for exercise, mae jogs miles then walks an additional to cool down. if her jogging speed is miles per hour faster than her walking speed and her total exercise time is , what is her walking speed?
Answers
Mae's walking speed is 10 miles per hour. This is calculated by considering the given information.
Let's assume Mae's walking speed is represented by the variable "x" (in miles per hour). According to the given information, her jogging speed would then be "x + 12.5" miles per hour.
To calculate Mae's exercise time, we can use the formula: time = distance / speed.
Mae jogs 27 miles at a speed of "x + 12.5" miles per hour, so her jogging time can be calculated as:
jogging time = 27 / (x + 12.5)
Mae walks an additional 3 miles at a speed of "x" miles per hour, so her walking time can be calculated as:
walking time = 3 / x
The total exercise time is given as 3 hours. Therefore, we can set up the equation:
jogging time + walking time = 3
Substituting the calculated values, we get:
27 / (x + 12.5) + 3 / x = 3
To solve this equation, we can start by multiplying all terms by x(x + 12.5) to eliminate the denominators:
27x + 27 * 12.5 + 3(x + 12.5) = 3x(x + 12.5)
Simplifying the equation:
\(27x + 337.5 + 3x + 37.5 = 3x^2 + 37.5x\)
Combining like terms:
\(30x + 375 = 3x^2 + 37.5x\)
Rearranging the terms to set the equation equal to zero:
\(3x^2 + 7.5x - 375 = 0\)
To solve this quadratic equation, we can use the quadratic formula:
x = (-b ± √(\(b^2\) - 4ac)) / (2a)
In this case, a = 3, b = 7.5, and c = -375. Substituting these values into the quadratic formula:
x = (-7.5 ± √(\(7.5^2\) - 4 * 3 * -375)) / (2 * 3)
x = (-7.5 ± √(56.25 + 4500)) / 6
x = (-7.5 ± √(4556.25)) / 6
Calculating the square root:
x = (-7.5 ± 67.5) / 6
Simplifying further:
x = (60 / 6) or x = (-75 / 6)
Since Mae's walking speed cannot be negative, the solution is x = 10.
Therefore, Mae's walking speed is 10 miles per hour.
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The complete question is:
For exercise, Mae jogs 27 miles then walks an additional 3 miles to cool down. If her jogging speed is 12.5 miles per hour faster than her walking speed and her total exercise time is 3 hours, what is her walking speed? The athlete's walking speed is
Related Questions
Solve for x, and find the angle.
Answers
Answer: x is equal to 35
Step-by-step explanation:
right angle is equal to 90 degrees
20+35=55
35+55=90
Find the total surface area of this cuboid 4m 5m 2.5m
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Answer:
use this formula and substitute
2(LxW)x2(LxH)x2(WxH) but if opened remove one of the 2s
The altitude of a triangular sign is 18 inches less than 3 times its base. Define the functions that describe the altitude and base of the triangle, and then use these functions to build an area function of the triangle
Answers
Functions to build an area function of the triangle , A = b2 + 2b.
What Altitude of a Triangle?A perpendicular line drawn from a triangle's vertex to its opposite side is the definition of a triangle's altitude. A triangle can be drawn with three altitudes because it has three sides. There are various types of elevations in triangles. When computing the area of a triangle, the altitude, also known as its height, is indicated by the letter.The section of a perpendicular line traced from a triangle's vertex to the side directly across from it is the triangle's altitude. The base of the triangle that the altitude touches forms a straight angle. It is often referred to as a triangle's height and is represented by the letter "h." The distance between the vertex and its opposing side can be calculated to determine its size. It should be remembered that every triangle has three altitudes that can be drawn from each of the vertices. See the intersection of the triangle's three elevations by paying attention to the triangle in the illustration below. The "Orthocenter" is this location.According to our question-
Let b = the base
altitude = 2b + 4
A = b(2b+ 4)/2
A = b(b + 2)
A = b2 + 2b
Hence, Functions to build an area function of the triangle , A = b2 + 2b.
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Explain how you can know whether a system of linear equations will have infinitely many solutions.
Answers
If the graphs of the linear equations are identical, then there are infinitely many solutions.
If the graphs are not identical, then there are not infinitely many solutions. In this case, there may be either no solutions (lines are parallel but not collinear) or one solution (the lines are not parallel but they intersect).
If a family has two children and there is a boy in the family, what is the probability that there is a girl
Answers
The probability of having a girl in the family is also 1/2 since there are only two potential outcomes.
The probability that a family with two children has a boy and a girl is 1/2 because there are two potential birth orders: boy then girl or girl then boy.
Since the order does not matter in this case, the probability is 1/2 + 1/2 = 1.
However, since the question specifies that the family has at least one boy, we can eliminate the girl-boy birth order and conclude that the probability that the family has a boy and a girl is 1/2.
Therefore, the probability of having a girl in the family is also 1/2 since there are only two potential outcomes.
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Quick algebra 1 question 25 points!
Only answer if you know the answer, quick shout-out to subtomex0, tysm for the help!
Answers
Answer:
1. Translate 5 units up (Fixed after a comment from subtomex0 - Thanks again!)
2. Vertical Compression by a scale factor of 3/8
3. Reflect across the y-axis, and shift 2 units to the left
4. Vertical stretch by a scale factor of 6, and shifting 1 unit up
5. Shifting 11 units to the left
6. Vertical stretch by a scale factor of 8
7. Vertical compression by a scale factor of 1/2, and reflection across the y-axis.
ind a parametric equation for a line through the point (1, -3, 5) and parallel to the vector 5i 3j − k . write your answer as a comma separated list of equations in x, y, z.
Answers
the parametric equation for the line is:
x = 1 + 5t
y = -3 + 3t
z = 5 - t
We can write the parametric equation of the line as:
x = 1 + 5t
y = -3 + 3t
z = 5 - t
where t is a parameter.
Note that the direction vector of the line is (5, 3, -1), which is parallel to the given vector 5i + 3j - k. We can see that the x-coordinate changes by 5t, the y-coordinate changes by 3t, and the z-coordinate changes by -t.
Since the line passes through the point (1, -3, 5), we substitute t=0 into the above equations to get:
x = 1
y = -3
z = 5
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5 ft, 6 ft, 12 ft
Do these side lengths form an enclosed triangle?
Choose (YES or NO)
Answers
What is the shortcut for multiplying mixed numbers?
Answers
To multiply mixed numbers, convert to improper fractions, cancel factors, multiply the remaining factors, and simplify if possible.
Increasing blended numbers can be tedious, yet there is an easy route that can work on the interaction. To duplicate blended numbers, convert them to ill-advised portions, then drop any elements that show up in both the numerator and denominator of the divisions. At long last, duplicate the leftover elements in the numerator and denominator and work on the subsequent division if conceivable. For instance, to duplicate 2 1/2 by 3 2/3, first proselyte them to inappropriate divisions, which are 5/2 and 11/3. Then, drop the variable of 2 in the numerator of the principal portion and the denominator of the subsequent division. The outcome is 55/3, which can be improved to 18 1/3. This alternate way can save time and assist understudies with taking care of augmentation issues all the more proficiently.
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journal articles and research reports are by far the most common secondary sources used in education.
Answers
Journal articles and research reports are widely recognized as the most common types of secondary sources used in education. In the field of education, secondary sources play a crucial role in providing researchers and educators with valuable information and scholarly insights.
Among the various types of secondary sources, journal articles and research reports hold a prominent position. These sources are often peer-reviewed and published in reputable academic journals or research institutions. They provide detailed accounts of research studies, experiments, analyses, and findings conducted by experts in the field. Journal articles and research reports serve as reliable references for educators and researchers, offering up-to-date information and contributing to the advancement of knowledge in the education domain. Their prevalence and credibility make them highly valued and frequently consulted secondary sources in educational settings.
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What are the steps to understanding this problem as well as the answers.
Answers
Step-by-step explanation:
1
\( \frac{1}{3 + 4i} \times \frac{3 - 4i}{3 - 4i} = \frac{3 - 4i}{25} = \frac{ 3}{25} - \frac{4i}{25} \)
2)
\( \frac{1}{3 - 4i} \times \frac{3 + 4i}{3 + 4i} = \frac{3 + 4i}{25} = \frac{ 3}{25} + \frac{4i}{25} \)
3)
1+0i
4)
\( \frac{3 - 4i}{3 + 4i} \times \frac{3 - 4i}{3 - 4i} = \frac{ - 7 - 24i}{25} = - \frac{7}{25} - \frac{24i}{25} \)
5)
3 - 4i
6)
\( \frac{3 + 4i}{3 - 4i} \times \frac{3 + 4i}{3 + 4i} = \frac{ - 7 + 24i}{25} = - \frac{7}{25} + \frac{24i}{25} \)
Rewrite the following equation in slope-intercept form. Y + 5 = 1 7 ( x + 7 )
Answers
Answer: y = 17x + 114
Step-by-step explanation:
The equation for the slope-intercept form is y = mx + b.
Arrange the equation so that it resembles y = mx + b.
You will do this by multiplying and subtracting so y is on the left side of the equation and mx + b is on the right side of the equation.
y + 5 = 17(x + 7)
y + 5 = 17x + 119
y + 5 - 5 = 17x + 119 - 5
y = 17x + 114
Answer:
Y = 17x + 114
Step-by-step explanation:
1. Y + 5 = 17 (x+7)
2. Y + 5 = 17x + 119 [Multiply the numbers in parenthesis by 17.]
3. Y = 17x + 114. [To keep the balance and move the 5 over, subtract it from 119.]
What is the simplified expression for 4 power 4 multiplied by 4 power 3 over 4 power 5?
Answers
To check the accuracy of a graduated cylinder, a student filled the cylinder to the mark of 25ml and then compared the measured volume to the actual volume using a buret. The results of five trails are recorded. The graduated cylinder is...
Answers
The graduated cylinder is being checked for accuracy by comparing the measured volume to the actual volume using a buret. The student filled the cylinder to the mark of 25ml and then recorded the results of five trials.
To determine if the graduated cylinder is accurate.
The measured volume from the cylinder should be close to the actual volume measured by the buret.
If the measured volume consistently matches the actual volume within an acceptable range, then the graduated cylinder can be considered accurate.
However, if there is a significant discrepancy between the measured and actual volumes in multiple trials, then the graduated cylinder may not be accurate and may require calibration or replacement.
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The accuracy of the graduated cylinder can be evaluated by comparing the measured volumes to the actual volumes using a buret. The student should analyze the results of the trials and calculate the average difference to draw a conclusion about the cylinder's accuracy.
To check the accuracy of a graduated cylinder, a student filled it to the mark of 25ml and compared the measured volume to the actual volume using a buret. The results of five trials are recorded.
To determine the accuracy of the graduated cylinder, the student needs to compare the measured volume to the actual volume. If the measured volume matches the actual volume, the graduated cylinder is accurate. However, if there is a discrepancy, the cylinder may be inaccurate.
The student performed five trials and recorded the results. By comparing the measured volumes to the actual volumes for each trial, the student can analyze the consistency of the measurements.
To draw a conclusion, the student should calculate the average difference between the measured volumes and the actual volumes for all five trials. If the average difference is small, it suggests that the graduated cylinder is accurate. Conversely, if the average difference is significant, it indicates that the cylinder may be inaccurate.
By comparing the results of the trials and calculating the average difference, the student can determine whether the graduated cylinder is accurate or not.
In conclusion, the accuracy of the graduated cylinder can be evaluated by comparing the measured volumes to the actual volumes using a buret. The student should analyze the results of the trials and calculate the average difference to draw a conclusion about the cylinder's accuracy.
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A plumber notices a faucet leaking of a rate of 2 milliliters per second.
What is the rate of the leak in liters per hour?
Answers
Answer:
it is 7200 Liters
Step-by-step explanation:
Brainliest?
The 5th term in a geometric sequence is 162. The 2nd term is 6, The sum of the 1st 5 terms is.
Answers
Answer:
Step-by-step explanation:
t2 = a*r
t2 = 6
t5 = a*r^4
t5 = 162
162/6 = ar^4 / ar
r^3 = 27
r = 3
6 = a*3
2 = a
Sum = a(r^n - 1)
=======
r - 1
n = 5
a = 2
r = 3
Sum = 2(3^5 - 1)
=======
2
Sum = 242
If I eat 5 cupcakes every 14 hours for 42 hours how many cupcakes is that
Answers
3 times 5= 15 cupcakes
Is 4/8 equivalent to 7/8
Answers
Answer:
is 7 more than 4 or 4 more than 7?
Step-by-step explanation:
JUST USE YOUR BRAIN!
Answer:
no
Step-by-step explanation:
of course not. since the denominators are the same, the numerators have to be equal. since the numerators aren't equal, the answer is no
Bob wants to catch an elevator before the door closes. He is 46ft away when the door starts to close. The door has to travel 4.2ft to fully close, and is closing at a rate of 1.5ft/s. Bob needs to get to the door while it is at least 0.7ft open. How fast does he have to run in order to catch the elevator? Give your answer in feet per second, and round to the nearest hundredth. Show your work here Enter your answer
Answers
Answer: Bob has to run at a speed of 21.31ft/s to catch the elevator.
Step-by-step explanation:
Let's call Bob's running speed "V".We know that the door is closing at a rate of 1.5ft/s, so the time it takes to close completely is 4.2ft / 1.5ft/s = 2.8 seconds.During this time, Bob has to travel 46ft to reach the elevator. So the time it takes Bob to reach the door is 46ft / V.We also know that the door needs to be at least 0.7ft open when Bob reaches it. So, the time that the door is open when Bob reaches it is 2.8s - (2.8s * 0.7ft / 4.2ft) = 2.8s - 0.6364s = 2.1636s.So, Bob has to cover 46ft in 2.1636s. Solving for V, we get:V = 46ft / 2.1636s = 21.31ft/s (rounded to the nearest hundredth).Therefore, Bob has to run at a speed of 21.31ft/s to catch the elevator.
m(x) = 3x2 + 2x - 11
Answers
Answer:
3x^2 + 2x - 11/x
how do i multiply 42 x 60 and round to the nearst hunderends
Answers
42x60=2520, and the nearest hundred is 2500
Drag each number from the box to complete the equations that follow. Each number may be used once,more than once, or not at all.12894(36:)--(36:= 5X3)-= 12
Answers
Notice that:
\(\begin{gathered} 5=9-4, \\ 36\div4=9, \\ 36\div9=4. \end{gathered}\)Therefore:
\(5=9-4=36\div4-36\div9.\)Also, notice that:
\(3\times8=24=12+12.\)Therefore:
\(12=12+12-12=3\times8-12.\)Answer:
\(\begin{gathered} (36\div4)-(36\div9)=5, \\ (8\times3)-12=12. \end{gathered}\)put the fractions in order from least to greatest 3/4 or 9/16 or 3/16 or 7/8 or 3/8
Answers
Answer:
3/16, 3/8, 3/4, 9/16, 7/8
Explanation:
To order the fractions from least to greatest, you can use the following steps:
Convert the fractions to a common denominator, if they have different denominators.
Compare the numerators of the fractions. The fraction with the smallest numerator will be the first.
If two or more fractions have the same numerator, compare the denominators. The fraction with the smallest denominator will be the first.
In this case, all fractions have different denominators so no need to convert them.
3/16 < 3/8 < 3/4 < 9/16 < 7/8
So the order from least to greatest is: 3/16, 3/8, 3/4, 9/16, 7/8
Amelia wants to buy 6 sausage Rolls. Each sausage rolls costs 84p.Amelia pays with a £20 note. Work out how much change Amelia will get from £20.
Answers
Answer:
15.6
Step-by-step explanation:
84 pence × 6 = 504
504 ÷ 100 = 5.4
20 - 5.4 = 15.6
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The average number of misprints per page in a magazine is whixch follows a Poisson's Probability distribution. What is the probability that the number of misprints on a particular page of that magazine is 2?
Answers
The probability that a particular book is free from misprints is 0.2231. option D is correct.
The average number of misprints per page (λ) is given as 1.5.
The probability of having no misprints (k = 0) can be calculated using the Poisson probability mass function:
\(P(X = 0) = (e^{-\lambda}\times \lambda^k) / k!\)
Substituting the values:
P(X = 0) = \((e^{-1.5} \times 1.5^0) / 0!\)
Since 0! (zero factorial) is equal to 1, we have:
P(X = 0) = \(e^{-1.5}\)
Calculating this value, we find:
P(X = 0) = 0.2231
Therefore, the probability that a particular book is free from misprints is approximately 0.2231.
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Question 13: The average number of misprints per page of a book is 1.5.Assuming the distribution of number of misprints to be Poisson. The probability that a particular book is free from misprints,is B. 0.435 D. 0.2231 A. 0.329 C. 0.549
Which equation represents a tangent function with a domain of all Real numbers such that x is not equal to pi over 4 plus pi over 2 times n comma where n is an integer?
Answers
The equation representing this function is y = tan(x)
The equation which represents a tangent function with a domain of all real numbers such that x is not equal to pi over 4 plus pi over 2 times n comma where n is an integer is:y = tan(x)The tangent function is one of the six trigonometric functions, which is abbreviated as tan. The inverse of the cotangent function is the tangent function. It is also referred to as the inverse tangent, arctan, or tan^-1.
It is defined by the ratio of the opposite side to the adjacent side of a right triangle. The tangent function is a periodic function with a period of π radians or 180°. Its value alternates between negative and positive infinity over each period.The tangent function is not defined at odd multiples of π/2, that is, (2n+1)π/2 for all integers n. This is because the denominator in the tangent function becomes zero, causing a vertical asymptote.
For example, the values of the tangent function for π/2, 3π/2, 5π/2, etc. are undefined. Therefore, the domain of the tangent function is all real numbers except for odd multiples of π/2. The notation for the domain is (-∞, -π/2) U (-π/2, π/2) U (π/2, 3π/2) U (3π/2, ∞).However, in this case, the domain is all real numbers except π/4 + nπ/2, where n is any integer.
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Determine the intercepts of the line
x intercept : ?,?
y intercept: ?,?
Answers
Answer:
x-intercept: 3 or (3,0)
y-intercept: -10 or (0,-10)
Step-by-step explanation:
1. The intercepts of a graph are points at which the graph intersects with the x - or y-axis.
2. Given the information above, the line intersects with the x-axis at (3,0) and the y-axis at (0,-10).
Therefore, the x-intercept is 3 or (3,0) and the y-intercept is -10 or (0,-10).
Create two imaginary numbers that multiply to get - 60 . (There are multiple solutions)
Answers
Answer:
10 x -6 = -60
Step-by-step explanation:
The number that multiplies to get -60 are (-2, 30), (-3, 20), (-4, 15), (-5, 12), (-6, 10), (2, -30), etc.
What is multiplication?
The fundamental concept of making the same number of additions repeatedly is represented by the action of multiplication. The results of multiplying two or more integers are known as the products, and the factors that are used in the multiplication are referred to as the factors.
Given:
The number is -60,
Factorize the number as shown below,
60 = 2 × 2 × 3 × 5
Here, the two numbers can be many, some of them are mentioned below,
-60 = 2 × (-30)
-60 = 3 × (-20)
-60 = 4 × (-15)
-60 = 5 × (-12)
-60 = 6 × (-10)
The number can be changed by changing the sign as shown below,
-60 = -2 × 30
-60 = -3 × 20
-60 = -4 × 15
-60 = -5 × 12
-60 = -6 × 10
Thus, the numbers are (-2, 30), (-3, 20), (-4, 15), (-5, 12), (-6, 10), (2, -30), etc.
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Consider this system of equations.
f(x)=x−4g(x)=−x−2
Plot the point that represents the solution to the equation f(x)=g(x).
Answers
We are given two functions.
\(f(x)=x-4\\g(x)=-x-2\)
The point that represents the equation \(f(x)=g(x)\), will also be the intersection of those two lines, meaning we can set the two equations equal to each other and solve for \(x\).
\(f(x)=g(x)\\x-4=-x-2\\2x=2\\x=1\)
Now that we are given the x value, we can plug this value back into either equation and solve for the y value.
\(f(1)=1-4\\f(1)=-3\)
The point of intersection will be \((1,-3)\).
Hope this helps!
Answer:
x=-1
Step-by-step explanation:
x-4=-x-2
x+x=-2+4
2x=-2
x=-1
Area of composite shapes
The following shape has 1 pair of
parallel sides.
7
2
7
8
*
-
-
-
3
What is the area of the shape?
CI
units?
Answers
Answer: 76
Step-by-step explanation:
The area of the given composite figure is 76 square units.
What is area?Area is the amount of space occupied by a two-dimensional figure. In other words, it is the quantity that measures the number of unit squares that cover the surface of a closed figure. The standard unit of area is square units which is generally represented as square inches, square feet, etc.
The given composite figure has three parts, two triangles and one rectangle.
Area of small triangle = 1/2 ×8×2
= 8 square units
Area of large triangle = 1/2 ×8×3
= 12 square units
Area of rectangle = Length×Height
= 8×7
= 56 square units
Total area = 8+12+56
= 76 square units
Therefore, the area of the given composite figure is 76 square units.
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