The surface area of the triangular prism is 891 square inches, calculated by finding the area of each face (two triangular and three rectangular) and adding them up.
To find the surface area of the triangular prism, we need to find the area of each face and add them up.
The triangular prism has two identical triangular faces and three rectangular faces. The triangular faces have base 9 inches, height 12 inches, and hypotenuse 15 inches. The area of each triangular face can be found using the formula for the area of a triangle:
Formula for area of each triangular face = (1/2) x base x height
= (1/2) x 9 x 12
= 54 square inches
The prism also has three rectangular faces, each with length equal to the base of the triangle (9 inches) and width equal to the height of the prism (29 inches). The area of each rectangular face can be found using the formula for the area of a rectangle:
Area of each rectangular face = length x width
= 9 x 29
= 261 square inches
Hence, the triangular prism's total surface area is:
Total surface area = 2(Area of each triangular face) + 3(Area of each rectangular face)
= 2(54) + 3(261)
= 108 + 783
= 891 square inches
Therefore, the surface area of the triangular prism is 891 square inches.
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Suppose you only found two ratios of yogurt to protein. Could you use the two ratios to draw a line on the coordinate plane and answer the question? How?
A ratio is a couple of numbers that are looked at. Part-to-part, part-to-entire, and entire-to-part correlations are examples of ratios. Units could conceivably be remembered for the ratios.
A two-layered plane framed by the crossing point of an upward line which is known as the y-axis and a horizontal line called the x-axis is known as a coordinate plane. These are a bunch of opposite lines that converge at nothing, which is known as the beginning. The axes partition the coordinate plane into four segments, every one of which is alluded to as a quadrant.
Requested matches are utilized to chart and find focuses on a coordinate plane. The arranged matches are dependably in the (x, y) structure where the primary number is the x-coordinate and the subsequent number is the y-coordinate. The principal coordinate lets you know how far to move along the x-axis, and the subsequent coordinate lets you know how far to go up or down the y-axis.
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the patient recovery time from a particular surgical procedure is normally distributed with a mean of 5.6 days and a standard deviation of 1.5 days. what is the probability of spending more than 4 days in recovery? (round your answer to four decimal places.)
The probability of spending more than 4 days in recovery is 0.8554
To calculate the probability of spending more than 4 days in recovery, we need to use the standard normal distribution since the patient recovery time from a particular surgical procedure is normally distributed with a mean of 5.6 days and a standard deviation of 1.5 days.
The standard normal distribution is a normal distribution with a mean of 0 and a standard deviation of 1.
If X is a normally distributed random variable with mean μ and standard deviation σ, then Z = (X-μ) / σ is a standard normal random variable.
So, P(X > 4) = P(Z > (4-5.6) / 1.5) = P(Z > -1.0667)
Using a standard normal distribution table, we find that P(Z > -1.0667) = 0.8554
Therefore, the probability of spending more than 4 days in recovery is 0.8554, rounded to four decimal places.
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Solve the expression below.
Answer:
3 2/3.
Probably the easiest question I've answered all day!
Find the surface area of a sphere with radius, r = 10 in.
Answer: ~1256.64
Step-by-step explanation:
The equation for the surface area of a sphere is 4πr². So you would substitute 10 in for r which would then be 4π10². That will get you 1256.63706 but rounded it would be approximately 1256.64.
Answer: [tex]\text{400}\pi \ \text{square inches}[/tex]
Step-by-step explanation:
Given: The radius of the sphere = 10 in.
The formula to calculate the surface area of the sphere is given by:
[tex]\text{Surface Area}=4\pi r^2[/tex], where r is the radius of the sphere.
For r = 10 in. we have
[tex]\text{Surface Area of the sphere}=4\pi (10)^2[/tex]
[tex]\implies \text{Surface Area of sphere}=4\pi (100)[/tex]
[tex]\implies \text{Surface Area of the sphere}=\text{400}\pi \ \text{square inches}[/tex]
[tex]400\pi =1256.64 \ \text{square inches}[/tex]Carolyn is 6 years older than alfred. six years ago she was twice as old as him. how old is each now?
Answer:
Now: Carolyn 18 yo, Alfred 12 yo
Step-by-step explanation:
Use X represent Alfred's age now, then Carolyn's age is (X+6)
6 years ago, their ages should be current age minus 6. So Alfred's age was (X-6), Carolyn's age was ((X+6)-6).
As 6 years ago, Carolyn's age was twice as Alfred's. So
((X+6)-6)=(X-6)×3
X=12 which is Alfred' current age
X+6=18 which is Carolyn' current age
The International Committee on the Taxonomy of Viruses estimates that 8.3% of the US population has COVID 19. The Center for Disease Control and Prevention has developed a diagnostic test for COVID 19 that is 98% accurate for people who have COVID 19 and 95% accurate for people who don't have it. The Center gives the test to a randomly selected person. What is the probability that diagnosis is correct? Round your answer to hundredth percent.
Let's first define some events:
A: The person has COVID-19.
B: The test result is positive.
Using the information provided, we can calculate the probability of a correct diagnosis using Bayes' theorem:
P(A|B) = P(B|A) * P(A) / [P(B|A) * P(A) + P(B|not A) * P(not A)]
where P(B|A) is the probability of a positive test result given that the person has COVID-19, P(A) is the prevalence of COVID-19 in the population (0.083 or 8.3%), P(B|not A) is the probability of a positive test result given that the person does not have COVID-19 (false positive rate, 0.05 or 5%), and P(not A) is the complement of P(A) (0.917 or 91.7%).
Plugging in the values, we get:
P(A|B) = (0.98 * 0.083) / [(0.98 * 0.083) + (0.05 * 0.917)]
= 0.6037 or 60.37%
Therefore, the probability that the diagnosis is correct is 60.37%, rounded to the nearest hundredth percent.
ANSWER THIS PLSSSS WHAT R THE NUMBERS IN THE MIDDLE!!
Answer:
Step-by-step explanation:
in the middle is 0 in the first one is -5 and last one is 5
This is due tomorrow!!!
The answer is option (d) "The volume of sphere can be interpreted as product of radius cubed and constant factor."
What is Volume?The volume of a three-dimensional object refers to the amount of space that it occupies. More specifically, it is a measure of the amount of enclosed space within a solid shape, like a cube, sphere, cylinder, or any other three-dimensional object. The formula for calculating volume of solid depends on its shape. The formula for the volume of a sphere, as mentioned in the previous question, is V=4/3πr³, where r is the radius of the sphere.
Volumes are typically measured in cubic units, like cubic meters, cubic centimeters, or cubic feet.
The statement that is true is: "The volume of sphere can be interpreted as product of radius cubed and constant factor."
The formula for the volume of a sphere, V=4/3πr³, shows that the volume is proportional to the cube of the radius. This means that if the radius of a sphere is doubled, the volume will increase by a factor of 2³=8. Similarly, if the radius is tripled, the volume will increase by a factor of 3³=27.
The constant factor in the formula, 4/3π, is a fixed value that applies to all spheres, regardless of their size. It is a constant because it does not depend on the radius of the sphere.
Therefore, we can interpret the formula for the volume of a sphere as the product of the radius cubed and a constant factor.
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Explain why the relationship between the height of these objects and the length of their shadows are approximately proportional.
The relationship between the height of these objects and their shadow length is approximately proportional because increase in height leads to increase in their length.
What is a direct proportional relationship?Direct proportional relationship is defined as the type of relationship whereby an increase in one variable leads to the increase in the other variable.
From the diagram given above, all the objects are of various heights and the length here f their shadow increased with increase in the heights of the objects.
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the origin of playing cards is debatable but what is definitely known is different countries had different suits. what comprised the suits in spanish cards?
Spanish playing cards have four suits: coins, cups, swords, and clubs, with each suit representing a different aspect of life, and consisting of ten numbered cards and three court cards.
Spanish playing cards traditionally have four suits: coins, cups, swords, and clubs. These suits are similar to the suits found in Italian and Latin American playing cards, but different from the suits found in French and German playing cards. The coins suit represents wealth and commerce, the cups suit represents love and pleasure, the swords suit represents warfare and justice, and the clubs suit represents agriculture and prosperity. Each suit typically contains ten numbered cards and three court cards: the knight, the queen, and the king.
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What is the properties of rhombus and rectangle and square?
There are some traits that rectangles, squares, and rhombuses have in common. These are also some differences between them. Rectangles, squares, and rhombuses all have 4 sides. If a shape is a rectangle the diagonal sides will be congruent. If a shape is a square all the sides will be congruent, the shape will also have a right angle. The diaganles of a rombus are perpendicular.
help me with this please
Answer:
10
Step-by-step explanation:
You want the determinant of the matrix ...
[tex]\left[\begin{array}{cc}1&-2\\3&4\end{array}\right][/tex]
DeterminantThe determinant of a matrix is a sum of products. Each product is the element of a row or column multiplied by its cofactor.
For a 2×2 matrix, this becomes the difference between the product of diagonal terms and the product of off-diagonal terms:
(1·4) - (3·(-2))
= 4 +6
= 10
__
Additional comment
The cofactor of term a[i, j] is (-1)^(i+j)·det(M[i,j]), where M[i,j] is the minor matrix obtained by removing row i and column j from the original. As you can see, this definition of a determinant is recursive.
The above describes the determinant of a 2×2 matrix. The determinant of a 3×3 matrix resolves to a sum of 6 3-element products. For larger matrices, the computation burden can be reduced by taking advantage of rows or columns containing zeros.
i need help pls!!!!! question is attached
The value of the investment after 3.5 years is approximately $2530.67.
Describe Principal Amount?The principal amount refers to the initial amount of money borrowed or invested, excluding any interest or additional fees. For example, if someone takes out a loan for $10,000, the principal amount is $10,000, and this is the amount that must be repaid to the lender, not including any interest that may accrue over time. Similarly, if someone invests $5,000 in a savings account, the principal amount is $5,000, and any interest earned on that amount will be calculated based on the principal amount. The principal amount is an important concept in finance and investing, as it determines the starting point for calculating interest, returns, and other financial transactions.
The formula for compound interest is:
[tex]A= P(1+\frac{r}{n} )^{nt}[/tex]
Where:
A = the final amount
P = the principal amount (initial investment)
r = the annual interest rate (as a decimal)
n = the number of times the interest is compounded per year
t = the time (in years)
In this case, we have:
P = 2000
r = 0.04 (4% as a decimal)
n = 12 (compounded monthly, so 12 times per year)
t = 3.5 (3.5 years)
Plugging these values into the formula, we get:
[tex]A= 2000(\frac{1+0.04}{12})^{12*3.5}[/tex]
A = 2000(1.00333333)⁴²
A ≈ 2530.67
Therefore, the value of the investment after 3.5 years is approximately $2530.67.
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forty-four percent of us adults have little confidence in their cars. you randomly select twelve us adults. find the probability that the number of us adults who have little confidence in their cars is (1) exactly six and then find the probability that it is (2) more than 7.
The proportion of adults who have little faith in their automobiles, or the chance of success (p), is 44%.
How does probability work?The probability of an event occurring is referred to as probability. We frequently have to make predictions about the future in real life. We may or may not be aware of the outcome of an event.
At the point when this happens, we broadcast that there is plausible that the occasion will happen.
In conclusion, probability can be put to great use in business as well as in this rapidly expanding field of artificial intelligence. By simply dividing the total number of outcomes by the favorable number of possibilities, the probability of an event can be calculated using the probability formula.
Given that "p" stands for probability—that is, the fact that 45 percent of adults in the United States have little faith in their automobiles—p = 0.45, the likelihood of failure is q = 1-p = 1 - 0.45.
The chance of success (p), or the percentage of adults who have little faith in their automobiles, is therefore 44%, with q =0.55.
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explain if a number is 5.32147 is rational or irrational number
Answer: yes it is rational because it’s not within a square root symbol
Step-by-step explanation:
Members of a running club volunteer to collect garbage they find on the ground one day each month. At the initial cleanup, the members collected six thousand, five hundred pounds of garbage. The club finds that they collect forty five% less trash at each subsequent monthly cleanup.
Define a unit for each quantity in the worksheet. Then enter a variable for the time and use this variable to write an expression for the amount of garbage collected.
Answer:3,575 lbs, or 45% less
Step-by-step explanation:
Unit for garbage collected: pounds (lbs)
Unit for time: month (mo)
Let's use "t" as the variable for time (in months).
Expression for the amount of garbage collected:
For the initial cleanup: 6,500 lbs
For subsequent cleanups: 45% less garbage collected each month, which means they collect 55% of the previous month's garbage. So, the expression for the amount of garbage collected each month (starting from the second month) would be:
0.55^(t-1) * 6,500 lbs
where "t" represents the number of months after the initial cleanup.
Note that for t=1 (i.e., the first subsequent cleanup), the expression evaluates to 0.55^(1-1) * 6,500 lbs = 6,500 * 1 = 6,500 lbs, which is consistent with the initial cleanup. For t=2, the expression evaluates to 0.55^(2-1) * 6,500 lbs ≈ 3,575 lbs, which is 45% less than the amount collected in the first subsequent cleanup.
Katie, Toby and Molly sold a total of 72 games at a car boot sale. The ratio of the numbers of games that they each sold is 5: 3: 1. How many more games did Toby sell than Molly?
Toby sold 16 more games than Molly.
What is ratio?A ratio is a comparison of two or more quantities of the same kind. It is often expressed as a fraction or with a colon (:). For example, the ratio of the number of boys to the number of girls in a class of 30 students could be 2:3, which means that for every two boys, there are three girls.
Let's start by finding the total number of parts in the ratio: 5 + 3 + 1 = 9.
Next, we can use the ratio to find out how many parts of the total each person sold:
Katie: 5/9 of 72 games = 40 games
Toby: 3/9 of 72 games = 24 games
Molly: 1/9 of 72 games = 8 games
To find out how many more games Toby sold than Molly, we can subtract Molly's sales from Toby's sales: 24 - 8 = 16.
Therefore, Toby sold 16 more games than Molly.
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Answer:
Toby sold 16 more games than Molly.
Step-by-step explanation:
Let's start by finding the total number of parts in the ratio: 5 + 3 + 1 = 9.
Next, we can use the ratio to find out how many parts of the total each person sold:
Katie: 5/9 of 72 games = 40 games
Toby: 3/9 of 72 games = 24 games
Molly: 1/9 of 72 games = 8 games
Then we subtract Toby's number of games by Molly's. (24-8)
Therefore, Toby sold 16 more games than Molly.
Help!!!! It’s due at 9:30 tomorrow
The two-column proofs of the segments are shown below
Proving that AG ≅ EDThe proof is as follows
Statement Reason
ABCD and BCDE are parallelogram Given
AG = BC Opposite sides of
parallelogram
ED = BC Opposite sides of
parallelogram
AG ≅ ED Substitution property (proved)
Proving that KLMN is a parallelogram
The proof is as follows
Statement Reason
KL || NM and ∠L ≅ ∠N Given
KN ≅ LM CPCTC
KL ≅ NM CPCTC
We've proved that the opposites sides are equal and parallel
So, KLMN is a parallelogram
Proving that STUV is a parallelogram
The proof is as follows
Statement Reason
ST || VU and W is midpoint of SU Given
SW = UW Definition of midpoint
VW = TW Definition of midpoint
VU = ST CPCTC
VS = UT CPCTC
We've proved that the opposites sides are equal and parallel
So, STUV is a parallelogram
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Hey guys I need help with 3 math problems the image is below please no is answering and I only need one homework to pass this year image is below giving brainliest
Answer:
I did the first image. I'm sorry but I don't remember fully how to do the other two, and I don't want to give you the wrong answer. GL
Step-by-step explanation:
Okay, for the first image if the perimeter is 48 you can divide that by 3 getting you 16. M=16.
8. Multiply the following:
a. (x3)(x2) =
b. (x7)(x10) =
c. (3s4)(-6s5) =
d. (-20x)(3x) =
Answer:
a. 6x^2
b. 70x^2
c. -360s^2
d. -60x^2
Step-by-step explanation:
Solve For X. Assume that lines which appear are tangent.
Option B :The solution for x in the given circle is x = 5 + 2√6 or x = 5 - 2√6 is near to value 5.
In the given figure, we have two tangents and a secant that intersects the circle at points A and B.
By the tangent-secant theorem, we know that the product of the lengths of the secant segment (AX) and the exterior segment (XB) is equal to the product of the lengths of the entire secant (AB) and the interior segment (CX).
So, we have:
AX * XB = AB * CX
Substituting the given values, we get:
(3 + x) * (7 - x) = 5 * 5
Expanding the left side and simplifying, we get:
[tex]21 - x^2 = 25 - 10x[/tex]
Bringing all the terms to one side and simplifying, we get:
[tex]x^2 - 10x + 4 = 0[/tex]
Using the quadratic formula, we get:
x = (10 ± √([tex]10^2 - 414[/tex])) / (2*1)
x = (10 ± √96) / 2
x = 5 ± 2√6
Therefore, the solutions for x are:
x = 5 + 2√6 or x = 5 - 2√6
So, the answer is (B) 5.
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PLEASE HELP ASAP?!!
Explain how to graph a polynomial function in factored form. What do the factors
mean in terms of the polynomial? What other ways have we learned to write a
polynomial function? Graph f(x) = (x - 2)²(x + 1)(x − 4). You may
-
handwrite your explanation if you would like. You can also attach a snip of the graph
to help explain your thinking.
Some terms to think about:
Factors, Zeros, x-intercepts, multiplicity, end behavior, degree of function
The x-intercepts (zeros), end behaviors, degree and multiplicity of the function f(x) = (x - 2)²·(x + 1)·(x - 4), can be used to graph the polynomial in factored form. Please find attached the graph of the polynomial created with MS Excel.
What is the difference between a zero and a root of a function?A zero is an input variable value that makes the value of the output to be zero. A root is a value that satisfies the equation.
The steps to graph the polynomial in factored form are;
1. Find the x-intercepts; The x-intercepts are obtained by setting each factor as being equivalent to zero and solve for x. The values obtained are the x-intercepts or the zeros of the function.
The specified function, f(x) = (x - 2)²·(x + 1)·(x - 4), the zeros are; x = 2, (with a multiplicity of 2), x = -1, and x = 4.
2. Determine the end behavior of the function: The degree and leading coefficient of a polynomial determines the end behavior of the polynomial.
The degree of a function is the highest exponent of the function. The highest exponent of x in the function f(x) is 4, therefore, the degree of f(x) is 4.
The leading coefficient is the coefficient of the term with the highest exponent of x. The leading coefficient of f(x) is therefore, the coefficient of the term with the highest exponent of x, which is 1
The even degree of f(x), (4), and the positive leading coefficient, (1), indicates that the end behavior is upwards on both ends.3. Determine the multiplicity of the zeros: The number of times a factor appears in the factored form determines the multiplicity of the zero of the factor.
The zero of x = 2 in the function has a multiplicity of 2 indicating that the graph touch and bounces upwards on the x-axis at x = 2.
The multiplicities of 1 of the of the zeros x = -1, and x = 4 indicates that the graph crosses the x-axis at the points x = -1, and x = 44. Determine the behaviour at the x-intercepts: The multiplicity of the zero determines the behavior of the graph at the x-intercept, such that an odd multiplicity indicates that the graph crosses the x-axis and an even multiplicity indicates that the graph touches the x-axis and bounces upwards or downwards at the point.
The information in the steps 1 – 4 can then be used to sketch the graph of the polynomial.
Please find attached the graph of the polynomial created with MS Excel, using the function, f(x) = (x - 2)²·(x + 1)·(x - 4)
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SOMEONE, PLEASE HELP ME!
Answer:
Find the heigh if a=550cm and r=7cm
C) 92.65%
To find the percent decrease in customers, we first need to find the difference in the number of customers between the two given hours.
Number of customers on Saturday from 6:00 p.m. to 7:00 p.m. = 68
Number of customers on Wednesday from 5:00 p.m. to 6:00 p.m. = 5
Difference in number of customers = 68 - 5 = 63
Next, we need to find the percent decrease in customers, which is given by:
(percent decrease) = (difference / original) x 100%
where "original" refers to the number of customers on Saturday from 6:00 p.m. to 7:00 p.m.
Plugging in the values, we get:
(percent decrease) = (63 / 68) x 100% ≈ 92.65%
Therefore, the percent decrease in customers from the given hour on Saturday to the given hour on Wednesday is approximately 92.65%.
A white-and-green spinner landed on white on 10 out of 14 spins. What is the experimental probability that the next spin will land on white? Write your answer as a fraction or whole number.
The experimental probability of the following spin landing on white is 5/7, or roughly 0.714 based on given events.
The number of times an event occurred divided by the total number of trials done is used to compute the experimental probability of the event. In this instance, there have been 14 trials, and the event is landing on white.
Out of 14 spins, the spinner landed on white 10 times, according to the information provided. the following is the experimental likelihood of landing on white:
Experimental probability is calculated as follows: White landings / total spins
10/14 is the experimental probability.
5/7 is the experimental probability.
Hence, the experimental likelihood that the following spin will land on white is 5/7, or roughly 0.714. It's crucial to keep in mind that this likelihood is just based on the small sample size of 14 spins and might not fully reflect the spinner's long-term chances of landing on white.
The design and balance of the spinner might affect the results, thus if there are any problems with its construction, the spinner may not be an accurate depiction of likelihood. The experimental probability might not be helpful in this situation to forecast future events.
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What is the area of the figure shown?
Answer:
41
Step-by-step explanation:
A = LW + (1/2)bh
A = 7 m × 5 m + (1/2)(3 m)(4 m)
A = 35 m² + 6 m²
A = 41 m²
The cylinder has height of 31mm and a volume of 4700mm³ what is the radius? (give ans to 2 d.p.) giving away 5 stars and a thanks
The radius of the cylinder is approximately 9.02 mm.
What is cylinder?
A cylinder is a three-dimensional shape that consists of two parallel and congruent circular bases that are connected by a curved lateral surface. It can be thought of as a stack of circular discs or coins of equal size, with a constant distance between them. The axis that passes through the center of the circular bases is called the axis of the cylinder.
The formula for the volume of a cylinder is:
[tex]$$ V = \pi r^2 h $$[/tex]
where [tex]$V$[/tex] is the volume, [tex]$r$[/tex] is the radius, and [tex]$h$[/tex] is the height.
We can rearrange this formula to solve for the radius:
[tex]$$ r = \sqrt{\frac{V}{\pi h}} $$[/tex]
Substituting the given values, we get:
[tex]$$ r = \sqrt{\frac{4700}{\pi \cdot 31}} $$[/tex]
Simplifying this expression, we get:
[tex]$$ r \approx 9.02\ \text{mm} $$[/tex]
Therefore, the radius of the cylinder is approximately 9.02 mm.
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The line plots represent data collected on the travel times to school from two groups of 15 students.
A horizontal line starting at 0, with tick marks every two units up to 28. The line is labeled Minutes Traveled. There is one dot above 4, 6, 14, and 28. There are two dots above 10, 12, 18, and 22. There are three dots above 16. The graph is titled Bus 47 Travel Times.
A horizontal line starting at 0, with tick marks every two units up to 28. The line is labeled Minutes Traveled. There is one dot above 8, 9, 18, 20, and 22. There are two dots above 6, 10, 12, 14, and 16. The graph is titled Bus 18 Travel Times.
Compare the data and use the correct measure of center to determine which bus typically has the faster travel time. Round your answer to the nearest whole number, if necessary, and explain your answer.
Bus 18, with a median of 13
Bus 47, with a median of 16
Bus 18, with a mean of 13
Bus 47, with a mean of 16
According to the given information, the correct answer is Bus 18, with a median of 13.
What is median?
The median is a measure of central tendency in statistics. It is the value that separates the dataset into two equal halves, with half the values being greater than the median and half being less than the median.
To compare the travel times of the two buses and determine which typically has the faster travel time, we need to look at the measures of central tendency.
The two common measures of central tendency are mean and median.
For Bus 18, the median is 13, which means that half of the students take less than 13 minutes to travel to school and half take more than 13 minutes. The mean can be calculated by finding the sum of all travel times and dividing by the number of students, but this information is not provided in the given line plot.
For Bus 47, the median is 16, which means that half of the students take less than 16 minutes to travel to school and half take more than 16 minutes. The mean can be estimated by calculating the average of all the travel times, which is:
(4+6+10+10+12+12+14+14+18+18+22+22+28+28+28)/15 = 16
Therefore, the mean travel time for Bus 47 is also 16.
Comparing the median travel times, we can see that Bus 47 has a higher median of 16 compared to Bus 18's median of 13. This suggests that the travel times for Bus 47 are typically longer than those for Bus 18, and therefore Bus 18 typically has the faster travel time.
Therefore, the correct answer is Bus 18, with a median of 13.
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Question 1C Answer to (a) is alpha-theta answer to (b) C=90-alpha will give brainliest
Please mark answer as brainliest
Answer:
(c) AE = x·cos(α)/sin(θ)
(d) BD = x·cos(α)cos(α-θ)/cos(θ)
Step-by-step explanation:
In the given diagram, you want expressions for (c) AE and (d) BD in terms of x, α, and θ.
C. AEThe law of sines can be used in ∆ACE to give the measure of AE.
[tex]\dfrac{AE}{\sin(C)}=\dfrac{CE}{\sin(\theta)}\\\\\boxed{AE=\dfrac{x\,\cos(\alpha)}{\sin(\theta)}}\qquad\text{where $\sin(C)=\cos(\alpha)$ and $CE=x$}[/tex]
D. BDThe length BD can be found in terms of AD and θ:
BD = AD·tan(θ)
The length AD can be found in terms of AE and (α-θ):
AD = AE·cos(α-θ)
Using the value of AE from part (c), we have ...
BD = AE·cos(α-θ)·tan(θ) = x·cos(α)cos(α-θ)·tan(θ)/sin(θ)
BD = x·cos(α)cos(α-θ)/cos(θ) . . . . . . . using tan/sin = 1/cos
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Additional comment
We assume angle EAC is θ throughout, as it is in part (a).
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[tex]\frac{(8^{3} -9^{0})}{7}[/tex]
Answer:
exact form-512/7
decimal form-73.1
Mixed number form-73 1/7
Step-by-step explanation:
PROOFS please fill in blanks need help badly !! would gratefully appreciate it
9. Given: U is the midpoint of ST, SVTW, VU =WU
Prove: SVU = ZTWU
For the given congruence triangle:
ΔSUV ≅ ΔTUW By Side Side Side (SSS) congruence ∠SVU ≅ ∠TWU BY CPCT Explain about the congruence triangle:Congruent triangles are triangles that are precisely the same size and shape. The word congruent has the sign. When the three sides and three angles of one triangle match the same dimensions as the three sides plus three angles of another triangle, two triangles are said to be congruent.
For the given data:
U is the midpoint of ST, SV ≅ TW, VU ≅ WU.Statement Reasons
U is the midpoint of ST Given
SV ≅ TW Given
VU ≅ WU Given
SU = UT U is the midpoint of ST
ΔSUV ≅ ΔTUW By Side Side Side (SSS) congruence
∠SVU ≅ ∠TWU BY CPCT
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