Applying the required rule or theorem, it can be concluded that the second biker is farther from the parking lot. The distance of the bikers to the parking lot are:
i. First biker = 17.0 km
ii. Second biker = 20.22 km
The path of travel of both bikers would form a triangle. Applying the Pythagoras theorem to the path of the first biker would give his distance from the starting point. While applying the cosine rule to the path of second rider would gives his distance to the starting point.
Thus,
a. To determine the distance of the first biker from the parking lot.
Let the required distance be represented by x. Applying the Pythagoras theorem, we have:
[tex]hyp^{2}[/tex] = [tex]adj 1^{2}[/tex] + [tex]adj 2^{2}[/tex]
[tex]x^{2}[/tex] = [tex]8^{2}[/tex] + [tex]15^{2}[/tex]
= 64 + 225
= 289
x = [tex]\sqrt{289}[/tex]
= 17
x = 17 km
Thus, the first biker is 17.0 km from the starting point.
b. To determine the distance of the second biker from the parking lot.
Let the required distance be represented by x. So that applying the cosine rule, we have:
[tex]c^{2}[/tex] = [tex]a^{2}[/tex] + [tex]b^{2}[/tex] - 2ab Cos θ
[tex]x^{2}[/tex] = [tex]8^{2}[/tex] + [tex]15^{2}[/tex] - 2(15*8) Cos (180 - 20)
= 64 + 225 - 240 Cos 160
= 289 - 240 * -0.5
[tex]x^{2}[/tex] = 289 + 120
= 409
x = [tex]\sqrt{409}[/tex]
= 20.2237
x = 20.22 km
Thus, the second biker is 20.22 km from the starting point.
Therefore, the second biker is farther from the parking lot.
A sketch of the path of travel for the two bikers is attached for more clarifications.
Visit: https://brainly.com/question/22699651
P = 6 ft. Find the length of side H.
3.5 ft
3 ft
2 ft
2.5 ft
Answer:
The answer is 2.5 ft.Step-by-step explanation:
Using Pythagoras theorem, let's find 'H'.=> H² = 2² + 1.5²=> H² = 4 + 2.25=> H² = 6.25=> √H² = √6.25=> H = 2.5Conclusion:
Therefore, the answer is 2.5 ft.
Hoped this helped.
[tex]BrainiacUser1357[/tex]
A student wants to check six websites. Four of the websites are social and two are school-related. After checking just two sites, she has to leave for school. What is the approximate probability that she checked a social website first, then a school-related website? 0. 042 0. 267 0. 533 0. 667.
The approximate probability that she checked a social website first, then a school-related website is 0.267.
First step is to calculate the Total number of websites
Total number of websites=Number of school websites+Number of social websites
Total number of websites=2+4
Total number of websites=6
Second step
Probability of checking the social website first
Probability of checking social website=Number of social websites/Total number of websites
Probability of checking social website= 4/6
Third step
Since one social website is checked which means that she is left with 3 social website and 2 school websites
Total number websites=2+3
Total number websites=5
Forth step
Probability of checking social website=Number of school websites/Total number websites
Probability of checking social website=2/5
Fifth step
Probability= 4/6 x 2/5 = 0.2666
Probability=0.267(Approximately)
Inconclusion the approximate probability that she checked a social website first, then a school-related website is 0.267.
Learn more about probability here:https://brainly.com/question/25688842
Answer:
0.267
Step-by-step explanation:
Total websites = school websites (2) + social websites (4) = 6
Checking social website = social websites (4) /Total websites (6) = 2/3
Total websites is 5
Checking social website = school websites (2) /Total websites (5)
4/6 x 2/5 = 0.2666
Answer: 0.267
Hope this helps :)
Steven has $150. John has J dollars. Steven has 30 less than 2 times the amount John has. How much does John have?
Answer:
J = 90
John has 90 dollars.
Step-by-step explanation:
We need to find how much money John has. To find how much J equals we need to break it down.
We already know that Steven has 150 dollars. We also know that he has 30 less than two times the amount John has.
Steven has 30 less than two times the amount John has.
So 150 + 30 = 180
180 is two times the amount John has.
Because 180 is two times the amount John has we need to divide by two.
180 ÷ 2 = 90.
J = 90. Therefore John has 90 dollars.
This question was tricky! I hope I helped a little! Have a great day!!
PLEASE HELP ME RNNNNN!!!!!! I NEED THE ANSWERS
I really need help don’t answer if your not giving the correct answer and it’s explanation!!!!
Answer:
(a) 0.4307
(b) 1.3906
Step-by-step explanation:
(a)[tex]\log_5{2}=\log_5{8^{\frac{1}{3}}}=\dfrac{1}{3}\log_5{8}=\dfrac{1.2920}{3}\approx0.4307[/tex]
__
(b)[tex]\log_5{\dfrac{75}{8}}=\log_5{3\cdot5^2\cdot8^{-1}}=\log_5{3}+2\log_5{5}-\log_5{8}\\\\=0.6826 +2-1.2920=1.3906[/tex]
-5⎜x - 3⎟ - 5 < 15
Pls
−5(|x−3|)−5<15
Step 1: Add 5 to both sides.
−5(|x−3|)−5+5<15+5
−5(|x−3|)<20
Step 2: Divide both sides by -5.
−5(|x−3|)
−5
<
20
−5
|x−3|>−4
Step 3: Solve Absolute Value.
|x−3|>−4
We know eitherx−3>−4orx−3<−(−4)
x−3>−4(Possibility 1)
x−3+3>−4+3(Add 3 to both sides)
x>−1
x−3<−(−4)(Possibility 2)
x−3<4(Simplify both sides of the inequality)
x−3+3<4+3(Add 3 to both sides)
x<7
Answer:
x>−1 or x<7
[tex](\sqrt[3]{5})^{2}[/tex]
Answer:
[tex](\sqrt[3]{5})^2=5^\frac{2}{3}[/tex]
Step-by-step explanation:
[tex](\sqrt[3]{5})^2[/tex]
[tex](5^{\frac{1}{3}})^2[/tex]
[tex]5^{\frac{1}{3}*2}[/tex]
[tex]5^\frac{2}{3}[/tex]
Remember that [tex](\sqrt[a]{x})^b=x^\frac{b}{a}[/tex]
What is equivalent to
4(b+5)
A line passes through the points (9,6) and (6,5). What is its equation in slope-intercept form?
Answer:
Y=X/3+3
Step-by-step explanation:
M= Y2-Y1/X2-X1
= 5-6/6-9
= -1/-3
= 1/3
sub x=6, y=5, M=1/3 into Y=MX+C
5=6/3+C
5=2+C
5-2= 2+C-2
3=C
pls help me with this:((
Answer:
9. A. One - to - One Correspondence
10. D. None of the above
9.) one to one correspondence
10.)one to many correspondence
Step-by-step explanation:
in 9 it shows that 1-4 are connected to different number
in 10 it shows that a is connected to 2 different numbers
Best answer gets brainiest! (plz help me!)
what is the circumference and the mass of Jupiter and Saturn combined? (both the circumference and mass)
Answer:
Total Circumference = 514, 170 miles
Total Mass = 2, 467, 000, 000, 000 metric tons
Step-by-step explanation:
hope this helps
Answer:
378,675 km (Saturn) + 449,197 km (Jupiter) = 827, 872 km (514,416 mi)
5.683 × 10^26 kg (Saturn) + 1.898 × 10^ kg (Jupiter) =568300000000000000000000018.98 kg (5.683 × 10^26)
Annette measured pepper plant sprouts and recorded the following lengths in
inches:
1/3 .0.75, 1/4 .0.5
If Annette ordered the lengths from least to greatest, which one would come
second?
Answer pls❤️❤️❤️
Answer:
Ask with your teacher.not to me
Answer:
1/4 , 1/3 , 0.5 , 0.75
Step-by-step explanation:
1 - Convert all numbers into fractions.
1/3 , 3/4 , 1/4 , 1/2
2 - Find the greatest common factor and apply it to all.
4/12, 9/12, 3/12, 6/12
3 - Order all into least to greatest.
3/12 , 4/12 , 6/12 , 9/12
4 - Convert back to normal forms.
1/4 , 1/3 , 0.5 , 0.75
Brainliest would be appreaciated! :-)
If i watch a movie at 7:00 pm and the movie lasts 1h 49m what time will it be when it finishes?
Answer:
it would finish at 8:49
Step-by-step explanation:
Have a nice day :)
Answer:
it's really simple seriously, but it will end at 8:49m
Step-by-step explanation:
how do you solve this do i need to plpug in the formula
Answer:
B. -2, 2
Step-by-step explanation:
Apparently, we're to presume that f(x) is the line that is graphed. It has a y-intercept of +1 and a slope (rise/run) of 1/2. Its equation is ...
f(x) = 1/2x +1
If we want points of intersection, we want to solve the equation f(x) = g(x) for the values of x that make it so.
1/2x +1 = √(x +2)
Squaring both sides, we get ...
1/4x² +x + 1 = x +2
1/4x² = 1 . . . . . . . . . . . . subtract x+1 from both sides
x² -4 = 0 . . . . . . . . . . multiply by 4, subtract 4
(x -2)(x +2) = 0 . . . . factor the difference of squares
x = -2, 2 . . . . . . . . . values of x that make the factors zero
The solutions to f(x) = g(x) are x = -2 and x = 2.
_____
Additional comment
The attached graph shows the x- and y-values at the points of intersection. The solutions to f(x) = g(x) are only the x-values, -2 and 2.
The square of (ax +b) is ...
(ax +b)² = a²x² +2abx +b²
The point-slope equation of a line is ...
y = mx + b . . . . . line with slope m and y-intercept b
What is the value of x?
74
138
69
148
Answer:
69
Step-by-step explanation:
All angles add up to 180 in a triangle.
Hope that helps
Find the values of x and y.
Answer:
x=68/9; y=38/3.
Step-by-step explanation:
1) according to the condition m(ABC)=m(DEF), then 6y-4=80, ⇒ y=38/3;
2) according to the condition AB=DE, then 10=3x-y. If y=38/3, then 10=3x-38/3; ⇒ x=68/9.
How many solutions does this equation have?
-2(t- 4) = 10 - 27
no solution
one solution
infinite solutions
two solutions
Answer:
t = 12.5
Step-by-step explanation:
Assuming you typed the equation correctly:
-2(t-4) = 10 - 27
-2(t-4) = -17
t-4 = 8.5
t = 12.5
So, there's only one solution
Barbara has some dimes and quarters. If she has 16 coins worth a total of $2.50, how many of each type of coin does she have?
Answer:
10 dimes and 6 quarters.
Step-by-step explanation:
2.50-25-25=2.00-10 dimes = 1.00-4 0.25=0
so
10 dimes and 6 quarters.
Answer:
10 Dimes and 6 Quarters.
Step-by-step explanation:
Important info:
16 Coins
Total = $2.50
Note:
Dimes = 0.10 Cents
Quarters = 0.25 Cents
Question to answer:
How many of each type of coin does she have?
Solution:
10 Dimes = $1.00
6 Quarters = $1.50
$1.00+$1.50 = $2.50
Therefore 10 Dimes and 6 Quarters = $2.50 and = 16 Coin.
HELP PLEASE FOR BRAINLIST!!!!!!!!!!!!
Answer:
a(x) and d(x)
hope that helps, have a good day!
dont forget my brainliest.
Step-by-step explanation:
The radius of a circle is 11 ft. Find its area in terms of π π.
Answer:
Area: 121π ft^2
(or just 380 ft^2)
What is the value of the expression
3-4 ?
Answer:
[tex]3 - 4 = 1[/tex]
✨✨
3-4
you just need to subtract 3 from -4
so , your answer is -1
can someone help me with this
[tex]R.H.S\\\\= (a+b)(a^2-ab +b^2)\\\\=a^3-a^2b +ab^2+ba^2-ab^2+b^3\\\\=a^3+b^3\\\\=L.H.S\\\\\text{Hence, proved.}[/tex]
The general equation for the geometric sequence -1, -2, -4, ... is a n = -1 · 2 n - 1 .
TrueFalse
[tex]\text{First term,}~ a = -1\\\\\text{Common ratio,}~ r = 2\\\\\text{Nth term} = ar^{n-1}=-1\cdot 2^{n-1}\\[/tex]
Answer:
true
Step-by-step explanation:
I had same question and said true so then it marked my as correct but then my computer screen turned black because its gay
don't know the answer pls help :p
Answer:
(b) increase the height so the slant height triples
Step-by-step explanation:
The lateral area is jointly proportional to the radius and the slant height of the cone. Increasing either one individually by a factor of 3 will triple the lateral area.
To triple the lateral area, you can ...
increase the height so the slant height triples
In the first week of July, a record people went to the local swimming pool. In the second week, fewer people went to the pool than in the first week. In the third week, more people went to the pool than in the second week. In the fourth week, fewer people went to the pool than in the third week. What is the percent decrease in the number of people who went to the pool over these four weeks?
Answer:
10%
Step-by-step explanation:
75 basketballs cost $1,143.75. Find the cost of 26 basketballs.
given the line y=-2x - 1 and the point (4,4) find the equation of the line perpendicular to the given line. PLEASE! Helppp
Answer:
(-6,-5)
Step-by-step explanation:
y2-y1
x2-x1
subtract then you get the answer
please help me to get the answers please read my questions
Answer: Where is the question.
Step-by-step explanation: Where is the question.
3. What is the slope of the line that passes through the points E(-1,4)
and F(2, 6)?
A.
3
2
C.
2
D.
NICO
B. -
al
NICO
3.
Find the Area and
Circumference of the
circle below.
מוח של
Use 3.24 for .
A=
C=
Answer:
you need to show the circumference, instead I cant help
The tallest man living is 251cm. How many meters tall is he?
In meters he would 2.51 meters.