A city is paving a bike path. The same length of path is paved everyday. After 4 days, there are 8 miles of path remaining to be paved. After 6 more days, there are 5 miles of path remaining to be paved.
a. Explain how you know the situation can be modeled by a linear equation.
b. Write an equation that gives the distance (in miles) as a function of the number of days since the project began.
c. In how many more days will the entire path be paved?
The linear equation is y = (-3/2)x + 14 and the number of days will be 10 days.
What is a linear equation?It is described as the relationship between two variables, and a straight line results from plotting the graph of the linear equation.
The equation is referred to as a linear equation in one variable if just one variable is contained in the linear equation.
It is given that:
A city is paving a bike path.
The same length of the path is paved every day. After 4 days, there are 8 miles of path remaining to be paved.
After 6 more days, there are 5 miles of path remaining to be paved.
The coordinates are (4, 8) and (6, 5)
The linear equation can be modeled:
[y - 5] = (5-8)/(6-4)[x-6]
y - 5 = -3/2[x - 6]
2y - 10 = -3x + 18
2y = -3x + 28
y = (-3/2)x + 14
Plug y = 0
(-3/2)x + 14 = 0
x = 28/3
x = 9.33 ≈ 10 days
Thus, the linear equation is y = (-3/2)x + 14 and the number of days will be 10 days.
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multiply (x+7) (x-7)
For which pairs of functions is (fOg)=12x
at a concession stand, five hotdogs and two hamburgers cost $11.50; two hot dogs and five hamburgers cost $13.00. find the cost of one hot dog and the cost of one hamburger.
As Mars revolves around the sun, it travels at a speed of approximately
15
miles per second. Convert this speed to miles per minute. At this speed, how many miles will Mars travel in
4
minutes? Do not round your answers.
Final answer:
To convert Mars' speed from 15 miles per second to miles per minute, multiply by 60 to get 900 miles per minute. Multiplying this by 4 gives the distance Mars will travel in 4 minutes, which is 3600 miles.
Explanation:
As Mars revolves around the sun, it travels at a speed of approximately 15 miles per second. To convert this speed to miles per minute, you simply multiply by the number of seconds in a minute:
15 miles/second × 60 seconds/minute = 900 miles per minute.
At this speed, to find out how many miles Mars will travel in 4 minutes, you multiply Mars' speed in miles per minute by the number of minutes:
900 miles/minute × 4 minutes = 3600 miles.
Therefore, Mars will travel 3600 miles in 4 minutes at the speed of 15 miles per second.
what transformation transforms (a,b) to ( a, -b)?
a) a translation of 1 unit down
b)a translation of 1 unit up
c)a reflection over the y-axis
d)a reflection over the x-axis
Which graph represents the solution set of the system of inequalities?
{3y≤2x+6
{ 2x+y>0 in one bracket
Make a table of ordered pairs for the equation.
y=−13x+4y=−13x+4
Then plot two points to graph the equation.
Solution-
The given equation,
[tex]y=-13x+4[/tex]
Then, we have to calculate two points that satisfy the equation,
Calculating y for x = 0,
[tex]y(0)=-13(0)+4=4[/tex]
So, point (0, 4) satisfies the equation.
Calculating y for x = 1,
[tex]y(1)=-13(1)+4=-13+4=-9[/tex]
So, point (1, -9) satisfies the equation.
Plotting the graph taking this two points, as shown in the attachment.
How can you equivalent ratio in order to compare ratios more precisely ?
What is 1,334 divided by 23? A) 53 B) 56 C) 57 D) 58
The answer is D 58
there 12 beads on the bracelet. 8 of the beads are purple. what percent of the beads are purple
There are 12 beads on the bracelet and 8 of the beads are purple. What percent of the beads are purple?
The fraction [tex]\frac{8}{12}[/tex] represents the number of purple beads on the bracelet out of all the beads on the bracelet.
To find what percent of the beads are purple, we can turn the fraction [tex]\frac{8}{12}[/tex] to a percent.
We can first reduce the fraction [tex]\frac{8}{12}[/tex] by dividing both the numerator and denominator by the Greatest Common Factor of 8 and 12 using 4.
8 ÷ 4 = 2
12 ÷ 4 = 3
Our reduced fraction is [tex]\frac{2}{3}[/tex]
2 ÷ 3 = 0.66666666666667
0.66666666666667 × 100 = 66.666666666667%
Therefore, 66.666666666667% of the beads on the bracelet are purple.
The temperature is 1 degrees Fahrenheit at dusk it is8 degrees colder at dawn what is the temperature at dawn ??
On a field trip there were 5 girls for every 8 boys. how many girls attended the 130-student field trip?
5. A map of Texas has the following scale.
1 cm = 50 km
The distance from Austin to Dallas measures 6 centimeters on the map. What is the actual distance ?
(1 point)
56 km
156 km
300 km
600 km
Answer; 300km .
Because 50x6 is 300.
Rebecca is at the zoo with her family. She sees 3 times as many elephants as cheetahs. There are 4 cheetahs. How many animals did she see all together?
Ava is 9 years old. Rose is 11 time as old as ava. How old is rose?
Is this graph discrete or continuous
WILL MARK BRANLIESTHELP ME PLZ
A jeweler needed two diamonds of exactly the same weight to make a ring. The first stone she selected weighed 0.642 carat, the second weighed 0.599 carat, and the third weighed 0.625 carat.
By how much did the heaviest stone outweigh the lightest?
0.043 carat
0.042 carat
0.041 carat
0.04 carat
Kaleb rode his bike at a rate of 10 mph for 2 hours. How far did he ride?
16 miles
20 miles
30 miles
36 miles
Please help me get this answer right
A crack in a water main pipe leaks 7 gallons of water each hour. What volume of water has moved though the crack after 9 hours?
Write a division story problem with 53 as the divisor and 2491 as the dividend
what does g-7=15 equal to?
Lydia makes 10 pancakes she tops each pancake with for blueberries how many blueberries does Lydia use in all use the break apart and distribute strategy and draw a number bond to solve
Multiplication is the process of multiplying, therefore, adding a number to itself for the number of times stated. The total number of blueberries that Lydia will need is 40 blueberries.
What is multiplication?Multiplication is the process of multiplying, therefore, adding a number to itself for the number of times stated. For example, 3 × 4 means 3 is added to itself 4 times, and vice versa for the other number.
Given that Lydia makes 10 pancakes she tops each pancake with blueberries. Therefore, the total number of blueberries that Lydia will need is,
Total number of blueberries
= Number of pancakes × Number of blueberries used on each pancake
= 10 pancakes × 4 blueberries per pancake
= 40 blueberries
As per the distribution strategy, we can draw 10 circles and then 4 mini circles on each circle to represent blueberries. Therefore, we can make the drawing as shown below.
Hence, the total number of blueberries that Lydia will need is 40 blueberries.
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Daniel's basic cell phone rate each month is $29.95. Add to that $5.95 for voice mail and $2.95 for text messaging. This past month Daniel spent an additional C dollars on long distance. His total bill was $62.35. How much did Daniel spend on long distance?
Answer: Daniel spent $23.5 on long distance
Step-by-step explanation:
Hi, to answer this question we have to write an equation with the information given.
So, Daniel's total bill (62.35) is equal to the sum of the cost of all the services: Basic cell phone rate (29.95); voice mail (5.95); text messaging (2.95); long distance (C)
Mathematically speaking:
29.95+5.95+2.95+C = 62.35
Solving for C
38.85+C =62.35
C =62.35-38.85
C =$23.5
Daniel spent $23.5 on long distance
what is the place value of the 8 in 0.829?
29,392.46
The 9 in the tens place is blank the value of the thousands place
Which expression is equivalent to the given expression? −(2n−6)
A)−2(n−3)
B)2(n−6)
C)2n−6
D) 2n + 6
Answer:
Option A [tex]-2(n-3)[/tex]
Step-by-step explanation:
we have
[tex]-(2n-6)[/tex]
Eliminate the parenthesis
[tex]-(2n-6)=-2n+6[/tex]
Verify each case
case A) [tex]-2(n-3)[/tex]
[tex]-2(n-3)=-2n+6[/tex]
therefore
[tex]-2n+6=-2n+6[/tex] -----> is true
case A is equivalent to the given expression
case B) [tex]2(n-6)[/tex]
[tex]2(n-6)=2n-12[/tex]
therefore
[tex]-2n+6\neq2n-12[/tex]
case B is not equivalent to the given expression
case C) [tex]2n-6[/tex]
we have that
[tex]-2n+6\neq2n-6[/tex]
therefore
case C is not equivalent to the given expression
case D) [tex]2n+6[/tex]
we have that
[tex]-2n+6\neq2n+6[/tex]
therefore
case D is not equivalent to the given expression
Which set of data could be used for the box-and-whisker plot shown below?
27, 35, 35, 32, 24, 34, 36, 27, 38
27, 35, 35, 32, 26, 32, 36, 27, 38
27, 35, 35, 32, 25, 34, 36, 27, 38
27, 35, 35, 32, 26, 34, 36, 27, 38
The dataset that can be used for box-and-whisker plot is 27, 35, 35, 32, 26, 34, 36, 27, 38.
What is the data set?A box plot is used to study the distribution and level of a set of scores. The whiskers represent the minimum value and the maximum value.
On the box, the first line to the left represents the lower (first) quartile. The next line on the box represents the median. The third line on the box represents the upper (third) quartile.
Minimum value = 26
Maximum value = 38
Q1 = 27
Median = 34
Q3 = 35
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Ribbon ones are made from strips of ribbon tied to sticks Connie has 84 feet of red ribbon 48 feet of blue ribbon and 72 feet of white ribbon she wants to cut the ribbon into equal links that are as long as possible so that no ribbon is wasted