Jeff bicycles 144 miles at the rate of r mph. The same trip would have taken 3 hours longer if he had decreased his speed by 4 mph. Find r (in mph).
His original speed was r =mph.
Answers
Jeff bicycles 144 miles at the rate of r mph. The same trip would have taken 3 hours longer if he had decreased his speed by 4 mph. The value of r is 16.
What is speed ?
The speed at which an object's position changes in any direction. The distance traveled in relation to the time it took to travel that distance is how speed is defined. Given that it only has a direction and no magnitude, speed is a scalar quantity.
144/r= t
144/(r-4)-144/r = 3
LCM r(r-4)
144r-144(r-4)/r(r-4)=3
Simplify [tex]$\frac{144 r-144(r-4)}{r(r-4)}: \frac{576}{r(r-4)}$[/tex]
[tex]\frac{576}{r(r-4)}=3[/tex]
Multiply both sides by r(r-4)
[tex]\frac{576}{r(r-4)} r(r-4)=3 r(r-4)[/tex]
Simplify
576=3 r(r-4)
Solve [tex]$576=3 r(r-4): \quad r=16, r=-12$[/tex]
r=16, r=-12
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Related Questions
A mug is 1/3 full. The mug contains 3/4 of a cup of water. Find the capacity of the mug. Write the answer as a fraction or mixed number in simplest form.
Please answer quick and add an explanation 0.0
Thank you!
Answers
Answer: 9/4
Step-by-step explanation:
The equation for this is 3/4 x 3 = 3/4 x 3/1 = 2 1/4
Simple 2 1/4 to fraction = 9/4
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The mug has a capacity of 2 1/4 cups of water, as per the given conditions.
Given that,
A mug is 1/3 full. The mug contains 3/4 of a cup of water. Find the capacity of the mug.
The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
Here,
As
1 / 3 of mug = 3 / 4 cups
1 of mug = 3/4 / [1/3]
1 of mug = 3×3 / 4
1 of mug = 9 / 4 cups or 2 1 / 4 cups
Thus, the mug has a capacity of 2 1/4 cups of water, as per the given conditions.
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120 thousand cars were manufactured in a country in the year 2004-OS. The production of cas
increased to 150 thousand in 2005-06. Find the percentage increase in the manufacture of cars.
Answers
Answer:
25% increase
Step-by-step explanation:
120 thousand cars were manufactured in a country in the year 2004-O5. The production of cars increased to 150 thousand in 2005-06. Find the percentage increase in the manufacture of cars.
(150 - 120) / 120 = 0.25
0.25 = 25% increase
Triangle ABC has the following measures: mA = 46°, m/B = 73°, and b = 32.3. What
is the length of side c?
Answers
The length of the side c is equal to 29.54 approximately to 2 decimal place, using the sine rule.
What is the sine ruleThe sine rule is a relationship between the size of an angle in a triangle and the opposing side.
For the triangle ABC, by sine rule;
a/sinA = b/sinB = c/sinC
We first derive the angle C as follows:
46° + 73° + C = 180° {sum of interior angles of a triangle}
C = 180° - 119
C = 61°
Thus by sine rule;
c/sin61° = 32.3/sin73°
c = (32.3 × sin61°)/sin73° {cross multiplication}
c = 29.5410
Therefore, by proper application of the sine rule we have the length of the side c to be equal 29.54 approximately to 2 decimal place.
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The area of a triangle is 36 cm2. The height of the triangle is 6 cm less than the base. What is the height of the triangle?.
Answers
Answer:
[tex]\huge{\boxed{\text{The height of the triangle is 6cm.}}}[/tex]
Step-by-step explanation:
This question requires us to use a system of equations.
The area of a triangle is (1/2) * (base) * (height).
Thus, if b = base, and h = height
[tex]\frac{1}{2} bh=36[/tex]
Additionally, from the problem, we know:
[tex]b=h+6[/tex]
Then, via substitution, we can get
[tex]\frac{1}{2} *(h+6)*h=36[/tex]
Then, simplify:
[tex]\frac{1}{2} h^2+3h=36[/tex]
[tex]\frac{1}{2} h^2+3h-36=0[/tex]
[tex](\frac{1}{2} h-3)(h+12)=0[/tex]
Thus, the height must equal either 6 or -12, and because height cannot intrinsically be negative, the height must be 6.
Hope it helps :) and let me know if you want me to elaborate.
can you answer this fast please please
Answers
Answer:
top option: The function is nonlinear and does not have a constant rate of change
Step-by-step explanation:
This is a parabolic function, meaning that it increases exponentially. Therefore, it is nonlinear and does not have a constant slope (rate of change).
Write the equation of the line passing through the points (-3,3) and (3,1).
The equation of the line is?
Answers
Answer:
y = -1/3x + 2
Step-by-step explanation:
Slope-intercept form of a linear equation is written as:
y = mx + b, where x and y are coordinates from one of the points on the line, m is the slope, and b is the y-intercept.
1. You'll first want to find the slope, m. Slope can be calculated from two points by using the equation (y1 - y2)/(x1 - x2). If you plug your two points into this equation for x and y (making sure that y1 and x1 are from the same point and y2 and x2 are from the other), you'll get,
(3 - 1)/(-3 - 3) = 2/-6 = -1/3
m = - 1/3
2. You can then plug your slope, m, into the slope-intercept form of the equation. Using one of your points (doesn't matter which, but I'll use (3,1)), you can solve for b, your y-intercept.
1 = -1/3(3) + b
1 = -1 + b
b = 2
3. Plug the variables into the equation.
For your final equation, plug the slope, m, and y-intercept, b, that you just found.
y = -1/3x + 2
Will give brainliest!!
Answers
explanation: the two remains a whole number, and the second part is 8 one hundredths, which goes to the second decimal spot
To convert the fraction 2 8/10 to a decimal, divide the numerator (8) by the denominator (10):
8/10 = 0.8Then, add the integer part (2) to the result:
2 + 0.8 = 2.8Therefore, the decimal representation of 2 8/10 is 2.8.
Identify each output value for the given input value if the rule of the table is to add -6.
Answers
The output values from the rule are -12, 2, 0, -6 and -10
How to determine the output valuesFrom the question, we have the following parameters that can be used in our computation:
Rule = add -6
This means that
Output = Input - 6
Using the values in the question, we have
Output = -6 - 6 = -12
Output = 8 - 6 = 2
Output = 6 - 6 = 0
Output = 0 - 6 = -6
Output = -4 - 6 = -10
The above represent the output values
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PLEEEEEEEEEEEEEEEEEEEEEEASEEEEEEEEEEEEEEEEE HELP
Answers
Answer:
Step-by-step explanation: with what????????????????????
Answer:
theres no image?
Step-by-step explanation:
7x9=(7 × 10) - (7 × ▲) what is the value of the triangle
Answers
Answer: 1
Step-by-step explanation:
Very simple both of them have the same base is 7. And we know that the number is 7x9, so the triangle is 1 because when both numbers have the same base, we will subtract the other number to get the answer!
Which of the following is equal to O BIN 22 26 day √3√2?
Answers
Answer:
3√3?
Step-by-step explanation:
Two cars leave for a vacation at the same time.
The drivers estimate how far they can travel in the first few hours.
Car B starts downtown.
Meanwhile, Car A starts 100 miles closer, heading to the same destination.
The graph shows the motion of each car.
Their speeds can be compared by comparing the steepness of the graphed line.
Use the drop-down menus to complete the statements.
Answers
Car A is travelling at a faster rate than Car B because its line on the graph is steeper.
What justifies measuring average speed?Average Understanding speed will help you better comprehend the pace of a travel. The speed may occasionally change while traveling. Finding the average speed becomes crucial in this situation so that you can get an idea of how quickly the travel will be finished.
What are typical speeds and an illustration?Divide the overall distance traveled by the time period to find the average speed. An someone traveling at an average speed of 40 miles divided by 40 minutes, or 1 mile per minute, would be driving 20 miles north and then 20 miles south to arrive at the same location (60 mph)
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PLEASE ANSWER NOWWW!!!!!!!!
Answers
Answer:
d
Step-by-step explanation:
its 3 to the right and top and its not a negative number so we don't go left
Answer:
Graph A
Step-by-step explanation:
The equation indicates the line has a positive slope and a y-intercept of 0. The only graph that corresponds to those conditions is Graph A.
Write an equation of the line that passes through $\left(-1,\ 3\right)$ and is parallel to the line $y=-3x+2$ .
Answers
The equation of the line that passes through point (-1, 3) and parallel to line y = 3x + 2 is
y = 3x + 4How to find the line that passes through point point (-1, 3)As a parallel line part of the qualities include that the slopes of the lines are equal
The equation of line is y = 3x + 2
The slope intercept form of the form as
y = mx + c
where
m = slope
c = intercept
x = input variables
y = output variables
Line has slope, m = 3, a new parallel line of slope 3 passing through point (-1, 3)
(y - y₁) = m (x - x₁)
y - 3 = 3 (x - -1)
y = 3x + 1 + 3
y = 3x + 4
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Note: Enter your answer and show all the steps that you use to solve this problem in the space provided.
What is the expression in factored form?
x
2
+
13
x
+
42
Answers
X^2 +7x+6x+42
X(x+7)+6(x+7)
Please help me solve!
Answers
Answer:
so I think the anwerst it all jedi younglings
The answers I really need the answers to this assignment
Answers
Answer:
Step-by-step explanation:
answer for 1 & 2 & 3
Emmett's seventh grade class is going on a field trip to a history museum. There are x students and y teachers going on the trip. Tickets for students are $10 each and tickets for teachers are $20 each. The history museum gave the class 20% off as part of a group promotion.
Pick all the expressions that represent the total cost of the field trip.
Answers
Expressions that represent the total cost of the field trip is
0.8{10x + 20y}.
What is Expression?A mathematical expression is made up of numbers, variables, and functions (such as addition, subtraction, multiplication or division etc.)
It is possible to compare expressions and phrases. In English, a phrase by itself could contain an action, but it doesn't constitute a full sentence.
As instances of expressions and how they connect to word phrases, consider the following:
Example: 3 + 7
The phrase "the product of three and seven"
Cost of Ticket for each student cost = $10
Cost of Ticket for each Teacher cost = $20
Let the total students be x
and, total number of teacher will be y
Total cost= 10x + 20y
As museum gives 20 % rebate for promotion
So, now total cost will be {10x + 20y} - 20/100 {10x + 20y}
So the required Expression would be 0.8{10x + 20y}.
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Which transformation results in the function, I would also like a explanation on how to do this.
Answers
The transformation that is results in the given function is a horizontal shrink of scale factor 1/4.
Which transformation results in function g(x)?Remember that for a function f(x), we define a horizontal shrink of scale factor k as:
g(x) = f(x*1/k)
Here we know that:
f(x) =x^2
g(x)= f(4x) = (4x)^2
Then this is equivalent to an horizontal shrink of scale factor of 1/4
Then the scale factor is k = 1/4, and the correct option is A.
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A turtle is 26.2 meters from a pond when it starts crawling toward the pond. The turtle crawls straight toward the pond at a
constant rate of 3.5 meters per minute.
Which equation models the distance of the turtle from the pond? (Let q represent the turtle's distance, in meters, from the
pond and p represent the number of minutes since it started crawling toward the pond.)
A. g=26.2-3.5
B.q=26.2p+3.3
C.q=26.2p-3.5
D.q=26.2+3.5p
Answers
The equation which models the distance of the turtle from the pond is q = 26.2 + 3.5p. Option D. is the answer
How to determine which equation models the distance of the turtle from the pond?
Given that:
A turtle is 26.2 meters from a pond when it starts crawling toward the pond
The turtle crawls straight toward the pond at a constant rate of 3.5 meters per minute
q represents the turtle's distance, in meters, from the pond and p represents the number of minutes since it started crawling toward the pond
The linear equation is of the form y = mx + c
where m is the rate of change and c is the starting point or y-intercept
m = 3.5 meters per minute, c = 26.2 meters
y = q ( turtle's distance) and x = p (number of minutes)
Thus, the equation models the distance will be:
q = 26.2 + 3.5p
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Omari buys a computer for $1,099. He
makes a down payment of 20%. His monthly
payments for the computer are $144. How
many months will it take Omari to finish
paying off the computer?
Answers
It will take 6 months for Omari to finish paying off the monthly payment for the computer.
What is the monthly payment?
The amount paid each month to repay the loan over the course of the loan is known as the monthly payment. When a loan is taken out, not only the principal, or the original lent amount, but also the interest that accrues, must be repaid.
Given, the total price of the computer = $1,099
down payment = 20% of $1,099 = $219.8
The remaining amount = $1,099 - $219.8 = $879.2
monthly payments for the computer = $144
Then, the total months to pay = 879.2/144 = 6 months
Hence, it will take 6 months for Omari to finish paying off the monthly payment for the computer.
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Please help me!At the beginning of spring, Jin planted a small sunflower in his backyard. The sunflower's height in inches, hh, after ww weeks, is given by the equation h=18+2.5wh=18+2.5w. What could the number 18 represent in the equation?
Answers
Answer:
The equation of the sunflower's height is h = 18+2.5w
Since the number 18 remains constant regardless of the change in number of weeks, we know that at the start h (w=0) = 18 + 2.5 x 0.
This means that, when Jin planted the sunflower, the sunflower's height was already 18 inches.
For such a reason, we can conclude that the number 18 could represent the sunflower's height at the start (original height).
--
Have a nice day!!
-2x+4y=17 + 3x-10y=-3
Answers
The values of x and y are -49/4 and -15/8 respectively for the given set of equations -2x + 4y = 17 and 3x - 10y = -3.
What is an equation?An equation is a combination of different variables, in which two mathematical expressions are equal to each other.
The given pair of equations,
-2x + 4y = 17 (1)
3x - 10y = -3 (2)
Multiply equation (1) with 3 and equation (2) with 2
-6x + 12y = 51 (3)
6x - 20y = -6 (4)
Add equation (3) and (4),
- 8y = 15
y = -15/8
Substitute the value of y in equation (1)
-2x + 4 (-15/8) = 17
-2x - 15/2 = 17
-2x = 49/2
x = - 49/4
The values of x and y for the given equations are -49/4 and -15/8 respectively.
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For the given equation the value of x and y will be 15/4 and 17/8 respectively
What is the equation?An equation is a statement that two expressions, which include variables and/or numbers, are equal. In essence, equations are questions, and efforts to systematically find solutions to these questions have been the driving forces behind the creation of mathematics.
It is given that, the equations are,
-2x+4y=17 -------(1)
3x-10y= -3
The value of x from equation 1 is,
-2x+4y=17
x=(17-4y)/2 -------(2)
Substitute the value of x in equation 2,
3x-10y=-3
3(17-4y)/2-10y= -3
y=17/8
The value of x is obtained as,
x=15/4
Thus, for the given equation the value of x and y will be 15/4 and 17/8 respectively
The question is incomplete the complete question is"solve the linear equation -2x+4y=17, 3x-10y=-3
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I need help on this question.
What is m
Answers
If so then..,
6x+10x+4x=180
20x=180
x=9
6x
6xX
6x9=54
4x
4xX
4x9=36
10x
10xX
10x9=90
Hope this helps
5 times the sum of a number and -2 equals 30
Answers
Answer: 5(x+-2) = 30
Step-by-step explanation:
Answer:
x=8
Step-by-step explanation:
5(x+(-2))=30
5x-10=30
+10 +10
5x=40
/5. /5
x=8
Hopes this helps please mark brainliest
What is the distance between the points (12 , -16) and (-10 , -16) in the coordinate plane?
Answers
Answer:
22
Step-by-step explanation:
Things To Keep In Mind:
(X, Y)
(12, -16) and (-10, -16) have the same Y, which means to find the distance all you have to do is subtract the Xs.
12 - -10
12 + 10
22
If there are any problems in this answer please tell me, thanks :)
Ron did not pay his credit card bill in full last month. He wants to pay it in full this month. On this month's bill, there is a mistake in the average daily balance. The
credit card company lists the average daily balance on his bill as $510.50. Ron computed it himself and found that it is $410.50.
a. The APR is 18%. What finance charge did the credit card company compute on Ron's bill?
b. If Ron's average daily balance is correct, what should the finance charge be?
Answers
The credit card company calculated a finance charge of $7.66 on Ron's bill if the annual percentage rate is 18%.
What is finance charges?A finance charge is any fee that represents the cost of credit or borrowing. It is the interest and fees charged for certain types of credit. It includes not only interest but also other charges like financial transaction fees.A financing charge is, to put it simply, any fee incurred when using credit. A finance charge is the total of all fees that are imposed incidentally to the extension of credit by the creditor and are paid directly or indirectly by the person to whom credit is extended, according to the Truth in Lending Act's legal definition.Your monthly statement from your credit card company will include a list of all finance charges in addition to your purchases and payments. Your card issuer will determine how your finance fee appears on your statement.The finance charge is the product of the average daily balance and the monthly percentage rate.
The annual percentage rate (APR) is 18% or 0.18.
$510.50× 0.18 / 12 =$7.66
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4 candy bars and 6 drinks cost $8.50. Which equation describes this situation if c equals
candy bars and d is drinks?
O4c+d=8.50
O4c+6d=8.50
O8d-8.50*
O6c+4d=8.50
Answers
Answer:
04c+06d=$8.50
Step-by-step explanation:
Kenji and his theater group are putting on a play. They need to make $373.50 to cover the
costs of the props and costumes. If they charge $4.50 for each ticket, how many tickets do
they need to sell to cover their costs?
Answers
Answer: 83 on the dot
Step-by-step explanation:83x4.50=373.50
the area of an equilateral triangle ABC is 50 cm² find AB
Answers
Answer:
Step-by-step explanation:
Length of side AB=a=10.75cm