t = time to hike up the hill
3-t is the time to hike down the hill
so 4t = 6(3-t)
4t = 18-6t
10t = 18
t = 18/10 = 1.8 hours to hike up the hill
1.8 hours = 1 hour 48 minutes
Answer:
The time it took him to climb up the hill is 1.8 hours.
Step-by-step explanation:
Here, t represents the the time it took him to climb up the hill,
Total time taken by it = 3 hours,
Thus, the time taken by it to climb down the hill = ( 3 - t ) hours.
Since, Trent hikes up a hill at 4 km/h,
⇒ Total distance covered by it to climb up = 4 t (Distance = Speed × Time)
Since, Trent go down a hill at 6 km/h,
⇒ Total distance covered by it to go down = 6(3-t)
We know that,
Total distance covered by it to climb up = Total distance covered by it to go down
⇒ 4t = 6(3-t)
Which is the required equation.
⇒ 4t = 18 - 6t
⇒ 10 t = 18
⇒ t = 1.8
Hence, the time it took him to climb up the hill is 1.8 hours.
janet's recipe calls for 6/8 cup of milk. what is this fraction in simplest form?
2/4
2/3
3/4
1/3
Can someone help me with this? Please look at the top, write it in standard form.
Algebraic Expressions Question
A company charges $59.99 for cable TV installation and $49.99 per month for basic cable service.
Part A
Write an algebraic expression to represent the total cost of m months of basic cable service, including installation.
Algebraic Expression: ________________
Part B
How much will it cost for installation and one year of basic cable service?
Explain:
Total Cost: ______________
This problem is continued on the next page.
Part C
After the first 12 months, the charge will be increased to $69.95 per month. What is the total cost of installation and basic cable service for the first two years?
Explain:
Part A.
We can create a linear equation from this problem. Let us say that C is total cost and m is number of months, therefore:
C = 59.99 + 49.99 m
Part B. For m = 12 months, the total cost is:
C = 59.99 + 49.99 * 12
C = $659.87
Part C. We have already calculated in part B the total cost for the 1st year:
C1 = $659.87
For the 2nd year, the equation becomes:
C = 59.99 + 69.95 m
C = 59.99 + 69.95 * 12
C2 = $899.39
Therefore the total cost C1 + C2 is:
$1,559.26
The total cost of m months of basic cable service, including installation, can be represented by the algebraic expression 59.99 + 49.99m. For installation and one year of basic cable service, the cost is 659.87. For the first two years, including installation and basic cable service, the cost is 1549.23.
Explanation:Part A:
To represent the total cost of m months of basic cable service, including installation, we can use the algebraic expression:
59.99 + 49.99m
Part B:
To calculate the total cost for installation and one year of basic cable service, we substitute 12 for m in the expression:
59.99 + 49.99(12) = 59.99 + 599.88 = 659.87
Part C:
For the first two years, the cost includes the installation and basic cable service for the first 12 months at $49.99 per month, and the following 12 months at $69.95 per month. So we write the expression as:
59.99 + 49.99(12) + 69.95(12) = 709.83 + 839.4 = 1549.23
Sofia wants to place a sticker 2 ½ inches long in the center of a switch box that is 3 ¾ inches wide. About how far from the edge will she place the sticker?
Please help
Which graph represents the function f(x) = −|x − 2| − 1?
The correct answer is C.
Thanks and have a good day :)
Can someone help me with these questions
Find the coordinates of the points of intersection of the graphs with coordinate axes: y=−1.5x+3
The coordinates for the points of intersection of the line y=-1.5x + 3 with the coordinate axes are (0,3) for y-axis and (2,0) for the x-axis.
Explanation:To find the points of intersection of the line with the coordinate axes, we will set the values of y and x to zero separately. So, let's start from the intersection of the line with the y-axis. For this, we set x=0 in the equation y = -1.5x + 3. Thus, y = 0*(-1.5) + 3 which gives us y = 3. So one point of intersection is (0,3). Next, finding the x-intercept requires setting y=0, which gives 0 = -1.5x + 3. Solving this equation, we get x = 3 / 1.5 or x=2. Hence, the other point of intersection is (2,0). Therefore, the coordinates for the points of intersections are (0,3) and (2,0).
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improper fraction of 1 7/8
WILL GIVE BRAINLIEST!
Simplify and express the answer as a decimal.
3(2.7+5)−23(2.7+5)−2
Enter your answer in the box.
The simplified expression is -202.2, which can be expressed as a decimal as -202.2.
Explanation:To simplify the expression, we need to perform the operations in order of operations (PEMDAS/BODMAS). First, we simplify the expressions inside the parentheses:
2.7 + 5 = 7.7
Next, we can rewrite the expression:
3(7.7) - 23(7.7) - 2
Now, we can multiply each term:
3 * 7.7 = 23.1
23 * 7.7 = 177.1
-23.1 - 177.1 - 2
Finally, we can combine like terms:
-202.2
The simplified expression is -202.2, which can be expressed as a decimal as -202.2.
Final answer:
To simplify the expression 3(2.7+5)−23(2.7+5)−2, we first evaluate the addition inside the parentheses and then perform the multiplication and subtraction step by step to get the final simplified answer as -156.
Explanation:
To simplify the expression 3(2.7+5)−23(2.7+5)−2, we first evaluate the addition inside the parentheses: 2.7+5 = 7.7.
Substituting this value back into the expression, we get 3(7.7) - 23(7.7) - 2.
Next, we perform the multiplication: 3(7.7) = 23.1 and 23(7.7) = 177.1.
Substituting these values back into the expression, we have 23.1 - 177.1 - 2.
Finally, we perform the subtraction: 23.1 - 177.1 = -154 and -154 - 2 = -156.
Therefore, the simplified answer as a decimal is -156.
A store manager realizes that he has too many jeans in stock. After he finished taking inventory, he has a total of 688 jeans. He decides to reduce the stock by having a buy one get one free sale. That means that every purchase will reduce this inventory by 2 pairs of jeans.
The expression below describes this situation.
688−2x
A. What does the expression represent?
A. the number of jeans sold with each purchase
B. the number of jeans the stock is reduced by from each sale
C. the total amount of jeans in stock after each sale
D. the number of jeans purchased
Answer:
Remaining amount of jeans after x sales = 688 - 2x
In this expression
2x = The number of jeans purchased.
-2 = The number of jeans the stock is reduced by from each sale.
2 = The number of jeans sold with each purchase.
Step-by-step explanation:
Given information:
Total number of jeans = 688
He decides to reduce the stock by having a buy one get one free sale. It means that every purchase will reduce this inventory by 2 pairs of jeans.
Average rate of change = -2
Let x be the number of purchase.
So, the total amount of jeans in stock after each sale is
Remaining amount of jeans after x sales = 688 - 2x
In this expression
2x = The number of jeans purchased
-2 = The number of jeans the stock is reduced by from each sale.
2 = The number of jeans sold with each purchase
fill in the blanks.
principal: $450
rate: ?
time: 3 years
interest earned: 67.50
new balance: ?
To find the missing rate and new balance, we used the simple interest formula. The rate was calculated to be 5% and the new balance after 3 years, including interest earned, was determined to be $517.50.
The subject in question here is simple interest calculation, which is a fundamental concept in finance and mathematic subjects. To solve for the missing rate and new balance, we can use the formula Interest = Principal x rate x time.
Principal: $450Rate: ? (We will solve for this)Time: 3 yearsInterest Earned: $67.50New Balance: ? (We will solve for this too)First, we rearrange the interest formula to solve for the rate:
Rate = Interest / (Principal x Time)
Plugging in the provided numbers:
Rate = $67.50 / ($450 x 3)
Rate = $67.50 / $1350
Rate = 0.05 or 5%
Now, we find the new balance using the formula:
New Balance = Principal + Interest
New Balance = $450 + $67.50
New Balance = $517.50
Therefore, the interest rate is 5% and the new balance after 3 years is $517.50.
Jamal hiked on two trails . the First trail was 5 1/3 miles long and the second trail was 1 3/4 times as long as the first.how many miles did jamal hiked?
In May 2009, exactly 20,336 tent campers stayed at Grand Canyon National Park. What was the average number of campers per day in May? (May has 31 days.)
Frank goes grocery shopping every 9 days Susan does her grocery shopping every sixth day the went shopping today and we're able to car pool how many days will pass before they can car pool again
The scatterplot and trend line show a positive correlation between advertising costs and sales. The slope was found using the points (6.4, 117) and (6.6, 120). What is the value of b in the equation of the trend line? y = 15x + b
The value of b in the equation of the trend line is 21
The equation of the trend line of the scatter plot is given as:
y = 15x + b
The points are given as: (6.4, 117) and (6.6, 120).
Using (6.4, 117), we have:
117 = 15 * 6.4 + b
Evaluate the products
117 = 96 + b
Subtract 96 from both sides
21 = b
Rewrite as:
b =21
Hence, the value of b in the equation of the trend line is 21
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Which absolute value function defines this graph?
Answer:
A. [tex]f(x)=-4|x+2|+3[/tex]
Step-by-step explanation:
We have been given an image of an absolute function. We are asked to find the formula for our given absolute function.
The formula of parent absolute function is [tex]f(x)=|x|[/tex] with vertex at (0,0)
We can see that the vertex of our given function is at [tex](-2,3)[/tex]. This means that our function is shifted to left by 2 units. We can represent this information as: [tex]f(x)=|x--2|=|x+2|[/tex]
We can also see that our graph is reflected across x-axis, so after reflection our function would be [tex]f(x)=-|x+2|[/tex]
We can see that our graph is shifted upwards by 3 units, so graph after shifting would be [tex]f(x)=-|x+2|+3[/tex].
Our graph is stretched vertically by a scale factor of 4, so after stretching our function would be [tex]f(x)=-4|x+2|+3[/tex].
Therefore, option A is the correct choice.
what is hundred-seventy as a fraction.
To convert 175% to a fraction, write it as 175/100 and then simplify by dividing both numerator and denominator by their greatest common divisor, 25, which gives a simplified fraction of 7/4.
One hundred seventy five percent as a fraction can be converted by writing the value of the percent as a fraction with a denominator of 100. To convert the percent to a fraction, we write 175% as 175/100. This fraction can then be simplified. To simplify, we can divide both the numerator and the denominator by their greatest common divisor, which is 25.
Here is the step-by-step simplification process:
Write 175% as a fraction: 175/100
Divide both the numerator and the denominator by 25: (175 ÷ 25) / (100 ÷ 25) = 7/4
The simplified fraction for 175% is therefore 7/4.
complete question given below:
What is one hundred seventy five percent as a fraction?
There are 7.2 milligrams of iron in a dozen eggs.Because there are 12eggs in a dozen,how many milligrams of iron are in 1egg?
-9(-4w^3+4-3v^2) i need the answer
ILL GIVE YOU 12 POINTS
How many pounds are in 9 kilograms?
Negative K over five equals seven over five
What is an equation of the line that is perpendicular to y + 1 = - 3 (x - 5) and passes through the point (4, -6)?
The equation of the line that is perpendicular to y + 1 = -3 (x - 5) and passes through the point (4, -6) is y = 1/3x - 22/3.
Explanation:
The subject of this question is Mathematics, specifically the topic of linear equations.
The line given in the question is y + 1 = -3 (x - 5). To find the equation of a line that is perpendicular to this given line and passes through the point (4, -6), we need to understand the concept of slope.
The equation of the given line can be rewritten as y = -3x + 15 -1, or y = -3x + 14. The slope of a line perpendicular to this line would be the negative reciprocal of -3, which is 1/3. Then, by using the point-slope form of a line, (y - y1) = m (x - x1), where m is the slope and (x1, y1) is the point through which the line passes (in this case, (4, -6)), we get: y - (-6) = 1/3 (x - 4) or y + 6 = 1/3x - 4/3.Simplifying, the equation of the perpendicular line is y = 1/3x - 4/3 - 6 or y = 1/3x - 22/3.
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If f(x) = –4x + 3 and g(x) = 3x2 + 2x – 4, find (f + g)(x).
A. (f + g)(x) = –2x – 1
B. (f + g)(x) = 3x2 + 6x + 7
C. (f + g)(x) = 3x2 – 2x – 1
D. (f + g)(x) = 4x – 1
Answer:
Correct option is:
C. (f + g)(x) = 3x² – 2x – 1
Step-by-step explanation:
f(x) = –4x + 3 and g(x) = 3x² + 2x – 4
We have to find (f + g)(x).
We know that (f+g)(x)=f(x)+g(x)
⇒ (f+g)(x)=-4x+3+3x²+2x-4
⇒ (f+g)(x)=3x²-2x-1
Hence, Correct option is:
C. (f + g)(x) = 3x² – 2x – 1
use the distributive property to simplify -5(-2f-6)
-5(-2f-6)
distribute by multiplying -5 by everything inside the parenthesis
-5 * -2f = 10f
-5 *-6 = 30
so you get 10f+30
The heaviest ball made by a bowling ball company weighs 16 pounds. Last week, the company shipped 10,000 of these balls. What was the total weight of these balls. Multiply 16 by 1 to find the weight of 1 of these balls. 16 x 1 = ____ ones = ____
Seema used compatible numbers to estimate the product of (–25.31)(9.61). What was her estimate? –250 –240 240 250
Answer:
-250
Step-by-step explanation:
Answer: yeah it's -250
Step-by-step explanation: just submitted the test
Points A(−1.5) and B(6) are marked on a number line. Find the coordinate of point M if it is known that AM:MB=1:2. Find all possible answers.
Final answer:
By adding the distance from A to M to A's coordinate, we find that M's coordinate is 1.
Explanation:
The question asks to find the coordinate of point M on a number line where point A has a coordinate of −1.5, point B has a coordinate of 6, and the ratio of the distances AM to MB is 1:2. To solve this, we first identify that AM and MB are segments on the number line with point M somewhere between A and B. Since AM:MB = 1:2, we know that for every unit distance from A to M, there are 2 unit distances from M to B.
The total distance between A and B is 6 - (−1.5) = 7.5 units. Dividing this distance in the ratio 1:2, implies that AM takes up one-third of the total distance and MB takes up two-thirds of the total distance. Therefore, AM = ¼ * 7.5 = 2.5 units. Adding this distance to the coordinate of A gives us the coordinate for M: −1.5 + 2.5 = 1. So, the coordinate of point M is 1.
sam is trying to lose weight and George is trying to gain weight. Sam's weight in pounds can be represented by the function f(x) = 240 - 2x, where x is the number of weeks since Sam started losing weight. Georges weight in pounds can be represented by the function g(x) = 180 + 4x, where x is the number of weeks since George started gaining weight.
What are the answers for the questions and can you check if I got the other one right please and thank you