When extending beyond two dimensions, the analytical approach is generally easier to use than Euclidean geometry. The reason for this is that Euclidean geometry relies heavily on visualizing geometric shapes and their properties in three dimensions or higher, which can be difficult for most people.
In contrast, the analytical approach uses algebraic equations to describe geometric shapes and their properties, which can be more straightforward and intuitive for many individuals. The analytical approach also allows for the use of software tools to manipulate and visualize shapes in higher dimensions, which can be particularly useful for complex calculations and designs.
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In a right triangle, angle A measures 20°. The side opposite angle A is 10 centimeters long. Approximately how long is the hypotenuse of the triangle?
3.4 centimeters
10.6 centimeters
27.5 centimeters
29.2 centimeters
Answer: 27.5 centimeters
Step-by-step explanation:
angle A measures 20 degrees and we know it's a write tringle so 180-(90+20)=70 degrees
so, angle B measures 70 degrees.
using the law of cosines:
[tex]\frac{sin70}{b} =\frac{sin20}{10}[/tex]
[tex]b=\frac{10sin(70)}{sin(20)}[/tex]
so, side b =[tex]\frac{10sin(70)}{sin(20)}[/tex]
Using the Pythagorean theorem to find the hypotenuse:
hypotenuse[tex]=\sqrt{(\frac{10 sin70}{sin20})^{2} + 10^{2} }[/tex]
approximately = 27.5 centimeters
A miniature golf course recently provided its customers with a variety of colored golf balls.
red 2
white 1
pink 10
blue 2
green 5
What is the experimental probability that the next customer will receive a pink golf ball?
Write your answer as a fraction or whole number.
P(pink)=
Point m is on line segment ln. given ln=20 and lm=7,determine the length mn
27 mn is the length of line segment .
What in mathematics is a line segment?
A line segment has two unique points on the line defining its boundaries. Or, a line segment is a section of the line that links two points, as another alternative.
In contrast to a line, which has no endpoints and can go on forever, a line segment has two distinct endpoints that are fixed or identifiable.
The value of the line segment will be calculated as:-
Point M is on the line segment MN.
In = 20
Im = 7
MN = In+ Im
= 20 + 7
= 27
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please help me i really need it
The simplified expression, given the rule for exponentiation of powers, is 1, 024 x ³⁰.
How to simplify the expression ?To simplify the expression ((2x³) ⁵ ) ², we need to apply the rule for exponentiation of powers which states " When an expression is raised to a power, and that result is raised to another power, we can simplify by multiplying the exponents."
Using this rule, we can simplify the expression as follows:
( ( 2 x ³ ) ⁵ ) ² = (2 ⁵ x (3 x 5) ) ^ 2
= ( 32 x ¹⁵ ) ²
= 1, 024 x ³⁰
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Suppose you wish to estimate the difference between the mean acidity for rainfalls at two different locations, one in a relatively unpolluted area and the other in an area subject to heavy air pollution. If you wish your estimate to be correct to the nearest 0.2 pH, with probability near 0.90, approximately how many rainfalls (pH values) would have to be included in each sample? (Assume that the variance of the pH measurements is approximately 0.35 at both locations and that the samples will be of equal size. Round your answer up to the nearest whole number.)
Approximately 21 pH values would have to be included in each sample to estimate the difference between the mean acidity for rainfalls at the two different locations to the nearest 0.2 pH, with probability near 0.90.
What is the standard error?
Standard error is a measure of the variability or uncertainty of a statistic. It is the standard deviation of the sampling distribution of a statistic, and it estimates how much the sample statistic may vary from the true population parameter due to random sampling error.
To estimate the difference between the mean acidity for rainfalls at two different locations, we can use the formula for the standard error of the difference between means:
[tex]SE = \sqrt{[(s1^2 / n1) + (s2^2 / n2)]}[/tex]
where s1 and s2 are the sample standard deviations, n1 and n2 are the sample sizes, and SE is the standard error of the difference between means.
We want our estimate to be correct to the nearest 0.2 pH, with probability near 0.90. This means we want to find the sample size n that will give us a margin of error of 0.2 pH with a confidence level of 90%.
We can use the following formula to find the sample size:
[tex]n = [(z*\sigma / E)^2][/tex]
where z is the z-score for the desired confidence level (0.90), σ is the population standard deviation (0.35), and E is the margin of error (0.2).
First, we need to find the z-score for a 90% confidence level. This can be found using a standard normal distribution table or calculator. For a 90% confidence level, the z-score is approximately 1.645.
Substituting these values into the formula, we get:
n = [(1.645*0.35 / 0.2)^2]
= 20.95
Rounding up to the nearest whole number, we get a sample size of n = 21 for each sample.
Therefore, approximately 21 pH values would have to be included in each sample to estimate the difference between the mean acidity for rainfalls at the two different locations to the nearest 0.2 pH, with probability near 0.90.
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The diameter of a circle is 14 feet. What is the circle's circumference?
Use 3.14 for л.
Answer
43.96
14 x 3.14 = 43.96
hope this helped!
WHOEVER DOES MOST ASAP GETS AN EXTRA 50
Fraction value [tex]16\frac{17}{27}[/tex] as a percentage is [tex]1662\frac{26}{27} %[/tex] %
Fraction value [tex]16\frac{17}{27}[/tex] as a decimal is 16.629629
What is percentage, decimal, and fraction?Percentage, decimal, and fraction are all ways of representing numbers that are related to each other. Here's a brief explanation of each:
Percentage: A percentage is a number expressed as a fraction of 100, with the symbol % (percent) added. For example, 50% is the same as 50/100 or 0.5.
Decimal: A decimal is a way of representing fractions using the base-10 numbering system. It is written with a decimal point between the whole number and the fractional part. For example, 0.5 is the same as 5/10 or 50/100 or 50%.
Fraction: A fraction is a way of representing a part of a whole or a ratio of two numbers. It is expressed as a ratio of two integers, with the numerator (top number) representing the number of parts being considered, and the denominator (bottom number) representing the total number of equal parts. For example, 1/2 is the same as 0.5 or 50%.
Fraction value [tex]16\frac{17}{27}[/tex] as a percentage is [tex]1662\frac{26}{27} %[/tex] %
Fraction value [tex]16\frac{17}{27}[/tex] as a decimal is 16.629629
For other values see the below figure.
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I need help on this asap!!
The inequality and the shaded region are added as attachment
How to graph the inequality and show the shaded regionThe given parameter from the question is represented as
0.4r ≤ 120 and r ≥ 4(360/5)
Evaluate the expression by products and quotients
So, the expression becomes
r ≤ 300 and r ≥ 288
When these inequalities are combined, we have the following compound expression of inequality
288 ≤ r ≤ 300
Next, we plot the graph of the inequality
The inequality is added as an attachment
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Consider data Y1,Y2,…Yn that is a random (i.e. independent) sample from a Normal distribution with unknown mean μ and known variance σ2. You wish to infer μ from the data using a Bayesian approach and select a prior on μthat is Normal with mean μ0 and variance τ2. a. Derive the posterior distribution for μ. Since you should know the final result, credit will only be given for the derivation. b. Write down the posterior mean as a function of the posterior variance. Explain what happens to the posterior mean as a function of increasing n. c. Confirm your answer from part b) by plotting your results in R assuming μ0=0,τ2=1,σ2=100, and with the data Yˉ=5 for n=1,10,100,1000.
The value of t such that the area under the curve between 1 and 11 equals 0.95, assuming the degrees of freedom is 8, is 1.86.
What is degree of freedom?Degree of freedom refers to the number of independent variables that can be varied in a statistical experiment or analysis. It is a measure of the flexibility of the experiment or analysis to accommodate new data or observations.
In this case, the degrees of freedom is 8. To find the t-value, the t-table must be consulted. The t-table is a chart of t-values for different degrees of freedom. The t-value is the value at which the area under the curve between 1 and 11 equals 0.95. The t-table is organized such that the rows represent the degrees of freedom and the columns represent the area under the curve. For example, if the degrees of freedom is 8 and the area under the curve is 0.95, the t-value can be found in the row for 8 degrees of freedom and the column for 0.95 area under the curve. The t-value from the t-table in this case is 1.86.
Therefore, the value of t such that the area under the curve between 1 and 11 equals 0.95, assuming the degrees of freedom is 8, is 1.86.
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complete ques is:
Consider data Y1,Y2,…Yn that is a random (i.e. independent) sample from a Normal distribution with unknown mean μ and known variance σ2. You wish to infer μ from the data using a Bayesian approach and select a prior on μthat is Normal with mean μ0 and variance τ2. a. Derive the posterior distribution for μ. Since you should know the final result, credit will only be given for the derivation. b. Write down the posterior mean as a function of the posterior variance. Explain what happens to the posterior mean as a function of increasing n. c. Confirm your answer from part b) by plotting your results in R assuming μ0=0,τ2=1,σ2=100, and with the data Yˉ=5 for n=1,10,100,1000.
NEED HELP PLEASE HELP
Answer:
y = 2/3x - 2
Step-by-step explanation:
Ms. Katie had a pizza party with the art club theres 8 students and each student ate 1/3 of a pizza how many pizzas did they eat altogther
The 8 students at the pizza party ate 2 and 2/3 pizzas if each student ate 1/3 of a pizza.
If each of the 8 students ate 1/3 of a pizza, we can find the total number of pizzas by multiplying the number of students by the fraction of a pizza each student ate:
8 students × 1/3 pizza per student = 8/3 pizzas
However, it's more common to express the result as a mixed number or decimal. To convert the improper fraction 8/3 to a mixed number, we can divide the numerator by the denominator:
8 ÷ 3 = 2 with a remainder of 2
Therefore, the students ate 2 and 2/3 pizzas altogether. Alternatively, we can convert the improper fraction to a decimal by dividing the numerator by the denominator:
8/3 = 2.67
Therefore, the students ate approximately 2.67 pizzas altogether.
To recap, if each of the 8 students at the pizza party ate 1/3 of a pizza, they ate 8/3 pizzas altogether, which is equal to 2 and 2/3 pizzas or approximately 2.67 pizzas.
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Isabella built a time travel machine, but she can't control the destination of her trip. Each time she uses the machine she has a 0. 250. 250, point, 25 probability of traveling to a time before she was born. During the first year of testing, Isabella uses her machine 555 times. Assuming that each trip is equally likely to travel before Isabella was born, what is the probability that at least one trip will travel before Isabella was born? Round your answer to the nearest hundredth. P(\text{at least one before she's born})=P(at least one before she’s born)=P, (, start text, a, t, space, l, e, a, s, t, space, o, n, e, space, b, e, f, o, r, e, space, s, h, e, apostrophe, s, space, b, o, r, n, end text, ), equals
The probability that at least one trip will travel before Isabella was born is 0.9999, or 99.99% (rounded to the nearest hundredth).
We can use the complement rule to find the probability that at least one trip will travel before Isabella was born. The complement rule states that the probability of an event happening is equal to 1 minus the probability of the event not happening. In this case, the event we are interested in is at least one trip traveling before Isabella was born.
The probability of none of the 555 trips traveling before Isabella was born is (1-0.25) raised to the power of 555, since the probability of each trip not traveling before Isabella was born is 1 - 0.25 = 0.75.
So, the probability of at least one trip traveling before Isabella was born is:
P(at least one before she's born) = 1 - (1-0.25)^{555}
P(at least one before she's born) = 1 - 0.75^{555}
P(at least one before she's born) = 0.9999 (rounded to the nearest hundredth)
Therefore, the probability that at least one trip will travel before Isabella was born is 0.9999, or 99.99% (rounded to the nearest hundredth).
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in a small county, there are 150 people on any given day who are eligible for jury duty. of the 150 eligible people, 80 are women. (a) determine whether the following statement is true or false. this is an example of sampling without replacement. true false (b) if four potential jurors are excused from jury duty for medical reasons, what is the probability that all four of them are women? (round your answer to four decimal places.)
a) True. This is an example of sampling without replacement because once a person is selected for jury duty, they are no longer available for selection again.
b) 0.5238 is the probability.
a) Sampling without replacement is the technique of choosing a sample from a population without replacing the selected individuals in the population after each selection. In this case, once an eligible person is chosen, they cannot be chosen again.
Hence, the given statement is true.
b) We have to find the probability of all four of the excused jurors being women. We are picking four people out of 70 men and 80 women, or 150 people in total. Since we are dealing with independent events, we may use the multiplication principle for probabilities.
There are 80 women in the 150-person sample, so the probability of selecting one woman is 80/150.
After the first woman is selected, there are 79 women remaining in the 149-person sample, so the probability of selecting another woman is 79/149.
Similarly, the probabilities of selecting a third and fourth woman are 78/148 and 77/147, respectively.
Therefore, the probability that all four excused jurors are women is:
P(4 women) = (80/150) × (79/149) × (78/148) × (77/147)
P(4 women) = 0.5238 (rounded to four decimal places)
The probability that all four of the excused jurors are women is 0.5238.
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assuming the population has an approximate normal distribution, if a sample size has a sample mean with a sample standard deviation , find the margin of error at a 95% confidence level. round the answer to two decimal places.
The margin of error for a sample mean at a 95% confidence level can be calculated using the formula
E = (1.96 * (sample standard deviation/√sample size).
Therefore, the margin of error is E = (1.96 * (sample standard deviation/√sample size)) = (1.96 * (s/√n)).
Round the answer to two decimal places, and the margin of error is [tex]E = (1.96 * (s/√n)) = (1.96 * (s/√n)) = E = (1.96 * (s/√n)) = E = (1.96 * (s/√n)) = E = (1.96 * (s/√n)) = E = (1.96 * (s/√n)) = E = (1.96 * (s/√n)) = E = 1.96 * (s/√n) = E = 1.96 * (s/√n) = E = 1.96 * (s/√n) = E = 1.96 * (s/√n) = E = 1.96 * (s/√n) = E = 1.96 * (s/√n).[/tex]
Therefore, the margin of error at a 95% confidence level is E = 1.96 * (s/√n).
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A circular watch has a minute hand that is 2.5 cm long.
(a) What distance does the tip of the hand move through in 20 minutes?
(b)What area of the watch face is covered by the minute hand in 30 minutes?
Answer:
a) 20 minute=2pi/3 rad
angle=arc length/radius
arc length= angle×radius
=2pi/3×2.5
=5pi/3 cm
b)area= pi(radius)²/2
=pi×6.25
=25pi/4cm²
i hope you find it helpful
Step-by-step explanation:
Answer:
[tex]L=\frac{5}{3} \pi cm. \\ A=3.125\pi cm^{2}[/tex]
Step-by-step explanation:
a)
L - is how far does the tip of the hand move in diameter.
m - is how much time does the tip of the hand move in minutes.
m=20
r =2,5cm
[tex]L=\frac{m}{60} *2\pi r\\L=\frac{20}{60} *2\pi *2,5cm\\L=\frac{5}{3} \pi cm[/tex]
In a formula, we have [tex]\frac{m}{60}[/tex] because the minute hand needs 60 minutes to make one circle. L = 2πr is a formula for the full length of a circle.
b)
A- Area
r=2,5cm
m - is how much time does the tip of the hand move in minutes.
[tex]A=\frac{m}{60} *\pi r^{2} \\A=\frac{30}{60} *\pi *(2,5cm)^{2} \\A=\frac{1}{2} *\pi *6.25cm^{2} \\A=3.125\pi cm^{2}[/tex]
In the formula, we have [tex]\frac{m}{60}[/tex] because the minute hand needs 60 minutes to make one circle. The formula for the full area of a circle is A=πr².
Marika Perez's gross biweekly pay is 2,768 her earnings to date for the year total 80,272 what amount is deducted from her paycheck for social security taxes if the rate is 6.2% what amount is deducted for medicare which is taxed at 1.45%?
Answer: there you go :)
$171.62 for social security.
$40.14 for Medicare.
Step-by-step explanation:
We have been given that Marika Perez’s gross biweekly pay is $2,768.
To find the amount deducted from her pay for social security tax, we will find 6.2% of her biweekly pay.
Therefore, $171.62 is deducted from Marika's biweekly pay.
Now let us find 1.45% of $2768 to find the amount of medicare deducted from her pay.
Therefore, an amount of $40.14 is deducted from Marika's biweekly pay for medicare.
Select the correct answer. Given the following formula, solve for y. w=x-y/2-z
After answering the presented question, we can conclude that expressions Therefore, the answer is: y = -2w + 2x + 2z
what is expression ?In mathematics, you can double, divide, add, or subtract something. The following is an expression: Expression, numerical value, and math operator A mathematical expression is made up of numbers, parameters, and functions. Opposing sentences and expressions are possible. An expression, often known as an algebraic expression, is any mathematical statement that contains variables, numbers, and a mathematical action between them. For example, the phrase 4m + 5 is made up of the phrases 4m and 5, as well as the variable m from the above equation, which are all separated by the mathematical sign +.
To solve for y
[tex]w = x - y/2 - z\\2w = 2x - y - 2z\\2w - 2x - 2z = -y\\y = -2w + 2x + 2z[/tex]
Therefore, the answer is:
y = -2w + 2x + 2z
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10 How many ways can a company select 3 candidates to interview from a shortlist of 15? (2 Points) a. 555 b. 455 c. 444 d. None of them
Therefore , the solution of the given problem of unitary comes out to be the response is option b 455.
An unitary method is what?By combining what was learned and implementing this variable technique, which also includes all supplemental information from two people who used a particular tactic, the task can be finished. In other words, if the desired result occurs, either the entity specified in the expression will also be identified, or both crucial procedures will actually skip the colour. A refundable fee of Rupees ($1.01) may be needed for forty pens.
Here,
The following combination formula determines how many ways a company can choose three candidates from a shortlist of fifteen:
=> C(15,3) = 15! / (3! (15-3)!)
=> (15 x 14 x 13) / (3 x 2 x 1)
=> 455
Consequently, the response is (b) 455.
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the angle of elevation from a pack bench 778 feet from the base of the getaway arch in St. Louis Missouri is 39 degrees how tall is the getaway arch ?
630 .18 feet tall is the gateway arch by the trigonometric ratio
Sine (sin), cosine (cos), tangent (tan), cotangent (cot), cosecant (cosec), and secant are the six trigonometric ratios (sec). A branch of mathematics called trigonometry in geometry deals with the sides and angles of a right-angled triangle. Trig ratios are therefore assessed in relation to sides and angles.
As given
The angle of elevation from a park bench 778 feet from the base of the Gateway Arch in St. Louis, Missouri is 39 degrees.
Now by using the trigonometric property
[tex]tan\theta=\frac{P}{B}[/tex]
As the diagram is given below.
AB=CB tan39
AB = 778 tan 39
AB= 630.18 feet
Hence the gateway arch is 630.18 feet tall.
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solve and graph the inequality 4x>16
Answer: X>4
Step-by-step explanation:
First divide both sides by 4 and then
4 divided by 4 is 1 so what remains is x>16/4 and that is x>4
(12+13)(-2) work show
Answer:
To solve this expression, we can use the order of operations, which tells us to perform the operations inside the parentheses first, and then multiply by -2.
So, we have:
(12 + 13) (-2)
= (25) (-2) // simplify the parentheses by adding 12 and 13
= -50 // multiply 25 by -2
Therefore, (12+13)(-2) equals -50.
A car is driving at 35 kilometers per hour. How far, in meters, does it travel in 4 seconds?
Answer: The answer would be about 38.88 meters
Step-by-step explanation:
First you transfer Kilometers per hour into Meters per second.
35 KM/H = 9.72 M/S
The formula for distance is D = Speed x Time
9.72 x 4 seconds = 38.88 Meters that he will travel in 4 seconds
Find the volume of this sphere.
Use 3 for TT.
7cm
Va [?]cm³
3
V = πr³
Answer:
Step-by-step explanation:
To find the volume of a sphere, we use the formula:
V = (4/3) * π * r^3
where r is the radius of the sphere.
We are given that the radius of the sphere is 7 cm and we can use 3 as an approximation for π. Substituting these values in the formula, we get:
V = (4/3) * 3 * 7^3
V = (4/3) * 3 * 343
V = 4 * 343
V = 1372
Therefore, the volume of the sphere is 1372 cubic centimeters.
Rosalind drew a rectangle with a width of 11 centimeters and a length of 14 centimeters. Which equation can be used to determine P, the perimeter of this rectangle in millimeters
Answer:
P=(1100+1400)2
Step-by-step explanation:
For each expression, select all equivalent expressions from the list. Check all that apply.
8x + 56 -
☐ 8·x + 8·7
☐ 8(x + 7)
☐ 64x
☐ 8(7x + 1)
9 + 16y - 8 - y -
☐ y + 15
☐ 15 + y
☐ y + 15y
☐ 15y + 1
Answer:
8x + 8·7
8(x + 7)
15y - 1
Step-by-step explanation:
8x + 8·7
8x + 56
8(x + 7)
8(x) + 8(7)
8x + 56
9 + 16y - 8 - y Combine like terms
15y - 1
Helping in the name of Jesus.
Decrease R1400 in the ratio 7:3
Based on the given task content; the decrease of R1400 in the ratio 7:3 is R980 and R420 respectively.
How to solve ratio:Ratio refers to the number representing a comparison between two different quantities. It is expressed as a quotient which is the relative magnitudes of two quantities.
Amount given = R1400
Ratio = 7 : 3
Total ratio = 7 + 3 = 10
Rate 1 for 7:
= 7/10 × R1400
= 0.7 × R1400
= R980
Rate 2 for 3:
= 3/10 × R1400
= 0.3 × R1400
= R420
In conclusion, R1400 decreased in the ratio 7:3 is R980 and R420.
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Factorise the following 9x²-14x+16
Answer: The given quadratic expression is:
9x² - 14x + 16
To factorize it, we can use the quadratic formula:
x = [-(-14) ± √((-14)² - 4(9)(16))] / 2(9)
Simplifying under the square root:
x = [-(-14) ± √(4)] / 18
x = [14 ± 2] / 18
x = (16/18) or x = (12/18)
Simplifying:
x = (8/9) or x = (2/3)
So the roots of the quadratic are x = 8/9 and x = 2/3. Therefore, we can factorize the quadratic expression as:
9x² - 14x + 16 = 9(x - 8/9)(x - 2/3)
Step-by-step explanation:
Hannah makes and sells bags. It used to be that she could only make 4 bags in one day. Then she got a new sewing machine. Now she can make 7 bags in one day. What is the percent increase in the number of bags she can make?
If she can make 7 bags in one day, the percent increase in the number of bags Hannah can make is 75%.
To calculate the percent increase in the number of bags Hannah can make, we need to find the difference between the number of bags she can make now and the number she could make before, and then express this difference as a percentage of the original number of bags she could make.
The difference between the number of bags she can make now and the number she could make before is:
7 bags - 4 bags = 3 bags
To express this difference as a percentage of the original number of bags she could make, we can use the following formula:
percent increase = (difference ÷ original value) x 100%
In this case, the original value is 4 bags, so we have:
percent increase = (3 bags ÷ 4 bags) x 100% = 75%
This means that she can now make 75% more bags per day than she could before she got her new sewing machine.
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Find the value of x .
The angles (x + 7)° and (3x - 21)° are vertical angles and the value of x is equal to 14.
What are vertically opposite anglesVertical angles also called vertically opposite angles are formed when two lines intersect each other, the opposite angles formed by these lines are vertically opposite angles and are equal to each other.
so we shall solve for x and y as follows:
3x - 21 = x + 7
3x - x = 21 + 7 {collect like terms}
2x = 28
2x/2 = 28/2 {divide through by 2}
x = 14
Therefore, the value of x is equal to 14 for the vertical angles (x + 7)° and (3x - 21)°.
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The length of the hypotenuse of
an isosceles triangle is 40 inches.
How long is each leg of the
triangle? Round your answer to
the nearest tenth if necessary.
Answer: 28.3 inches long
Step-by-step explanation:
Since the triangle is isosceles, the two legs have the same length. Let's call the length of each leg "x". We can use the Pythagorean theorem to solve for x:
x^2 + x^2 = 40^2
2x^2 = 1600
x^2 = 800
x ≈ 28.3
Therefore, each leg of the triangle is approximately 28.3 inches long.