In ΔXYZ, ∠Y=90° and ∠X=73°. ∠ZWY=80° and XW=80. Find the length of ZY to the nearest 100th.
Answers
Answer:
Solution given:
Y=90°
∠X=73°.
∠ZWY=80°
and XW=80.
ZY=?
We know that
In right angled triangle ∆ XYZ
Tan 73=[tex] \frac{p}{h} [/tex]
3.27=[tex] \frac{yz}{xy} [/tex]
3.27×[xy]=yz
xw+wy=[tex] \frac{yz}{3.27} [/tex]
wy=[tex] \frac{yz}{3.27} [/tex]-80...........(1)
again
In right angled triangle WYZ
Tan 80=[tex] \frac{yz}{wy} [/tex]
5.67×wy=yz
wy=[tex] \frac{yz}{5.67} [/tex]
yz=5.67×wy............................................(2)
Equating equation 1&2
[tex] \frac{yz}{5.67} [/tex]=[tex] \frac{yz}{3.27} [/tex]-80
[tex] \frac{yz}{3.27} [/tex]-[tex] \frac{yz}{5.67} [/tex]=80
5.67yz-3.27yz=80*5.67*3.27
2.4yz =1483.272
yz=[tex] \frac{1483.272}{2.4} [/tex]
yz=618.03
:.y=618.03unit.the length of ZY to the nearest 100th is 618.
Related Questions
two bicycle riders start from the same point and ride in opposite directions. one rider is moving twice as the other. in 3 hours, they are 72 miles apart. find the rate of each rider.24
Answers
Let the speed of one rider = x
The speed of the second rider would e 2x ( twice as fast)
The total speed of the two riders would be x + 2x = 3x
Speed = Distance / time
Using the numbers:
3x = 72/3
Simplify:
3x = 24
Divide both sides by 3:
x = 8
The speed of one rider is 8 miles per hour
The speed of the second rider is 2(8) = 16 miles per hour.
Find the measure of COA. Then, classify the angle.
Answers
Answer:
The Angle COA=110°
An Obtuse Angle
Which equation is true?
Answers
Answer:
The third option
Step-by-step explanation:
[tex]\frac{-56}{8} = -7[/tex]
Find an equation of the line that passes through the point (2, 4) and is perpendicular to the line 4x + 9y - 2 = 0 (let x be the independent variable and y be the dependent variable.
Answers
Answer:
y = 9/4x -1/2
Step-by-step explanation:
4x + 9y -2=0
solve for y: 4x-2=-9y
(4x-2)/-9 =
y =4/-9x-2/9
perpendicular means reciprocal of slope. So 4/-9 changesz to 9/4
For the point plug in y and x:
9/4*2+b=4
b = -0.5
I attached graph as proof
is x=2a solution 10 3x+4=12 show work don't just say yes or no
Answers
9514 1404 393
Answer:
x = 2 2/3 is the solution; x = 2 is not a solution.
Step-by-step explanation:
The solution is ...
3x +4 = 12 . . . . . . given
3x = 8 . . . . . . . . . .subtract 4
x = 8/3 = 2 2/3 . . . divide by 3
x = 2 is not a solution. The correct solution is x = 2 2/3.
PLZ HELP PLZ PLZ this is my last final plz
A restaurant sells soups and salads. Soup costs $5.50, and a salad costs $8. On a particular day, the restaurant sells 58 items and makes $371.50.
Which system of equations can be used to find the amount of soup, x, and salad, y, the restaurant sold?
OA
5.50x = 58
8y = 371.50
OB.
5.50x = Sy
58x = 371.50y
x + y = 58
Oc.
5.50x + 8y = 371.50
x+y = 371.50
OD.
5.50x + 8y = 58
Answers
Answer:
b
Step-by-step explanation:
18. If an apprentice can do a piece of work in 24 days, and the apprentice and
instructor together can do it in 6 days, how long would it take the instructor to do
the work alone?
18. If an apprentice can do a piece of work in 24 days, and the apprentice and
instructor together can do it in 6 days, how long would it take the instructor to do
the work alone?
Answers
Answer:
the number of days when instructor do the work alone is 8 days
Step-by-step explanation:
Given that
The apprentice can do the work in 24 days
And, the apprentice and instructor together can do it in 6 days
We need to find out the number of days when instructor do the work alone
So,
[tex]= \frac{1}{6} - \frac{1}{24} \\\\= \frac{4 - 1}{24} \\\\= \frac{3}{24} \\\\= \frac{1}{8} \\\\= 8[/tex]
hence, the number of days when instructor do the work alone is 8 days
pioneers are buying mules to trek across the country. each of the 5 wagons require e mules to pull them. write the equation to express the relationship between the total mules d they need to and all the wagons. x=1y
Answers
Answer:
d = 5e
Step-by-step explanation:
Number of wagons = 5
Number of miles per wagon = e
Total number of mules = d
Hence, relationship between total mules d needed will be ;
Total mules = number of wagons * Numbe rof mules per wagon
d = 5e
PLEASE PLEASE PLEASE HELP!
use the distributive property to express the sum 24 + 30 with a common factor multiplied by a sum of two whole numbers with no common factor
Answers
Answer:
6(4+5)
Step-by-step explanation:
You are wrapping a birthday gift that is packaged in a specially made pyramid-shaped box. The base of the box measures 10 inches by 9 inches and the slant height is 6 inches. How much paper do you need to wrap the box
Answers
Answer:
2826 inches^2
Step-by-step explanation:
The general formula for the total surface area of a regular pyramid is
T.S.A.=12pl+B
Where p represents the perimeter of the base, l the slant height and B the area of the base.
The perimeter of the base is.
p=2L+2W
P=2*10+2*9
P=20+18
P= 38 inches
The area of the base is.
B=10*9
B=90in^2
T.S.A.=12(38)(6)+90
T.S.A=2736+90
T.S.A=2826 inches^2
Hence the paper needed is 2826 inches^2
Which numbers are rational?
Select each number that is correct.
23.429
10
13
151
8/7
-4.93
Answers
Answer:
All of them.
Step-by-step explanation:
Rational numbers are defined as the numbers that can be expressed as the ratio of two integers(a/b) where b must be a non-zero number. The rational numbers display a terminating characteristic and they also contain repeating, as well as, recurring digits. All the given numbers are rational as they can be written in the form of p/q.
23.429 = It can be written as a fraction. So, it is a rational number.
10 = 10 is a whole number and it can be written in the form of a/b i.e. 10/1. So, it is a rational number.
13 = 13 also can be written in ration form as 13/1. Therefore, it is also a rational number.
151 = It can be written as 151/1. Hence, it is a rational number.
8/7 = It is already mentioned in the form of a/b. So, it is a rational number.
-4.93 = since it is an integer, it will surely be a rational number.
Read the sentence.
The young soldier had been stationed overseas for two years. When it was time to come home, he decided to surprise his mom. It was a poignant moment when the soldier reunited with his mom.
What is the meaning of poignant?
A) touching
B) pitiful
C) relaxing
D) lonely
Answers
Answer: A
Step-by-step explanation:
The meaning of poignant is "touching", option A is correct.
What is Poignant?The meaning of poignant is touching or emotionally moving.
The word "poignant" is used to describe something that is deeply touching or emotionally moving.
It is often used to describe situations or experiences that evoke strong feelings of sadness, nostalgia, or sentimentality.
In the given sentence, the word "poignant" is used to convey the emotional impact of the soldier reuniting with his mother after two years of being stationed overseas.
The word suggests that the moment was very emotional and deeply touching for both the soldier and his mother, likely evoking feelings of happiness, relief, and nostalgia.
Hence, the meaning of poignant is "touching", option A is correct.
To learn more on Poignant click:
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please help me do this question
Answers
Answer:
2/10
Step-by-step explanation:
Im pretty sure its 2/10
have a great day:)
Points A,B, and C form a triangle. Complete the statements to prove that the sum of the interior angles of ABC is 180 degrees
Answers
Answer:
Step-by-step explanation:
Statements Reasons
1). Points A, B and C form the triangle 1). Given
2). Let DE be a line passing through 2). Definition of parallel lines
B and parallel to AC
3). ∠3 ≅ ∠5 and ∠1 ≅ ∠4 3). Theorem of Alternate
interior angles
4). m∠1 = m∠4 and m∠3 = m∠5 4). Definition of alternate angles
5). m∠4 + m∠2+ m∠5 = 180° 5). Angle addition and definition
of straight lines
6). m∠1 + m∠2+ m∠3 = 180° 6). Substitution
Panchito needs to make 80 ml of a 39% alcohol solution. He is going to make it by mixing a 50% alcohol solution with a 6% alcohol solution. How much if each should he use?
Answers
Answer:
60ml of the 50% alcohol solution and 20ml of the 6% alcohol solution
Step-by-step explanation:
We can build a system of equation for solve this problem
x = first solution
y = second solution
x + y = 80
0.5x + 0.06y = 80 * 0.39
x + y = 80
0.5x + 0.06y = 31.2
x = 80 -y
0.5(80-y) + 0.06y = 31.2
40 - 0.5y + 0.06y = 31.2
-0.44y = -8.8
y = 20
x = 80 - 20 = 60
5^2 - 3(3 -1) =
SHOW YOUR WORK STEP BY STEP PLS
Answers
I think this is right
Answer:
x = 19
Step-by-step explanation:
Let's start solving:
5² - 3(3-1) = x
Multiply 5 and 5 and also multiply 3(3-1)
25 - (9-3) = x
Subtract 6 from 25
25 - 6 = x
Simplify
x = 19
If my answer is incorrect, pls correct me!
If you like my answer and explanation, mark me as brainliest!
-Chetan K
Which of the following statements best describes the difference between net income and gross profit? a. Gross profit considers operating expenses while net income does not. b. Net income considers operating expenses while gross profit does not. c. Gross profit deducts taxes while net income does not. d. Net income deducts taxes while gross profit does not. Please select the best answer from the choices provided A B C D
Answers
Answer:
its b
Step-by-step explanation:
edg 20/21
if it is correct i will mark as brainlist or i will report
Answers
Answer:
The number of non-positive integral values of [tex]k[/tex] are contained in the following set:
[tex]S_{k} = \{-1, 0\}[/tex]
Step-by-step explanation:
Let be the following second order polynomial:
[tex]x^{2}-(k + 1)\cdot x + (k^{2}+k -8) = 0[/tex], [tex]k \le 0[/tex] (1)
Whose roots can be found by the Quadratic Formula:
[tex]x_{1,2} =\frac{k + 1\pm \sqrt{k^{2}+2\cdot k +1 - 4\cdot k^{2}-4\cdot k +32 }}{2}[/tex]
[tex]x_{1,2} = \frac{k+1}{2} \pm \frac{\sqrt{33-2\cdot k -3\cdot k^{2}}}{2}[/tex]
Based on the statement, we have the following system of inequations:
[tex]\frac{k+1}{2} + \frac{\sqrt{33 - 2\cdot k -3\cdot k^{2}}}{2} > 2[/tex] (2)
[tex]\frac{k+1}{2} - \frac{\sqrt{33 - 2\cdot k -3\cdot k^{2}}}{2} < 2[/tex] (3)
By (2) we have:
[tex]k + 1 + \sqrt{33-2\cdot k -3\cdot k^{2}} > 4[/tex]
[tex]\sqrt{33 -2\cdot k - 3\cdot k^{2}} > 4 - (k + 1)[/tex]
[tex]33 - 2\cdot k -3\cdot k^{2} > [4 - (k+ 1)]^{2}[/tex]
[tex]33 - 2\cdot k -3\cdot k^{2} > 16 -8\cdot (k+1)+(k+1)^{2}[/tex]
[tex]33 - 2\cdot k - 3\cdot k^{2} > 16-8\cdot k -8 + k^{2}+2\cdot k + 1[/tex]
[tex]33 - 2\cdot k -3\cdot k^{2} > 9 -6\cdot k + k^{2}[/tex]
[tex]0 > 4\cdot k^{2}-4\cdot k -24[/tex]
[tex]4\cdot k^{2}-4\cdot k -24< 0[/tex]
[tex]4\cdot (k^{2}-k-6) < 0[/tex]
[tex]k^{2}-k - 6 < 0[/tex]
[tex](k -3)\cdot (k+2) < 0[/tex]
The solution is:
[tex]k \in (-2, 3)[/tex]
Likewise, we get the following expression from (3):
[tex]k^{2}-k - 6 > 0[/tex]
[tex](k -3)\cdot (k + 2) > 0[/tex]
The solution is:
[tex]k \in (-\infty, -2)\,\cup\,(3, +\infty)[/tex]
The number of non-positive integral values of [tex]k[/tex] are contained in the following set:
[tex]S_{k} = \{-1, 0\}[/tex]
HELPPP
PLLS
DUE RN
WILL
GIVE BRAINLIST
X
X
X
X
Answers
Answer:
33% of the people preferred onions
can i get brainliest now lol
A point with a positive x-coordinate and a negative y-coordinate is reflected over the y-axis.
Which sentence describes the coordinates of the new point?
Answers
This is because the y-axis is vertical, so reflecting across it means you will change the sign of the x-value, and the sign of the y-value will stay constant. Since we start off with a positive x and negative y, we will end up with a negative x and negative y.
Solve for y
3 times 10 ^ 2y = 3600
Answers
Answer:
y≈1.778 (or y=log(3600)/2 or y=log(6)+1)
Step-by-step explanation:
10^2y=3600
log(10^2y)=log(3600)
2y=log(36)+log(100)
2y=log(6²)+2
2y=2log(6)+2
2y-2=2log(6)
y-1=log(6)
y=log(6)+1
y≈1.778
Maya wants to determine the area of a circle. She uses a compass and ruler to draw a circle that has a radius of r. She then inscribes a regular octagon within the circle, as shown above. The octagon is divided into 8 congruent triangles, and each of the 8 interior angles measure 45°.
She then labels the height and base of one of the triangles within the circle. She labels the height h, and the base, b.
She then makes three claims about her work.
Determine whether each claim Maya makes is correct. Select True or False for each claim.
Answers
Answer:
1st one is true, 2nd is true and 3rd is false
Step-by-step explanation:
If cose < 0 and cote > 0, then the terminal point determined by e is in:
A. quadrant 4.
B. quadrant 1.
C. quadrant 3.
D. quadrant 2.
Answers
If not let me know please and sorry if it is wrong:)
If cos < 0 and cot > 0, then the terminal point is determined by
C. quadrant 3.
What are reference angles according to quadrats?We have I, II, III, IV quadrants.In quadrant I the referece angle Ф is Ф.
In quadrant II the referece angle Ф is (π - Ф).
In quadrant III the referece angle Ф is (π + Ф).
In quadrant IV the referece angle Ф is (2π - Ф).
We know, cos is -ve on III and IV quadrants, and cot = 1/tan is +ve on I and III quadrant.
Therefore, The combined condition cos < 0 and cot > 0 satisfies on the II quadrant.
learn more about quadrants here :
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Evaluate the following complex expression. (4+ i) 2= + i (-4 i)(3 i)= i 3(9- i)= - i (5+2 i)(3-7 i)= - i (8+5 i)+2(3 i-4)= i (4+6 i)-(-4- i)= + i
Answers
Answer:
Operations on Complex Numbers (page 2 of 3) ... Simplify (2 – i)(3 + 4i). (2 – i)(3 + 4i) = (2)(3) + (2)(4i) + (–i)(3) + (–i)(4i). = 6 + 8i – 3i – 4i2 = 6 + 5i – 4(–1) ... exact same techniques for simplifying complex-number expressions as you do for polynomial ... Suppose you have the following exercise:
Step-by-step explanation:
Solve the system of equations using substitution or graphing.
y= -x2 + 4x + 5
y= x + 1
OA) (-1,0) and (6,7)
OB) (-1,0) and (4,5)
C) (1, 2) and (4,5)
D) (1, 2) and (6,7)
Answers
6 There were 35 children and 10 adults at a cookout. What is the ratio of children to total people at the cookout?
Answers
Cab 1 charges $1 per kilometer. Cab 2 charges $0.50 per kilometer and a $4 base charge. Solve for the value of k(kilometers ) that the 2 cab companies would cost the same.
Answers
Answer:
k=8
Step-by-step explanation:
Cab 1 : 1/km
Cab2: 0.5 /km with Base charge =4
x=0.5 x+4
x-0.5x=4
0.5x=4
4/0.5=x
x=8
Assume x=k
k=8
A theater sells adult tickets for $11 and child tickets for $6. At one show, the theater sold 180 tickets and received $1740.
How many adult tickets were sold? Enter the answer in the box.
Answers
A = adult, C = child
Total tickets = 180
Total cost = $1740
A + C = 180
11A + 6C = 1740
Use any method
I will use elimination
(A + C = 180) * 6
6A + 6C = 1080
11A + 6C = 1740
Subtract both sides
-5A = -660, A = 132
Solution: 132 adult tickets
Write the equation in either slope-intercept or point-slope form for the
line that goes through (1,1) and (3,-5). *
Answers
Answer:
y = mx + b
m = (-5-1)/(3-1)
m = -3
1=(-3)1 + b
b= 4
y= -3x + 4
A collection of books is set up into 34 rows. The first row has 96 books, and each row after that one
has 2 less books than the preceding row. (a) How many total books are there in the structure and (b)
how many books are in the 17th row?
Answers
Answer:
Part A: 3197
Part B: 62
Step-by-step explanation:
Part A: To make this easier just multiply 96 books by 34 rows which is 3264 books, but then since you are taking away 2 books for every row, multiply 2 by the 34 rows which is 68 but since the first row starts at 96 we will take away 1 row from the 68 which is 67. Then subtract 67 from the 3264 books and get 3197 books.
Part B: To make this easier just multiply 17 by 2 since we know for every row, 2 books are taken away and that equals 34 so subtract 34 from 96 and get 62.
Answer:
a(17) = 64
Step-by-step explanation:
you can create an arithmetic sequence formula as follows:
a(n) = a(1) + d(n-1) where a(1) is the first value and d is the common difference
a(17) = 96 -2(17-1)
a(17) = 96 - 32
a(17) = 64