Andrew is hiking in a mountainous area of a state park. Use the given key features to sketch a graph.
y-intercept: Andrew starts at an elevation of 0 feet.
Extrema: Andrew's maximum elevation is 800 feet.
Increasing: At the start of the hike, Andrew's elevation increases steadily for 30 minutes. Then he stops to rest for 5 minutes.
Decreasing: Andrew hikes back to his starting point for the final 20 minutes.
Answers
Using the features, a piece-wise function is defined, and the graph is sketched at the end of this answer.
A piece-wise function is a function that has multiple definitions, depending on the value of the input.
He starts at 0 feet, and reaches a maximum elevation of 800 feet in 30 minutes, with a steady(linear) increase thus, for the first 30 minutes, the definition is:
[tex]h(t) = \frac{800}{30}t, 0 \leq t < 30[/tex]
For the next 5 minutes, he stops to rest, at the maximum elevation of 800 feet, thus, the definition is:
[tex]h(t) = 800, 30 \leq t < 35[/tex]
For the final 20 minutes, he descends 800 meters, at a linear rate, thus:
[tex]h(t) = 800 -\frac{800(t-35)}{20} = 800 - 40(t - 35), 35 \leq t \leq 55[/tex]
Using these definitions, the graph is sketched at the end of this answer.
A similar problem is given at https://brainly.com/question/13205719
Related Questions
A clothing business finds there is a linear relationship between the number of shirts, n ,it can sell and the price, p , it can charge per shirt. In particular, historical data shows that 1000 shirts can be sold at a price of $66, while 10000 shirts can be sold at a price of $48. Give a linear equation in the form p
Answers
Answer: p = [tex]\frac{-n}{500} +68[/tex]
Step-by-step explanation:
Let n represent the number of shirts and p represent the price, the there is a linear relationship between n and p, then the model equation is given as:
p = mn + b, where
m = slope and b is the intercept
From the question, when n = 1000, p = $66
And, when n = 10,000 , p = $48
The formula for finding slope is given as:
m = [tex]\frac{y_{2}-y_{1} }{x_{2} -x_{1} }[/tex]
[tex]y_{1} = 66[/tex]
[tex]y_{2} = 48[/tex]
[tex]x_{1} = 1000[/tex]
[tex]x_{2} = 10000[/tex]
substituting the values,
m = [tex]\frac{48-66}{10000-1000}[/tex]
m = [tex]\frac{-18}{9000}[/tex]
m = [tex]\frac{-2}{1000}[/tex]
m = [tex]\frac{-1}{500}[/tex]
The linear equation thus becomes
p = [tex]\frac{-n}{500}+b[/tex]
To find the value of b, substitute p = 66 and n =1000 into the equation
That is,
66 = [tex]\frac{-1000}{500}+b[/tex]
66 = -2 + b
68 = b
Therefore b = 68
The linear equation is therefore
p = [tex]\frac{-n}{500} +68[/tex]
pls help ASAPPPP11!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answers
Answer:
It's between 0 and 1
Step-by-step explanation:
1/64 = 0.015625
The perimeter of a triangle is 65 cm. The
lengths of the sides are x cm, x+8 cm, and
X+ 12 cm.
What is the length, in cm, of the longest side of
the triangle?
Answers
[tex]▪▪▪▪▪▪▪▪▪▪▪▪▪ {\huge\mathfrak{Answer}}▪▪▪▪▪▪▪▪▪▪▪▪▪▪[/tex]
The longest side measures :
[tex]27\: \: cm[/tex][tex] \large \boxed{ \mathfrak{Explanation}}[/tex]
Perimeter of a triangle is equal to sum of measures of its all three sides, that is :
[tex]x + x + 8 + x + 12[/tex]and according to the question, the perimeter of the triangle is = 65 cm
so, let's equate both the expressions to find value of x :
[tex]x + x + 8 + x + 12 = 65[/tex][tex]3x + 20 = 65[/tex][tex]3x = 65 - 20[/tex][tex]3x = 45[/tex][tex]x = 45 \div 3[/tex][tex]x = 15[/tex]The longest side of the Triangle is :
[tex]x + 12[/tex][tex]15 + 12[/tex][tex]27 \: \: cm[/tex]27cm
Step-by-step explanation:
(xcm) + (x+8cm) + ( x+ 12cm) = 65cm
Open Bracket
xcm + x+8cm + x+12cm = 65cm
3x+ 20cm = 65cm
Collect like terms
3x = 65cm - 20cm
3x = 45cm
Divide both sides by 3
3x/3 = 45cm/3
x = 15cm
The longest side of the triangle =( x+12cm)
= (15+12)cm= 27cm
1/5 divided by 2/3 help meee loll
Answers
Answer:
3/10 or 0.3
Hope this helps
the awnser is 0.3 .......................
An investor invests $525 in stock. For each month following, the stock increased at a rate of $25 per
month
Identify the slope of the linear relationship. Explain what the slope represents in the context of the
problem
• identify the y-intercept of the linear relationship. Explain what the y-intercept represents in the
context of the problem.
Create a model/build the function/write the equation in slope-intercept form to represent the total
value of the stock, f (2), based on the number of months, I.
Answers
Answer: f(x) = mx+ b
slope = m = $25 / month
This means that for every month (x) that goes by, the total value of the stock (f(x)) will increase by $25.
y-intercept = b = $525
This is the amount of money in the account at time = 0. This will be equal to the original investment of $525.
f(x) = mx+ b = 25x + 525
Step-by-step explanation:
help me with this please
Answers
Answer: 65
Step-by-step explanation:
Can someone plsss help me with the 2 one
Answers
Answer: [tex]\sqrt{73}[/tex] for number 7
Step-by-step explanation:
a²+b²=c²
3²+8²=c²
9+64=c²
[tex]\sqrt{73}=\sqrt{c^2}\\\sqrt{73}=c[/tex]
george is building a fence at a consent rate of 1/3 section of fence every 1/2 hour at the rate. what fraction represents the section iof fence george can build per hour
Answers
Is 12 × –1 positive or negative? positive negative Submit
Answers
Answer:
it's a negative number. the answer would be
Step-by-step explanation:
-12
I WILL GIVE YOU BRAINYIST IF YOU ANSWER THIS FOR ME
Answers
Answer:
A
Step-by-step explanation:
Answer:
a
Step-by-step explanation:
Write a unit rate for each situation . 20$ saved in 4 weeks
Answers
Answer:
so the answer is 5
Step-by-step explanation:
20/4=5
May I please receive help?
Please???
Answers
Answer:
m1 is 25 and m2 is 50
Step-by-step explanation:
Answer:
25
Step-by-step explanation:
x+2x=75
Find the EQUATION of the line through (-10,-12) and (-15,3). Use the form y=mx+b.
Answers
Y=-3x-42
Please mark brainliest. Thank you
3over 7 = blank over 35
Answers
Let blank be x
[tex]\\ \sf\longmapsto \dfrac{3}{7}=\dfrac{x}{35}[/tex]
[tex]\\ \sf\longmapsto 7x=35(3)=105[/tex]
[tex]\\ \sf\longmapsto x=\dfrac{105}{7}[/tex]
[tex]\\ \sf\longmapsto x=15[/tex]
Classify the quotient as positive, negative, or zero - 25 ÷ - 5
Answers
Answer:
-25÷-5= 5 The quotent is positive.
Step-by-step explanation:
positive+positive=positive
negative+negative= positive
positive+negative=negative
negative+positive=negative
triangular field having the length of sides are 42m, 34m and 20m respectively. find the area of the field (need this answ with full explanation)
Answers
Answer:
[tex]A = 336[/tex] [tex]m^{2}[/tex]
Step-by-step explanation:
Using the formulas
[tex]A=\sqrt{s(s-a)(s-b)(s-c)}[/tex]
[tex]s=\frac{a+b+c}{2}[/tex]
Solving for [tex]A[/tex]
[tex]A=\frac{1}{4} \sqrt{-a^{4}+2(ab)^{2} +2(ac)^{2} -b^{4} +2(bc)^{2}-c^{4} }[/tex]
[tex]=\frac{1}{4} *\sqrt{-42^{4} +2*(42*34)^{2}+2*(42*20)^{2} -34^{4} +2*(34*20)^{2} -20^{4} }[/tex]
[tex]=336m^{2}[/tex]
Answer:
✌ just because that what the answer is I just know it cuz im right
8z + 6 = 7z + 4
I need help with it please show the steps
Answers
The ratio of men to women working for a company is 4 to 5. If there are 110 women working for the company, what is the total number of employees?
Answers
Answer:
198
Step-by-step explanation:
?/4 110/5
cross-multiply 4*110
440
divide 440/5
88 men
add total employees
110 women + 88 men = 198
Someone help me I will mark you as brain
Answers
Answer:
- 1
Step-by-step explanation:
-3 (-3) -10
9 - 10 = -1
PLEASE HELP!!
(04.03)
Given the function g(x) = 5(2)^x, compare the average rate of change from x = 1 to x = 2 and from x = 3 to x = 4.
How many times greater is the average rate of change from x=3 to x=4 than from x=1 to x=2?
О 4 times
O 5 times
O 2 times
O The average rate of change of Section B is not greater than the average rate of change of Section A.
Answers
Answer: Choice A. 4 times
========================================================
Explanation:
We'll be using this formula
[tex]m = \frac{f(b)-f(a)}{b-a}[/tex]
to compute the average rate of change (AROC) from x = a to x = b. Note how this is effectively the slope formula because y = f(x).
To start things off, we'll compute the AROC from x = 1 to x = 2.
[tex]m = \frac{g(b)-g(a)}{b-a}\\\\m = \frac{g(2)-g(1)}{2-1}\\\\m = \frac{5(2)^2-5(2)^1}{2-1}\\\\m = \frac{10}{1}\\\\m = 10\\\\[/tex]
Do the same for the AROC from x = 3 to x = 4.
[tex]m = \frac{g(b)-g(a)}{b-a}\\\\m = \frac{g(4)-g(3)}{4-3}\\\\m = \frac{5(2)^4-5(2)^3}{4-3}\\\\m = \frac{40}{1}\\\\m = 40\\\\[/tex]
The jump from m = 10 to m = 40 is "times 4", which is why choice A is the final answer.
In a student president race student A received 9 votes received by student B if student A received 540 votes, how many votes did student B receive?
Answers
Answer: 60 Votes
Step-by-step explanation:
540 divded by 9 which equals 60 votes.
So Student B received 60 votes.
60 votes was received by student B.
540/9=60
hi pls help me thanksss
pls provide me with workings thankss :)
Answers
Step-by-step explanation:
(i)
Using cos(a - b) = cos a cos b + sin a sin b
[tex]\frac{4}{5}[/tex] = cos a cos b + [tex]\frac{1}{5}[/tex]
cos a cos b = [tex]\frac{4}{5} -\frac{1}{5} = \frac{3}{5}[/tex]
(ii)
Using cos(a + b) = cos a cos b - sin a sin b
cos(a + b) = [tex]\frac{3}{5}-\frac{1}{5}=\frac{2}{5}[/tex]
(iii)
Using cot a = [tex]\frac{cos a}{sin a}[/tex]
[tex]=(\frac{cos A}{sin A} )(\frac{cos B}{sin B} )[/tex]
[tex]=\frac{cos A cos B}{sin A sin B}[/tex]
[tex]=\frac{\frac{3}{5} }{\frac{1}{5} }[/tex] [tex]=\frac{3}{5}[/tex] × [tex]5[/tex]
= 3
please give me a brainliest answer
Can someone help me with number 8 :(
Answers
Answer:
a1=5
d=9-5=4
a20=5+19×4=81
A 144-inch board is cut into two pieces. One piece is five times the length of the other. Find the length of the shorter piece.
The shorter piece is inches long.
Answers
Answer:
shorter piece is 28.8 inches
Step-by-step explanation:
Answer28.8
Step-by-step explanation:
28.8 x 5 = 144
Find the upper quartile for the data. {9, 6, 13, 8, 8, 10, 9.5, 8, 7.5, 8.5}
A. 9
B. 9.5
C. 10
D. 8.5
Answers
Answer:
the answer is 9.5 (B)
Step-by-step explanation:
Hi I really need help with this question, ANSWERS ONLY, I'll give 35 POINTS, PLEASE
What is the positive conterminal angle to -32° that is between 500° and 1000° and a negative conterminal angle to -32° that is between -500° and -50°?
positive coterminal angle:
negative coterminal angle:
Answers
Answer:
0° and 90°, it's Ql. If between 90° and 1800 QQ. ... Find a positive and a negative conterminal angle for the given angle.
Step-by-step explanation:
The positive and negative coterminal angles to -32° are:
Positive coterminal angle = 688°
Negative coterminal angle = -392°
What is a coterminal angle?Coterminal angles are those whose terminal sides and beginning sides coincide.
The given angle measure is -32°.
The positive coterminal angle is:
-32° + 360°
= 328°
Since the angle is not between 500° and 1000°, add 360° one more times:
328° + 360°
= 688°
The negative co-terminal angle is:
-32° - 360°
= -392°
Hence, the positive and negative coterminal angles to -32° are:
Positive coterminal angle = 688°
Negative coterminal angle = -392°
Learn more about coterminal angles:
https://brainly.com/question/23093580
#SPJ6
plz help answer the following questions
Answers
a³-a²b-ab²+b³hihihihihihihi
Answers
Which statement correctly compares the shapes of the distributions?
Team A's scores
58 60 62 64 66 68 70 72 74 76 78 80 82 84 86 88 90 92 94 96 98 100
Team B's scores
58 60 62 64 66 68 70 72 74 76 78 80 82 84 86 88 90 92 94 998 100
O A. Team A's scores are symmetric, and team B's are negativ
skewed.
O B. Team A's scores are symmetric, and team B's are positively
skewed.
O C. Team A's scores are negatively skewed, and team B's are
symmetric.
D. Team A's scores are positively skewed, and team B's are
Answers
The statement that compares the distribution shapes is (C) Team A's scores are negatively skewed, and team B's are symmetric.
How to interpret the distribution shapes?From the complete question (see attachment for box plots), we have the following highlights:
Team A scores has more points at the left. This represents a negative skewTeam B scores has more points at the center. This represents a symmetric skewnessHence, the statement that compares the distribution shapes is (C) Team A's scores are negatively skewed, and team B's are symmetric.
Read more about skewness at:
https://brainly.com/question/24309209
#SPJ1
Item 1
What is the slope of the line on the graph?
WORTH 20 POINTS
Enter your answer in the box.
Answers
Answer:
-2
Step-by-step explanation:
Hope it helps