typical form of distribution assumed in technical stock market analysis and other statistical investigations is the normal distribution. The mean and the standard deviation are the two variables that make up the standard normal distribution.
The sampling distribution of p hat follows a normal distribution thus,
Mu Subscript p hat = p
Here, the value of p = 0.12
Hence, the value of Mu Subscript p hat = p = 0.12. Option 1 is the correct answer.
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Answer:
A. Mu Subscript p hat = p = 0.12
Step-by-step explanation:
The table represents a function.
A 2-column table with 4 rows. The first column is labeled x with entries negative 4, negative 1, 3, 5. The second column is labeled f of x with entries negative 2, 5, 4, negative 8.
What is f(5)?
–8
–1
1
8The table represents a function.
A 2-column table with 4 rows. The first column is labeled x with entries negative 4, negative 1, 3, 5. The second column is labeled f of x with entries negative 2, 5, 4, negative 8.
What is f(5)?
–8
–1
1
8
The value of function f(5) is 8.
What do you mean by function?A function is defined as a relation between a set of inputs having one output each. A function is a relationship between inputs where each input is related to exactly one output. Every function has a domain and codomain or range. A function is generally denoted by f(x) where x is the input.
The general representation of a function is y = f(x).
Injective function or One to one function: When there is mapping for a range for each domain between two sets.
Surjective Function or Onto function: When there is more than one element mapped from domain to range.
Polynomial function: The function which consists of polynomials
Inverse function: The function which can invert another function.
Given:
x with entries -4, -1, 3 and 5.
f(-4) = 2
f(-1) = 5
f(3) = 4
f(5) = 8
The value of f(5) is 8.
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Answer: f(5) is -8
Step-by-step explanation:
took the quiz
the product 2√3 and 3√12 in simplified form is
The product of 2√3 and 3√12 in simplified form is 6√36. To simplify this expression, we can first multiply 2 and 3 to get 6. Then, we can simplify the square root of 3 and the square root of 12 by finding their prime factorizations:
√3 = √(3 * 1) = √3
√12 = √(12 * 1) = √(2^2 * 3) = 2√3
So, 2√3 = 2 * √3 = 2 * √3
And, 3√12 = 3 * 2√3 = 6√3
Finally, the product of 2√3 and 3√12 is 6 * 6√3 = 6√36.
At MeDonald's four cheeseburgers and three medium fries have a total of 2290 calories.Six cheeseburgers and two medium fries have 2560 calories. How many calories does each
Item contain?
Answer:
350 calories
Step-by-step explanation:
see the attachment.
Calories in one cheeseburgers = 135
And, Calories in one medium fries = 583
We have to given that,
At McDonald's four cheeseburgers and three medium fries have a total of 2290 calories.
And, Six cheeseburgers and two medium fries have 2560 calories.
Let us assume that,
Calories in one cheeseburgers = x
And, Calories in one medium fries = y
Hence, We get;
4x + 3y = 2290 . (i)
6x + 3y = 2560 .. (ii)
From (i);
3y = 2290 - 4x
Substitute above value in (ii);
6x + (2290 - 4x) = 2560
6x - 4x + 2290 = 2560
2x = 2560 - 2290
2x = 270
x = 270 / 2
x = 135
From (ii);
6 x 135 + 3y = 2560
810 + 3y = 2560
3y = 2560 - 810
3y = 1750
y = 1750/3
y = 583
Therefore, Calories in one cheeseburgers = 135
And, Calories in one medium fries = 583
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two paintings in an art display have shapes that are similar figures. the similarity ratio is 9:7. the perimeter of the smaller painting is 6 meters. which is the perimeter of the larger painting to the nearest tenth?
Two paintings in an art display have shapes that are similar figures. the similarity ratio is 9:7 and the perimeter of the smaller painting is 6 meters therefore the perimeter of the larger painting to the nearest tenth is 7.7 meters.
What is Perimeter?This is referred to as the total distance around a two-dimensional shape.
Perimeter of the smaller painting is 6 meters and similarity ratio is 9:7
9 = x
7 = 6
7x = 54
x = 54/7 = 7.7 meters.
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pour le carnaval un fleuriste dispose de 283 roses et 397 tulipes. il décide de décorer de façon identique le plus grand nombre de chars pour accompagner les carnavalier. après avoir décorer le chars il lui reste 3 roses et 2 tulipes.
combien a t-il décorer de chars et quelle est la composition de chaque décor?
Answer:
I don't understand French
Step-by-step explanation:
A hotel swimming pool measures 20 m by 8m.The hotel manager wants to put a 2 m wide deck around the pool. Caluculate the area of the deck.
Louise is planning to renovate her house. She intends to spend no more than $30 000. She has
$20 000 to invest in an account that pay 4.28% compounded monthly. How long will it take
Louise to meet her goal? Show your work. Round your answer to the nearest tenth of a year.
Answer: To solve this problem, we can use the formula for calculating the future value of an investment:
FV = PV * (1 + r/n)^(nt)
where:
FV is the future value of the investment
PV is the present value of the investment (the initial amount Louise has to invest)
r is the annual interest rate (4.28%)
n is the number of times the interest is compounded in a year
t is the number of years the investment is made
Since the interest is compounded monthly, we need to convert the annual interest rate to a monthly rate:
r/12 = 4.28% / 12 = 0.3566666666666667%
Now, we can use the formula to calculate the future value of Louise's investment:
FV = $20,000 * (1 + 0.3566666666666667%)^(12t)
We can use trial and error or iterative methods to find the value of t that satisfies the condition: FV = $30,000.
A quick approximation is to use the formula for simple interest:
FV = PV * (1 + r * t) = $20,000 * (1 + 0.0428 * t)
t = ($30,000 - $20,000) / ($20,000 * 0.0428) = 2.857142857142857 years, or approximately 2.9 years.
This is an approximation, but it should be close to the actual answer. To get a more accurate answer, we can use an iterative method, such as Newton-Raphson or bisection, to solve for t in the formula above.
Step-by-step explanation:
can someone explain as well so i can understand......A savings account with simple annual interest rate of 3.92% and an initial deposit of $5,460.75 yields a final account balance of $6,370.51 after 51 months. Part A: Using the rate and term as the simple interest account, calculate the final account balance if the initial deposit is invested for the same number of months, with interest compounded semiannually. Show all work. (3 points) Part B: Compare that simple interest final account balance with the compound interest final account balance. (2 point)
Answer:
Step-by-step explanation:
To calculate the final account balance for a savings account with an initial deposit of $5,460.75, compounded semiannually with an interest rate of 3.92%, for 51 months, we need to use the formula:
A = P * (1 + r/n)^(nt)
where A is the final account balance, P is the initial deposit, r is the interest rate (as a decimal), n is the number of times the interest is compounded in a year, t is the number of years, and nt is the number of compounding periods.
In this case, n = 2 (since the interest is compounded semiannually), r = 3.92%/100 = 0.0392, t = 51 months / 12 months/year = 4.25 years, and nt = 2 * 4.25 = 8.5.
Substituting the values into the formula, we get:
A = $5,460.75 * (1 + 0.0392/2) ^ (8.5)
A = $5,460.75 * 1.0196^8.5
A = $5,460.75 * 1.2408
A = $6790.32
So, the final account balance if the initial deposit is invested with interest compounded semiannually is $6790.32.
B) Comparing the final account balance of the simple interest account and the compound interest account, we can see that the compound interest account yields a higher balance ($6790.32) than the simple interest account ($6370.51). This is because compounding interest allows for the interest earned in one period to be reinvested, so the interest earns interest in future periods, which increases the overall amount of interest earned over time. In contrast, simple interest is calculated only on the initial deposit, so the amount of interest earned remains constant over time.
Find the common factor of all the terms of the polynomial 16x² - 14x.
Answer:
The common factor of all the terms of the polynomial 16x² - 14x is:
2x
Step-by-step explanation:
We are given a polynomial:
16x²-14x
We have to find the common factor of all terms.
First we factorize each term separately and then see the common factor.
16x²=2×2×2×2×x×x
14x=2×7×x
We observe that the common factor is:
2x
Hence, the common factor of all the terms of the polynomial 16x² - 14x is:
2x
Answer:
2x
Step-by-step explanation:
16 = 2^4
14 = 2 × 7
Common factor of 16 and 14 is 2.
x² = x × x
x = x
Common factor of x² and x is x
The common factor of the two terms is 2x.
Lena estimate is there a bottle contains 500 mm of water but actually contains 473 mm of water what is the percent error and Lena's estimate rounded to the nearest 10th of a percent HURRY FAST PLS!!!
5.4% is the percent error .
What is the formula for errors?
The difference between the estimated value and the actual value in relation to the actual value is given as a percentage and is known as the percent error.
The relative error is multiplied by 100 to calculate the % error, in other words. The absolute value of the difference between the measured value and the actual value is divided by the actual value, then multiplied by 100 to get the percent error.
= 500 - 473/500 * 100
= 27/500 * 100
= 5.4%
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1. An awning that covers a sliding glass door that is 88 inches tall forms an angle of 50' with the wall.
The purpose of the awning is to prevent sunlight from entering the house when the angle of elevation
of the Sun is more than 65'. See the figure. Find the length of L of the awning. Round to the nearest
Inch.
What is the area of ∆AOB?
The Area of Rhombus is 97.5 cm².
What is area of Rhombus?The area of a rhombus is equal to half the product of the lengths of the diagonals. The formula to calculate the area of a rhombus using diagonals is given as, Area = (a × b )/2 where, a and b are the diagonals of the rhombus.
Given:
As, diagonals of rhombus bisect perpendicularly.
so, In triangle OAD using Pythagoras theorem
AD² = OD² + OA²
10² = 7.8² + OD²
OD= 6.25 cm
So, length of BD = 2 x 6.25 = 12.5 cm
Now, area of Rhombus = 1/2 x a x b
= 1/2 x 15.6 x 12.5
= 97.5 cm².
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Which graph shows the function y = 3x - 5 ?
The solution is, Option A. Line X
What is a straight line?A straight line is an endless one-dimensional figure that has no width. It is a combination of endless points joined both sides of a point and has no curve.
here, we have,
We have to identify the line which represents the function f(x) = 3x - 5
The given equation is y = 3x -5, in which slope of the line should be 3 and y- intercept is -5.
In these lines line x is having y-intercept as -5.
Line x passes through (1, 2) and (0, -5)
So slope of the given line will be = y2 - y1/ x2 - x1
= -5-2/ 0-1
= 3
Therefore, option A : Line X is the answer.
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rachel's coffee shop makes a blend that is a mixture of two types of coffee. type a coffee costs rachel per pound, and type b coffee costs per pound. this month, rachel made pounds of the blend, for a total cost of . how many pounds of type a coffee did she use?
Rachel's Coffee Shop used 33 pounds of type A coffee at a cost of $4.20 per pound, and four times as many pounds of type B coffee at a cost of $5.50 per pound, to create a blend costing a total of $864.60.
Let's use the variable "x" to represent the number of pounds of type A coffee used in the blend.
The amount of type B coffee used in the mix was four times that of type A, therefore we can write:
number of pounds of type B coffee = 4x
The total cost of the blend is given as $864.60, so we can write an equation based on the cost:
[tex]4.2x + 5.5(4x) = 864.60[/tex]
Simplifying and solving for x, we get:
[tex]4.2x + 22x = 864.60[/tex]
[tex]26.2x = 864.60[/tex]
[tex]x = 33[/tex]
As a result, the mix contained 33 pounds of type A coffee.
To check our answer, we can substitute x = 33 into the equation we used to solve for it and verify that the total cost is indeed $864.60.
[tex]4.2(33) + 5.5(4*33)[/tex]
= [tex]138.6 + 726.0[/tex]
= [tex]864.6[/tex]
The total cost matches, so our answer is correct.
Therefore, Rachel's Coffee Shop used 33 pounds of type A coffee in the blend.
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The complete question is:
A blend made by Rachel's Coffee Shop combines two different kinds of coffee. Rachel pays $4.20 per pound for type A coffee and $5.50 for type B coffee. This month's blend cost $864.60 and included four pounds more of type B coffee than type A. How many pounds of coffee of type A were consumed?
120 pens and pencils triple the number of pens than pencils how many pens
If number of pencils are triple the number of pens, then the number of pens is 30
Total number of pens and pencils = 120
Number of pencil is triple the number of pens
Consider the number of pens as x
Number of pencils = 3x
Sum of the pens and pencils = 120
Then the equation will be
Number of pens + Number of pencils = Sum of number of pens and pencils
Substitute the values in the equation
x + 3x = 120
Add the like terms
(1 + 3)x = 120
4x = 120
Move 4 to the right hand side of the equation
x = 120 / 4
x = 30
Therefore, the number of pens is 30
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Ticket lines are huge around the Colossal Arena. The Boulders, one of the most popular rock groups ever, are giving a concert on Saturday. When the tickets went on sale Monday, 500 were sold in the first hour, 560 tickets were sold in the second hour, and 640 tickets were sold in the third hour. After the second hour, the increase in ticket sales every hour was 20 more than the increase of the previous hour. If sales continue at that rate, in what hour will 10,000 tickets be sold for the Boulders concert?Explain your answer in detail
If after the second hour, the increase in ticket sales every hour was 20 more than the increase of the previous hour, it will take 12 hours to sell 10,000 tickets for the Boulders concert.
To solve this problem, we need to find the number of hours it will take to sell 10,000 tickets for the concert. We are given the number of tickets sold in the first three hours and the rate at which ticket sales increase each hour after the second hour.
Let's denote the number of tickets sold in the fourth hour by "x". Then, the number of tickets sold in the fifth hour will be "x + 20", and the number of tickets sold in the sixth hour will be "x + 40", and so on.
Using this information, we can set up an equation to find "x":
500 + 560 + x + (x + 20) + (x + 40) + ... = 10,000
Simplifying the equation, we get:
3x + 1020 + 20n = 9500
where "n" is the number of hours after the third hour.
Solving for "n", we get:
n = (10,000 - 1020 - 3x) / 20
Now, we need to find the value of "x" that satisfies this equation. We can do this by testing different values of "x" until we find the one that gives an integer value for "n".
Let's start by trying "x = 640 + 20 = 660". Plugging this value into the equation, we get:
n = (10,000 - 1020 - 3(660)) / 20 = 9
We arrived at this solution by using the given information about the rate of increase in ticket sales and setting up an equation to solve for the number of hours it will take to sell 10,000 tickets. We then tested different values of "x" until we found the one that satisfied the equation and gave an integer value for "n".
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ANSWER ASAP
Three points of a parallelogram are (4, 3), (-4 3), and (2, -3).
What are the coordinates of the 4th point that would complete the parallelogram?
Given parallelogram points are (4,3),(-4 3), and (2, -3).
Let's say A= (4,3) , B=(-4 3) ,C=(2, -3) and D=(x, y)
Parallelogram defined as opposite sides are equal and parallel to each other.
From the properties of parallelogram :
We can say diagonals bisect each other.
From this we can easily find 4th point of parallelogram by using mid point concept.
Mid point formula
(X,Y)=[tex](\frac{x_{1} +x_{2}}{2},\frac{y_{1} +y_{2}}{2})[/tex]
Find mid point between AC line
midpoint (X,Y)= [tex](\frac{4 +2}{2},\frac{3-3}{2})[/tex]
(X,Y)=[tex](\frac{6}{2},\frac{0}{2})[/tex]
(X,Y)=(3,0)
Find mid point between BD Line
Mid point (X,Y)= [tex](\frac{-4 +x}{2},\frac{3+y}{2})[/tex]
Mid point of AC and BD are equal to each other
(3,0)=[tex](\frac{-4 +x}{2},\frac{3+y}{2})[/tex]
Equate x-coordinate and y-coordinate.
[tex]3=(\frac{-4 +x}{2})[/tex] and [tex]0=(\frac{3+y}{2})[/tex]
6=-4+x and 0=3+y
x=10 and y=-3
Therefore ,the coordinates of the 4th point is D(x, y)=(10,-3)
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The coordinates of the fourth point that would complete the parallelogram are (10, -3).
What is Parallelogram?A parallelogram is defined as a special type of quadrilateral that has both pairs of opposite sides parallel and equal.
We know A, B, and C, where A = (4, 3), B = (-4, 3), and C = (2, -3).
To determine the fourth point, which represents D.
First, we need to find the vector representing side AB.
Subtracting the coordinates of point B from the coordinates of point A. So:
AB = A - B = (4, 3) - (-4, 3) = (8, 0)
Next, we need to find a point that is on the line that is parallel to AB and passes through point C.
The vector CD (where D is the point) is equal to AB. So:
CD = AB = (8, 0)
We know that C = (2, -3),
We can start by adding CD to C to get D:
D = C + CD = (2, -3) + (8, 0) = (10, -3)
Therefore, the coordinates of the fourth point are (10, -3).
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Use your understanding of transformations and key features to write the slope-intercept equation of this linear function.
Enter the correct answer in the box by replacing the values of m and b.
The slope-intercept equation of this linear function is y = -3x + 5.
What is the point-slope form?Mathematically, the point-slope form of a straight line can be calculated by using this mathematical expression:
y - y₁ = m(x - x₁) or y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)
Where:
m represents the slope.x and y are the points.Based on the information provided, we can logically deduce the following data points on the line:
Points on x-axis = (0, 1).Points on y-axis = (5, 2).At point (0, 5), a linear equation of this line can be calculated in slope-intercept form as follows:
y - 5 = (2 - 5)/(1 - 0)(x - 0)
y - 5 = -3(x - 0)
y = -3x + 5
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8x^{2}-8x8x
2
−8x from -6x^{2}-10x+4−6x
2
−10x+4.
The value of the equation 8x² - 8x + 2 -( 6x² - 10x + 4) is 2x² + 2x - 2.
How to illustrate the equationIt should be noted that an equation simply has to do with the statement that illustrates the variables given. In this case, it is vital to note that
two or more components are considered in order to be able to describe the scenario.
It is important to note that an equation is the mathematical statement which can be made up of two expressions which are connected by an equal sign.
The equation can be illustrated thus:
8x² - 8x + 2 -( 6x² - 10x + 4)
8x² - 8x + 2 - 6x² + 10x - 4
= 2x² + 2x - 2
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Use the following data sets to answer the question.
Set {12, 9, 30, 1, 15, 10,
A:
12}
Set
B:
9, 30, 12, 3, 16, 11,
18}
Which statement about the shape of the data is true?
Both sets have the same median, but Set A has a larger mean.
O Both sets have the same median, but Set B has a larger mean.
O Set B has a larger mean and median than Set A.
O Set A has a lower median but a higher mean than Set B.
Answer:
Both have the same median but set A has a larger mean.
Step-by-step explanation:
You're welcome.
j–18≥1 Need help pls
Answer:
j≥19
hope this helpss :))
Now look at the exponential expression you found to be equivalent to 100,000 • 1/100,000 can you use addition or multiplication on the powers of this exponential expression to simplify it if not which operation works and which one doesn’t
The expression simplifies to 1, which means that 100,000 • 1/100,000 is equal to 1.
The exponential expression that is equivalent to 100,000 • 1/100,000 is:
[tex](10^5) * (10^-5)[/tex]
To simplify this expression using addition or multiplication on the powers, we can use the property of exponents that states:
[tex]a^m *a^n = a^{(m+n)[/tex]
This means that when we multiply two numbers with the same base, we can add their exponents to simplify the expression. However, this property does not work for division, as we need to subtract the exponents instead.
Using this property, we can simplify the expression as follows:
[tex](10^5) * (10^-5) = 10^{(5-5)} = 10^0 = 1[/tex]
Therefore, the expression simplifies to 1, which means that 100,000 • 1/100,000 is equal to 1. We can see that in this case, addition and multiplication do not help us simplify the expression, but we can use the exponent property to do so.
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a= 340 rounded to the nearest 10
b= 49.8 rounded to 1 DP
Find the minimum of a × b
Answer: First, we'll round the values of A and b:
A = 340 rounded to the nearest 10 = 340
b = 49.8 rounded to 1 decimal place = 49.8
Next, we'll find the product of A and b:
A × b = 340 × 49.8 = 16872
Finally, we'll find the minimum of A × b:
Minimum of A × b = 16872
So, the minimum value of A × b is 16872.
Step-by-step explanation:
Need answers stat trigonometry
The required measure of x is given in each triangle are given as,
2. x = 74.01 3. 25.09 4. x = 23.78
5. x = 26.64 6. x = 21.03° 7. x = 39.55°
If you know the lengths of two sides of a right triangle, you can use trigonometric ratios to calculate the measures of one (or both) of the acute angles.
Here,
2.
For the given triangle
Apply the trigonometric ratios,
Tan 62 = x/25
x = 25 tan62
x = 74.01
Similarly,
3. x = 11/sin26 = 25.09
4. x = 32sin48 = 23.78
5. x = 29/cos12 = 29.64
6. cosx = 14/15 = 21.03°
7. tanx = 19/23 = 39.55°
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how many solutions do 2(x-4)=2x-8 have
The equation 2(x - 4) = 2x - 8 has infinitely many solutions.
What is an Equation?An equation is the statement of two expressions located on two sides connected with an equal to sign. The two sides of an equation is usually called as left hand side and right hand side.
Given equation is 2(x - 4) = 2x - 8.
Solving this,
Using the distributive property, a (b + c) = ab + ac, 2(x - 4) = (2 × x) - (2 × 4).
Substituting in the original equation,
(2 × x) - (2 × 4) = 2x - 8
2x - 8 = 2x - 8
2x - 2x = -8 + 8
0 = 0
Right hand side and left hand side are equal if we put any value for x.
So it has infinitely many solutions for x.
Hence the given equation has infinitely many solutions.
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