Triangle $ABC$ has side lengths $AB = 9$, $AC = 10$, and $BC = 17$. Let $X$ be the intersection of the angle bisector of $\angle A$ with side $\overline{BC}$, and let $Y$ be the foot of the perpendicular from $X$ to side $\overline{AC}$. Compute the length of $\overline{XY}$.
Answers
Answer:
[tex]\dfrac{72}{19}[/tex]
Step-by-step explanation:
Consider triangle ABC. Segment AX is angle A bisector. Its length can be calculated using formula
[tex]AX^2=\dfrac{AB\cdot AC}{(AB+AC)^2}\cdot ((AB+AC)^2-BC^2)[/tex]
Hence,
[tex]AX^2=\dfrac{9\cdot 10}{(9+10)^2}\cdot ((9+10)^2-17^2)=\dfrac{90}{361}\cdot (361-289)=\dfrac{90}{361}\cdot 72=\dfrac{6480}{361}[/tex]
By the angle bisector theorem,
[tex]\dfrac{AB}{AC}=\dfrac{BX}{XC}[/tex]
So,
[tex]\dfrac{9}{10}=\dfrac{BX}{17-BX}\Rightarrow 153-9BX=10BX\\ \\19BX=153\\ \\BX=\dfrac{153}{19}[/tex]
and
[tex]XC=17-\dfrac{153}{19}=\dfrac{170}{19}[/tex]
By the Pythagorean theorem for the right triangles AXY and CXY:
[tex]AX^2=AY^2+XY^2\\ \\XC^2=XY^2+CY^2[/tex]
Thus,
[tex]\dfrac{6480}{361}=XY^2+AY^2\\ \\\left(\dfrac{170}{19}\right)^2=XY^2+(10-AY)^2[/tex]
Subtract from the second equation the first one:
[tex]\dfrac{28900}{361}-\dfrac{6480}{361}=(10-AY)^2-AY^2\\ \\\dfrac{22420}{361}=100-20AY+AY^2-AY^2\\ \\\dfrac{1180}{19}=100-20AY\\ \\20AY=100-\dfrac{1180}{19}=\dfrac{1900-1180}{19}=\dfrac{720}{19}\\ \\AY=\dfrac{36}{19}[/tex]
Hence,
[tex]XY^2=\dfrac{6480}{361}-\left(\dfrac{36}{19}\right)^2=\dfrac{6480-1296}{361}=\dfrac{5184}{361}\\ \\XY=\dfrac{72}{19}[/tex]
Related Questions
Triangle ABC is translated using the rule (x, y) ? (x + 1, y ? 4) to create triangle A?B?C?. If a line segment is drawn from point A to point A? and from point B to point B?, which statement would best describe the line segments drawn?
Answers
Answer:
The line segments AA' and BB' are parallel and congruent
Step-by-step explanation:
we know that
When the transformation is a translation, the figure does not change its shape or dimensions,
so
AA'=BB'=CC'
therefore
The line segments AA' and BB' are parallel and congruent
Translation involves moving a function away from its original position.
The statement that describes the line segments is:
Both lines would be parallel and congruent
The translation is given as:
[tex]\mathbf{(x,y) \to (x + 1, y - 4)}[/tex]
Translation is a rigid transformation.
This means that, the image and the pre-image would have the same measure.
So, when a line is drawn from A to A' and B to B'
The lines would be parallelThe lines would be congruentAssume the coordinates of A and B are:
[tex]\mathbf{A = (2,3) }[/tex]
[tex]\mathbf{B = (-4,6) }[/tex]
Apply transformation
[tex]\mathbf{A' = (2 + 1, 3 - 4) = (3,-1)}[/tex]
[tex]\mathbf{'B = (-4 + 1, 6 - 4) = (-3,2)}[/tex]
The distance of lines AA' and BB' is calculated using:
[tex]\mathbf{d = \sqrt{(x_2 -x_2)^2 + (y_2 - y_1)^2 }}[/tex]
So, we have:
[tex]\mathbf{AA' = \sqrt{(2 -3)^2 + (3 - -1)^2 = \sqrt{17}}}[/tex]
[tex]\mathbf{BB' = \sqrt{(-4 --3)^2 + (6 -2)^2 = \sqrt{17}}}[/tex]
Notice that:
[tex]\mathbf{BB' = AA' = \sqrt{17}}}[/tex]
Because translation is a rigid transformation, then lines AA' and BB' would also be congruent
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Which of the following equations is of the parabola whose vertex is at (2, 3), axis of symmetry parallel to the y-axis and p = 4?
A.)y-3 = 1/16 (x-2)^2
B.)y+3 = -1/16 (x+2)^2
C.)x-2 = 1/16 (y-3)^2
Answers
Answer:
option A.) y-3 = 1/16 (x-2)^2
Step-by-step explanation:
we know that
If the axis of symmetry is parallel to the y-axis, then we have a vertical parabola
The equation of a vertical parabola is equal to
[tex]4p(y-k)=(x-h)^{2}[/tex]
where
(h,k) is the vertex
In this problem we have
(h,k)=(2,3)
p=4
substitute
[tex]4(4)(y-3)=4(4)(x-2)^{2}[/tex]
[tex]16(y-3)=(x-2)^{2}[/tex]
[tex](y-3)=(1/16)(x-2)^{2}[/tex]
Answer:
option A.) y-3 = 1/16 (x-2)^2
Step-by-step explanation:
Please help me with this last part. The other parts are fine.
Answers
These percentiles on small data sets are confusing. We have 8 data points. So the median is the average of the 4th and 5th.
The upper quartile, 75th percentile, is between the 6th and 7th data point of the 8. I calculated its index as (8-1)*.75=6.25. One definition of upper quartile has us just pick the next one up, 36 here. Another definition has us interpolate. Since 6.25 = (3/4) 6 + (1/4) 7 we take (3/4) 33 + (1/4) 36 = 33.75 as a 75th percentile. It's hard for me to choose without knowing what you were taught.
Which is an example of SRS (simple random sample)? a. Putting all the names of the 50 elementary students sitting in the auditorium into a large fishbowl and pulling out only 10 names b. Calling households at random with the area code 312; after completing the survey with the homeowner, surveying others living in the same home c. Stopping every thirteenth person who leaves the local hardware store with a bag, showing they purchased an item d. Listing in alphabetical order the 100 players in the league, then beginning at the top of the list and calling players until you have spoken to 10 players
Answers
Answer:
a. Putting all the names of the 50 elementary students sitting in the auditorium into a large fishbowl and pulling out only 10 names
Step-by-step explanation:
When one does simple random sampling picture it like a lottery. (This is actually a good example) It is a type of smapling that is done where a smaller portion of the whole population is chosen to participate in the research. It is called random because everyone in the population has an equal chance to be selected. Although the other examples are random sampling as well, they are more systematic than simple.
Answer:
A
Step-by-step explanation:
The peroson above is correct
To the nearest tenth the value of x that satisfies 2x = −2x + 11 is
Answers
Answer:
2.8 (from 2.75 because of rounding)
Step-by-step explanation:
2x = -2x + 11
Add 2x on both sides
4x = 11
Divide 4 on both sides
x = 11/4
x = 2.75
Round to nearest tenth
x is about 2.8
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Answer:
x = 2.8
Step-by-step explanation:
2x = - 2x + 11 Add 2x to both sides.
2x+2x = -2x+2x + 11 Combine
4x = 11 Divide by 4
4x/4 = 11/4
x = 2 3/4
x = 2.75
Rounded to the 10th place, you would get 2.8
In the triangles, and .
Which statement correctly compares and ?
and are the same length.
is longer than .
is shorter than .
is shorter than or the same length as .
Answers
Answer:
answer is B just got 100%
Step-by-step explanation:
In this triangle, what is the value of X?
Enter your answer, rounded to the nearest tenth, in the box.
X=
PLEASEEE HELP 12p!!! BRAINLIEST IF CORRECT!!
Answers
Answer:
The measure of angle x is [tex]26.1\°[/tex]
Step-by-step explanation:
we know that
In the right triangle of the figure, the tangent of angle x is equal to divide the opposite side to angle x by the adjacent side to angle x
so
[tex]tan(x)=\frac{26}{53}[/tex]
[tex]x=arctan(\frac{26}{53})=26.1\°[/tex]
please help asap will mark brainlest
Answers
Answer: -79, 21, 46, 80
Step-by-step explanation:
-79, 21, 46, 80
79 is a negative number making it the smallest. After -79 just order the numbers in the consecutive order of how you count.
Hope this helped!
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To solve this system of equations by elimination, what operation could be used to eliminate the y-variable and find the value of x? 2x ? 4y = 6 ?3x + 3y = 9 A) add 3 times the second equation to 4 times the first equation B) add 4 times the second equation to 3 times the first equation C) subtract 3 times the second equation from 4 times the first equation D) subtract 4 times the second equation from 3 times the first equation
Answers
Step-by-step explanation:
4y=6 (first equation)
3x+3y=9(second equation)
we know if a=a, a+x=a+x,ax=ax
now we add 3 times
4y=6(=)12y=18
now add 4 times
12x+12y=36
now we can eliminate the y and will be
12x=18
x=1,5
2x=3
PLEASE HELP ASAP I WILL MARK BRAINLIEST!! If measures 65°, what is the measure of WZ?
Answers
Answer:
180-65=115
Step-by-step explanation:
Straight line always measures 180 degrees, take 180 and subtract 65 thats your answer.
Answer:
115 dude
Step-by-step explanation:
you just substract 65 with 180 and then you get 115
Solve for x. -3 + 8x - 5 = -8 A. -2 B. -1 C. - 3 4 D. 0
Answers
Answer:
D
Step-by-step explanation:
Answer:
0
Step-by-step explanation:
-3+5
-8+8x=-8
divide both sides by 8
x=0
A pizza restaurant charges for each pizza and adds a delivery fee. The cost (c), in dollars, to have any number of pizzas (p) delivered to a home is described by the equation c = 11p + 5.
Each pizza costs $5 and the delivery fee is $11
The cost of 11 pizzas is $16
Each pizza costs $11 and the delivery fee is $5
The cost of 5 pizzas is $11
Answers
Answer:
Each pizza costs $11 and the delivery fee is $5
Step-by-step explanation:
We assume you want an interpretation of the equation.
The total cost of an order is the sum of any fixed cost (such as a delivery fee) and the variable cost.
Here, the variable cost is the cost of some number of pizzas. It is proportional to the number of pizzas. In the equation, it is represented by 11p, where p is the number of pizzas. The cost of each pizza must be $11, since the cost of p pizzas is 11p.
The equation's two parts are a fixed cost of $5 and a variable cost of $11 per pizza. The best description is ...
Each pizza costs $11 and the delivery fee is $5
The cost (c) to have any number of pizzas (p) delivered is calculated using the equation c = 11p + 5. This implies that each pizza costs $11 and the delivery fee is $5.
Explanation:The question involves the concept of linear equations in mathematics. In this particular case, the equation is c = 11p + 5. This equation denotes the cost (c) of pizzas delivered where each pizza prices ($11 each) is multiplied by the number of pizzas (p) and then added to the delivery fee ($5). Therefore, the third option, 'Each pizza costs $11 and the delivery fee is $5' is the correct interpretation of the equation.
To find out the cost of any number of pizzas, you would substitute that number in for 'p' in the equation. For instance, the cost of 5 pizzas would be calculated as 5 * $11 + $5 = $60.
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Can mutually exclusive events have an intersection of events? Explain your answer
Answers
Answer:
no
Step-by-step explanation:
exclusive pertains to one, hence the phrase, exclusive.
Mutually exclusive events or disjoint events are two events that don’t have anything in common. Nothing in common means NO INTERSECTION.
Answer: No!
Five friends are going to the theater. They have purchased a row of five seats with an aisle on either end. James doesn't want to sit next to Jill Betty and Herb are dating and want to sit next to each other Bob must sit on an aisle Provide a seating order that conforms to the above rules. An example of an invalid seating order is: James, Betty, Herb, Bob, Jill The above arrangement is invalid because: Bob is not sitting on an aisle. Specify the seating order as the names separated by s (as in the above example). Please be sure to spell the names correctly, including capitalization.
Answers
Answer:
Bob, Jill, Betty, Herb, James
Final answer:
A valid seating arrangement for the five friends is either Bob, Betty, Herb, James, Jill, or Jill, James, Herb, Betty, Bob. Each arrangement adheres to all given conditions: Bob is on an aisle, Betty and Herb are seated together, and James is not sitting next to Jill.
Explanation:
To solve the seating problem for the five friends going to the theater, we must adhere to the conditions: Bob must sit on an aisle, James cannot sit next to Jill, and Betty and Herb want to sit next to each other. Bearing in mind that there's an aisle on either side of the row of five seats, we can begin by placing Bob on an aisle seat since he must sit on one. This can either be the first seat on the left or the right. Since James doesn't want to sit next to Jill, we can't place Jill next to Bob if we sit James on the other end to maximize distance between them. Betty and Herb must sit together, which can only happen in the three seats left in the middle.
Here is a seating arrangement that satisfies all conditions: Bob, Betty, Herb, James, Jill. In this arrangement, Bob is on an aisle, Betty and Herb are seated together, and James is not sitting next to Jill.
Alternatively, if we place Bob on the other aisle, we get: Jill, James, Herb, Betty, Bob. Again, all conditions are met. Bob is on an aisle, Betty and Herb are sitting together, and James is not sitting next to Jill.
please Simplify 3^2x3^3
Answers
Answer:
[tex]243[/tex]
Step-by-step explanation:
[tex]3^2*3^3 = 9 * 27[/tex]
[tex]9 * 27 = 243[/tex]
Answer:
243
Step-by-step explanation:
[tex]3^2*3^3[/tex]
To solve your equation, employ the use of PEMDAS.
According to PEMDAS, exponents come before multiplication, so we can simply the 3 squared and the 3 cubed first.
3 squared is the same as 3 x 3, which is 9.
3 cubed is the same as 3 x 3 x 3, which is 27.
Thus, our new equation is
[tex]9*27[/tex]
Simply do the multiplication and you have your simplified answer.
[tex]9*27=243[/tex]
Jace has consumed 1,500 calories so far today. He has also burned off 400 calories at the gym. He would like to keep his daily calorie total to 1,900 calories per day. How many calories does he have left to consume for the day? Is 1,100 a viable solution to this problem?
===================================
Yes; 1,100 is less than 1,500.
No; 1,100 is more than the 400 he burned off at the gym.
No; 1,100 will cause him to exceed 1,900.
Yes; 1,100 is less than 1,900
Answers
Answer:
No, it will cause him to exceed 1900.
Step-by-step explanation:
1,500 - 400 = 1,100 (his total after the gym)
1,100 + 1,100 exceeds 1,900. He wants to keep his total below 1,900, so this is not a viable solution.
Answer:
No; 1,100 will cause him to exceed 1,900.
Step-by-step explanation:
The rationale for this problem is basic.
Jace established a diet restricted to 1900kcal.
If he started 1500kcal and burned 400kcal in the gym, Jane's partial jump is 1100 calories.
Thus, it can still eat the total of 1900-100 = 800kcal.
Any value over 800kcal will exceed the tax threshold and will disrupt Jane's results.
Based on the model N(1154,81) describing steer weights, what are the cutoff values for
a) the highest 10% of the weights?
b) the lowest 20% of the weights?
c) the middle 40% of the weights?
Answers
7. The number +10 can be used to indicate a
A. 10-degree rise in temperature.
B. decrease in salary of $10.
C. withdrawal of $10.
D. loss of 10 pounds.
Answers
Hello There!
The number +10 can be used to indicate a 10-degree rise in temperature.
This is because this is an increase. All of the other options are a decrease meaning that there going down from where they were originally.
If it takes Tom 15 minutes to eat a burger and then 5 minutes to eat a portion of fries, how many burgers and portions of fries would he be able to eat in one hour?
Answers
Tom could eat 4 burgers and 12 portions of fries.
Answer:
3
Step-by-step explanation:
15 minutes for one burger and another 5 for one portion of fries. If he has to eat a portion of fries after each burger that's 20 minutes. An hour is only 60 minutes allowing only enough time to eat 3 burgers and portions of fries. Simply because 60 divided by 20 is 3.
Which set of boxes containing tiles with the letters A, B, C, and D meet the following conditions?
In Box 1, P(A) > P(B)
In Box 2, P(B) + P(C) + P(D) = 1
In Box 3, P(D) = 2P(C)
Answers
Answer:
your choice is correct
Step-by-step explanation:
In your selected set of boxes, ...
Box 1 has p(A) = 2/6 > p(B) = 1/6
Box 2 contains only B, C, and D.
Box 3 has P(D) = 4/6 = 2*P(C) = 2*2/6
Need help with a math question PLEASE HELP
Answers
Answer:
57%
Step-by-step explanation:
From the table you can state that:
the total number of students is 10,730the number of students receiving Finincial Aid is 6,101Use the definition of the probability
[tex]Pr=\dfrac{\text{The number of favorable outcomes}}{\text{The number of all possible outcomes}}[/tex]
So,
the number of favorable outcomes = 6,101the number of all possible outcomes = 10,730Hence, the probability is
[tex]Pr=\dfrac{6,101}{10,730}\approx 0.5685\approx 57\%[/tex]
The results of a common standardized test used in psychology research is designed so that the population mean is 135 and the standard deviation is 30. A subject earns a score of 198. What is the z-score for this raw score?
z-score=
Answers
Answer:
2.1
Step-by-step explanation:
Mean+z score(Standard deviation)=raw score
Let the z score be z
135+z(30)=198
30z=63
z=2.1
The z-score is a measure of how many standard deviations a score is from the mean. In this case, where the test was designed with a mean of 135 and a standard deviation of 30, a score of 198 results in a z-score of 2.1.
Explanation:The z-score represents how many standard deviations an element is from the population mean. In this particular case, the results of a standardized test designed with a population mean of 135 and a standard deviation of 30 are given. A subject has a test score of 198.
To calculate the z-score, you use the formula: z = (X - μ) / σ. Where X is the score, μ is the mean, and σ is the standard deviation.
Substitute the given values into the formula:
z = (198 - 135) / 30
z = 2.1
So a test score of 198 would yield a z-score of 2.1.
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In order to avoid a training violation, 85% of your store's employees must complete diversity training by the end of the week. You have 142 employees at your store and 91 have currently completed the training. How many more employees must complete the training by the end of the week to avoid a training violation? 15 20 25 30 45
Answers
Multiply the number of total employees by 85%:
142 x 0.85 = 120.7, round to 121
121 total people need to complete the training.
Now subtract the number of people who already took the training:
121 - 91 = 20
20 more people need to take it.
I DONT WANT TO FAIL!!!! PLEASE HELP ME WITH THE CORRECT ANSWER, WILL MARK AS BRAINLIEST!!!
What is the solution to the system of linear equations? {4x+3y=543x+9y=108 Enter your answer in the boxes.
Answers
Answer:
x = -24
y = 66
Step-by-step explanation:
12x+9y = 102
12x+16y = 432
---------------------
y = 66
4x + (66*3) = 102
198-102 = -96
-96 / 4 = -24
Answer:
solution is [tex](6,10)[/tex]
Step-by-step explanation:
[tex]4x+3y=54[/tex]
[tex]3x+9y=108[/tex]
WE use elimination method to solve for x and y
Multiply the first equation by [tex]-3[/tex]
[tex]-12x-9y=-162[/tex]
[tex]3x+9y=108[/tex]
Now add both the equations, we will get
[tex]-9x=-54[/tex]
Divide by [tex]-9[/tex] on both sides
[tex]x=6[/tex]
Now we plug in the x value in first equaiton and find out y
[tex]4x+3y=54[/tex]
[tex]4(6)+3y=54[/tex]
[tex]24+3y=54[/tex], subtract 24 on both sides
[tex]3y=30[/tex]
Divide both sides by 3
[tex]y=10[/tex]
So solution is [tex](6,10)[/tex]
Find the measure of angle ABC.
A. 124
B. 97
C. 56
D. 51
Answers
Answer D. 51
Step-by-step explanation:
Sum of the interior angles of a triangle is up to 180
.: 32+(2x-15) + (x-5) = 180
Group like terms
2x+x =180 - 32 + 15 + 5
When - and + sign cross equal sign it turns to the opposite
3x = 168
x= 168/3
.: X =56
Now put x = 56 in (x - 5)
Angle ABC = 51
168/3 = x
X= 56 and now substitute 56 for x and u get ur angles 51 and 97
In a recent year,there were approximately 45 million moviegoers in a certain country, of these about 4/5 were ages 24-34. Find the approximate number of people ages 24-34 who attended the movies in that year.
Answers
Answer:
36 million
Step-by-step explanation:
(4/5)×(45 million) = (4/5×45) million = 36 million
Approximately 36 million people aged 24 to 34 attended movies that year.
Answer: 36 million.
Step-by-step explanation:
Hi, to answer this question we simply have to multiply the total number of moviegoers (45 million) 4/5 (moviegoers between ages 24-34 )
Mathematically speaking:
45m x 4/5 =45 x 4/5= 36 million
it can also be solved like this:
45,000,000 x 4/5 = 36,000,000
The approximate number of people ages 24-34 who attended the movies in that year were 36 million.
What is the surface area of the regular pyramid below
Answers
Answer:
C. 864 units²Step-by-step explanation:
We have the square in the base and four triangles on the lateral surface.
The formula of an area of a square:
[tex]A_{\square}=a^2[/tex]
a - side lenght
We have a = 16. Substitute:
[tex]A_{\square}=16^2=256[/tex]
The formula of an area of a triangle:
[tex]A_{\triangle}=\dfrac{bh}{2}[/tex]
b - base
h - height
We have b = 16 and h = 19. Substitute:
[tex]A_{\triangle}=\dfrac{(16)(19)}{2}=152[/tex]
The Surface Area:
[tex]S.A.=A_{\square}+4_{\triangle}[/tex]
Substitute:
[tex]S.A.=256+4(152)=256+608=864[/tex]
Answer: it C. 864 units²
Step-by-step explanation: I just did it
Write your answer without using negative exponents.
(w^5)^-7
Answers
Answer:
1/(w^35)
Step-by-step explanation:
According to the rules of exponents, you need to multiply both -7 and 5 such that you get...
w^(-35)
Since you cannot have a negative exponent according to the question, you simplify by...
w^-x means that you do 1/(w^-x)
1/(w^35)
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How to find the legs of a right triangle with only the hypotenuse?
Answers
Let x = legs of right triangle.
The set up would be:
x^2 + x^2 = (hypotenuse)^2
Understand?
To find the legs of a right triangle with only the hypotenuse known, the Pythagorean theorem is used. Without extra information like an angle or one leg length, it's impossible to find the specific leg lengths due to the infinite possibilities of right triangle configurations with the same hypotenuse length.
The question involves finding the lengths of the legs of a right triangle when only the length of the hypotenuse is known. Utilizing the Pythagorean theorem, which states that in a right triangle the square of the hypotenuse (c) is equal to the sum of the squares of the other two sides (a and b), expressed as a² + b² = c². To find the lengths of the legs (a and b) given the hypotenuse (c), one needs additional information such as the angle of the triangle or the length of one of the legs.
Without such information, it is not possible to determine the specific lengths of the legs because there are infinitely many right triangles with different sets of leg lengths that could have the same hypotenuse length. Therefore, to address this problem, one might use trigonometry if any angle is known, or apply other relevant context or given data.
Need help with a math question
Answers
Answer:
0.000032,0.00000.64
Step-by-step explanation:
For this case, it can be observed that the sequence is performed by multiplying each term by 0.2:
We have to:
[tex]0.1 * 0.2 = 0.02\\0.02 * 0.2 = 0.004\\0.004 * 0.2 = 0.0008\\0.0008 * 0.2 = 0.00016\\0.00016 * 0.2 = 0.000032\\0.000032 * 0.2 = 0.0000064[/tex]
Answer:
The next terms are:
[tex]0.000032\\0.0000064[/tex]