Does this graph show a proportional relationship? Why or why not?
A bicyclist was traveling from the village to the railroad station with a speed of 15 mph and he was coming back to the village with a speed of 10 mph. Find the distance from the village to the railroad station, if it’s known that it took 1 more hour for the bicyclist to get back to the village.
Since, a bicyclist was traveling from the village to the railroad station with a speed of 15 mph and he was coming back to the village with a speed of 10 mph.
Let the time taken in traveling from village to the railroad station be 't' hours
Distance is calculated by the formula:
[tex] d= s \times t [/tex]
So, the distance traveled from village to the railroad station is:
[tex] d=15 \times t [/tex]
Since, the time taken in traveling from railroad station to the village is 1 hour more = 't+1' hours
So, the distance traveled from railroad station to the village is:
[tex] d=10 \times (t+1) [/tex]
Therefore, distance traveled from village to railroad station is equals to the distance traveled from railroad station to the village.
So, [tex] 15 \times t=10(t+1) [/tex]
[tex] 15t=10t+10 [/tex]
[tex] 5t=10 [/tex]
So, t=2
Therefore, distance from village to railroad station = [tex] 15 \times t [/tex]
= [tex] 15 \times 2 [/tex]
= 30 miles.
Therefore, the distance from village to railroad station is 30 miles.
The distance from the village to the railroad station is 30 miles
Speed is the ratio of distance to time taken. It is given by:
Speed = distance/time
Let d represent the distance from the village to the rail station.
When Going at a speed of 15mph, let us assume he spent a hour, hence:
15 = d/a
d = 15a
When coming at a speed of 10mph, let us assume he spent b hour, hence:
10 = d/b
d = 10b
Therefore:
15a = 10b
But it took 1 more hour for the bicyclist to get back to the village, hence b = a + 1, hence:
15a = 10(a + 1)
15a = 10a + 10
5a = 10
a = 2 hours
d = 15a = 15(2) = 30 miles
Therefore, the distance from the village to the railroad station is 30 miles
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15 POINT QUESTION
Francine solves the system of equations using the linear combination method. 4x+3y=−1
3x−5y=4
Which steps would allow her to eliminate the x terms in the system of equations?
A) Multiply 4x+3y=−1 by 4. Multiply 3x−5y=4 by 3. Add the resulting equations together.
B) Multiply 4x+3y=−1 by −4 . Multiply 3x−5y=4 by 3. Add the resulting equations together.
C) Multiply 4x+3y=−1 by 3. Multiply 3x−5y=4 by −4. Add the resulting equations together.
D) Multiply 4x+3y=−1 by 5. Multiply 3x−5y=4 by 3. Add the resulting equations together.
Write the time 8:30 then write this time in two other ways using words
The time 8:30 can be written in two other ways using words: eight thirty and half past eight.
Explanation:The time 8:30 can be written in two other ways using words as follows:
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The time 8:30 can be written in words as 'Half past eight' and 'Thirty minutes past eight'. These phrases show the same time but express it in different ways.
Explanation:The time 8:30 can be written in two other ways using words. One way is to say 'Half past eight'. Another way is 'Thirty minutes past eight'. These phrases encapsulate the same time but offer variation in how the time can be expressed verbally or in writing.
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whats 324589 times 789024???
circle O has a circumference of 132 feet. what is the approximate area of the circle?
You can use the given circumference of 132 feet to find the radius using the formula C=2πr. Once the radius is found to be approximately 21 feet, use the formula for the area of a circle, being A=πr², to calculate an area of approximately 1386 square feet.
Explanation:To find the area of a circle when you know the circumference, you can use the formula for the circumference of a circle, which is C = 2πr (C is the circumference and r is the radius). From the circumference, we can find the radius.
Let's rearrange the formula for r: r = C / 2π . Plugging in the given value, r = 132 / 2π approximately equals 21 feet.
Next, we use the area of a circle formula A = πr² and plug in the radius to calculate the area. Here, A = π * (21)^2 that gives us an area of approximately 1386 square feet.
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A hiker walks an average rate of 2 miles per hour. Write a multiplication equation to find how long it will take for the hiker to walk 11 miles?
Please help me asap will give brainliest
I really need help!! God bless you.
Whats the surface area? WILL GIVE BRAINIEST!
How to find the surface area of certain 3 dimensional shapes
A $140 car stereo is marked up 50% and then discounted 50% will the final price of the car stereo be #140
How does the volume of a cone change if its radius and height are both tripled? A. B. C. D.
The volume of the cone changes by a factor of 27
How does the volume of the cone change
From the question, we have the following parameters that can be used in our computation:
Volume of a cone
The volume of a cone is calculated using
[tex]V = \frac13\pi r^2h[/tex]
When the radius and height are both tripled, we have
R = 3r
H = 3h
So, the new volume is
[tex]V_2 = \frac13\pi R^2H[/tex]
Substitute the known values into the equation
[tex]V_2 = \frac13\pi (3r)^2 * 3h[/tex]
Evaluate
[tex]V_2 = \frac13\pi 9r^2 * 3h[/tex]
So, we have
[tex]V_2 = \frac13\pi r^2h * 27[/tex]
Recall that
[tex]V = \frac13\pi r^2h[/tex]
So, we have
[tex]V_2 = 27V[/tex]
This means that the volume of the cone changes by a factor of 27
Question
How does the volume of a cone change if its radius and height are both tripled? A. 3 B. 9 C. 27 D. 81
Interpret the scatter plot of the data for the amount of paint used to paint signs of various lengths based on the shape of the distribution
Answer:
The shape of the points in the scatter plot resemble an increasing exponential equation.
Step-by-step explanation:
As you can tell it increases because it is going up on the graph.
Which number is equivalent to 43/12?
A fraction is a way to describe a part of a whole. The correct option is B.
What is a Fraction?A fraction is a way to describe a part of a whole. such as the fraction ¼ can be described as 0.25.
What is Mixed Fraction?A mixed fraction is a fraction that contains a whole number and a fraction whose denominator is greater than the numerator. A mixed fraction can be converted as,
2 1/2
= (2×2 + 1)/2
= 5/2
= 2.5
Given that the number that is equivalent to 43/12 can be found as shown below.
43/12
= 3 ⁷/₁₂
= 3 + 7/12
= 3 + 0.58333333
= 3.58333333
[tex]= 3.58\overline3[/tex]
Hence, the correct option is B.
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∠1 and ∠2 are vertical angles. ∠2 has a measure of 63°.
What is the measure of ∠1 ?
Enter your answer in the box.
Vertical angles are formed when two lines intersect. The measure of the ∠1 when ∠1 and ∠2 are vertical angles is 63°.
What are vertical angles?Vertical angles are a pair of angles formed when two lines intersect each other, these angles are always opposite to each other and measure the same.
We know about the vertical angles, therefore, if the pair of angles ∠1 and ∠2 are vertical angles, then the measure of the two angles is equal.
Now, as it is given that the measure of the ∠2 is 63° and ∠1 and ∠2, therefore,
∠1 = ∠2 = 63°
Hence, the measure of the ∠1 when ∠1 and ∠2 are vertical angles is 63°.
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Draw a picture to show how to find12+37
What are the coordinates of the point on the directed segment from K (-5,-4) to L (5,1) that partitions the segment into a ratio of 3 to 2?
the length of a rectangular garden is 5 feet longer than its width. The garden is surrounded by a 2-foot-wide sidewalk. The sidewalk has an area of 76 square feet. Find the dimensions of the garden.
Final answer:
By setting up equations based on the given information about the garden and the sidewalk around it, and then solving for the width, we find that the width of the garden is 5 feet, and its length is 10 feet.
Explanation:
Let's denote the width of the garden as w feet. Therefore, the length of the garden can be represented as w + 5 feet, since it is mentioned that the length is 5 feet longer than its width. Surrounding the garden, there is a 2-foot-wide sidewalk which affects the overall dimensions of the combined area (garden plus sidewalk). The width and length of this entire area would thus be w + 4 and w + 9 respectively, adding 2 feet on each side for the sidewalk.
To find the area of just the sidewalk, which is given as 76 square feet, we first calculate the area of the entire (garden plus sidewalk) rectangle, and then subtract the area of the garden. The equation for the area of the entire rectangle is (w + 4)(w + 9), and for the garden alone, it's w(w + 5). The difference between these areas gives us the area of the sidewalk:
(w + 4)(w + 9) - w(w + 5) = 76
Expanding and simplifying this equation gives us a quadratic equation to solve for w. Simplifying further:
w^2 + 13w + 36 - w^2 - 5w = 76
8w + 36 = 76
8w = 40
w = 5
Therefore, the width of the garden is 5 feet and the length is 10 feet (5 + 5).
Katenka cross country skied a trail that was 3/4 mile each way. after skiing 2/3 of the trail she turned around. What fraction of a mile did katenka ski before she turned around.
I’m not sure about this question. Please help thanks!
Which of the following represents seventh root of x to the sixth power in exponential form
WILL GIVE BRAINLIESTTT HELP PLEASE
Briana surveys five students from four different classrooms. She asks them about the number of hours they spend on the Internet every day. This is the data from her survey: classroom A: 0, 0, 0, 1, 1 classroom B: 1, 1, 1, 2, 2 classroom C: 2, 3, 3, 3, 4 classroom D: 1, 2, 2, 2, 3 Which classroom's data has the highest center of distribution?
classroom A
classroom B
classroom C
classroom D
Thank you!
Answer:
Classroom C
Step-by-step explanation:
all you do is add it then divide it by 5 and boom
in rectangle abcd measure of angle d =(3x+15) measure b =(6x-42) find measure of angle a
meagan has $1.10 in dimes nickels and pennies she has three times as many nickels as pennies and the number of dimes is two less than the number of pennies how many dimes nickels and pennies dose she have please help
John uses 9 eggs to make 5 breakfast burritos. How many burritos can he make 27 eggs
BRAINLIEST IF CORRECT PLEASE SHOW WORK:)
Evaluate. 8 2/9 −7 1/6
A: 1/18
B: 1 7/18
C: 1 1/3
D: 1 1/18
Hannah has 11 toothpicks that are the same length.Name the types of triangles and quadrilaterals Hannah can make if she uses only one toothpick for each side of each figure
Answer:
Step-by-step explanation:
Given that Hannah has 11 toothpicks that are the same length
When she uses only one toothpick for each side then we see that all sides would be equal whether quadrilateral or triangle.
Hence she can make equilateral triangles, rhombuses or squares out of these 11 toothpicks
Either one equilateral triangle, and 2 rhombuses, or one equil. triangle and 2 squares or 1 equil triangle with 1 square, 1 rhombus or 2 equil triangles with one square or rhombus
The flat surfaces of a 3D shape are called what? Faces Edges Vertices
The flat surfaces of a 3D shape are called faces.
The faces serve as the two-dimensional polygonal areas that define the boundaries of a 3D object. In geometry, for instance, a cube is a common 3D shape that has six faces, each of which is a square. Each face is bordered by edges, which are the straight lines where two faces meet, and the corners of the faces are known as vertices (or vertex in singular form).
Examining various 3D shapes, such as the tetrahedron, which has four triangular faces, and the octahedron with its eight triangular faces, provides a clearer understanding of how faces constitute the polyhedron's shape.