The passenger's velocity relative to the road is calculated by subtracting the passenger's speed from the bus's speed since they are moving in opposite directions. Thus, the passenger's velocity relative to the road is 12 km/h south.
Explanation:The passenger's velocity relative to the bus is 3.0 km/h towards the back of the bus. However, given that the bus is moving south at 15 km/h, the passenger's velocity relative to the road is actually the bus's speed subtracted by the passenger's speed (as they're moving in opposite directions). Therefore, the passenger's velocity relative to the road is 15 km/h - 3.0 km/h = 12 km/h towards the south or simply 12 km/h south.
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The following diagram shows parallel lines cut be a transversal. What is the measure of Angle 2?
The angles in transverse parallel lines are related through some theorems such as vertical angles, corresponding angles, etc. the measure of [tex]\angle 2[/tex] is [tex]50^o[/tex]
Given the attached diagram
First, we solve for x using the corresponding angle theorem
[tex]5x + 55 = 2x + 100[/tex] ---- corresponding angles are equal
Collect like terms
[tex]5x - 2x = 100 - 55[/tex]
[tex]3x = 45[/tex]
Divide both sides by 3
[tex]x = 15[/tex]
We then solve for [tex]\angle 2[/tex] using the straight line theorem
[tex]\angle 2 + 5x + 55 = 180[/tex] ---- sum of angles on a straight line
Substitute 15 for x
[tex]\angle 2 + 5 \times 15 + 55 = 180[/tex]
[tex]\angle 2 + 75 + 55 = 180[/tex]
Collect like terms
[tex]\angle 2 =- 75 - 55 + 180[/tex]
[tex]\angle 2 =50[/tex]
Hence, the measure of [tex]\angle 2[/tex] is [tex]50^o[/tex]
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explain why the gcf of two numbers is sometimes 1
Answer:
The number 1 is common factor between any set of numbers, but, sometimes is the only common factor.
Step-by-step explanation:
This happens when the numbers do not have common prime factors, like 5 and 7.
Since 1 is a prime number, you can consider it the common primer factor of every set of numbers.
Remember:
If 'a' is a number, a prime factor of it would be 1, since a*1=a
What number has the value as 50 tens
Write a real world problem that could be solved by using the equation 3x-25= 125. Then solve the equation
Answer:
There can be many example for this equation like:
1. There are three friends and all have the same amount of money. Together they give $25 in a restaurant and they are left with $125. How much money did each have?
We can solve this like:
Let each friend had 'x' money so three friends had 3x money.
They gave out $25, means 3x-25 and are left with $125.
So, complete equation becomes :
[tex]3x-25=125[/tex]
Solving for x we get;
[tex]3x=125+25[/tex]
[tex]3x=150[/tex]
x = 50
So, each friend had $50.
A pizza bot travels at an average rate of 4 mph it is sent on a delivery toy house 1.5 miles away how long will it take the bot to make the delivery every time back to the restaurant
The pizza bot will take approximately 22.5 minutes to make the delivery and return to the restaurant.
Explanation:To calculate the time it will take the pizza bot to make the delivery and return to the restaurant, we can use the formula:
Time = Distance / Speed
In this case, the distance is 1.5 miles (one way), and the speed is 4 mph. So, the time it will take for the pizza bot to make the delivery and return to the restaurant is:
Therefore, it will take the pizza bot approximately 0.375 hours, or 22.5 minutes, to make the delivery and return to the restaurant each time.
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What is the greatest common factor of 49 and 84?
A square rug has an area 100 ft2. Write the side length as a square root. Then decide if the side length is a rational number.
The rug has side length______ft.
The side length of the square rug is 10 feet and it is a rational number since it can be written as a ratio of two integers.
Explanation:The area of a square is computed by squaring the length of one of its sides. The area of the rug is given as 100 square feet. Therefore, we can set up the following equation to find the side length:
S^2 = 100
Where 'S' represents the side length. To solve for 'S', we take the square root of both sides of the equation.
Therefore, S = √100
The square root of 100 is 10, so the side length of the rug is 10 feet.
Therefore, the rug has a side length of 10 ft. Since '10' can be expressed as a ratio of two integers, it is a rational number.
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Write your own story problem using mixed numbers that need to be scaled up. The problem should
have at least five mixed numbers that will be scaled up. Be sure to show all your work, explain your
steps in your solution (including changing improper fractions to mixed numbers), and write a complete
answer to your problem. Your answer should include units for the mixed numbers, if needed.
I do not understand the question, I cannot conduct a problem can somebody just give a mixed number problem or whatever and I will calculate it on my own. I am not asking you to do my work just to give me an example of what my teacher wants.
Thanks
The diameter of the moon is about 3,476 kilometers. The distance from Earth to the moon is about 384,400 kilometers.About how many moons could be lined up in a row between Earth and the moon? Round to the nearest whole number.
Answer: About 111 of moons could be lined up in a row between Earth and the moon .
Step-by-step explanation:
Given : The diameter of the moon is about 3,476 kilometers.
The distance from Earth to the moon is about 384,400 kilometers.
Then , the number of moons could be lined up in a row between Earth and the moon will be :-
[tex]384,400\div3,476\\\\=110.586881473\approx111\text{ Rounded to the nearest whole number }[/tex]
Hence, about 111 of moons could be lined up in a row between Earth and the moon .
Find k such that the equation kx^2+x+25k=0 has a repeated solution.
Final answer:
The value of k for the equation kx^2 + x + 25k = 0 to have a repeated solution can be found by setting the discriminant to zero. Solving for k, we find that k = 0.1 and k = -0.1 are the values that yield a repeated solution for this quadratic equation.
Explanation:
To find the value of k such that the equation kx^2 + x + 25k = 0 has a repeated solution, we need to use the discriminant of a quadratic equation. The discriminant D is given by D = b^2 - 4ac. For a quadratic equation to have a repeated solution, its discriminant must be zero (D = 0). In this equation, a = k, b = 1, and c = 25k. Plugging these values into the discriminant formula gives us:
D = 1^2 - 4(k)(25k)
Setting D to zero and solving for k will give us the value(s) of k for which the equation has a repeated solution:
0 = 1 - 100k^2
k = ± 0.1
Therefore, there are two values of k that make the original equation have a repeated solution: k = 0.1 and k = -0.1.
X is distributed with mean 6 and standard deviation 2 and Y=2X+5. Find the mean and standard deviation of the Y distribution.
Is 13/16 rational or irrational
The number 13/16 is a rational number because it can be expressed as a ratio of two integers.
Explanation:The number 13/16 is a rational number. A rational number is any number that can be expressed as a ratio of two integers, where the denominator (the number below the division line) is not zero. In this case, the number 13/16 can be expressed as a ratio of two integers: 13 and 16. Therefore, 13/16 is considered to be a rational number, not an irrational number. In contrast, an irrational number cannot be stated as a ratio of two integers. Examples of irrational numbers include the square root of two and pi.
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What is the rational number equivalent to 3.24 repeating?
A. 3 6/97
B. 3 28/99
C. 3 8/33
D. 3 10/32
Answer:
C
Step-by-step explanation:
Took the test got it right
The graph shows the cost for cherries and apples.
Which statement is true about the unit costs shown in the graph?
The unit cost for cherries is greater because the slope is greater than the slope for apples.
The unit cost for cherries is greater because the slope is less than the slope for apples.
The unit cost for apples is greater because the slope is greater than the slope for cherries.
The unit cost for apples is greater because the slope is less than the slope for cherries.
Answer:
The unit cost for cherries is greater because the slope is greater than the slope for apples.
Explanation:
Slope is the rate of change of a line. The slope of the graph for cherries is greater; we can see this because the line is steeper.
Since the slope is greater, the unit cost is greater.
The statement that represents the unit cost in the graph is that the unit cost for cherries should be more as the slope is more than the slope for apples.
The following information should be considered:
Slope refers to the changing in the rate with respect to the line.Also, the graph slope for cherries should be more as there is a steeper line as compared with the apple one.Also, if the slope is more, so the units cost should be more that means there is a direct relationship between each other
Therefore we can conclude that the first option is correct.
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1.3(8-b)+3.7b=-5.2
Solve the equation
a number increased by seven
Betty's height is 2/3 of Jinlan's height. Find the ratio of Betty's height to Jinlan's height.
How does the product 110 x n compare to the product 11 x n?
Find the value of x. Then the measure of each angle
According to Dolbear’s law, you can predict the temperature T (in degrees Fahrenheit) by counting the number x of chirps made by a snowy tree cricket in 1 minute. For each rise in temperature of 0.25°F, the cricket makes an additional chirp each minute. a. A cricket chirps 40 times in 1 minute when the temperature is 50°F. Write an equation in slope-intercept form that represents the temperature in terms of the number of chirps in 1 minute.
Answer:
the temp is 65 and there was 224 chirps
Step-by-step explanation:
6 men can complete a job in 20 days.if the men work at the same rate.how many more are needed to complete the job in 12 days
Need help solving this problem
Is this function or non function
you want to model the speed of a motorcycle which unit would be appropriate for measuring the quantity
Solve and check x / 6 equals 12 / 9
x/6 = 12/9
x = 12/9 * 6
x = 8
check:
8/6 = 1.3333
12/9 = 1.3333
How many positive 4-digit integers have only odd digits?
Answer:
[tex]5^4 = 625[/tex]
Step-by-step explanation:
There are 5 possible odd digits to choose from: 1,3,5,7,9.
When we chose our first digit, we have 5 choices (the possible odd digits). For every one of those 5 choices, we can chose our second digit in 5 different ways again, then we have 5*5 = 25 ways for choosing our first two digits. We can do the same again, as for every one of the 25 first two digits, we can chose our third digit in 5 different ways (again, the odd numbers). So we multiply it by 5 again. Repeating this one more time, because we have 5 different ways to chose our fourth digit. At the end we will have
[tex]5*5*5*5 = 5^4 = 625[/tex]
This is a commun counting technique.
Alex Rode her skateboard her velocity changed from 3m/s to 1m/s in 4 seconds. What was her acceleration?
1/2(4x−5)+52=10
x=
A:5
B:8
C:12
D:20
3/4k+3/8k=12
k=
1.4x+2.6x=−16
X=-13
X=-4
X=-48
X=19
1/3(3+2x)−1=10
A:x= 6 2/3
B:x=15
C:x=20
D:x=5
The ratio of the side length of Square AA to the side length of Square BB is 4:94:9. The side length of Square AA is 1212 yards. What is the perimeter of Square BB?
How can you show 198.000 as a power of using an exponents