a) the distance of the man from is friend is 140.59 ft
b) the distance between his friend and the base of the cliff is 39.26 ft
How to calculate the distance of the man from is friend?It is given that a man on a 135-ft vertical cliff looks down at an angle of 16°13' and sees his friend.
So, the vertical cliff, the line of sight of the man and the line joining his friend and the base of the cliff, forms a right angled triangle.
The angle 16°13' is the angle between the the vertical cliff and the line of sight of the man.Here the distance of the man from is friend is actually the hypotenuse of the right angled triangle.We know that, in a right angled triangle,
cosФ= [tex]\frac{base}{hypotenuse}[/tex], where Ф is the angle between the base and hypotenuse
In the right angle triangle we can write,
cos(16°13')= [tex]\frac{135}{hypotenuse}[/tex]
⇒ hypotenuse = 140.59 ft
∴ the distance of the man from is friend is 140.59 ft
How to find the distance from his friend and the base of the cliff?Here, the distance between his friend and the base of the cliff is actually the perpendicular of the right angled triangle.We know that, in a right angled triangle,
sinФ= [tex]\frac{perpendicular}{hypotenuse}[/tex], where where Ф is the angle between the base and hypotenuse
sin(16°13')= [tex]\frac{perpendicular}{140.59}[/tex]
⇒ perpendicular = 39.26 ft
∴ the distance between his friend and the base of the cliff is 39.26 ft
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Answer:
Step-by-step explanation:
Given that (-1,-1) is on the graph of f(x), find
the corresponding point for the function
f(x - 5).
Answer:
(-1, -6)
Step-by-step explanation:
f(x -5) is another way to say f(x) - 5
And f(x) - 5 is going down the y axis 5 points, so you end at (-1, -6)
2. Write two numbers that are opposites and each more than 6 units away from 0.
Answer:
-7, 7
Step-by-step explanation:
Opposites are basically two numbers that are at different sides of the number line. For example, -2 and 2 are opposites because they are the same distance away from 0 on a number line making them opposites. To make an opposite just take a positive number, and then add a negative to it. (8, -8)
PLEASE ANSWER
What
is the value of x?
Enter
your answer in the box.
X=
Answer: 20°
Step-by-step explanation:
Set up your work like this and solve.
3x+50=6x-10
60=3x
20°=x
use the Pythagorean theorem to find L
Answer:
l = Square root of 10
Use the equation, y = 5.4x + 36, to find the value of y when x = 10.
Answer: y= 90
Step-by-step explanation: 5.4(10)+36 = y
54+36= 90
Answer:
y = 90
Step-by-step explanation:
Use substiution.
Y= 5.4(10) + 36
y=54+36
y=90
number of solutions to y = 3x - 2 and y = x - 1
Answer:
(z+3)^3=2i
x^3−8=0
(z+6)^2=2i+4
Step-by-step explanation:
hope this is what u are looking for
If the radius of a circle is 3.21 mm, what is the area of the circle? 32.35 mm2 10.08 mm2 20.162 129.42 mm2
Answer:
32.35mm2
Step-by-step explanation:
3.21 squared is 10.3041
and Multiply 10.3041 by pi(3.14) to get 32.354
A spinner with 4 equal sections (red, blue, green, yellow) is spun 43 times. About how many times would you predict it lands on blue? Explain.
Answer:
11 times
Step-by-step explanation:
Sample space = {red, green, blue, yellow)
Probability of landing blue in a single spin ;
P(blue) = required outcome / Total possible outcomes
P(blue) = number of blue / sample space
P(blue) = 1/4
Number of spins = 43
Expected number of times it'll land on blue :
P(blue) * number of spins
1/4 * 43 = 10.75
About 11 times
Answer:
Step-by-step explanation:
The answer is
An amusement park sold 276 discount tickets and 299 full-price tickets. What percentage of the tickets sold were discount tickets?
Answer:Percentage of discount tickets =48%
Step-by-step explanation:
Percentage of discount tickets = Number of discount tickets / total num ber of tickets x 100
But Total number of tickets = Discount tickets + full-price tickets
= 276 +299
= 575 tickets
Percentage of discount tickets = 276/575 x 100/1
0.48 x 100= 48 %
What point(s) are 100units away from point -1? Can you pls respond quickly!
Answer:
Look below.
Step-by-step explanation:
FYI: Im a bit confused on what this question is asking but I am responding based on what I believe the question is asking.
The point 100 spaces to the left of -1 would be (-101,0) and the point 100 spaces to the left of -1 would be (100,0).
The point(s) 100 spaces to the left of -1 would be (- infinity, -1) and the point(s) 100 spaces to the right would be (-1, infinity).
Benjamin spent $31.20 on ten gel pens. How much did each pen cost?
Answer:
$3.12
Step-by-step explanation:
31.20 divided by 10 = 3.12
A can lid has a radius of 3 in. What is the area of the can lid?
Answer:
28.27
Step-by-step explanation:
A=(pi)(3^2) = 28.27
Answer:
28.27 in²
Step-by-step explanation:
Area of a circle = πr²
π3^2 = 9π ≈ 28.27
12, 17, 22... find the 35th term
Answer:
a₃₅ = 182
Step-by-step explanation:
There is a common difference d between consecutive terms, that is
d = 17 - 12 = 22 - 17 = 5
This indicates the sequence is arithmetic with n th term
[tex]a_{n}[/tex] = a₁ + (n - 1)d
where a₁ is the first term and d the common difference
Here a₁ = 12 and d = 5 , then
a₃₅ = 12 + (34 × 5) = 12 + 170 = 182
bestie help
Ok bestie thank you;)
Answer:
Chloe swam further. 16/40 to 25/40
Step-by-step explanation:
2/5 5/8
Find greatest common factor of 5 and 8 which is 40.
5x8=40 so multiply the same at the top.
2/5=16/40
5/8=25/40
16/40<25/40.
Chloe swam further
b) Write down an expression for the nth term of the following sequence.
9,
14,
19,
24,
Answer:
32,41,51,62,74,87,101
Great Valley State Park charges $10 per car for admission to its camping grounds and $17.50 per night for a campsite.
Write a function rule to represent the total cost of camping at Great Valley as a function of the number of nights camped.
C = Total Cost
n = Number of nights camped
Answer:
C = 17.50n + 10
Step-by-step explanation:
You can plug the numbers into the equation 'y = mx + b' to get your answer.
What single percentage change is equivalent to a 12% decrease followed by a 18% increase?
Given:
12% decrease followed by a 18% increase.
To find:
The single percentage change is equivalent to the given set of percentages.
Solution:
Let the initial value be 100.
After 12% decrease, the value is:
[tex]v_1=100-\dfrac{12}{100}\times 100[/tex]
[tex]v_1=100-12[/tex]
[tex]v_1=88[/tex]
After 18% increase, the value is:
[tex]v_2=88+\dfrac{18}{100}\times 88[/tex]
[tex]v_2=88+15.84[/tex]
[tex]v_2=103.84[/tex]
The initial value is 100 and the new value in 103.84. So, it represents increase in the value. So, increase percentage is
[tex]Increase\%=\dfrac{\text{New -Initial}}{\text{Initial}}\times 100[/tex]
[tex]Increase\%=\dfrac{103.84-100}{100}\times 100[/tex]
[tex]Increase\%=3.84[/tex]
Therefore, the value increased by 3.84%.
Dennis got 85 percent of the questions on the math test correct, which was out of 40. what was his actual mark?
Answer:
34/40
Step-by-step explanation:
85/100 cross multiply x/40
100x/100=3400/100
x=3400/100
3400/100=34
x=34
Picture included
(Sorry about my handwriting)
Hope this helps!! :)
Stay safe and have a wonderful day/night!!!!!
Brainliest?!?!
Lucia has 18 pieces of ribbon that she uses to decorate presents. One ribbon's length is 5/6 of a yard. How many yards of ribbon does Lucia have?
Answer: 15 yards
Step-by-step explanation:
From the question, we are given the information that Lucia has 18 pieces of ribbon that she uses to decorate presents and that the length of one ribbon is 5/6 of a yard.
Therefore, the number of yards of ribbon that Lucia has will be gotten by multiplying 5/6 by the total pieces of ribbon. This will be:
= 5/6 × 18
= 15 yards
There are 30 students in Mrs. Krzyzewski's class. None of them has a first name that begins with the letter "U" or the letter "Y." Eight of her students have first names that begin with "A," five have first names that begin with "E," two have first names that begin with "I", and three have first names that begin with "O."
Based on this data, what is the probability that a randomly-selected student from Mrs. Krzyzewski's class has a first name that begins with a consonant?
Answer:
i need help with this question too so can any one help us
Step-by-step explanation:
i need help as well cuhhhhh
¿Cuál es la ecuación de la recta que pasa por el punto? (-1,-5) y tiene una
pendiente de - 1?
Answer:
y=-1x-6
Step-by-step explanation:
y-y1=m(x-x1)
y-(-5)=-1(x-(-1)
y+5=-1(x+1)
y+5=-1x-1
y=-1x-5-1
y=-1x-6
Find the length of the third side. If necessary, round to the nearest tenth.
Answer:
12
Step-by-step explanation:
Use the pythagorean theorem.
THIS HAS TO BE TURNED IN AT 3:15! HEWP!
Help with #2!
Answer:
A, and C
Step-by-step explanation:
Can someone pls help me with this?
Answer:
5 is d
6 is a
Step-by-step explanation:
HELP PLEASE! I NEED SO MUCH HELP. IM SO LOST!!
I don’t how to do these does anybody know how?
Hello what grade is this for?
Eight $300 is marked down by 20% find the sale price rounded to the nearest dollar (show work) 
Answer:
300 - (20/100)=$240 sale price of the suit after 20% discount.
Step-by-step explanation:
300 - (20/100)* 300 =
300 - (1/5) * 300 =
300 - 60 =
$240
Not sure how to do this problem.
The graph below shows the solution set of which inequality?
Answer:
D x^2 smaller than or equal 4
Step-by-step explanation:
if you tried to get a number on the number line and put it to fit in the equation it will just end to equal or smaller than 4