In ΔXYZ, ∠Y=90° and ∠X=16°. ∠ZWY=42° and XW=260. Find the length of ZY to the nearest integer. (9th grade honors geometry)
Answers
Step-by-step explanation:
[tex] \tan(16) = \frac{y}{260 + x} \\ (260 + x) \times \tan(16) = y \\ 74.55 + 0.286x = y \\ y = 0.286x + 74.55[/tex]
[tex] \tan(42) = \frac{y}{x} \\0.9 x = y[/tex]
[tex]0.9x = 0.286x + 74.55 \\ 0.614x = 74.55 \\ x = 121.42[/tex]
[tex]y = 0.9x \\ y = 109.27 = 109[/tex]
The length of ZY is [tex]109.27[/tex]
What is Trigonometry?
Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles. The field emerged in the Hellenistic world during the 3rd century BC from applications of geometry to astronomical studies.
What is length?
Length is a measure of distance. In the International System of Quantities, length is a quantity with dimension distance. In most systems of measurement a base unit for length is chosen, from which all other units are derived. In the International System of Units system the base unit for length is the meter.
According to question, In ΔXYZ, ∠Y=90° and ∠X=16°. ∠ZWY=42° and XW=260.
We have to find the the length of ZY.
Let the length of ZY be [tex]x[/tex] and WY be [tex]y[/tex]
From the given question and figure
[tex]tan16[/tex]°[tex]=\frac{y}{260+x}[/tex]
⇒[tex]tan16[/tex]°×[tex](260+x)=y[/tex]
⇒[tex]y=0.286x+74.55[/tex]
Now,[tex]tan42[/tex]°[tex]=\frac{y}{x}[/tex]
⇒[tex]y=0.9x[/tex]
From both the above equation,
[tex]0.9x=0.286x+74.55[/tex]
⇒[tex]x=121.42[/tex]
[tex]y=0.9x=109.27[/tex]
Hence, we can conclude that the length of ZY is [tex]109.27[/tex]
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Related Questions
Find the value of x and y.
20
X
12
у
X =
y =
Answers
Answer:
Step-by-step explanation:
Therefore: The slope is: m=1. The y -intercept is: b=12 or (0,12)
a baby goraffe is about 6 1/2 feet tall at birth and grows about 1/2 foot per month for its first year. The function h=1/2m+61/2 represents the total height h of a baby giraffe for any number of months m within ita firat year. How much taller is the giraffe at the end of the month 11 than at the end of month 2
Answers
Answer: 4 and 1/2 ft (or 4.5 ft) taller.
Step-by-step explanation:
The function h(m) = (1/2)*m + (6 + 1/2) represents the height (on feet) of the giraffe as a function of the number of months, m.
We want to find the difference in the height between month 11 and month 2, then we need to find:
difference = h(11) - h(2)
We can directly calculate this:
difference = [ (1/2)*11 + (6 + 1/2)] - [(1/2)*2 + (6 + 1/2)]
difference = (1/2)*11 - (1/2)*2 = (1/2)*(11 - 2) = (1/2)*(9) = 9/2
And we can write 9 = 9 + 1, then:
difference = 9/2 = (8 + 1)/2 = 8/2 + 1/2 = 4 + 1/2
And this is in feet, then the girrafe is (4 and 1/2) ft taller on month 11 than on month 2.
Please help me now!!!!
Answers
Answer:
20
Step-by-step explanation:
Answer:
Hello! I hope you are having a great day~
Here is the answer:
Mean Absolute Deviation (MAD): 4.33
Step-by-step explanation:
Mean absolute deviation (MAD) of a data set is the average distance between each data value and the mean. Mean absolute deviation is a way to describe variation in a data set. So the average distance is 4.33! It has already been rounded to the hundredth place
A triangle is dilated by scale factor of 1/5 in a rotated night degrees clockwise about the origin why is the image similar to the pre image
Answers
9514 1404 393
Answer:
conditions for similarity are not violated by the transformation
Step-by-step explanation:
Dilation changes linear measures proportionally, and has no effect on angles. Rotation changes neither lengths nor angles. Hence the dilated, rotated triangle has the same angles as the original, and has proportional side lengths. Those are the requirements for figures to be similar, so the triangles are similar.
Answer:
The corresponding angles of the triangles are congruent
The image is a reduction of the pre-image
Neither the dilation nor the rotation change the shape of the triangle
Explanation:
For shapes to be similar:
1- there should be a ratio between the sides
2- angles in first shape should be congruent to angles in second shape
Now, a scale factor of 0.2 means that the sides of the image are 0.2 of the length of the original shape. However, angles are not changes
Let's check the choices:
1- The corresponding sides of the triangles are congruent:
This option is incorrect as dilation changes the lengths of the sides
2- The corresponding angles of the triangles are congruent:
This option is correct as neither dilation nor rotation alters the measures of the angles
3- The corresponding sides of the image are 5 times as long as those of the pre-image:
This option is incorrect as the sides of the image are only 0.2 times as long as those of the pre-image
4- The image is a reduction of the pre-image:
This option is correct as the sides of the image are 0.2 times those of the pre-image which means that the shape is reduced
5- Neither the dilation nor the rotation change the shape of the triangle:
This option is correct as both dilation and rotation are rigid transformations that do not alter the shape of the triangle (a triangle remains a triangle only with different side lengths)
6- The rotation reduces the size of the triangle:
This option is incorrect as rotation does not alter the size of the shape. It only changes its position
Hope this helps :)
-4x-2y=-12
solve the system of equations
Answers
1 2/3 - 3/5 as fraction
Answers
Answer:
1 1/15 or 16/15
Step-by-step explanation:
Find the common denominator.
25/15 - 9/15 = 16/15
Have a nice day!!
Hope this helps!!
Someone please help!! asap!!
Answers
Answer:
14.308-665544906576543214990
Type the correct answer in the box. Use numerals instead of words. If necessary, use / for the fraction bar(s).
Vlewer's Age Group
Excellent
Good
Average
Poor
Marginal Total
16-25
52
113
42
12
7
26-35
33
97
50
5
9
36-45
58
12
28
34
132
46-55
25
17
22
12
76
56+
12
5
3
8
28
Marginal Total
180
126
70
70
446
Note: A rating of good or excellent means the audience liked the movie, while a rating of poor means the audience disliked
the movie.
A movie producer conducted a survey after a preview screening of her new movie to find out how the film would be received by viewers from
different age groups. The table shows the numbers of viewers in different age groups who rated the film excellent, good, average, and poor.
%. Write your
Out of the total respondents, the percentage of respondents from the 46-55 age group who rated the film excellent is
answer up to two decimal places.
Reset
Next
Answers
The results of a linear regression are shown below.
y = ax + b
a=-1.15785
b = 139.3171772
r= -0.896557832
r2 = 0.8038159461
Which phrase best describes the relationship
between x and y?
1) strong negative correlation
2) strong positive correlation
3) weak negative correlation
4) weak positive correlation
Answers
Answer:
2 hopefully this helps you with work
The best describes the relationship between x and y will be;
⇒ Strong negative correlation.
What is linear expression?A linear expression is an algebraic statement where each term is either a constant or a variable raised to the first power.
Given that;
The results of a linear regression are shown below,
⇒ y = ax + b
⇒ a = -1.15785
⇒ b = 139.3171772
⇒ r = -0.896557832
⇒ r₂ = 0.8038159461
Now,
With the value of r we have both the information about the sign of the relationship and the strength of this relationship.
⇒ As the value of r is negative, we can conclude that the correlation between x and y is negative.
Also, as the absolute value of r is close to 1, we can conclude that this relationship is strong.
And, The strength can also be seen in the value of r2, which is also close to 1, but this value does not give information about the sign.
Thus, The value of the slope a, being negative, can also tell us that the relation between x and y is a negative correlation.
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1. Maya had a dozen white eggs
and a dozen brown eggs in her
refrigerator. She used 6 white
eggs and 8 brown eggs to make
breakfast. How many eggs does
she have left?
Answers
Answer:
6 white & 4 brown
Step-by-step explanation:
12-6=6
12-8=4
MATRIX X IS SHOWN BELOW
Answers
Answer:
4
Step-by-step explanation: thast it
Answer: 40
Step-by-step explanation:
401(<) the contributions are tax deductible, and income generated by the account is
401(k), the contributions are taxable when deposited, but when the money is withdrawn at retirerment they are
In a traditional
In a Roth
Answers
Answer:
First Blank: Traditional
Second Blank: (the other choice, besides exempt)
Third Blank: Roth
Fourth Blank: Taxes exempt
Step-by-step explanation:
I got 5/5 on the test by reading through the other guys answer.
In a traditional 401(k), it is tax deferred because the income earned isn't taxed until the money is withdrawn.
What is income tax?Income tax is a tax applied on individuals or entities concerning income or profit earned by them.
A 401 k is a qualified tax-advantaged saving retirement plan. Usually, The 401K plans are employer-sponsored. Employee contributions to the 401 k plans are deducted from the payroll before the taxes can be calculated.
This means that the employee contribution is not taxed at the time it's withheld by the employer.
The amounts saved are invested in market securities such as shares and companies bonds. The tax due from the money from the investment is deferred to the time of withdrawal.
The employee are needed to pay taxes on contributions and investments earning every financial year.
In a traditional 401(k), it is tax deferred because the income earned isn't taxed until the money is withdrawn.
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Which set of ordered pairs represents a function?
{(-7,-1), (7,-1),(-9,3), (-9,2)}
{(3,5), (7,9),(4,4), (3,3)}
{(3,-2), (-7,6),(-5, -8), (3, -6)}
{(0,2).(-9,7),(-6, -1),(-2,2)}
Answers
Answer:
The last one
Step-by-step explanation:
Answer:
{(0,2), (-9,7), (-6, -1), (-2,2)}
Step-by-step explanation:
You can see if points are a function by seeing if the first value in the parenthesis (X value) and if they are the same, the points are not a function. The only points where the first value in the parenthesis are not the same is in the fourth set of points.
find the measure of the missing angle to the nearest degree, with showing your work.
Answers
[tex]\cos\theta=\frac{10}{14}\\ \\
\theta=\cos^{-1}\frac{10}{14}\\ \\
\theta=44^o [/tex]
12. x + y = 4
And the next question is
13. -7 x = y
Pls answer ASAP and explain why!! Thank you!!
Answers
Answer:
[tex]x = - \frac{2}{3} \: \: \: y = \frac{14}{3} [/tex]
Step-by-step explanation:
Since we know -7x=y we use the substitution method and plug it in the top equation.
[tex]x + - 7x = 4[/tex]
[tex] - 6x = 4[/tex]
[tex]x = - \frac{4}{6} [/tex]
or x=-2/3
Then plug it back in the the bottom equation
[tex] - 7( \frac { - 2}{3} ) = y[/tex]
y=14/3
Mary Chapman had been working at First Savings for 18 years when she
became permanently disabled and could not continue to work. She was 50 years
old and had planned to retire in 12 years. Her final average salary was $34,500.
First Savings' rate of benefits is 2%. What is Chapman's monthly disability
benefit?
Answers
Answer:
17250
Step-by-step explanation:
1
1 point
The force, I needed to move a rock varies inversely as the length, L, of the crowbar used. When the length is 80 cm, the force needed is 1.5 N. Find the force needed when
the length of the crowbar is 120 cm
Type your answer..
3
Answers
9514 1404 393
Answer:
1.0 N
Step-by-step explanation:
When the length increases by the factor 120/80 = 3/2, the force required is multiplied by the inverse of this: 2/3.
The required force is ...
(2/3)(1.5 N) = 1.0 N
Can someone solve this please
Answers
Question 48= 98 Fahrenheit
Question 49= 127 millimeters
Last question= 2 inches
If a rectangular prism has a width of 5, a height of 4, and a length of 9, what is the volume of this prism if it was dilated by a scale 1/2?
Answers
Answer:
90
Step-by-step explanation:
5x4x9=180
180x.5=90
hope this is what you were looking for!
Which is the measure of
A) 93* B)113* C)138* D)180*
Answers
Answer:
A) 93 degrees
Step-by-step explanation:
a is supplementary to 93 degrees so A=180-87=93
Answer:
<A+87=180(linear pair)
<A=180-87=93°
is required value of <A
In 2071 the monthly salary of the Chief justice of
Nepal was Rs. 53580. If 1 % tax was levied on firs
Rs. 300000 and certain rate on remaining so that the
chief justice paid Rs. 4537 monthly tax. How much
was the tax percentage on remaining? (Ans: 15%)
Answers
Answer:
Step-by-step explanation:
There must be an error—or multiple errors—in the question. Rs 300,000 doesn't make sense, because that would mean he was due a tax refund.
Rs 30,000 doesn't work, either, because that would mean he was paying 18% tax, not 15%.
If a 1% tax was levied on the first Rs 25,000, then he would pay Rs 4,287 on on the remaining Rs 28,580, which would work out to 15%.
Which graph represents the parametric equations x = 1 – t2 and y = 2t, where 0 ≤ t ≤ 5?
ANSWER: A
Answers
After plotting the above equation on the coordinate plane, we can see the graph of the function.
What are parametric equations?A parametric equation in mathematics specifies a set of numbers as functions of one or more independent variables known as parameters.
We have two parametric equations:
x = 1 – t² and
y = 2t
t = y/2 and
0 ≤ t² ≤ 5
1 ≤ 1 - t²≤ 4
1 ≤ x≤ 4
Plug the above value in x = 1 – t²
x = 1- (y/2)²
x = 1 - y²/4
4x = 4 - y²
y² = 4(1 - x)
Thus, after plotting the above equation on the coordinate plane, we can see the graph of the function.
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This question is worth 2 points! Allison makes and sells beaded necklaces. She charges a flat fee of $5 per necklace, and $1.50 per bead that she adds. If Jennifer, who wants to purchase a necklace, has $34 to spend, how many beads can she add to her necklace? Explain the process you used to solve, and tell what your answer is.
Answers
Answer:
19 beads
Step-by-step explanation:
If Jennifer has 34$ she automatically loses 5$ because that's the fee for the necklace. So, you subtract 34 from 5 and you get 29. After that you divide 29 by 1.50 and you get 19.333333. But, since you can't get 1/3 of a bead Jennifer can only buy 19 beads.
Can anyone help explain this my daughter is 7 does not understand it
Answers
Dawn is playing a word game. The scores for her first nine words are:
14, 23, 9, 15, 17, 22, 24, 17, 21
Which best describes her scores?
Answers
Answer:
The minimum is 9 the maximum is 24 and the range is 9
Step-by-step explanation:
The minimum is 9 and the maximum is 24 and the range is 15
What is the range of a set of observations?The difference between the highest and lowest values in the observation is known as the range of the observation.
Given here: 14, 23, 9, 15, 17, 22, 24, 17, 21
Clearly max. value =24 and min. value=9
∴ Range= 24-9
=15
Hence, The minimum is 9 and the maximum is 24 and the range is 15
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I have a question, do you think School is necessary during a pandemic? If so then explain why
Answers
Answer:
Step-by-step explanation: Honestly, I don't dislike school. With the rather boring state we're in, school is generally a passtime. But, It depends on your emotional health. Some kids have their parents or relatives getting infected, which takes a toll. And now, teachers barely let us skip for any reason, even if it's more emotional health. So, I would say yes and no.
Brady has a card collection with 32 baseball cards, 64 football cards, and 24 baseball cards. He wants to arrange the cards in equal piles, with only one type of card in each pile.
Answers
So you will have 4 piles of baseball cards, 8 piles of football cards, and 3 piles of baseball cards again
(I think you meant basketball cards and if not add 3+4=7 so you get 7 baseball cards if it wasn’t a typo)
Hope this helps :)
Please help will give correct answer brainliest
what information is necessary to prove that the two triangles are similar by the AA similarity theorem? show your work
Answers
Answer:
Step-by-step explanation:
Let us begin with the AA Similarity definition. It states that if two angles of one triangle are congruent to two angles of another triangle, then the triangles are similar.
This means that we need:
An angle of one triangle that is congruent to an angle of the other triangle.Another angle of one triangle that is congruent to another angle of the other triangle.For this problem, it is unclear that there are more than one angles that are congruent to each other. We see that angle <DEF and <ABC are congruent, but the problem does not give any other angles. In another case, we must find one more to prove similarity by the AA similarity theorem.
i got 413 pointssssssssssssssssssssss who wants em cuz i am leaving brainlry for answers
Answers
Answer:
ayooo i'll take it
Step-by-step explanation:
thanks
Answer:
Ooh a couple more for 100 points!!
Step-by-step explanation:
The population of a small town is growing at a rate of 5% per year. If the population right now is 22 000, What will the population be 10 years from now?
Answers
Answer:
35,836
Step-by-step explanation:
I had this question before and I believe this is correct.
Answer:
the population 35,836 in 10 years.
Step-by-step explanation:
The numbers representing the population in consecutive years create a geometrical sequence with:
a1 = 22,000
and
q = 1 + 0.5 = 1.05
We are asked to find the population after
10 years. This number is the eleventh term in the sequence, so we are looking for:
a11 = a1 ⋅ q^10 = 22, 000 ⋅ (1.05)^10
After substitution of given data we have:
a11 ≈ 35, 836
*Answer:* "After 10 years the population will be 35, 836."