Christa's distance from school is represented by y=-100x +1300.
Stephen's distance from school is represented by y= -60x +1000.
Using the slope and y-intercept from each equation, find out who lives
farther from school and who walked to school faster.
Answers
Answer:
Christa walked faster and farther than Stephen.
Step-by-step explanation:
Answer:
Step-by-step explanation:
If you think of the y-axis is the "distance" axis (in feet for example), and the x-axis as the time axis (in minutes for example), then what you have is a velocity graph (velocity is the distance traveled divided by the time it takes to get there). If you haven't moved at all, your time is 0 (ON the y-axis) and the distance value (the y-intercept) is where you started. In other words, if no time has gone by, I haven't moved from my initial position yet. So the y-intercept of both of those equations serves as the intial distance each is from school.
In the equation y = mx + b, b is the y-intercept. The y-intercept in Christa's equation is 1300 (in feet) which means that before she leaves her house for school (no time has gone by yet), her initial distance from school is 1300 feet. Likewise, for Stephen. The y-intercept in his equation is 1000, so his initial distance from school is 1000 feet. Christa lives farther away than does Stephen.
Now for the rate they are each walking...
Rate is also (sort of the same thing as) velocity. It is represented in our equation by the m. In a "regular" slope-intercept equation, this would be the slope. Slope is the rate at which something is changing. Since our graph is a velocity graph--distance over time--our slope represents the distance each covers for every minute they walk. Christa's velocity is 100 feet per minute and Stephen's is 60 feet per minute. From this we can determine that Christa walks faster because she covers more feet per minute than does Stephen.
The equations are both negative because they are shortening their distances to the school. By this I mean that as they continue walking to school and the amount of time that goes by gets greater, the distance they are from the school gets smaller.
Hope this helps you understand what linear equations actually mean to the real world!
Related Questions
Given that ƒ(x) = 3x – 1 and g(x) = 4x2 – 5x + 7, find (ƒ – g)(x)
Answers
Answer:
The answer is - 4x² + 8x - 8
Step-by-step explanation:
ƒ(x) = 3x – 1
g(x) = 4x2 – 5x + 7
(ƒ – g)(x) = 3x - 1 - ( 4x² - 5x + 7)
That's
3x - 1 - 4x² + 5x - 7
Group like terms
- 4x² + 3x + 5x - 1 - 7
The final answer is
- 4x² + 8x - 8
Hope this helps you.
29:PLEASE HELP Solve the inequality x+6<-2
Answers
Answer:
x<-8
Step-by-step explanation:
x+6<-2
subract 6 from both sides
x+6-6<-2-6
x<-8
HELP ME PLEASE PLEASE IM BEGGING
Answers
Answer:
a, No
Step-by-step explanation:
We can just substitute the numbers (x, y) into the inequality to see if the inequality is valid.
y=40
5(4) + 8 = 28
"<" means the number on the left is smaller than the number on the right.
40 is not smaller than 28, so in this inequality,
(4, 40) is not valid in y<5x+8
PLEASE HELP!!!
The model below represents 4x+(-4) -- 2x+8
What is the value of x when solving the equation 4x+(-4) --2x+8 using the algebra tiles?
X-2
Answers
Answer:
x=6
Step-by-step explanation:
4x-4=2x+8
Get all x's to one side. Subtract 2x from both sides.
2x-4=8
Isolate x. Add 4 to both sides.
2x=12
Divide both sides by 2 to get x.
12/2=6
x=6
Answer:
2 A.K.A. C. this answer is really late i think but for people in the future this is the answer lol
PLZ HELP ASAP--------->
Answers
Malachy, Sushil and Fiona share some sweets in the ratio 1:3:1. Malachy gets 5 sweets. How many did Sushil get?
Answers
Answer:
Sushil got 15 sweets
Step-by-step explanation:
we can use law of indices property as shown below
a:b:c = ax:bx:cx
that if we multiply each term of ratio by same number , the ratio does not change
____________________________
given
Malachy, Sushil and Fiona share some sweets in the ratio 1:3:1.
let
Malachy gets 1x sweets
sushil gets 3x sweets
Fiona gets 1x sweets
but given that
Malachy got 5 sweets
thus
1x = 5
x = 5
Sushil got 3x sweets = 3*5 = 15 sweets.
Sushil got 15 sweets.
If y varies jointly as x and z and inversely as the square of w, and y =3 when x=3, z=10 and w=2, then y=4 when x=4 z=20 w=4
Answers
Answer:
0.4 ; 0.8
Step-by-step explanation:
Given that :
y varies jointly as x and z and inversely as the square of w
y ∝ xz ∝ 1/w^2
y = kxz/w^2 - - - - (1)
Given that y =3 when x=3, z=10, w=2
Inputting the values into (1)
3 = (k*3*10) / 2^2
3 = 30 × k / 4
k × 30 = 3 × 4
k × 30 = 12
k = 12/30
k = 0.4
B.) Given that ;
y=4 when x=4 z=20 w=4
Input values into (1)
y = kxz/w^2
4 = ( k * 4 * 20) / 4^2
4 = (k * 80) / 16
k * 80 = 16 * 4
k * 80 = 64
k = 64 / 80
k = 0.8
Answer:
False
Step-by-step explanation:
Took the test and got it wrong
*QUICK HELP PLEASE
Which pairs of angles are adjacent? Select all that apply.
Answers
Answer:
1 and 3; 1 and 4; 2 and 3; 2 and 4
Step-by-step explanation:
Adjacent angles are those with a common side and common vertex (corner point). Of your choices, the ones provided above are the ones that meet the needs of adjacent angles.
A mural inspired by a photograph measures 108 inches by 180 inches. The scale of the photograph to the mural is 1 in.:12 in. What are the dimensions of the photograph?
Answers
Answer:
9x9
Step-by-step explanation:
Divide 108/12
108/12=9
you have a 9x9 photo
hope this helps!
PLEASE HELP ME Logan has twice as many contacts in his phone as Marcus. Janet has 8 more then 1/3 of the number of contacts that Marcus has. Marcus has 243 contacts in his phone. How many more contacts does Logan have than Janet?
Answers
John who is 5 ft tall is standing 20 feet away from a tree, and you measure the angle of elevation to be 38∘. How tall is the tree? Find your answer to the nearest tenth.Instructions: Find the missing length indicated.
Answers
Answer:
5√17=
20.6
Step-by-step explanation:
[tex]adj \: = 5 \\ opp \: = 20 \\ hyp \: = \: \\ pythagoras \: theorem \: \: = \\ {hyp}^{2} = {opp}^{2} + {adj}^{2} [/tex]
[tex] {hyp \:}^{2} = {20}^{2} + {5}^{2} \\ {hyp }^{2} = 400 + 25 \\ {hyp}^{2} = 425 \\ \sqrt{ {hyp}^{2} } = \sqrt{425} [/tex]
[tex]hypotenuse \: = 5 \sqrt{17} [/tex]
The tangent or tanθ in a right-angle triangle is the ratio of its perpendicular to its base. The height of the tree is 20.6257 feet.
What is Tangent (Tanθ)?The tangent or tanθ in a right-angle triangle is the ratio of its perpendicular to its base. it is given as,
[tex]\rm Tangent(\theta) = \dfrac{Perpendicular}{Base}[/tex]
where,
θ is the angle,
Perpendicular is the side of the triangle opposite to the angle θ,
The base is the adjacent smaller side of the angle θ.
The digram for the given condition is given below. Now, in ΔABC, the tangent value for ∠A can be written as,
tan(38°) = BC/AB
tan(38°) = 5 feet / AB
AB = 6.3997 feet
Now, in ΔABC and ΔADE for ∠A the value of the tangent can be written as,
tan(38°) = BC/AB = ED/AD
5/6.3997 = ED/(20 + 6.3997)
ED = 20.6257 feet
Hence, the height of the tree is 20.6257 feet.
Learn more about Tangent (Tanθ):
https://brainly.com/question/10623976
#SPJ2
At a certain car rental company, it costs $39.95 per day and $0.06 cents per mile to rent a car. How much would it cost to rent a car for 2 days and drive 150 miles?
Answers
Answer: $88.90
Step-by-step explanation:
$39.95 x 2 + 0.06 x 150
Sue has a crate, open at the top, in the shape of a cuboid. The internal dimensions of the crate are 36cm long by 36cm wide by 60cm high. Sue has a stick of length 90cm. She places the stick in the crate so that the shortest possible length extends out above the top of the crate. A) Calculate the length of the stick that extends out of the crate. B) Calculate the angle the stick makes with the base of the crate.
Answers
Answer:
Step-by-step explanation:
When the stick is placed along the diagonal of the cuboid , shortest possible length will extend out above top of the crate .
Length of the diagonal
= [tex]\sqrt{36^2+36^2+60^2}[/tex]
= 78.69 cm
the length of the stick that extends out of the crate
= 90 - 78.69
= 11.31 cm
If θ be the angle made by stick with the base
cosθ = hypotenuse of base / diagonal of cuboid
=[tex]\frac{\sqrt{2}\times36 }{78.69}[/tex]
= [tex]\frac{50.90 }{78.69}[/tex]
θ = 50°
Answer: This is the answer to B) 47.9 degrees
Step-by-step explanation:
Pythagoras: a^2+b^2=c^2
36²+36²=C²
√2592=C
C=50.9cm
Used Trigonometry: SOH CAH TOA
Tan=Opposite/Adjacent
Tan=60/50.9
The angle stick makes when it meets the base:
Tan^-1(60/50.9)
=49.7˚
From the information given, what is the biggest flaw in the study? A health researcher randomly selected 500 high school students from the city of Oak Grove. In a private interview the researcher asked the students whether they had ever used drugs. She concluded that only 8% of the high school students of Oak Grove have ever used drugs.
Answers
Answer:
The correct answer is - The setting may discourage honest responses.
Step-by-step explanation:
In this particular setting of research and interview regarding this research may not produce hones results as the question is too direct to ask students if they had ever used drugs.
Research should be anonymous and should avoid the questions that can lead to bias results like this case that may lead to dishonest results.
Thus, the correct answer is : The setting may discourage honest responses.
(17x10)-(17x4)=(17 x ?)
Answers
Answer:
6
Step-by-step explanation:
6 is the answer
? =6
Answer:
6
Step-by-step explanation:
1. 17 * 10 = 170
2. 17 * 4 = 68
3. 170 - 68 = 102
4. 102 / 17 = 6
A new hockey stick costs $57.00 at the sporting goods store. If there is a 6%
sales tax, what is the actual cost of the hockey stick?
Answers
Answer:
$60.42
Step-by-step explanation:
0.06 x $57 = $3.42
$57 + $3.42 = $60.42
Hope this helped! :)
Please help ASAP Payton collected data to show the relationship between the number of hours he practices and the number of errors he makes when playing a new piece of music. The table shows his data. Which is the approximate slope of the line of best fit for the data? –5.5 –4.5 –2.0 –1.0
Answers
Answer:
Option B.
Step-by-step explanation:
The general equation of best fit line is
[tex]y=ax+b[/tex]
where, a is the slope of best fit line and b is y-intercept.
Using graphing calculator a=-4.54762 and b=43.7143. So equation of best fit line is
[tex]y=-4.54762x+43.7143[/tex]
Here,
[tex]Slope=-4.54762[/tex]
[tex]Slope\approx -4.5[/tex]
Note: In alternate method, you can use the below formula to find slope.
[tex]m=\dfrac{\overline{x}\cdot \overline{y}-\overline{xy}}{(\overline{x})^2-\overline{x^2}}[/tex]
Therefore, the correct option is B.
Answer:
B: -4.5
Step-by-step explanation:
edg2021
y ≈ -4.548x + 43.714 is the entire equation. So -4.548 or -4.5 is the slope.
Sonya made a graph showing the first ten minutes of her drive to the movies. A graph with time on the x-axis and speed on the y-axis. The graph increases, increases rapidly, and then remains constant. Which description is the best interpretation of the graph? Sonya left her house and accelerated as she drove toward the highway entrance. She increased her speed as she drove up the ramp to the highway and then drove a constant speed on the highway. Sonya backed out of her driveway at a constant speed and then accelerated until she reached the street where the movie was playing. She stopped the car. Sonya drove down her driveway at a constant speed until she reached the street. She turned and drove down the street at a constant speed. Her car went slower as she drove up a hill. At the top of the hill she drove into the parking lot of the movie theater. Sonya accelerated as she drove down her driveway. She accelerated on the street on her way to the highway entrance. She waited for a red light, then accelerated onto the highway.
Answers
Answer:
Sonya left her house and accelerated as she drove toward the highway entrance. She increased her speed as she drove up the ramp to the highway and then drove a constant speed on the highway.
Step by step explanation:
The first scenario is the best match for the increasing slope, (leaving the house and accelerating) rapidly increasing slope (increasing speed on ramp) and level line (constant speed on the highway).
The best interpretation of the graph is,
Sonya left her house and accelerated as she drove toward the highway entrance. She increased her speed as she drove up the ramp to the highway and then drove a constant speed on the highway.
What is Acceleration?When a point or an object moving in a straight line , the acceleration is the rate at which velocity changes with time, in terms of both speed and direction.
Here, we have,
The first scenario is the best match for the increasing slope, (leaving the house and accelerating) rapidly increasing slope (increasing speed on ramp) and level line (constant speed on the highway).
Hence, The best interpretation of the graph is,
Sonya left her house and accelerated as she drove toward the highway entrance. She increased her speed as she drove up the ramp to the highway and then drove a constant speed on the highway.
To learn more on Acceleration click:
https://brainly.com/question/2303856
#SPJ3
What is one of the zeros of the function shown in this graph?
Answers
Answer:
-4 or 2Step-by-step explanation:
the x-intercepts of the graph are the zeros of the quadratic function
Which of the sets of ordered pairs represents a function? (1 point)
A = {(2, 7), (1, −5), (7, 2), (2, −9)}
B = {(5, 3), (−2, −9), (−3, 8), (9, 3)}
Answers
Answer:
B = {(5, 3), (−2, −9), (−3, 8), (9, 3)}
Step-by-step explanation:
A function has no repeating inputs (x-values). One input is assigned to exactly one output.
In set 'A', the input of two is repeated.
A = {(2, 7), (1, −5), (7, 2), (2, −9)}
In set 'B', there are no repeating inputs.
Set 'B' is a function.
Brainilest Appreciated.
Mrs smith invests £30,000 (some in a 5% account, some in an 8% account). After the year shes earned £2100. How much did she put in each account? PLEASE HELP!!
Answers
Answer:
She deposited £10,000 in the 5% yield account and deposited £20,000 in the 8% yield account
Step-by-step explanation:
Let the amount she put in each account be £x and £y respectively
Total amount deposited is ;
x + y = 30,000 ••••••(i)
Now, let’s look at the earnings:
in the £x , amount earned would be;
5/100 * x = 5x/100
For the £y, amount earned would be;
8/100 * y = 8y/100
Adding both gives the total which is £2,1000
5x/100 + 8y/100 = 2,100
Multiply through by 100
5x + 8y = 210,000 ••••••••(ii)
From the first equation, we know that
x = 30,000 -y
Let’s put this into the second
5(30,000-y) + 8y = 210,000
150,000-5y + 8y = 210,000
3y = 210,000 -150,0000
3y = 60,000
y = 60,000/3
y = £20,000
So mathematically;
x = 30,000-y
x = 30,000 -20,000
x = £10,000
Find the range of the given function y = 5x + 2, where x > -2.
Answers
Answer:
Its -3,2,7
Step-by-step explanation:
Simply put, you plug in all values greater than -2. Which is what thst function tells you.
NEED HELP ASAP ‼️‼️I BELIEVE ANSWER IS C
Answers
Answer:
I agree with your answer C!!
Step-by-step explanation:
Find the area of this triangle..
Answers
Answer:
39.936 ( not rounded )
Step-by-step explanation:
Use Pythagorean theorem
a^2 + 6.4^2 = 9^2
height = 6.24 (rounded to nearest hundredth)
1/2 * base * height = area
1/2 * 12.8 * 6.24
= 39.936 ( not rounded )
Gwendolyn shot a coin with a sling shot up into the air from the top of a building. The graph below represents the height of the coin after
x seconds.
Answers
Answer: A
Step-by-step explanation:
Which answers are equivalent to the fraction below? Check all that apply
12/16
A.1/2 B.6/8 C2/3 D.2/6 E.3/4 F.6/4
Answers
Answer: e
Step-by-step explanation: 12/16 6/8 3/4
Answer:
B and E.
Step-by-step Explanation:
B: 6/8
6*2=12
8*2=16
12/16
E: 3/4
3*4=12
4*4=16
12/16
Hope this helps!!!!!
Find the value of x in the triangle
shown below.
Answers
Answer: 55
Step-by-step explanation:
There are two sides that are equal (5 and 5). That means that this is an isoceles triangle. The unmarked angle and the x angle are equal to each other because isoceles triangles have also have two equal angles. Because every triangle has 180 degrees, that means that all three angles added up should equal 180.
Since the unmarked and x angle are equal you can write the equation out as 180=70+2x. Subtract 70 from both sides to get the variable and nonvariable on different sides.
110=2x. Divide both sides by 2(in order to isolate the variable). X is 55
Hope this helped you:)
This service is NOT important when comparing banks: a: Debit card design. b:Hours of operation. c:Convenience of location. D:Monthly fees and minimum balance required.
Answers
Answer:
A.
Step-by-step explanation:
Debit card design really has nothing to do with banks but has to do with personal preference. If you are comparing banks, you would want to see when they are open, how much you would need to deposit to start an account, that kind of stuff.
Given that y is directly proportional tox, and when y = 8 when x=
10.
(a) Write down the equation of y in terms of x.
(b) Find the value of y when x = 25.
8
(c) Find the value of x when y==
25
Answers
Answer:
see explanation
Step-by-step explanation:
(a)
Given that y is directly proportional to x then the equation relating them is
y = kx ← k is the constant of proportion
To find k use the condition y = 8 when x = 10. then
8 = 10k ( divide both sides by 10 )
0.8 = k
y = 0.8k ← equation of proportion
(b)
when x = 25, then
y = 0.8 × 25 = 20
(c)
when y = 25, then
25 = 0.8x ( divide both sides by 0.8 )
x = 31.25
Use the graph to complete the given statements. Enter the letters A, B, C, or D in the boxes.
The function with the lowest output values as x approaches infinity is _. The function with the greatest output values as x approaches infinity is _.
Answers
The function with the lowest output values as x approaches infinity is A.
The function with the greatest output values as x approaches infinity is B