The position of an open-water swimmer is shown in the graph. The shortest route to the shoreline is one that is perpendicular to the shoreline. Write an
equation that represents this path.
Answers
*attachment contains the omitted graph
Answer:
[tex] y = -\frac{4}{3}x + 9 [/tex]
Step-by-step explanation:
The equation that represents the path of the swimmer to the shoreline can be represented in the slope-intercept form, given as [tex] y = mx + b [/tex].
Where,
Slope (m) = the negative reciprocal of the slope of the shoreline, since it is perpendicular to it = ??
y-intercept (b) = ??
Find the slope of the shoreline using, (0, 1) and (4, 4):
[tex] m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{4 - 1}{4 - 0} = \frac{3}{4} [/tex].
Since the slope of the shoreline is ¾. The slope of the path of the swimmer would be the negative reciprocal of ¾.
The negative reciprocal of ¾ = -⁴/3.
The slope of the swimmer's path = -⁴/3.
Using the coordinate of the point of the swimmer (6, 1), and the slope of the path, we can find b, the y-intercept of the path.
Substitute x = 6, y = 1 and m = -⁴/3 into y = mx + b, to find b.
Thus:
1 = (-⁴/3)(6) + b
1 = -8 + b
Add 8 to both sides
1 + 8 = b
9 = b
b = 9
Substitute m = -⁴/3 and b = 9 into y = mx + b.
✅The equation that represents the path would be:
[tex] y = -\frac{4}{3}x + 9 [/tex]
Related Questions
Jake plans to use a ramp to make it easier to move a piano out of the back of his truck. The back of the truck is 83 centimeters tall and the ramp is 158 centimeters long
Answers
Given :
Height of the ramp, h = 83 cm.
Length of ramp, L = 158 cm.
To Find :
Length of the base of the ramp.
Solution :
Let length of the base is l.
By Pythagoras theorem :
L² = h² + l²
[tex]l=\sqrt{L^2-h^2}\\\\l=\sqrt{158^2-83^2}\\\\l=134.44\ cm[/tex]
Therefore, length of the base is 134.44 cm.
Hence, this is the required solution.
Ada bought 90 feet of for $20.70. She needs 30 more feet. If the unit price is the same, how much will she pay for the extra 30 feet of ?
Answers
Answer:
Step-by-step explanation:
20.70/90= 0.23 per foot
30*.23= 6.90
It'll cost $6.90 for 30 more feet.
Jeff sells popcorn for $3 per bag. To make a profit each day, he needs to sell at least $120 worth of popcorn. He has sold $36 worth of popcorn today. Which inequality can be used to find the number of bags of popcorn, p, Jeff still needs to sell today to make a profit?
Answers
Answer:
The inequality tha can be used to find how many more bags of popcorn Jeff still needs to sell today to make a profit is
x - 12 ≥ 40.
Step-by-step explanation:
Let us represent the number of bags of popcorn as p
Jeff sells popcorn for $3 per bag. To make a profit each day, he needs to sell at least $120 worth of popcorn.
We have the equation:
$3 × p ≥ $120
3p ≥ $120
p ≥ 120/3
p ≥ 40 bags
He must sell at least 40 bags to make a profit
He has sold $36 worth of popcorn today.
1 bag is $3
Hence, he has sold
$36/$3 = 12 bags of popcorn
Which inequality can be used to find Jeff still needs to sell today to make a profit?
This equality is given as:
x - 12 bags ≥ 40 bags
x - 12 ≥ 40
x ≥40 - 12
x ≥ 28 bags
She still need to sell 28 more bags of popcorn.
Politician Alec and Candidate Simeon are running for governor. The latest surveys show that Politician Alec has 47% of the vote, while Candidate Simeon has 42% of the vote. The news report, however, states that this survey has a 6 % margin of error. What interval describes Politicians Alec's chances of winning the election?
Answers
Answer:
(41%, 53%)
Step-by-step explanation:
Given that:
Politician Alec's vote = 47%
Candidate Simeon = 42%
Margin of Error = 6%
Interval which describes Alec's chances of winning
Chances of Alec winning (p) = 47%
Margin of Error = 6%
Interval :
p ± margin of error
47% ± 6%
47% - 6% ; 47% + 6%
(41%, 53%)
Write and solve an equation to find the number.
Ten less than half of a number(x) is 6.
Answers
Answer:
x = 32
Step-by-step explanation:
[tex]\frac{1}{2}[/tex]x-10 = 6
Isolate the x.
[tex]\frac{1}{2}[/tex]x = 6+10
Simplify.
[tex]\frac{1}{2}[/tex]x = 16
([tex]\frac{1}{2}[/tex]x × 2 = [tex]\frac{2}{2}[/tex]x) Find x.
[tex]\frac{2}{2}[/tex]x = 16 × 2
Simplify.
[tex]\frac{2}{2}[/tex]x = 32
half of x = x/2
ten less = -10
please help asap ;-;
Answers
Answer:
D.
Step-by-step explanation:
Both have a slope or "rate of change" of 1/2 because going from (0,5)-->(2,6) on the first one you go right 2 units and up 1 and slope is rise over run or y/x values in this case it would be 1/2 and on the bottom function you can see it goes from (0,-2)-->(4,0) and this goes right 4 units and up 2 units same principal applies you get 2/4 which is equal to 1/2 also it being negative or not doesn't change whether the two functions have the same rate of change.
The average emergency room cares for 300 patients each day. There are 20 nurses on duty at the emergency room each day, and they share the patient load equally.
Answers
Answer: 15
Step-by-step explanation:
You didn't say what you need to calculate but I guess that you want to calculate the number of patients each nurse will get.
Number of patients = 300
Number of nurses = 20
Number of patients to each nurse will be:
= Number of patients / Number of nurses
= 300/20
= 15
Each nurse gets 15 patient
Answer:
Step-by-step explanation:
There are 1$$ patients in the sample space.
There are 2$$ nurses on duty each day.
P(N)=3$$, is the probability that a patient will be assigned to a specific nurse.
Correct answers:
1$300$2$20$3$\frac{1}{20}$
The sample space is the set of all possible outcomes of an experiment. Here, there are 300 possible patients.
The event is a grouping of the outcomes in the sample space. Here, there are 20 possible nurses that a patient may have.
When the 300 patients are assigned equally to 20 nurses, that is equal to 15 patients per nurse. The probability of a patient being assigned to a specific nurse, N, is the comparison of being assigned to that nurse's patients versus all possible patients: P(N)=15/300=1/20.
Teresa bought 8 packages of paper. Each package contained 10 pads of paper, and each pad of paper cost $2. How many pads of paper did Teresa buy? How much did Teresa spend?
A.
80 pads of paper; $160
B.
18 pads of paper; $20
C.
18 pads of paper; $36
D.
80 pads of paper; $36
1 / 10
Answers
Step by step
add 5m{3-m} and 5m {2+m} is
Answers
(2+m)si thats wat i got, hope its right
pls answer asap
thx................
Answers
Answer:
3. 1mL
Step-by-step explanation:
There are 1000mL in a Liter so if you divide a liter in 1000 parts one part is 1mL
On a bird-watching trip, Tai and Mei counted 94 birds.
Of these, 55 of the birds were sparrows. Which value
is a reasonable estimate of the percent of sparrows in
the birds Tai and Mei counted?
Answers
however, it is estimating so depending on the answer choices it would be around 55-60% or so
For what values of x is the inequality (x-4)2 > true?
Answers
Answer:
You multiply both sides of this inequality by −1, we get −4 > −2.
Please answer, I’m struggling allot
Answers
Answer: -3
Step-by-step explanation:
y2-y1/x2-x1
(1,0)
(0,3)
3-0/0-1 = -3/1
Which of the following statements about a plane is not true
Answers
if p (x) =30(x+4)+26 what is the value of p(-8)
Answers
=30(-4)+26
= -120+26
=94
A local Latin restaurant specializes in Peruvian, Cuban, and Tex-Mex cuisines in their recipes. Lomo Saltado, “Beef Stir-fry,” is considered a family meal. The restaurant uses the following function to determine the total cost for customers who choose to have the Lomo Saltado meals delivered, where x represents the number of Lomo Saltado meals purchased. C(x) = 12.09x + 5 What does 12.09 represent in terms of the cost?
Answers
Answer:
The cost per meal not including the $5
Step-by-step explanation:
or whatever is says something like that
Answer:
55
Step-by-step explanation:
its eay you just
Joy's Tea Shop has caffeinated tea and decaffeinated tea. During the lunchtime rush, the tea shop served 60 teas in all, 30% of which were caffeinated. How many caffeinated teas did the tea shop serve?
Answers
Answer:
18
Step-by-step explanation:
whats the nearest thousandth of 2.8151
Answers
Answer:
To round off a number to the nearest 1000, check the hundredth digit of the number. Round off the number to the previous thousand if the hundredth digit is 0, 1, 2, 3 and 4. Round off the number to the next thousand if the thousandth digit is 5, 6, 7, 8 and 9. Examples: Consider the numbers 6567 and 6281.
4. John gets a new job and receives a $700 signing bonus. After that, he makes $250 a day
What is the y intercept of the equation that describes the situation
I need to know if the answer is y=700
Answers
Answer:Yes the answer would be 700 since that is the starting amount.
Step-by-step explanation:
Oscar is offered jobs at two different dog-walking companies. At company A he would earn $50 a day, plus $6 for each dog walk. At Company B, he would earn $20 a day, plus $9 for each dog walk. How many dogs would Oscar have to walk to earn the same amount at both companies in a day? How much would he earn for walking that number of dogs? *
Answers
Answer:
he should walk 4 dogs in order to earn same amount
I need help with this question
Answers
Answer:
Its B
Step-by-step explanation:
you have to subtract 320-70 to get 250. If you didn't you be able to divide 5 cleanly
I REALLY NEED HELP PLEASEEE
A shark is swimming 60 feet below the surface of
the ocean. There is a fish that is 25 feet deeper
in the water. Use the expression (-60) + (-25) to
describe the fish’s location relative to the surface
of the ocean
Answers
Answer:
- 85 ft
Step-by-step explanation:
-60 - (-25) =-85
Divide 2 3/4 divided by 3
Answers
Answer:
11/12
Step-by-step explanation:
Convert to improper fractions : 2 3/4 = 11/4
Divide denominator by 3: 11/4 ÷ 3 = 11/12
Out of 200 people eating at a diner, 70% ordered
sandwiches. How many people ordered
sandwiches?
Answers
Answer:
140 people
Step-by-step explanation:
The number is 140 people. 140 people ordered sandwiches.
What is a percentage?A ratio or value that may be stated as a fraction of 100 is called a percentage. And it is represented by the symbol '%'.
Given:
Out of 200 people eating at a diner,
70% ordered sandwiches.
To find the number of sandwiches ordered:
Use percentage formula,
let n be the number of sandwiches ordered.
So, n = 70 x 200 / 100
n = 14000/100
n = 140
Therefore, 140 people ordered sandwiches.
To learn more about the percentage;
https://brainly.com/question/24159063
#SPJ2
Diego's family car holds 14 gallons of fuel. Each day the car uses 0.6 gallons of fuel. A warning light comes on when the remaining fuel is 1.5 gallons or less. Write an inequality to determine the number of days Diego's father can drive the car without the warning light coming on. 10 points 14− 0.6t > 1.5 14− 0.6t < 1.5 14+ 0.6t > 1.5 14+ 0.6t < 1.5
Answers
Answer:
[tex]14-0.6t>1.5[/tex]
Step-by-step explanation:
The amount of fuel the car holds is fixed i.e., 14 gallons
The amount of fuel consumed every day is 0.6 gallons
Warning light comes on when the fuel level is 1.5 gallons or less.
Let t be the number of days the car runs for
So the amount of fuel consumed in all the days must be less than 1.5.
The equation will be
[tex]14-0.6t>1.5\\\Rightarrow -0.6t>1.5-14\\\Rightarrow -0.6t>-12.5\\\Rightarrow 0.6t<12.5\\\Rightarrow t<\dfrac{12.5}{0.6}\\\Rightarrow t<20.83[/tex]
So, the number of days the car can be driven without the warning light coming on is less than 20.83 days.
Hence, the required inequality is [tex]14-0.6t>1.5[/tex].
1.Which system of linear inequalities is graphed?
Answers
Lisa hikes 9 miles in 2 hours. At this rate, how far does she hike in hours?
O 2 miles
O4 miles
O 3 miles
O 3 miles
Answers
please Help 3 ×__=15
Answers
Answer:
3 x 5 = 15
Step-by-step explanation:
15 / 3 = 5
OR
3 + 3 + 3 + 3 + 3 = 15
(1 2 3 4 5)
OR
5 + 5 + 5 = 15
(1 2 3)
I hope this was helpful to you! If it was, please consider rating, pressing thanks, and marking my answer Brainliest. It would mean a lot :) Have a great day!
Answer:
Hey mate here is your answer. Hope it helps you
Step-by-step explanation:
Let the unknown number be x,
3 *x=15
x= 15/3
=5
The answer is 5.
whats 500000 x 700=
heyyyyy
Answers
Answer:
PERIOD
Step-by-step explanation:
A student solved log4(2x – 12) = 3, as shown.
Step 1: 2x – 12 = 34
Step 2: 2x – 12 = 81
Step 4: 2x = 93
Step 5: x = 46.5
Explain the error and find the correct solution.
Answers
Answer:
The error is in Step 1. They translated from logarithmic to exponential form incorrectly.
The student should have used 4 as the base and 3 as the exponent. This would result in 64, not 81, on the right side of the equation.
The correct answer is x = 38.
Step-by-step explanation:
Answer:
The error is in Step 1. They translated from logarithmic to exponential form incorrectly.
The student should have used 4 as the base and 3 as the exponent. This would result in 64, not 81, on the right side of the equation.
The correct answer is x = 38.
Step-by-step explanation:
Step-by-step explanation: