Answer:
Total length of the biking trail is 14 units
Step-by-step explanation:
The trail starts from point P(-3, 2) and touches points Q(1, 2), R(1, -1) and S(8, -1).
We have to calculate the total length of the biking trail.
Since distance between two points are represented by
d = [tex]\sqrt{(x-x')^{2}+(y-y')^{2}}[/tex]
So length of PQ = [tex]\sqrt{(1+3)^{2}+(2-2)^{2}}[/tex]
PQ = [tex]\sqrt{(4)^{2}}[/tex]
PQ = 4 units
QR = [tex]\sqrt{(1-1)^{2}+(2+1)^{2}}[/tex]
QR = [tex]\sqrt{(3)^{2}}[/tex]
QR = 3 units
RS = [tex]\sqrt{(8-1)^{2}+(-1+1)^{2}}[/tex]
RS = [tex]\sqrt{(7)^{2}}[/tex]
RS = 7 units
Now total biking trail = PQ + QR + RS
= 4 + 3 + 7
= 14 units
Total length of the biking trail is 14 units
Answer:
The answer is 14 units
Step-by-step explanation:
A math teacher gave her class two tests. 76% of the class passed the first test. 58% of the class passed both tests. What is the approximate probability that a student who passed the second test, given that he passed the first test.
A rug is shaped like a rectangle who's per Perimeter there's 192 feet the length is five times longer with find the length and the width
Why does a calculator return an error when trying to find inverse sine of 1.055?
Answer:
1.055 is outside the domain of the sine function.
Step-by-step explanation:
When we are taking the inverse sine, we are finding an angle that gives a value of 1.055.
The sine function NEVER gives a value greater than 1 or less than -1. The domain of the sine function is between -1 and 1, inclusive.
So wanting to know which angle gives a sine value of 1.055 is futile. Sine can never be greater than 1.
That's why the calculator gives an error, because 1.055 is outside the domain of the sine function.
You have learned about special right triangles. Using that knowledge, you decide to take a square cake with 10-inch sides and divide it diagonally to form two special right triangles. Find and explain how you know the exact (no decimals) measure of the hypotenuse.
Now find the exact diagonal measure of cakes that are an 8-inch square, a 12-inch square, and a 15-inch square.
Did you discover a shortcut that works with any square cake? Explain.
Please show your work
The hypotenuse of a right triangle formed by dividing a square cake diagonally can be found using the Pythagorean Theorem, with the shortcut that the hypotenuse is the side length of the square multiplied by √2. Examples include a hypotenuse of 10√2 inches for a 10-inch square, 8√2 inches for an 8-inch square, 12√2 inches for a 12-inch square, and 15√2 inches for a 15-inch square.
Finding the Hypotenuse of Right Triangles in Squares
To find the length of the hypotenuse in a right triangle that is formed by dividing a square cake diagonally, we use the Pythagorean Theorem which states that for a right triangle with sides a and b and hypotenuse c, the relation is c = √(a ² + b ²). Since the sides of the square are equal in length, for a square with 10-inch sides, the hypotenuse will be √(10 inches ² + 10 inches ²) = √(100 + 100) = √200 inches = 10√2 inches.
For the other square cakes:
8-inch square: Hypotenuse = √(64 + 64) = 8√2 inches
12-inch square: Hypotenuse = √(144 + 144) = 12√2 inches
15-inch square: Hypotenuse = √(225 + 225) = 15√2 inches
The shortcut discovered is that the length of the hypotenuse is always the side length of the square multiplied by √2, because each side of the square forms a right triangle with equal sides when the square is divided diagonally.
A bus traveled on a level road for 4 hours at an average speed of 20 miles per hour faster than it traveled on a winding road. The time spent on the winding road was 5 hours. Find the average speed on the level road if the entire trip was 449 miles.
To solve this problem, we must recall that the formula for velocity assuming linear motion:
v = d / t
Where,
v = velocity
d = distance
t = time
For condition 1: bus travelling on a level road
v1 = d1 / t1
(v2 + 20) = (449 – d2) / 4 --->1
For condition 2: bus travelling on a winding road
v2 = d2 / t2
v2 = d2 / 5 --->2
Combining equations 1 and 2:
(d2 / 5) + 20 = (449 – d2) / 4
0.8 d2 + 80 = 449 – d2
1.8 d2 = 369
d2 = 205 miles
Using equation 2, find for v2:
v2 = 205 / 5
v2 = 41 mph
Since v1 = v2 + 20
v1 = 41 + 20
v1 = 61 mph
Therefore the average speed on the level road is 61 mph.
A medical plan requires a patient to pay a $25.00 copay plus 20% of all charges incurred for a medical procedure. If the average bill for a patient is between $200 and $800, find the range of the original bill.
How many four-digit even numbers are possible if the leftmost digit cannot be zero
There are 4500 four-digit even numbers possible when the leftmost digit cannot be a zero.
Explanation:The question is about finding out the number of four-digit even numbers possible given that the first or leftmost digit cannot be a zero. In a four-digit even number, the last digit (rightmost) should be an even number, i.e., 0, 2, 4, 6, or 8. Hence, there are 5 possibilities for the last digit.
Next, since the leftmost digit cannot be a zero, it leaves us with 9 possibilities (1-9). Lastly, the middle two digits can be any digit from 0 to 9, so there are 10 possibilities each for the second and third digits.
Therefore, the total number of four-digit even numbers under the given conditions is found by multiplying these possibilities: 9 (for the first digit) * 10 (for the second digit) * 10 (for the third digit) * 5 (for the last digit) = 4500.
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To find the number of four-digit even numbers where the leftmost digit cannot be zero, there are 9000 possibilities.
Explanation:To find the number of four-digit even numbers where the leftmost digit cannot be zero, we need to consider the following:
Choose the digit for the leftmost position (excluding zero). This can be done in 9 ways.Choose the digits for the other three positions (including zero for even numbers) in 10 ways each (0-9).By multiplying the number of choices for each position, we get the total number of four-digit even numbers without leading zeros: 9 * 10 * 10 * 10 = 9000.
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What's the answer to the equation;
√2y+3=11
Translate this sentence into an equation; 14 less than Julie's score is 62. Use the variable m to represent Julie's score.
a car dealership has 55 cars and 11 vans.what is the ratio of cars to vans? wriiten as a fraction in simplest form?
Evaluate the limit, if it exists. (if an answer does not exist, enter dne.) lim h→0 (5 + h)−1 − 5−1 h
PLEASE help me...Suck at math. find the following using the given triangle.
A(-3, 9) and B(5, 9) are the endpoints of the diameter of a circle. Use these points to find the standard equation of the circle.
What is the probability that a fair die never comes up an even number when it is rolled six times? (note: enter the value of probability in decimal format and round it to three decimal places.)?
A small company repairs home computers. In the past 200 days, it has been quite busy, taking in and repairing 2 computers on 52 of those days; 3 computers on 84 of those days; 4 computers on 40 of those days; and 5 computers on 24 of those days. Build a probability distribution for the number of computers repaired on any given day, show it is a valid distribution, and calculate its mean and variance.
how many miles can you drive with 13.2 gallons of gasoline
Keeping in mind that a functions rate of change is measure of how fast the function is increasing or decreasing what does the slope of a linear function indicate?
Answer: A linear function is represented as a straight line. The slope of the line gives the function’s rate of change.
Step-by-step explanation: Plato sample answer
Mike is taking a social studies test. mike was only able to finish 1/6 of the test in 1/2 an hour. How long will it take him to finish the test.
1/6 = 1/2 hr
2/6 = 1 hr
6/6-1/6 = 5/6 left of the test
2/6 + 2/6 = 4/6 = 2 hours
4/6 + 1/6 = 2 + 1/2 = 2 1/2
so 2 1/2 more hours
What is the height of a cylinder with a volume of 315 pi cubic meters and a radius of 6 meters? 8.75 meters 12.25 meters 26.25 meters 52.5 meters
Since this cylinder has a radius of 6 meters, its height is equal to 8.75 meters.
Given the following data:
Radius of cylinder = 6 m.
Volume of cylinder = 315π m.
How to calculate the height of this cylinder?Mathematically, the volume of a cylinder is calculated by using this formula:
V = πr²h
Where:
h is the height.r is the radius.Substituting the given parameters into the formula, we have;
315π = π × 6² × h
315π = 36πh
h = 315/36
Height, h = 8.75 meters.
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The course for a walkathon is 6 miles long. If Chloe wants to walk 50 miles during the walkathon, how many times must she walk the course?
divide 50 by 6
50/6 = 8.333
so she has to walk it 8.33 times
round answer as needed.
Your employer offers you a choice of wage scales: a monthly salary of $2800 plus commission of 8% of sales or a salary of $3300 plus a 6% commission. At what sales level would the options yield the same salary?
At the 25,000 salary scale, the options yield will be the same salary the answer is 25,000.
What is percentage?It's the ratio of two integers stated as a fraction of a hundred parts. It is a metric for comparing two sets of data, and it is expressed as a percentage using the percent symbol.
We have:
Your employer offers you a choice of wage scales:
A monthly salary of $2800 plus a commission of 8% of sales or
A salary of $3300 plus a 6% commission.
First choice of wage scale:
= 2800 + 0.08s
Second choice of wage scale:
= 3300 + 0.06s
2800 + 0.08s = 3300 + 0.06s
0.08s - 0.06s = 3300 - 2800
0.02s = 500
s = 25,000
Thus, at the 25,000 salary scale, the options yield will be the same salary the answer is 25,000.
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Atmospheric pressure decreases by about 11.8% for every 1000 meters you climb. The pressure at sea level is 1013 millibars (a unit of pressure). Construct an exponential model to represent the atmospheric pressure at a given altitude in thousands of meters. Use your model to determine the atmospheric pressure at an altitude of 4000 meters.
(Express your answer in millibars rounded correctly to the nearest tenth.)
write each fraction as a sum or difference
2m-5/9
Evaluate the integral. (3 + 1/4 u^4 − 2/3 u^9) du
Two identical twins can only be distinguished by the characteristic that one always tells the truth and the other always lies. One twin tells you of a lucky number pair: "When I multiply my first lucky number by 3 and my second lucky number by 6, the addition of the resulting numbers produce a sum of 12. When I add my first lucky number and twice my second lucky number, the sum is 5." Which twin is talking? How do you know?
The axis of symmetry for a quadratic equation can be found using the formula x =-b/2a , where a and b are coefficients in the quadratic equation and x represents the values along a vertical line on the coordinate plane. When the equation is solved for a, such that b is the numerator of the resulting fraction, what is the denominator of the fraction?
2x
–2x
1/2x
–1/2x
The answer is B on edgen.
What statement regarding the diagram is true?
Drag the tiles to the correct boxes to complete the pairs. A team of 10 players is to be selected from a class of 6 girls and 7 boys. Match each scenario to its probability.
Answer:
Here you go!
Step-by-step explanation:
a triangular prism has height of 10cm and a base area of 12cm. a rectangular prism has height of 10cm and base dimensions of 3 cm and 4 cm. do the solids have the same volume?
Matthew currently has enough money to buy 45 toy cars. If the cost of each car was 10 cents less, Matthew could buy 5 more cars. How much money does Matthew have to spend on toy cars?