Answer:
Jon's hiding spot is closer to the starting point.
Step-by-step explanation:
Jon's final position forms a triangle with sides 100 ft and 120 ft respectively with an angle of 180 - 45 = 135 between them. Since the angle between the 100 ft direct east and 120 ft direction is 45, since Jon turns 45 after moving for 100 ft and then moves another 120 ft to his final destination.
Also, Lisa's final position forms a triangle with sides 120 ft and 100 ft respectively with an angle of 180 - 32 = 148 between them. Since the angle between the 120 ft direction west and 100 ft direction south of west is 45, since Lisa turns 32 after moving for 120 ft and then moves another 100 ft to her final destination.
Using the cosine rule,
a² = b² + c² - 2abcosФ, we find the length of the third side of each triangle which is their distance from the starting point.
So, for Jon
a² = b² + c² - 2abcosФ where b = 100 ft, c = 120 ft and Ф = 135°
Thus,
a² = (100 ft)² + (120 ft)² - 2(100 ft)(120 ft)cos135°
a² = 10000 ft² + 14400 ft² - 24000 ft²cos135°
a² = 10000 ft² + 14400 ft² - 24000 ft²(-0.7071)
a² = 24400 ft² + 16970.56 ft²
a² = 41370.56 ft²
a = √(41370.56 ft²)
a = 203.4 ft
for Lisa
a'² = b'² + c'² - 2a'b'cosФ' where b = 120 ft, c = 100 ft and Ф = 148°
Thus,
a'² = (120 ft)² + (100 ft)² - 2(120 ft)(100 ft)cos148°
a'² = 14400 ft² + 10000 ft² - 24000 ft²cos148°
a'² = 14400 ft² + 10000 ft² - 24000 ft²(-0.8481)
a'² = 24400 ft² + 20353.15 ft²
a'² = 44753.15 ft²
a' = √(44753.15 ft²)
a' = 211.56 ft
a' ≅ 211.6 ft
Since a = 203.4 ft < a' = 211.6 ft,
Jon's hiding spot is closer to the starting point.
pls answer asap no wrong answers pls
Answer:
401.92
Step-by-step explanation:
The formula used the calculate the volume of a cylinder is
πr^2h
π= 3.14
H= 8
r= 4
Volume= 3.14 × 4^2 × 8
= 3.14 × 16×8
= 401.92
Hence the volume is 401.92
The total cost in dollars to buy uniforms for the company staff can be found using the function c=14.95x+7.95, where x is the number of uniforms bought. If there are at least 30 people but not more than 35 people on the staff, what is the domain of the function for this situation?
Answer: the answer is D
Step-by-step explanation:
The domain is the x-values and can not be greater than 35.
Answer:
Step-by-step explanation:
Please help me with question number 2
Answer:
2. The area of the side walk is approximately 217 m²
3. The distance away from the sprinkler the water can spread is approximately 11 feet
4. The area of the rug is 49.6
Step-by-step explanation:
2. The dimensions of the flower bed and the sidewalks are;
The diameter of the flower bed = 20 meters
The width of the circular side walk, x = 3 meters
Therefore, the diameter of the outer edge of the side walk, D, is given as follows
D = d + 2·x (The width of the side walk is applied to both side of the circular diameter)
∴ D = 20 + 2×3 = 26
The area of the side walk = The area of the sidewalk and the side walk = The area of the flower bed
∴ The area of the side walk, A = π·D²/4 - π·d²/4
∴ A = 3.14 × 26²/4 - 3.14 × 20²/4 = 216.66
By rounding to the nearest whole number, the area of the side walk, A ≈ 217 m²
3. Given that the area formed by the circular pattern, A = 379.94 ft.², we have;
Area of a circle = π·r²
∴ Where 'r' represents how far it can spread, we have;
π·r² = 379.94
r = √(379.94 ft.²/π) ≈ 10.997211 ft.
Therefore, the distance away from the sprinkler the water can spread, r ≈ 11 feet
4. The circumference of the rug = 24.8 meters
The circumference of a circle, C = 2·π·r
Where;
r = The radius of the circle
π = 3.1
∴ For the rug of radius 'r', C = 2·π·r = 24.8
r = 24.8/(2·π) = 12.4/π = 12.4/3.1 = 4
The area = π·r²
∴ The area of the rug = 3.1 × 4² = 49.6.
Can some one awnser the following
Answer:
-11
Step-by-step explanation:
find the gradient of a line that is perpendicular to 8y+4x=5
Answer:
gradient = 2
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope (gradient) and c the y- intercept )
Given
8y + 4x = 5 ( subtract 4x from both sides )
8y = - 4x + 5 ( divide the terms by 8 )
y = - [tex]\frac{1}{2}[/tex] x + [tex]\frac{5}{8}[/tex] ← in slope- intercept form
with gradient = - [tex]\frac{1}{2}[/tex]
Given a line with gradient m then the gradient of a line perpendicular to it is
[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{-\frac{1}{2} }[/tex] = 2
2 is the gradient of a line that is perpendicular to 8y+4x=5
What is slope of Line?The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane
The slope of line can also be called ad gradient of a line.
The standard form of line or slope intercept form of a line is given by
y=mx+c
where m is the slope of line and c is the y intercept.
The given equation of line is 8y+4x=5
We need to convert the equation of line to Slope intercept form
8y=5-4x
Divide both sides by 8
y=5/8-4/8x
y=-1/2x+5/8
So m is -1/2.
Two lines are said to be perpendicular if m₁m₂ =-1
if m₁=-1/2
then we need to calculate m₂
-1/2m₂=-1
m₂=2
Hence gradient of a line that is perpendicular to 8y+4x=5 is 2.
To learn more on slope of line click:
https://brainly.com/question/14511992
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how do you get 0.1 x 2.4
Answer:
the answer is .24
Step-by-step explanation:
when you multiply 0.1 x 2.4 it equals out to .24
0.1 x 2.4= .24
help also dont mind karl
Answer:
15/8
Step-by-step explanation:
the mixed answer is 1 7/8
but also the answer is 15/8
Suppose you have a bag with 50 letters tiles in it and 9 of the tiles are the letter m. If you pick a letter tule at random from the bag, probability that is the letter m is 9/50
Answer: True- [tex]\dfrac{9}{50}[/tex]
Step-by-step explanation:
Given
There are 50 letter tiles
9 of them is m letter
Favorable outcomes to draw an m letter tile is 9
The total ways to draw a single tile is 50
Probability is the ratio of favorable to the total outcomes
[tex]P=\dfrac{9}{50}[/tex]
So, the given statement is true
During her ride home from school, Dana sees 15 cars driven by men and
34 cars driven by women. What is the experimental probability that the
next car Dana sees will be driven by a man?
Answer: 30%
Step-by-step explanation:
A linear function that represents the number of video games purchased at an electronics store is compared to a different linear function that represents the amount of money the store made that day. Describe the key features of the functions that are needed to determine if these lines intersect
Answer:
The key features needed to determine if these two linear functions intersect would be their y-intercept and their slopes. We need this information because it would allow us to graph these two linear functions, and if we can graph them, we can see if these lines intersect.
Step-by-step explanation:
Took the "quiz"
(Please mark Brainliest)
BER33333 Solving a word problem with two unknowns using a linear...
Devaughn is 8 years older than Sydney. The sum of their ages is 104. What is Sydney's age?
years old
Х
$
?
Answer:
56
Step-by-step explanation:
x+x+8=104
2x=96
x=48
48+8=56
To get the paint color moss green, 2 parts
violet paint is mixed with 3 parts yellow
paint. How many parts yellow paint
should be mixed with 5 parts violet
paint to make moss green paint?
It is the assumption of staff at NSA that 96% of students will graduate on time. Last year 150 out of 154 students graduated on time. What is the p-value and z-score of the graduation rate at NSA?
a. p = .625, z = .73
b. p = .73, z = .625
c. p = .96, z = 1.976
d. p = 1.10, z =0.986
Is the staff at NSA correct in assuming that 96% of NSA students will graduate on time?
Yes
No
Can anyone help me with this math equation?
Answer:
2/9
Step-by-step explanation:
1/3=3/9
5/9-3/9=2/9
Answer:
2/9
Step-by-step explanation:
1/3= 3/9
5/9 - 3/9 = 2/9
hope this helps
what is the answer to this fraction 4/8+2/8+4/8
Answer:
1 2/8 OR 1 1/4
Step-by-step explanation:
4/8 + 2/8 + 4/8 =
6/8 + 4/8 =
10/8 =
1 2/8 OR 1 1/4
Hope that helps!
Can some one plz help i really dont wna failll plzzz
LINKS WILL BE REPORTED
helppppppppppppppppp
Answer:
64 degrees.
Step-by-step explanation:
We are given that angle QRP is 32 degrees.
We are also given that angle PRS is 84 degrees.
Add those two angles to get the measure of angle QRS.
measure of angle QRS= 116 degrees.
Same-side interior angles are supplementary
So,
116+ angle PQR= 180
subtract both sides by 116.
PQR=64
Therefore the measure of angle PQR is 64 degrees.
I hope this helps
If £2000 is placed into a ban account that pays 3% compound interest per year how much will be in the account after 2 years
Answer:£2121.8
Step-by-step explanation:
Given
Principal money [tex]P=[/tex]£2000
rate of interest is [tex]R=3\%[/tex]
time period [tex]T=2\ yr[/tex]
The amount by compound interest is given by
[tex]A=P[1+\frac{R}{100}]^T[/tex]
Putting values
[tex]\Rightarrow A=2000[1+0.03]^2\\\Rightarrow A=2121.8[/tex]
So, after two years it will be £2121.8
what is the slope of a line parallel to the line whose equation is y=2/3x+7 fully simplify your answer
Answer:
2/3
Step-by-step explanation:
When a line is parallel to another, it means that there are never going to be any solutions(they won't ever intersect each other.) To do so, the slope of the lines have to be the same. It doesn't matter what the y-intercept is.
So the slope of the second line is going to be the same as the first line: 2/3
Please help me answer this question
Answer:
254.34 ft^2
Step-by-step explanation:
The equation for area of a circle is π*r^2, where r is the radius of the circle. So we do 3.14*9^2 for the answer
Answer:
254.34 ft
Step-by-step explanation:
radius (9)
multiply it by itself (9x9)
so then you get 81
then the two radius squared (81) is multiplied by pi (3.14)
what is the equation that the line goes through (1,-2) and is parallel to y=3x-3?
A. y-1=3(x+2)
B. y+2= -1/3(x-1)
C. y=3x+2
D. y+2=3(x-1)
Answer:
Step-by-step explanation:
Parallel lines have the same slope.
Point-slope equation for line of slope 3 that passes through (1,-2):
y+2 = 3(x-1)
The diameter of a basketball rim is 18 inches. A standard basketball has a circumference of 30 inches. What is the distance between the ball and the rim in a shot in which the ball goes exactly in the center of the rim? Show your work.
Answer:
4.2 inches
Step-by-step explanation:
Basketball rim:
diameter = 18 inches
r = 18/2 = 9 inches
Ball:
Circumference of ball = 30 inches
2πr = 30 inches
[tex]2*3.14*r = 30\\\\r = \frac{30}{2*3.14}\\\\r = 4.8 inches[/tex]
Distance between the ball and the rim in a shot when the ball goes exactly in the center of the rim = radius of the rim - radius of the ball
= 9 - 4.8
= 4.2 inches
I NEED HELP WITH THIS
ichi ni san ñya arigato
Find the surface area of a pringles can that has a radius of 1.6 inches and a height of 9.8 inches. (Find the WHOLE surface area, including the top cover.
Answer:
10.55
Step-by-step explanation:
I dont Know what to put here
But Anwer Pls
Answer:
QR, QT
Step-by-step explanation:
A radii is a line from the center of the circle to the circumfrence of the circle.
In this case the radii are QR, QT, and QK because they all start from the center of the circle which is point Q and stop at the circumfrence of the circle.
Since QK isn't an answer choice the only answers are ...
QR and QT
help pleaaseee rons of points and brainliest just need help.
Since both equations equal y they need to equal each other.
2x - 5 = -3x + 10
Add 3x to both sides:
5x -5 = 10
Add 5 to both sides
5x = 15
Divide both sides by 5
X = 3
Now solve for y by replacing x with 3:
Y = 2(3)-5 = 6-5 = 1
Y = -3(3)+ 10 = -9+ 10 = 1
Check: replace y with 1 and solve for x:
1 = 2x -5
Add 5 to both sides
6 = 2x
Divide both sides by 2
X = 3 ( True)
|x +2], if x>-1
Plz help
Answer:
Step-by-step explanation:
greater than 1 , is your teacher just giving you brain teaser questions? these seem like they are .. "out in the weeds" type of questions, not really useful math :/
given 4p = 18-5q. Calculate
i) value when q is 2
ii) value when p is 2
Answer:
i). 2 ii). 2
Step-by-step explanation:
i). 4p = 18 - 5(2)
4p = 18 - 10
4p = 8
p = 2
ii). 4(2) = 18 - 5q
8 = 18 - 5q
-10 = - 5q
q = 2
Write an equation for esch line in Slope Intercept Form
Answer:
Step-by-step explanation:
Y intercept is at (0,1) so b=1
slope is go 4 down 1 right so slope is -4
Equation is
-4x+1=y