a. The recursive formula to represent the sequence is aₓ = aₓ₋₁ + 10.
b. The explicit formula to represent the sequence is aₓ = 50 + 10x.
c. We have $310 in savings after 26 weeks.
What is sequence?
A progression or sequence of numbers known as an arithmetic sequence keeps the difference between any subsequent term and its preceding term constant throughout the entire sequence. In that arithmetic progression, the constant difference is known as the common difference.
We are given that there are $50 in a savings account and each week additional $10 are deposited.
a. Let x be the number of weeks
a₀ = $50
aₓ = aₓ₋₁ + 10
So, the recursive formula to represent the sequence is aₓ = aₓ₋₁ + 10.
b. Let x be the number of weeks.
So, the explicit formula is given by
aₓ = 50 + 10x
c. Now, we are given x = 26.
So, by substituting this, we get
⇒ a₂₆ = 50 + 10 * 26
⇒ a₂₆ = 50 + 260
⇒ a₂₆ = $310
Hence, the required solutions have been obtained.
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Two gears turn together. Each time Gear A makes 36 turns, Gear B makes 27 turns. How many turns does Gear A make When Gear B makes 90 turns?
In the proportion, Gear A makes 120 turns when Gear B makes 90 turns.
What is Proportion?
A proportion is a statement that two ratios or fractions are equal. It shows the relationship between two or more quantities that are proportional to each other.
The gears have a fixed ratio of rotations, which is determined by the number of teeth on each gear.
To find out how many turns Gear A makes when Gear B makes 90 turns, we can set up a proportion:
=> [tex]\frac{36}{27} =\frac{ x}{90}[/tex]
where x is the number of turns Gear A makes.
To solve for x, we can cross-multiply:
=> 36 × 90 = 27 × x
=> 3240 = 27x
=> x = 120
Therefore, Gear A makes 120 turns when Gear B makes 90 turns.
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Solve the problem in the picture please!
x^2-16÷ (x-16 )(x+4)
= (x^2)-(4^2)÷ (x-16)(x+4)
= (x+4)(x-4)÷ (x-16) (x+4)
=(x-4)÷(x-16)
Write a mathematical expression to represent the following statement.
'Two less than a number plus twenty.'
Answer: (n - 2) + 20
Step-by-step explanation:
We will create a mathematical expression using the statement given. 'Less' implies subtraction, let n be a number.
'than a number' ➜ n
'Two less' ➜ - 2
'plus twenty.' ➜ + 20
'Two less than a number plus twenty.' ➜ (n - 2) + 20
If the width of a pool is 60 ft and the perimeter is 200 ft How long is the pool
Answer: The pool is 40 feet long.
Step-by-step explanation: 60ft) = 2 x 100ft = 200ft. Answer. The pool is 40 feet long.
a) Write 1 as a decimal rounded to 1 significant figure.
b) Write
2
as a decimal rounded to 3 significant figures.
Since it is less than 5, we do not round up, and our final answer is 2.00.
What is decimal round?Decimal rounding is a process of changing a number to a certain number of decimal places, based on a specified rounding rule. In decimal rounding, the digits to the right of the specified decimal place are examined to determine whether rounding is necessary. If the digit immediately to the right of the specified decimal place is 5 or greater, the number is rounded up by adding 1 to the last digit of the specified decimal place. If the digit is less than 5, the number is rounded down by simply dropping the digits to the right of the specified decimal place.
(a). To round 1 to 1 significant figure, we only keep the leftmost digit, which is 1. Therefore, 1 rounded to 1 significant figure is 1.
(b) . To write 2 as a decimal rounded to 3 significant figures, we start by identifying the leftmost significant digit. In this case, it is the digit 2. We then count two more digits to the right, which gives us 2.00. Finally, we look at the next digit, which is 0. Since it is less than 5, we do not round up, and our final answer is 2.00.
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Think about a density curve that consists of two line segments. The first goes from the point (0, 1) to the point (0.7, 1). The second goes from (0.7, 1) to (0.9, 2) in the xy-plane. What percent of observations fall between 0.7 and 0.9? Rstudio
a) 0.20
b) 1.00
c) 0.05
d) 0.30
e) 0.50
0.20 is percent of observations fall between 0.7 and 0.9.
What use does percentage serve?
The simplest way to use percentages is to compare two numbers, with the second number being rebased to 100. Consider that we are curious about the proportion of employed women who are female. If this proportion is equal to 1/2, then generally speaking, there is one employed woman for every two men.
Density curve consists of two line segments .
first line goes from the point (0,1) to the points (0.7 , 1) . second line goes from (0.7 , 1) to (0.9 , 2 ) in the xy plane .
then percentage of observation fall below 0.20 and is 0.20.
percentage = 20% = 0.20
area of rectangle = ab
= 0.2 * 1
= 0.20
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Find the domain and range for y=4x^2+24x+13 and f(x)=-5x+20x-7
All real numbers make up the domain of a linear function, hence the domain of [tex]f(x)=-5x+20x-7[/tex] is [tex](-\infty , \infty )[/tex] . The range of a linear function is also the set of all real numbers, hence [tex]f(x)=-5x+20x-7[/tex] has a range of (-[tex]\infty[/tex], [tex]\infty[/tex]).
What is domain and range?For the formula, [tex]y = 4x2 + 24x + 13[/tex]
All real numbers make up the domain of a polynomial function, hence the domain of y=4x2+24x+13 is [tex](-\infty , \infty )[/tex]
We can use calculus or the square root method to determine the function's range. At x=-3, where y=1, the function's minimal value is found. As a result, the function's range is [tex][1, \infty )[/tex].
Using the formula [tex]f(x)=-5x+20x-7:[/tex]
Using related words together, we obtain [tex]f(x)=15x-7.[/tex]
Therefore, All real numbers make up the domain of a linear function, hence the domain of [tex]f(x)=-5x+20x-7[/tex] is [tex](-\infty , \infty )[/tex] . The range of a linear function is also the set of all real numbers, hence [tex]f(x)=-5x+20x-7[/tex] has a range of (-[tex]\infty[/tex], [tex]\infty[/tex]).
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Help with math problems
Answer:
Step-by-step explanation:
Sorry, i can't "add up to five attachments" because i say only answer.
1.(−24,8)
2.[−3,1]
3.[−3,4]
4. (−3,5)
5 and 6 no answer (check my attachments)
7. (−∞,−8)v(4,+∞)
8 (−∞,1)v(7,+∞)
9. (−∞,−3]v[6,+∞)
10. (−∞,−3]v[2,+∞)
11. (−∞,∞)
12. (−∞,∞)
13. (−∞,−[tex]\frac{21}{4}[/tex]]v[[tex]\frac{15}{4}[/tex],+∞)
14.[-[tex]\frac{4}{5}[/tex],[tex]\frac{8}{5}[/tex]]
15. (-[tex]\frac{17}{3}[/tex];5)
16. (−∞,−14]v[22,+∞)
17. no answer (how 5 and 6)
18. (−∞,∞)
19. (−2,[tex]\frac{2}{3}[/tex])
20. (−∞,−4)v(−[tex]\frac{2}{3}[/tex],+∞)
Add the expressions.
the quantity negative 8 minus one fourth times p end quantity plus the quantity five eighths times p minus 7 end quantity
negative 3 over 12 times p plus negative 1
7 over 16 times p minus 1
3 over 8 times p minus 15
7 over 8 times p plus negative 15
Please help me and tell me what is did wrong I picked The second one
An addition of the quantity negative 8 minus one fourth times p end quantity plus the quantity five eighths times p minus 7 end quantity is: C. 3 over 8 times p minus 15.
What is an expression?In Mathematics, an expression is sometimes referred to as an equation and it can be defined as a mathematical equation which is typically used for illustrating the relationship that exist between two (2) or more variables and numerical quantities (number).
Based on the information provided above, we have the following mathematical expressions:
Expression = -8 - 1/4(p)
Expression = 5/8(p) - 7
By adding the two expressions, we have:
Addition = -8 - 1/4(p) + 5/8(p) - 7
Addition = -8 - p/4 + 5p/8 - 7
Addition = -15 +(-p/4 + 5p/8)
Addition = -15 +(-2p + 5p)/8
Addition = -15 + (3p)/8
Addition = 3p/8 - 15
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Solve the problem in the picture please!
Answer:
C. -7
Step-by-step explanation:
A rational expression will always be undefined when the denominator = 0 because we can't divide by 0.
-7 + 7 = 0 so -7 is the only number which makes the expression undefined
Scott Salman, a travel agent, is paid on variable commission, is married, and claims four withholding allowances. He receives 3% of the first $20,000 in sales, 4% of the next $10,000 in sales, and 6% of all sales over $30,000. This week he has sales of $45,550 and the following deductions: FICA, Medicare, federal withholding, state disability insurance, state withholding, a retirement contribution of $45, a savings bond of $50, and charitable contributions of $20. Find his net pay after subtracting all of his deductions.
Scott Salman's net pay after subtracting all of his deductions is $1,620.26.
How To calculate Scott Salman's net pay?
To calculate Scott Salman's net pay, we need to first calculate his commission earnings and then subtract all of his deductions.
Commission Earnings:
3% of the first $20,000 in sales = $600
4% of the next $10,000 in sales = $400
6% of all sales over $30,000 = 6% × ($45,550 - $30,000) = $930
Total commission earnings = $600 + $400 + $930 = $1,930
Now we can calculate his gross pay by adding his commission earnings to his base salary:
Gross Pay:
Base salary = 0 (not given)
Commission earnings = $1,930
Total gross pay = $1,930
Next, we need to calculate his deductions. We'll assume the following rates for each deduction:
FICA: 7.65%
Medicare: 1.45%
Federal withholding: based on the IRS tax tables (not provided)
State disability insurance: 1%
State withholding: based on the state tax tables (not provided)
Retirement contribution: $45
Savings bond: $50
Charitable contributions: $20
Deductions:
FICA = 7.65% × $1,930 = $147.45
Medicare = 1.45% × $1,930 = $27.99
Federal withholding = based on the IRS tax tables (not provided)
State disability insurance = 1%×$1,930 = $19.30
State withholding = based on the state tax tables (not provided)
Retirement contribution = $45
Savings bond = $50
Charitable contributions = $20
Total deductions = $147.45 + $27.99 + $19.30 + $45 + $50 + $20 = $309.74
Finally, we can calculate Scott Salman's net pay by subtracting his total deductions from his gross pay:
Net Pay:
Gross pay = $1,930
Total deductions = $309.74
Net pay = $1,930 - $309.74 = $1,620.26
Therefore, Scott Salman's net pay after subtracting all of his deductions is $1,620.26.
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Express the following argument mathematically and give the rule(s) that could be used to prove or disprove them. a. The children are sick. The doctors are not here. Therefore the doctors are not here and the children are sick. [2 marks]?
Answer:
Step-by-step explanation:
Let A represent "The children are sick."
Let B represent "The doctors are not here."
Argument: A and ¬B
Rule(s) used to prove or disprove: Conjunction (AND)
Help plssssssssssssssss
The measure of 1/2 of the circumference of a circle is 157 feet. What is the radius of the circle, to the nearest foot?
A rectangle has side lengths of 5 inches and 5–√ inches. Which statement must be true about the area of the rectangle?
The area of a rectangle is represented by an irrational number because the product of the two side lengths is an irrational number. This is because the product between an integer and an irrational number leads to another irrational number, which is the right answer.
What is the area of the rectangle?A rectangle is a four-sided flat geometric form with right angles on all four sides. It is a quadrilateral, which implies that it has four sides. A rectangle's opposite sides are parallel and equal in length, whereas its adjacent sides are perpendicular to one other. A rectangle's area is computed by multiplying its length by its width, and its perimeter is computed by summing the lengths of all four sides.
According to this question, we know the lengths of the two sides of the rectangle, the length of a side is an positive integer and the length of the other one is an positive irrational number. The area of the rectangle is the product of the two sides lengths mentioned above.
By algebra, we know that the product between an integer and an irrational number leads to other irrational number. Therefore, the area of the rectangle is represented by an irrational number.
A = 3 x [tex]\sqrt{5}[/tex]
A = 3[tex]\sqrt{5}[/tex]
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The complete question is: A rectangle has side lengths of 3 inches and 5–√ inches. Which statement must be true about the area of the rectangle?
find the length of the arc
(50 points)
can mark brainly
Answer: i'm going to assume, this needs to be a full answer
meaning this would be
43.9823 inches (or 44 if fully rounded)
basically, to find arc length, you take the given degrees shown (210) and divide it over the full length of the circle (360)
dividing this gives us 58.333333 (repeated forever) or 7/12
then we need to find the circumference, which is c=pid (or c=pi times diameter)
so we would do 24 multiplied by 3.14159 (this is standard amount of numbers for naturally calculating pi in equations) and we get 75.39816
finally, we need to multiply 75.39816 to 7/12, and we will get 43.98226
which when rounded to the 4th digit will give us 43.9823
Answer with step-by-step explanation:
The formula to find the arc length of a circle is:
[tex]\sf \red {Arc\: length = \frac{\theta}{360} *2 \pi r}[/tex]
PQ major arc length
[tex]\sf Arc\: length = \frac{\theta}{360} *2 \pi r\\\\\sf Arc\: length = \frac{210}{360} *2 \pi*12\\\\\sf Arc\: length = \frac{15825.6}{360} \\\\\sf Arc\: length = 43.96\: in[/tex]
PQ minor arc length
[tex]\sf Arc\: length = \frac{\theta}{360} *2 \pi r\\\\\sf Arc\: length = \frac{150}{360} *2 \pi*12\\\\\sf Arc\: length = \frac{11304}{360} \\\\\sf Arc\: length = 31.4\: in[/tex]
Let a, b, and m be positive integers, where = a, and
4
=b. Which of the following numbers could be m?
The only number that could m is 480 as it is both divisible by 4 and 6. Thus, option J is correct.
What do you mean by term Integers?A whole number that can be either positive, negative, or zero is known as an integer. It is a number without a decimal or fractional component. Integer examples include: -3, -2, -1, 0, 1, 2, 3, etc
Lets check if 4 and 6 are divisible by both a and b and is a positive integer,
F. 124:
124/4 = 31, is a positive integer
124/6 = 20.6 is a not positive integer
Thus, 124 is not m.
G. 222:
222/4 = 55.5, is a not positive integer
Thus, 222 is not m.
H. 310:
310/4 = 77.5, is a not positive integer
Thus, 310 is not m.
J. 480:
480/4 = 120, is a positive integer
480/6 = 80 is a positive integer
Thus, 480 is m.
K. 544:
544/4 = 136, is a positive integer
544/6 = 90.6 is not a positive integer
Thus, 544 is not m.
Thus, The only number that could m is 480 as it is both divisible by 4 and 6. Thus, option J is correct.
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Complete question:
Jasmine owns her own housekeeping business. She charges $50 to clean a house with 3 bedrooms and 2 bathrooms. She charges $75 to clean a house with 3 to 4 bathrooms. It takes Jasmine 3 hours to clean a house with 2 bathrooms and 4 hours to clean a house with 3 or 4 bathrooms. How much more does Jasmine make per hour cleaning a larger house compared to a smaller house?
Jasmine makes $2.08 more per hour cleaning a larger house compared to a smaller house.
Define the term pricing strategy?Pricing strategies refer to the methods and techniques used by businesses or companies to set the prices of their products or services.
Let's first calculate the hourly rate Jasmine charges for cleaning a house with 2 bathrooms:
She charges $50 for a house with 3 bedrooms and 2 bathrooms, and it takes her 3 hours to clean it, so her hourly rate is:
⇒ $50 ÷ 3 hours = $16.67/hour
Now let's calculate the hourly rate she charges for cleaning a house with 3 or 4 bathrooms:
She charges $75 for a house with 3 to 4 bathrooms, and it takes her 4 hours to clean it, so her hourly rate is:
⇒ $75 ÷ 4 hours = $18.75/hour
Therefore, Jasmine makes $18.75/hour cleaning a larger house compared to $16.67/hour cleaning a smaller house.
To find out how much more Jasmine makes per hour cleaning a larger house compared to a smaller house, we can subtract the hourly rate for a smaller house from the hourly rate for a larger house:
⇒ $18.75/hour - $16.67/hour = $2.08/hour
So, Jasmine makes $2.08 more per hour cleaning a larger house compared to a smaller house.
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solve for y
3(3y-8)=21
Answer:
y = 5
Step-by-step explanation:
3(3y-8)=21
expand:
9y - 24 = 21
+24 to both sides to get 9y on its own.
9y = 45
divide both sides by 9 to get y on its own.
therefore
y = 5
hope this makes sense!
Answer: Solve for
y
by simplifying both sides of the equation, then isolating the variable.
y≈−1.21698677,2.94165923
Step-by-step explanation:
If his teacher used a 95% confidence interval to correctly estimate the true percentage of correct answers that he should have scored on this exam, what possible grades could the teacher reasonably assign to Gabriel
The possible range of scores is given as follows:
Anything from 21% to 59%.
The percentage that is typically assigned is given as follows:
40%.
What is a confidence interval of proportions?A confidence interval of proportions has the bounds given by the rule presented as follows:
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which the variables used to calculated these bounds are listed as follows:
[tex]\pi[/tex] is the sample proportion, which is also the estimate of the parameter.z is the critical value.n is the sample size.The confidence level is of 95%, hence the critical value z is the value of Z that has a p-value of [tex]\frac{1+0.95}{2} = 0.975[/tex], so the critical value is z = 1.96.
The parameters for this problem are given as follows:
[tex]\pi = 0.4, n = 25[/tex]
Then the lower bound of the confidence interval is given as follows:
0.4 - 1.96 x sqrt(0.4 x 0.6/25) = 0.21.
The upper bound of the confidence interval is given as follows:
0.4 + 1.96 x sqrt(0.4 x 0.6/25) = 0.59.
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I need help answering the this
When p = 0. 1, the mean of the sampling distribution would be 65. 5 and the standard deviation would be 7.6769.
When p = 0.5, the mean of the sampling distribution would be 327.5 and the standard deviation would be 12.7984 .
How to find the mean and standard deviation ?To find the mean and standard deviation of the sampling distribution of the sample proportion, we can use the following formulas:
p = 0.1
Mean:
μ p = n x p = 655 x 0.1 = 65.5
Standard Deviation:
σ_p = √(n x p x (1 - p)) = √(655 x 0.1 x (1 - 0.1)) = √(655 x 0.1 x 0.9) = √(58.95)
σp = 7.6769
When p = 0.5
Mean:
μ p = n x p = 655 x 0.5 = 327.5
Standard Deviation:
σ p = √(n x p x (1 - p)) = √(655 x 0.5 x (1 - 0.5)) = √(655 x 0.5 x 0.5) = √(163.75)
σp = 12.7984
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The three data sets have MAD value of 7,9 and 11. Match the data sets to the apporopriate MAD value with out actuly making a calculation.
Based on the general properties of the MAD and the characteristics of the data sets, these matches seem reasonable.
What is data set?In statistics, a dataset is a collection of data that is organized in a specific way. Typically, a dataset consists of multiple data points, where each data point represents an observation or measurement of a particular variable or set of variables.
We can make some general observations to match the data sets to the appropriate MAD value without actually calculating them:
The MAD measures the average distance between each data point and the median of the data set.
Therefore, the larger the MAD value, the more spread out the data set is.
Data set 1 will have the smallest MAD value, since it is the most tightly clustered around the median.
Data set 3 will have the largest MAD value, since it is the most spread out around the median.
Data set 2 will have a MAD value between those of data sets 1 and 3.
Based on these observations, we can match the data sets to the appropriate MAD value as follows:
Data set 1 has the smallest MAD value (7).
Data set 2 has a medium MAD value (9).
Data set 3 has the largest MAD value (11).
Of course, without actually calculating the MAD values, we can't say for certain whether these matches are correct.
Therefore, based on the general properties of the MAD and the characteristics of the data sets, these matches seem reasonable.
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which of the following statements is false 1) sin45=cos45 2)cos110=sin80 3)sin30=cos40 5) sin0=cos90
The false statement is 3)sin30=cos40.
This is because the sine of 30 degrees is 0.5, whereas the cosine of 40 degrees is approximately 0.766. These two values are not equal to each other.
The following claims, however, are accurate:
The sine of 45 degrees is equal to the cosine of 45 degrees (both are equal to approximately 0.707).The cosine of 110 degrees is equal to the sine of 80 degrees.The sine of 0 degrees (or any multiple of 360 degrees) is equal to 0, and the cosine of 90 degrees (or any odd multiple of 90 degrees) is also equal to 0.Therefore, the false statement is 3)sin30=cos40.
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Factor 16x2 – 49.....
Answer:
(4x+7)(4x-7)
Step-by-step explanation:
Use DoS (x+y)(x-y)=x^2-y^2
A composite figure is shown.
A five-sided figure with two parallel sides. The shorter one is 43 centimeters. The height of the figure is 34 centimeters. The portion from the vertex to the perpendicular height is 21 centimeters. The portion from a point to a vertical line created by two vertices is 16 centimeters.
Which of the following represents the total area of the figure?
1,432 cm2
2,091 cm2
2,507 cm2
2,520 cm2
2091 square meters represents the total area of the figure.
What is the example polygon?
A polygon is any two-dimensional shape formed by straight lines. Triangles, hexagons, pentagons, and quadrilaterals are examples of polygons.
Polygons are flat two-dimensional shapes with straight sides that are completely closed. The sides should be straight, not curved. However, polygons can have any number of sides. The word polygon comes from the Greek word "polgonos".
This figure is called a pentagon and has the shape of a trapezoid.
To find its area, we can calculate the area of the trapezoid, which is given by:
A = (b1 + b2)/2 * h
where b1 and b2 are the lengths of the parallel sides and h is the height.
In this case, the length of b1 is 43 meters and the length of b2 is 18 meters, and the height is 34 meters, so the area of the trapezoid is:
A = (43 + 16)/2 * 34 + (43 + 21) * 34
A = 1003 + 1088
A = 2091 square meters.
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Need help with this
5. The value of angle LNM in the given circle is 54 degrees. 7. The value of angle ABC is 51 degrees.
What is a circle?A circle is a two-dimensional shape made up of a collection of points that are spaced uniformly apart from one another (called the radius) on a plane. The fixed point is referred to as the circle's origin or centre, and the fixed distance between each point and the origin is referred to as the radius. The centre, the radius, and the diameter of a circle may be seen in the following illustration.
5. The angle subtended by the two chords is half the measure of the angle at the center.
Thus,
angle LNM = 1/2 (angle LPM)
Substitute the value of angle LPM = 108, thus:
angle LNM = 1/2(108) = 54 degrees.
Hence, the value of angle LNM in the given circle is 54 degrees.
7. For measure angle ABC we have:
16x-26 = 2(5x+11)
16x-10x = 22+26
6x=48
x = 8
Substituting the value of x we have:
5(8) + 11 = 40 + 11 = 51
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The oblique pyramid has a square base.
An oblique pyramid has a square base with a base edge length of 2 centimeters. The vertical height of the pyramid is 3.75 centimeters.
What is the volume of the pyramid?
2.5 cm3
5 cm3
6 cm3
7.5 cm3
Answer:
5cm^3
Step-by-step explanation:
22-1x5-4 to the second
The value of a given arithmetic expression is 1.
We have given that an arithmetic expression -
22-(1×5)-4 to the seccond
So we can write it -
22-(1×5)-4²
we shall solve it with the help of the BODMASS rule
BODMAS Rule: The BODMAS Rule is a crucial mathematical tool for resolving issues. It is a technique for using an arithmetic expression to resolve mathematical problems. The abbreviation BODMAS stands for brackets, order of powers or roots, division, and multiplication. S indicates for subtraction, whereas A stands for addition.
according to BODMASS
first, solve the brackets and square,
=22-(5)-16
now subtract all
=22-21
=1
The complete question is
Solve the given arithmetic expression -
22-(1×5)-4 to the seccond
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On a certain day, Miquel. had a credit of $75 in her checking account and spent $240. Which represents the total change in his account that day?
A. $315
B. $365
C. -$135
D. -$165
SHOW YOUR WORK!!
Answer:
B. $365
Step-by-step explanation:
CIRCLES GEO !!
7. Is DE tangent to circle C
8. ST is tangent to circle Q. Find the value of r.
9. Find the value(s) of x.
The value of x is approximately equals to 30.4 and the value of r is approximately 9.24.
What is circle ?
In geometry, a circle is a two-dimensional shape consisting of all points that are a fixed distance (called the radius) from a given point (called the center). A circle is a set of points that are equidistant from the center.
Is DE tangent to circle C?
Yes, DE is tangent to circle C. This is because a tangent to a circle is a line that intersects the circle at exactly one point, and in this case, DE intersects circle C at point E and only touches the circle at that point.
ST is tangent to circle Q. Find the value of r.
Since ST is tangent to circle Q at point T, the radius of the circle Q is perpendicular to ST at T. Therefore, triangle SRT is a right triangle, where RS is the hypotenuse and ST is the adjacent side to the angle at S. We can use the Pythagorean theorem to find the length of the hypotenuse:
We know that ST = 10 and RT = r, so we can substitute these values to get:
[tex]RS^{2}[/tex] = 100+ [tex]r^{2}[/tex]
We also know that RS = 2r, so we can substitute this value to get:
4[tex]r^{2}[/tex]= 100 + [tex]r^{2}[/tex]
3[tex]r^{2}[/tex] = 100
[tex]r^{2}[/tex] = 100/3
r ≈ 9.24
Therefore, the value of r is approximately 9.24.
Find the value(s) of x.
Since AB is a diameter of circle C, triangle ABC is a right triangle with right angle at B. Therefore, we can use the Pythagorean theorem to find the length of BC:
We know that AB = 26 and AC = x + 8, so we can substitute these values to get:
[tex](x + 8)^{2}[/tex]= 676 + [tex]BC^{2}[/tex]
We also know that BC = x - 2, so we can substitute this value to get:
[tex](x + 8)^{2}[/tex]= 676 + [tex](x - 2)^{2}[/tex]
[tex]x^{2}[/tex]+ 16x + 64 = 676 + [tex]x^{2}[/tex]- 4x + 4
20x = 608
x = 30.4
Therefore, the value of x is 30.4.
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