Answer:
57.33
Step-by-step explanation:
For a triangle: 3 angles sum up to be 180
(z-39)+(z+47)+z=180
3z=180+39-47
z=172/3
z=57.3333
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Let P(1,2,1), Q(1,0,-1), R(2,2,0) be the vertices of a parallelogram with adjacent sides PQ and PR. Find the other vertex S.
Given:
The vertices of a parallelogram are P(1,2,1), Q(1,0,-1), R(2,2,0).
PQ and PR are the adjacent sides of the parallelogram.
To find:
The coordinates of vertex S.
Solution:
We know that, the diagonals of a parallelogram bisect each other.
Let the coordinates of the vertex S are (a,b,c).
In the given parallelogram PS and QR are the diagonals. It means their midpoints are same.
[tex]\left(\dfrac{1+a}{2},\dfrac{2+b}{2},\dfrac{1+c}{2}\right)=\left(\dfrac{1+2}{2},\dfrac{0+2}{2},\dfrac{-1+0}{2}\right)[/tex]
[tex]\left(\dfrac{1+a}{2},\dfrac{2+b}{2},\dfrac{1+c}{2}\right)=\left(\dfrac{3}{2},\dfrac{2}{2},\dfrac{-1}{2}\right)[/tex]
On comparing both sides, we get
[tex]\dfrac{1+a}{2}=\dfrac{3}{2}[/tex]
[tex]1+a=3[/tex]
[tex]a=3-1[/tex]
[tex]a=2[/tex]
Similarly,
[tex]\dfrac{2+b}{2}=\dfrac{2}{2}[/tex]
[tex]2+b=2[/tex]
[tex]b=2-2[/tex]
[tex]b=0[/tex]
And,
[tex]\dfrac{1+c}{2}=\dfrac{-1}{2}[/tex]
[tex]1+c=-1[/tex]
[tex]c=-1-1[/tex]
[tex]c=-2[/tex]
Hence, the coordinates of vertex S are (2,0,-2).
It's camping season! Ernie and Bert set up their tents 15 m from
each other. Ernie has Tent 1 and Bert has Tent 2. The angle
between the line of sight from Bert's tent to the shower and the
line of sight from Bert's tent to Ernie's tent is 78 degrees. If
Ernie's tent is 19m away from the shower, is Bert 's tent closer or
further away from the shower and by how much? In your
calculations, round your angles to the nearest whole degree and
side measurements to the nearest tenth of a metre.
1
2
Answer:
The answer is "21.6".
Step-by-step explanation:
Let A stand for tent 1
Let B stand for tent 2
Let C be a shower
Using cosine formula:
[tex]c= \sqrt{b^2 +a^2 - 2ab\cdot \cos(C)}\\\\[/tex]
[tex]= \sqrt{(19)^2 + (15)^2 - 2\cdot 19 \cdot 15 \cdot \cos(78^{\circ})}\\\\= \sqrt{361 + 225 - 570\cdot \cos(78^{\circ})}\\\\ = \sqrt{586- 570\cdot \cos(78^{\circ})}\\\\= 21.6\\\\[/tex]
Therefore, you need to reduce the similarity from B to C which is the length from tent 2 to shower:
Tent 2 Distance to Dusk = 21.6m
Bert's tent is 21.6m away from the shower
Determine the difference. 3/4 – 5/16 =?
Answer:
[tex]\frac{3}{4} -\frac{5}{16} =\frac{3(4)}{4(4)} =\frac{5}{16} =\frac{12}{16} -\frac{5}{16} =\frac{7}{16}[/tex]
Answer:
7/16
Step-by-step explanation:
3/4 - 5/16
Get a common denominator of 16
3/4 *4/4 -5/16
12/16 - 5/16
7/16
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Answer: move each corner (where you see the right triangles) 2 units to the left and three units up. Then, draw the quadrilateral.
Step-by-step explanation:
which of the following is q point slope equation of a line that passes through the point (5,2)and (-1,-6)
Answer:y - y1 = m(x + x1)
m = (y2 - y1)/(x2 - x1) = (-6 - 2)/(-1 - 5) = -8/(-6) = 4/3
y - 2 = 4/3(x - 5) is a possible answer
y + 6 = 4/3(x + 1) is also a possible answer
Step-by-step explanation:
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Find the length of AC
A. 12.84
B. 43.92
C. 12.28
D. 40.16
Answer: 40.16
Step-by-step explanation:
The length of the side AC will be 12.28 units. The correct option is C.
What is trigonometric indentity?
Trigonometric Identities are equality statements that hold true for all values of the variables in the equation and that use trigonometry functions. There are numerous distinctive trigonometric identities that relate to a triangle's side length and angle.
Given that the hypotenuse of the triangle is 42 and the angle B is 17 degrees.
The side AC will be calculated as below:-
sin(47) = P / 42
AC = 42 x sin42
AC = 12.27
Therefore, the length of the side AC will be 12.28 units. The correct option is C.
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I’ll give you Brainliest if you answer this!
Answer:
17
Step-by-step explanation:
please help, it’s urgent !
Answer:
f(-10) = 2 times -10 + 1
= -19
f(2) = 2^2
= 4
f(-5) = 2 times -5 + 1
= -9
f(-1) = (-1)^2
= 1
f(8) = 3-8
= -5
Step-by-step explanation:
pleas help
given parallelogram ABCD find m<ADB
Answer:
∠ ADB = 19°
Step-by-step explanation:
Consecutive angles in a parallelogram are supplementary, sum to 180° , so
∠ CDA = 180° - ∠ DAB = 180° - 138° = 42°
Then
∠ ADB + ∠ CDB = 42° , that is
∠ ADB + 23° = 42° ( subtract 23° from both sides )
∠ ADB = 19°
4.8 yd
6 yd
1
4.5 yd
5 yd
7 yd
Find the volume of the composite solid. Round your answer to the nearest hundredth.
A. 244.36 B. 264.79 C. 304.51 D. 330.84
Answer:
A
Step-by-step explanation:
The composite solid is made up of a cone and a rectangular prism.
Volume of the composite solid = volume of the cone + volume of the rectangular prism
✔️Volume of Cone = ⅓*π*r²*h
Where,
r = 4.8 yd
h = √(6² - 4.8²) = √12.96 = 3.6 yd
Substitute
Volume of cone = ⅓*π*4.8²*3.6
= 86.86 yd²
✔️Volume of rectangular prism = l*b*h
Where,
l = 7 yd
w = 5 yd
h = 4.5 yd
Substitute
Volume of prism = 7*5*4.5 = 157.5 yd²
✔️Volume of composite solid = 86.86 + 157.6 = 244.4 yd² (which is close to 244.36 yd²)
Write a linear equation in point slope form with the given slope of 1/4 and passing through the point (8,-3)
Answer:
The equation is
y=1/4x-3
Answer:
y = 1/4x - 5
Step-by-step explanation:
If gradient or slope (m) equal to 1/4
then y - y¹ = m( x - x¹) ..........(1)
where the line happen to be passing through the point given above
therefore let x¹ be 8.........(2)
and y¹ be -3...............(3)
substitute (3) and (2) into (1)
we have y -(-3) = 1/4 (x - 8)
so 4(y+3)= (x-8)
4y = x - 8 - 12
therefore y = 1/4x - 5
Sixty out of every 100 pieces of candy is red. Which Indicates the
proportion of red candies? **
60
60/100
60/40
40/100
Answer:
The proportion of red candies is 60/100.
Step-by-step explanation:
Given that sixty out of every 100 pieces of candy is red, to determine which indicates the proportion of red candies, the following calculation must be performed:
60 red candies out of 100 total candies
60/100
Therefore, the ratio of red candies is 60/100.
Find the missing length indicatedOk
Answer:
x = 135
Step-by-step explanation:
find z-score for the standard normal distribution with mean 0 and standard deviation 1 with the probability 0.9850
Answer:
z-score=2.17
Step-by-step explanation:
We are given that
Mean, [tex]\mu=0[/tex]
Standard deviation, [tex]\sigma=1[/tex]
Probability, p-value=0.9850
We have to find z-score for the standard normal distribution with mean 0 and standard deviation 1 with the probability 0.9850.
To find the z score for the standard normal distribution we will use z-table.
From z- table we get
p-value =0.9850 when z -score=2.17
[tex]\implies[/tex]z-score corresponding to p-value=2.17
Therefore, the z-score for the standard normal distribution with mean 0 and standard deviation 1 with the probability 0.9850=2.17
Danielle needs to walk 3 miles. If she wants to reach her destination in 45
minutes ( hour), how fast does she need to walk?
A. 135 miles
per hour
B. 2.25 miles per hour
C. 15 miles per hour
D. 4 miles per hour
Answer:
4 miles per hour
Step-by-step explanation:
3 miles
Change the 45 minutes to hours
45 minutes * 1 hour/60 minutes = 3/4 hour
3 miles ÷ 3/4 hour
Copy dot flip
3 * 4/3
4 miles per hour
a ball is thrown from a height of 4 feet with an intial upward velocity of 40 ft per second. The ball's height h (in feet) after t seconds is given by the following. h=4+40t-16t^(2 )Find the values of t for which the ball's height is 26 feet.
Answer:
Step-by-step explanation:
you need o solve 26=4+40t-16t^2
the equation becomes:
the equation becomes:-16t^2+40t+4-26=0
the equation becomes:-16t^2+40t+-22=0 or8t^2-20t+11=0
8t^2-20t+11=0, a=8 , b=-20 c=11 the discriminant =b^2-4ac=(-20)^2-4x8x11=48
t1=(20-squarootof48)/16 =13/16 =0.81 seconds t2=27/16=1.68 second I rounded my answers
Does anyone know this?
Answer:
C
Step-by-step explanation:
Rationalize the denominator by multiplying [tex]\frac{\sqrt{5}}{\sqrt{5} }[/tex]. The denominator will become 5, while the numerator will be 3[tex]\sqrt{100}[/tex]. This is equal to 30/5, which is 6.
Hope this helps!
A roller coaster descended 32.3 ft in one minute. How would you show this using an integer?
A. -32.3
B. +32.3
C. 32.3-
D. 32.3+\
Answer:
Step-by-step explanation:
a
Ivan and kate live 42 miles apart. ivan leaves his house at 8:00 a.m. and bikes towards kate's house at a constant speed of 12 mph. kate leaves her house at 9:30 a.m. but bikes towards ivan at constant speed of 18 mph. at what time will they meet?
Answer:
10:18am
Step-by-step explanation:
The time at which they meet, given that Ivan leaves his house at 8:00 A.M. and bikes towards Kate's house at a constant speed of 12 mph, while Kate leaves her house at 9:30 A.M. but bikes toward Ivan at a constant speed of 18 mph is 10:18 A.M.
How is the speed of a body, related to the distance it travels and the time it takes?The speed of a body is given as the ratio of the distance it travels and the time it takes. Thus, it can be shown as:
Speed = Distance/Time.
The other equations formed from this are:
Distance = Speed*Time
Time = Distance/Speed.
How to solve the question?In the question, we are given that Ivan and Kate live 42 miles apart.
We are asked for the time at which they meet, given that Ivan leaves his house at 8:00 A.M. and bikes towards Kate's house at a constant speed of 12 mph, while Kate leaves her house at 9:30 A.M. but bikes toward Ivan at a constant speed of 18 mph.
The time for which Ivan travels alone is from 8:00 A.M. to 9:30 A.M., that is, 1.5 hours.
The distance covered by Ivan at a constant speed of 12 mph during this time can be shown as,
Distance = Speed*Time,
or, Distance = 12*1.5 = 18 miles.
The distance left to be covered now is, 42 - 18 miles = 24 miles.
After 9:30 A.M., both Ivan and Kate are biking toward each other.
Thus, their relative speed moving toward each other is the sum of their speeds.
Thus, the relative speed = 12 + 18 = 30 mph.
Thus, the time taken by them after 9:30 A.M. to meet can be shown as:
Time = Distance/Speed,
or, Time = 24/30 = 0.8 hours = 48 minutes.
Thus, Ivan and Kate meet at 9:30 + 48 minutes = 10:18 A.M.
Thus, the time at which they meet, given that Ivan leaves his house at 8:00 A.M. and bikes towards Kate's house at a constant speed of 12 mph, while Kate leaves her house at 9:30 A.M. but bikes toward Ivan at a constant speed of 18 mph is 10:18 A.M.
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PLEASE HELP ME NOW PLEASE
9514 1404 393
Answer:
x = 12
Step-by-step explanation:
Angle U is supplementary to the arc intercepted by the tangents.
5x +10 = 180 -110
5x = 60 . . . . . . subtract 10 and simplify
x = 12 . . . . . . . . divide by 5
6. A sporting goods store receives an order of 100 baseball caps, of which 22 are green. If 1 of
the 100 caps is selected at random, what is the probability it will not be green?
A. 39/50
B. 11/25
C. 11/50
D. 1/2
Answer:
[tex]\text{A. }39/50[/tex]
Step-by-step explanation:
The probability that a randomly selected cap will not be green is equal to the number of non-green caps divided by the total number of caps.
Since there are 100 caps total and 22 are green, there must be [tex]100-22=78[/tex] non-green caps.
Divide this by the total number of caps (100) to get the probability that a randomly selected cap will not be green:
[tex]\frac{78}{100}[/tex]
Simplify by dividing both the numerator and denominator by 2:
[tex]\frac{78}{100}=\boxed{39/50}[/tex]
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Step-by-step explanation:
if u like this answer plz mark as brainlist
Angle formed by each blade = 40°
So, total angle formed by 3 blades
= 40° × 3 = 120°
Total angle of a circle = 360°
Ratio of angle formed by total circle to angle formed by the 3 blades
= 360° : 120°
= 360 : 120
= 3 : 1
Total area of circle
= πr²
= π(3m)²
= π9m²
Let the area of blades be x.
So, area of total circle : x = 3 : 1
= π9m² : x = 3 : 1
= π9m²/x = 3/1
= π9m²/3 = x/1
= π9m²/3 = x
= π3m² = x
So, the area of all three blades is π3m².
13/16= (-5/4) + g
G= what
NEDD HELP NOW plz
Using Suitable property Evaluate :
(10)3 – (2)³ – (8)3
Answer:
480
Step-by-step explanation:
(10)3- (2)3- (8)3
1000- 8- 512
= 480
Please mark mee brainlist....
If you have a right triangle with legs a =6 and b= 8, what is the value of the hypotenuse? show work.
Answer:
10
Step-by-step explanation:
1. [tex]6^{2} + 8^{2} = c^{2}[/tex]
2 [tex]100 = c^{2}[/tex]
3. c = 10
Which ratio represents the tangent of an angle?
a. adjacent/hypotenuse
b. opposite/hypotenuse
c. adjacent/opposite
d. opposite/adjacent
Answer:
option d.opposite / adjacent
Step-by-step explanation:
opposite /adjacent ratio represents the tangent of an angle .
hope it is helpful to you ☺️
Answer:
D.
Step-by-step explanation:
From the trigonometry shortcuts we can use the acronyms:
SOH CAH TOA
for an arbitrary angle Ф, plug in the length of the sides:
sin(Ф) = opposite/hypotenuse
cos(Ф) = adjacent/hypotenuse
tan(Ф) = opposite/adjacent
Triangle plz help me find B,b and c
Answer:
B = 55°
b = 17.1 (rounded to the nearest tenth)
c = 20.9 (rounded to the nearest tenth)
PLZZZZZZ HELP WILL GIVE BRAIN THING AND EXTRA POINTS !What is the least common denominator of the rational expressions below?
Answer:
D is the least common denominator
R0,180 is the same rotation as ____.
R0,-180
R-90,180
R90,180
R0,90
A pollster obtains a list of all the residential addresses in a certain town, and uses a computer random number generator to choose 150 of them. The pollster visits each of the 150 households and interviews all the adults in each of the household about their television viewing habits. What kind of sampling is this
Answer:
Cluster sampling.
Step-by-step explanation:
Samples may be classified as:
Convenient: Sample drawn from a conveniently available pool.
Random: Basically, put all the options into a hat and drawn some of them.
Systematic: Every kth element is taken. For example, you want to survey something on the street, you interview every 5th person, for example.
Cluster: Divides population into groups, called clusters, and each element in the cluster is surveyed.
Stratified: Also divides the population into groups. However, then only some elements of the group are surveyed.
In this question:
People divided into groups, by households.
Each member of the households(group) is surveyed, so cluster sampling.