Luis and Raul are riding their bicycles to the beach from their respective homes. Luis proposes that they leave their respective homes at the same time and plan to arrive at the beach at the same time. The diagram shows Luis's position at two points during his ride to the beach. Write an equation in slope-intercept form to represent Luis's ride from his house to the beach. If Raul lives 5 miles closer to the beach than Luis, at what speed must Raul ride for the plan to work?
If x represents the time in hours since the ride began and y represents the remaining distance from the beach, then the equation
_____
represents Luis's ride from his house to the beach.
Answers
Answer:
equation: y=-7.5x+15 and Raul must ride at a speed of 5 mi/hr
Step-by-step explanation:
[tex]\frac{y2-y1}{x2-x1}[/tex] to find out the slope. [tex]\frac{6-11.25}{1.2-0.5}[/tex]=[tex]\frac{-5.25}{0.7} = -7.5[/tex]
Then you fill x and y to find out the y intercept
[tex]11.25=-7.5*0.5+b[/tex]
[tex]11.25=-3.75+b\\11.25+3.75=15\\[/tex]
Y intercept= 15
then you put it in the equation:
y=-7.5x+15
Since Raul lives 5 miles closer and Luis is 5 miles away, he needs to go at 5 miles an hour to get to the spot.
That is 5 miles/hour
The distance and time, as presented in this question are illustrations of linear equations.
The linear equation is: [tex]y = -7.5x + 15[/tex]He must plan to ride at 4.5 miles per hour, if he lives 5 miles closerFrom the diagram, we have:
[tex](x_1,y_1) = (0.5,11.25)[/tex]
[tex](x_2,y_2) = (1.2,6)[/tex]
Start by calculating the slope (m)
[tex]m = \frac{y_2 - y_1}{x_2 -x_1}[/tex]
So, we have:
[tex]m = \frac{6 - 11.25}{1.2 - 0.5}[/tex]
[tex]m = \frac{-5.25}{0.7}[/tex]
[tex]m = -7.5[/tex]
The equation is then calculated using:
[tex]y = m(x - x_1) + y_1[/tex]
This gives
[tex]y = -7.5(x - 0.5) + 11.25[/tex]
[tex]y = -7.5x + 3.75 + 11.25[/tex]
[tex]y = -7.5x + 15[/tex]
Calculate distance, when [tex]x = 5[/tex]
We have:
[tex]y = -7.5 \times 5 + 15[/tex]
[tex]y = -22.5[/tex]
The speed (s) is then calculated as:
[tex]s = \frac{22.5}{5}[/tex]
[tex]s = 4.5[/tex]
Hence, he must plan to ride at 4.5 miles per hour
Read more about linear equations at:
https://brainly.com/question/11897796
Related Questions
2 COLLUM PROOFS 1 question
Answers
Answer:
1. <AOB and <XOZ are vert. <'s 1. Given
m<AOB = 80 m<XOZ = 6x+5
2. m<AOB = m<XOZ 2. Vertical <'s are congruent
3. 80 = 6x+5 3. Substitution
4. 75 = 6x 4. Subtraction Property of equality
5. 12.5 = x 5. Division Property of equality
Step-by-step explanation:
2p + 3 = 5 - 6p
what is the value of p in the equation?
Answers
Answer:
p=1/4
Step-by-step explanation:
original: 2p+3=5-6p
move variable to one side: 2p+6p=5-3
combine like terms: 8p=2
answer :p=2/8
simplify answer (final answer): p=1/4
2p+3=5-6p
2p+6p+3=5
2p+6p=5-3
8p=5-3
8p=2
Answer: p=1/4
what is the measure of <4?
Answers
Answer:
i not sure but i think its 125
Step-by-step explanation
60% sure is 125
An is a mathematical statement that shows two expressions are equal using an equal sign.
Answers
No! Because a mathematical statement is actually a statement that is either true or false not a statement that shows two expressions are equal using an equal sign!
Answer:
fix the awser
Step-by-step explanation:
Raj is deciding between two cell phone plans, A and B, which are both linear functions. The monthly charge for plan A according to the number of minutes used is shown in the table.
Monthly Charge for Plan A
Minutes used, x
Monthly charge ($), y
0
14.45
3
14.84
6
15.23
9
15.62
12
16.01
Plan B has the same monthly base charge as plan A, but it charges a different amount per minute used. If the total monthly charge for plan B is $22.10 when 45 minutes are used, what is the slope of the linear function that represents the cost of plan B?
0.13
0.17
0.39
0.45.
Answers
Answer:B is the correct answer (0.17)
Step-by-step explanation:
how do i solve for x
Answers
Answer:division if you just use the derivative
Step-by-step explanation:
What is the product of (−4)⋅(−4)⋅(−4)⋅y⋅y using exponents
Answers
Answer:
[tex](-4)^{3[/tex]*[tex]y^{2}[/tex]
This should be right.
Scott wrote the number 39 on the board and said that it was a prime
number because it was an odd number. Is he correct? Explain why
or why not.
Answers
how many loonies are in 1 quarter
Answers
25 loonies i think but im not so sure
What is the value of 5/z when z=2
Answers
2
−6−
56
=−3−
14
=−6.742
5/(2) = 2.5 or 5/2
The track star runs 100m at a rate of 10.4m/s. How long did it take to run 100m?
0.1 m/s
9.65
1040m/s
0.1s
Answers
Answer:
Time, t = 9.615 secs.
Explanation:
Speed can be defined as distance covered per unit time. Speed is a scalar quantity and as such it has magnitude but no direction.
Mathematically, speed is given by the equation;
[tex]Speed = \frac{distance}{time}[/tex] ....equation 1
[tex]Time = \frac{distance}{speed}[/tex] .....equation 2
Given the following data;
Distance = 100m
Speed = 10.4m/s
Substituting into equation 2;
[tex]Time = \frac{100}{10.4}[/tex]
Time, t = 9.615 secs.
pls help now
A person is trying to find the height of a flagpole or AB. This person is 1.5 m tall and is
standing at DC. A mirror is placed at point M. This mirror is 6 m away from the person and 120 m away from the flagpole. Angles BMA and DMC are congruent. Find the height of the flagpole or BA.
Answers
Answer:
30 m. Your welcome
Step-by-step explanation:
Answer:
30m tall
Step-by-step explanation:
1.5/6 = x/120
Switch sides; cross multiply:
x/120 = 1.5/6
Multiply both sides by 10 and simplify:
x/12 = 5/2
Multiply both side by 12 and get 30m
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Answers
Answer:
3.5
Step-by-step explanation:
Answer:
0.35( I see that's a lot of help* )
The answer is 0.35 because...
Each row is 10 and there is 3 rows full,
1 row is half full, so that equals 5, and then
you add up all of the numbers and you will get 35.
But, in this case, you need it to be a decimal so you just make it 0.35
Hope this helps! <3
solve the equation. Enter your answer in the box.
Answers
which expressions are equivalent to -56z+28?
choose 2 correct answers:
a: 1/2 x (28z + 14)
b: (-1.4z + 0.7) x 40
c: (14 -7z) x (-4)
d: (8z - 4) (-7)
e: -2(-28z -14)
Answers
Answer:
e
Step-by-step explanation:
Make sure all words are spelled correctly.
Try different keywords.
Try more general keywords.
Try fewer keywords
S =4LW + 2WH; S = 96, L= 7, W= 3.
H=
Help please
Answers
Answer:
H = 2
Step-by-step explanation:
Order of Operations: BPEMDAS
Step 1: Define
S = 4LW + 2WH
S = 96
L = 7
W = 3
Step 2: Substitute and Evaluate for H
96 = 4(7)(3) + 2(3)H
96 = 84 + 6H
12 = 6H
H = 2
Answer:
H = = 2 H W + 4 L W
Step-by-step explanation:
Substitute the given value into the function and evaluate.
S = 4 L W + 2 W H = = 2 H W + 4 L W
S = 96 = = 2 H W + 4 L W
L = 7 = = 2 H W + 4 L W
W = 3 = = 2 H W + 4 L W
H = = 2 H W + 4 L W
I hope this helps!
Please Mark Brainliest
Sorry If I Overcomplicated it!
Triangles ABC and DBC have the following characteristics:
BC is a side of both triangles
∠ACB and ∠DCB are right angles
AC ≅ DC
Which congruence theorem can be used to prove △ABC ≅ △DBC?
AAS
SSS
HL
SAS
Answers
Answer please. For money.
Answers
x = 21.75 (third option)
lol i accidentally added a comment sorry
Ricky and James sold beef for a school fundraiser. Ricky sold 52 pounds and James sold 21 pounds. If their total combined sales were $1,168, how much does each pound of beef cost?
A. 16.00
B. 17.50
C. 13.50
D. 17.00
Answers
pleaseee help me solve this
Answers
hello! here is your answer
Answer:
1) ∠2 ≅ ∠7
⇒ they are corresponding angles
2) ∠5 ≅ ∠9
⇒ they are alternate interior angles
3) ∠4 ≅ ∠7
⇒ they are vertically opposite angles
4) if ∠3 ≅ ∠8, then p║q
⇒ they are corresponding angles
5) ∠3 ≅ ∠9
⇒ they are vertically opposite angles
6) m∠2 + m∠3 = 180
⇒ they are co-interior angles
7) ∠4 is vertical to ∠7
8) ∠2 and∠3 are same side interior angles
9) ∠5 corresponds to ∠8
10) one alternate exterior pair is ∠1 and ∠8
hope it helps you!!
Max has 3 textbooks and 2
notebooks in his backpack. The total
weight of his backpack and its
content is 10,5 pounds. Each
textbook weighs 2.5 pounds. Each
notebook weighs 0.25 pound. What
is the weight of Max's empty
backpack?
Answers
Answer:
2 pounds
Step-by-step explanation:
2•.25=.5
7.5+.5=8
10.5-8=2.5
Max’s empty backpack weighs 2.5 pounds
Fiften is 30 percent of what number?
Answers
Answer:
50
hope it helps
Step-by-step explanation:
Answer:
50
Step-by-step explanation:
The way you solve this is by creating an inequality of
30 15
---- = ----
100 x
So you cross multiply which would give you 30x = 1500, then you divide by 30 on both sides leaving you with 50. If you want to check it, you can then multiply 50 by .30 which would give you 15.
Please help with this question, thank you.
Answers
Answer:
the conclusion is that AC and CB are equal distances because the midpoint is half of the line. hope this helps:)
An elephant can drink up to 6,400 fluid
ounces of water a day. How many gallons of
water can an elephant drink per day?
Answers
Answer:
50 gallons
Step-by-step explanation:
A students wants to help her mother in their family store in displaying canned goods. Her mother instructed that the canned should be piled in triangular pile by starting 40 canned goods in the bottom row, 36 in the second row, 32 in the third row, and so on. If the pattern is consistent, how many canned goods will be there in the 7th row?
Answers
Answer: The number of canned goods in 7th row = 64.
Step-by-step explanation:
The given numbers of canned goods in every row( starting from first ) is represented as
40 , 36, 32, ...
There is a common difference between numbers(d)= 4
∴ Its is an Arithmetic progression.
First term (a) = 40
nth term in A.P. : [tex]a(n)= a+(n-1)d[/tex]
7th term in this A.P. = 40+(7-1)(4)=40+(6)(4)=40+24=64
So, the number of canned goods in 7th row = 64.
help me asp and explain please
Answers
Okay so, to get C you add the ones inside the triangle together.
42+58=100 Then the last angle will be 80, because when you add the three inside the triangle, you should get 180
42+58+80=180
To get D, you have to subtract 180 and 58, because 58+d will be a straight angle.
180-58=121
To get B and A, you would also have another straight angle (c, b, and a)
180-80=100
I believe that B=A, so, with the remaining 100, both A and B equal 50.
50+50+80=180
Does this help??
Answer:
a° = 58°
b = 42°
c° = 80°
d° = 122°
Step-by-step explanation:
d° can be found because a straight line has an angle of 180°.
180° - 58° = 122°
Because the angles of a triangle add up to 180°, we can find c°
58° + 42° = 100°. 180° - 100° = 80°
You can find a° subtracting 180 and d°, which is 122. 180° - 122° = 58°
You can do the same thing for b°. 180° - 42° = 138°. 180° - 138° = 42°
You can check this because b° + c° + a° should equal 180°.
58° + 42° + 80° = 180°
I hope this helps :)
3.5−2.46=1.16
Describe Maysa's error. Explain how you would use a model or place-value concepts to help Maysa build understanding. Give the correct answer in your explanation.
Answers
The correct answer for the given subtraction is:
3.5 - 2.46 = 1.04
How to solve the subtraction?
Here we want to find the subtraction between two numbers in decimal form:
3.5 - 2.46 = 1.16
Now, this is clearly wrong, as 0.46 is smaller than 0.5, so the decimals after the decimal point are incorrect, now let's solve it again.
First, we can rewrite these two numbers as:
3.5 = 3 + 0.5
2.46 = 2 + 0.46
Then the subtraction can be rewritten as:
3.5 - 2.46
(3 + 0.5) - (2 + 0.46)
Now we group like terms:
(3 - 2) + (0.5 - 0.46)
1 + (0.50 - 0.46)
1 + (0.04)
Now we group that, so we get:
1 + (0.04) = 1.04
This is the correct answer to the given subtraction.
If you want to learn more about subtractions:
https://brainly.com/question/25421984
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Help ASAP ‼️If m∠A=5x-12 m∠B=2x+18 ∠A and ∠C are supplementary and ∠B and ∠C are supplementary, find x.
Answers
Combine like terms.
-m + 4m - 5m - (-9)
o not use any spaces in your answe
Answers
Because u add like terms and distribute the negative into the parenthesis
Answer:
9 - 2m
Step-by-step explanation:
-m + 4m - 5m - (-9)
-m + 4m = 3m
3m - 5m - (-9)
3m - 5m = - 2m
-2m - (-9)
-(-9) = 9
9 - 2m
10x - 4 = 16
What does x equal to?
Answers
Answer:
x = 2
Step-by-step explanation:
First isolate the variable:
10x - 4 = 16
+4 +4
10x = 20
Then get x by itself:
10x = 20
x = 20/10
x = 10