The equestrian's father will catch up to her at 2:00 pm by using the concept of relative speed and calculating the time it will take for him to close the gap between them.
Explanation:The student's father will catch up to the equestrian at 2:00 pm. To solve this problem, we can use the concept of relative speed. The equestrian starts riding away from the house at 10 miles per hour (mph) at 10:00 am. By noon, when the father starts chasing her on his scooter at 15 mph, the equestrian is already 20 miles away (2 hours × 10 mph).
Since the father's speed is 15 mph and the equestrian's speed is 10 mph, the father is closing the gap at a speed of 15 mph - 10 mph = 5 mph. To cover the 20 miles gap, the father will need 20 miles / 5 mph = 4 hours. Therefore, if the father starts at noon, he will catch up to her at 4 hours later, which is 2:00 pm.
A climber is on a hike. After 2 hours he is at an altitude of 400 feet. After 6 hours, he is at an altitude of 700 feet.
What is the average rate of change?
A 75 feet per hour
B 200 feet per hour
C 116 feet per hour
D 100 feet per hour
the function p(t)=350e^-.2t represents the population of a city, in thousands, t years after 2010. determine the population of the city in 2014
1/5n -3/4 + 7/10n
Need to simplify
ABC has vertices A(0,6) B(4,6) C(1,3). Sketch a graph of ABC and use it to find the orthocenter of ABC. Then list the steps you took to find the orthocenter including any necessary points or slopes you had to derive.
To find the orthocenter of triangle ABC with vertices A(0,6), B(4,6), and C(1,3), one must plot the triangle, calculate the slopes of its sides, find the slopes and equations of the altitudes, and determine their intersection point, which is the orthocenter.
The question involves finding the orthocenter of the triangle ABC with vertices A(0,6), B(4,6), C(1,3). To find the orthocenter, we have to identify the altitudes of the triangle and find their point of intersection. Here are the steps:
Plot the points A(0,6), B(4,6), C(1,3) on the Cartesian coordinate system and draw the triangle ABC.Find the slopes of the sides of triangle ABC: The slope of AB is 0 (horizontal line), the slope of BC and AC can be found using the formula [tex](y_2 - y1) / (x_2 - x1)[/tex].Determine the slopes of the altitudes: The slope of an altitude is the negative reciprocal of the slope of the side it is perpendicular to.Find the equations of the lines representing the altitudes by using the point-slope form of the equation of a line, which involves a point on the line (vertex of the triangle) and the slope you've just found.Calculate the point of intersection of any two altitudes. The intersection point is the orthocenter of the triangle.Upon completing these steps, the point of intersection is the orthocenter of the triangle ABC.
Select the equation of the line that passes through the point (3, 5) and is perpendicular to the line x = 4.
y = 5
x = 5
y = 4
x = 3
Ashley's penny bank is 1/4 full. After she adds 400 pennies, it is 2/3 full. How many pennies can Ashley's bank hold?
I know the answer, but how to solve?
Working alone mona can paint a room in 4 hours. lisa can paint the exact same room in 3 hours. how long should it take to paint the room if they work together?
To find out how long it would take Mona and Lisa to paint the room together, we need to calculate their combined work rate. Mona can paint the room in 4 hours, so her work rate is 1/4 of the room per hour. Lisa can paint the room in 3 hours, so her work rate is 1/3 of the room per hour. Their combined work rate is 7/12 of the room per hour. Therefore, it would take them approximately 1 hour and 43 minutes to paint the room together.
Explanation:To find out how long it would take Mona and Lisa to paint the room together, we need to calculate their combined work rate. Mona can paint the room in 4 hours, so her work rate is 1/4 of the room per hour. Lisa can paint the room in 3 hours, so her work rate is 1/3 of the room per hour. To calculate their combined work rate, we add their individual work rates: 1/4 + 1/3 = 3/12 + 4/12 = 7/12 of the room per hour. Since they are working together, we can use their combined work rate to determine how long it would take to paint the entire room. The formula to calculate time is: Time = Work / Rate. In this case, the work is the entire room, which is 1, and the rate is 7/12 of the room per hour. Therefore, the time to paint the room when they work together is: Time = 1 / (7/12) = 12/7 hours, or approximately 1 hour and 43 minutes.
Write a real-world prblem in which you would need to convert pints to cups
For each function, what is the output of the given input?
For f(x) = 4x+7, find f(4)
Answer:
f(4)=23
Step-by-step explanation:
Plug 4 in to the function
f(4)=4(4)+7
f(4)=16+7
f(4)=23
Final answer: 23
You measure a piece of rope and find its length to be 13 m. Find the percent error of this measurement.
Convert 1.50 μm² to square meters.
what's is width of a rectangle with an area of 5/8 in and a length of ten inches
A dvd costs $20 the sales tax is 6.5% how much sales tax do you have to pay
Which equation, when graphed, has x-intercepts at (−1, 0) and (−5, 0) and a y-intercept at (0, −30)?
f(x) = −6(x + 1)(x + 5)
f(x) = −6(x − 1)(x − 5)
f(x) = −5(x + 1)(x + 5)
f(x) = −5(x − 1)(x − 5)
Answer:
Option A
Step-by-step explanation:
The equation has x intecepts at -1 and -5.
Hence function would be of the form
a(x+1)(x+5) for some real a.
To find a, let us use y intercept
When x =0 we have y =a(1)(5)
y intercept is given as -30
i.e. 5a = -30
a=-6
So
f(x) = -6(x+1)(x+5)
Option A is the right answer.
In 1992, jason bought a gallon of gas for $1.23. yesterday, he bought a gallon of gas for $2.19. what is the percentage increase of the price of a gallon of gas from 1992 to yesterday? if necessary, round to the nearest tenth of a percent.
Answer:
39.7
Step-by-step explanation:
why is a circle not a polygon
Let's first go over the definition of a polygon.
A polygon a figure formed by coplanar segments. The segments are called sides.
A circle is not considered a polygon because it's formed by a curve rather than line segments.
find three solutions of the equation y=2
A child takes a nap averaging three hours and gets an average of 12 hours of sleep at night. Nap time and night time sleep can each vary by 30 mins. What are the possible time lengths for the child's nap and night time sleep? ...?
Final answer:
The possible time lengths for the child's nap are 2.5 to 3.5 hours, and for night time sleep are 11.5 to 12.5 hours, as each can vary by up to 30 minutes.
Explanation:
The question asks about the possible time lengths for a child's nap and night time sleep, given that each can vary by 30 minutes. The average nap time is three hours, so the possible nap lengths range from 2.5 hours (3 hours - 30 minutes) to 3.5 hours (3 hours + 30 minutes). Similarly, the average night time sleep is 12 hours, meaning the possible night time sleep lengths range from 11.5 hours (12 hours - 30 minutes) to 12.5 hours (12 hours + 30 minutes).
The child's nap can be from 2.5 to 3.5 hours and night sleep from 11.5 to 12.5 hours, totaling a possible sleep range of 14 to 16 hours per day.
Explanation:The child's nap time can vary by 30 minutes from the average of 3 hours, meaning the possible lengths for nap time range from 2.5 hours to 3.5 hours. Similarly, the night time sleep also has a variability of 30 minutes from the average of 12 hours, which gives a range of 11.5 hours to 12.5 hours for night time sleep. Therefore, the possible lengths for the child's total sleep time can range from a minimum of 14 hours (2.5 hours nap + 11.5 hours night) to a maximum of 16 hours (3.5 hours nap + 12.5 hours night).
Which of the following are not congruence theorems for right triangles? Check all that apply.
A. LA
B. HL
C. AA
D. HA
E. HH
F. LL
Answer:
E. HH, C. AA
Step-by-step explanation:
Got these from the quiz
the table below represents the total number of laps jessica swam in the pool this summer.
week 1 18 laps week 2 28 laps week 3 38 laps week 4 48 laps
if the linear function representing the number of laps jessica swam each week is f(w)=10w+8. what does the 10 represent in this function?
In the function f(w) 10w+8, the number 10 represents the number of laps Jessica increased her swim by each week.
To find out what the coefficient 10 represents in the linear function f(w) = 10w + 8, we need to understand the structure of the function.
In this function:
- w represents the week of the summer.
- f(w) represents the number of laps Jessica swam in week w.
- The coefficient 10 is multiplied by w, indicating a relationship.
Since the linear function represents the number of laps Jessica swam each week, the coefficient 10 represents the number of laps Jessica increased her swim by each week.
So, the correct answer is: C. The number of laps Jessica increased her swim by each week
Complete question:
The table below represents the total number of laps Jessica swam in the pool this summer:
Week Laps
1 18
2 28
3 38
4 48
If the linear function representing the number of laps Jessica swam each week is f(w) 10w+8, what does the 10 represent in this function?
The number of laps Jessica swam in total
The week of the summer that Jessica swam
The number of laps Jessica Increased her swim by each week
A The number of laps Jessica swam in week
Factor the expression.
9x^2 + 48x + 64
What is the amount of sales tax owed on a $39 jacket if the tax rate is 5%?
A sample of carbon-12 has a mass of 6.00 g. How many atoms of carbon-12 are in the sample?
I have the answer but I don't understand how to solve it.
b+c=10/a
solve for a ...?
To solve the equation b + c = 10/a for a, isolate a on one side of the equation by multiplying both sides by a, distribute a to both terms inside the parentheses, and then solve for a by dividing both sides by (b + c).
Explanation:To solve the equation b + c = 10/a for a, we need to isolate a on one side of the equation. We can start by multiplying both sides of the equation by a to get rid of the denominator:
a(b + c) = 10
Next, we can distribute a to both terms inside the parentheses:
ab + ac = 10
Finally, we can solve for a by dividing both sides of the equation by (b + c):
a = 10 / (b + c)
Given that the hypotenuse of this right triangle is 25 cm long and that tan(θ) = 3find the values of x and y, accurate to the nearest tenth.
Answer:x ≈ 7.9; y ≈ 23.7
Step-by-step explanation:
The right triangle above you can use SOHCAHTOA and determine that tanθ =
y
x
. Replacing tanθ with 3 you get
3 =
y
x
3x = y
Then use the Pythagorean Theorem to
x2 + y2 = 252. Replace y with 3x
x2 + 9x2 = 625
10x2 = 625
x2 =
625
10
x =
25
10
= 7.9
Since,
y = 3x
y = 3(7.9) = 23.7
Kalon has $175 and needs to save at least $700 for a new computer. If he can save $35 per week, what is the minimum number of weeks Kalon will need to save to reach his goal?
A.10 weeks
B.12 weeks
C.15 weeks
D.20 weeks
8x + 2y= 10
Solve the equation for y ...?
HELP ASAP PLEASE!!!
In the past 3 years, Hannah’s savings account has earned $90 in interest. She initially deposited $600. What simple annual interest rate is the bank paying on this account?
A. 2.7%
B. 3.5%
C. 4.0%
D. 5.0%
Marge has 4 more than 2 times as many books as Susan. If Marge has 22 books and x is the number of books that Susan has, the relationship can be written as 4 + 2x = 22. How many books does Susan have?
8
9
10
11