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Randy and Wade started riding a bike at noon. Noon is 12 pm. Both of them are heading towards each other and 60km.
let
speed of wade = x
speed of Randy = 4 + x
They met each other at 1:30 pm. 12 pm to 1:30 pm is 1 hour 30 minutes(1.5 hours). Both of them will cover a total distance of 60km.
[tex]\begin{gathered} \text{speed}=\frac{dis\tan ce}{\text{time}} \\ \text{speed}\times time=dis\tan ce \end{gathered}[/tex]Therefore,
[tex]\begin{gathered} 1.5x+1.5(4+x)=60 \\ 1.5x+6+1.5x=60 \\ 3x=60-6 \\ 3x=54 \\ x=\frac{54}{3} \\ x=18\text{ km/hr} \end{gathered}[/tex]speed of wade = 18km/hr
speed of Randy = 4 + 18 = 22km/hr
Related Questions
Jess's age is six years less than three times Ethan's age. The product of their ages is 45. What are their ages? Hint: Write an equation to represent the product of their ages, using x to represent Ethan's age, then solve this quadratic equation. Connect each person to their correct age.
Answers
Jess's age is six years less than three times Ethan's age. The product of their ages is 45. What are their ages?
Hint: Write an equation to represent the product of their ages, using x to represent Ethan's age, then solve this quadratic equation. Connect each person to their correct age.
Let
x ------> Ethan's age
y -----> Jess's age
we have that
y=3x-6 -------> equation A
xy=45 ------> equation B
substitute equation A in equation B
x(3x-6)=45
solve for x
3x^2-6x=45
3x^2-6x-45=0
Solve using the formula
so
a=3
b=-6
c=-45
substitute
[tex]x=\frac{-(-6)\pm\sqrt[]{-6^2-4(3)(-45)}}{2(3)}[/tex][tex]\begin{gathered} x=\frac{6\pm\sqrt[]{576}}{6} \\ \\ x=\frac{6\pm24}{6} \end{gathered}[/tex]the solutions for x are
x=5 and x=-3 (is not a solution)
Find the value of y
y=3(5)-6
y=9
therefore
Ethan's age is 5 years
Jess's age is 9 years
What’s the correct answer answer asap for brainlist
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Answer: 3 years it started in Europe in 1914 and the USA got involved in 1917
Step-by-step explanation:
"People who are generous help those in need however they can."
To which theory of ethics is the person who made this statement likely appealing?
Conventionalism
Virtue-based ethics
Kantian deontology
Egoism
Answers
Answer: Conventionalism
Step-by-step explanation:
The person who made the statement, "People who are generous help those in need however they can," is appealing to virtue-based ethics.
What is Virtue ethicsVirtue ethics is a way of thinking about what is right and wrong. It focuses on becoming a good person and practicing good qualities.
This focuses on helping people develop good qualities such as being generous, caring, and kind. In this situation, the statement means that being kind and helping people who need it is seen as doing the right thing.
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The table to right gives the projections of the population of a country from 2000 to 2100.Answer parts (a) through (c).
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c.
As found in part (a), the data in the table can be represented by the linear model as follows,
[tex]f(x)=2.928x+270.641[/tex]Here, 'x' is the number of years after year 2000.
To find: The population in 2080 as predicted by the model.
The value of 'x' corresponding to the year 2080 can be obtained as follows,
[tex]\begin{gathered} x=2080-2000 \\ x=80 \end{gathered}[/tex]Substitute the value of 'x' in the model for population,
[tex]\begin{gathered} f(80)=2.928\cdot(80)+270.641 \\ f(80)=234.24+270.641 \\ f(80)=504.881 \\ f(80)\approx504.9 \end{gathered}[/tex]Thus, the population in 2080 will be 504.9 million approximately, as predicted by the linear model.
Simplify and express in " a + bi " form.Show Detailed Step By Step Calculations
Answers
So, let's simplify
(8 - 10i) - (22 - 6i) =
8 -10i -22 +6i = (adding like terms)
-4i -14i
30. Landscaping Calculate the area (in square feet) of a flower garden shaped like a circular sector withradius 60 ft and central angle 33 degrees.31. In problem 30; if shrubs are planted every 2 ft along the outer border of the garden, how many shrubsare needed?
Answers
Explanation
the area of a circular sector is given by
[tex]\begin{gathered} \text{Area}_{sc}=\frac{\theta}{360}\pi r^2 \\ \text{where r is the radius and }\theta\text{ is the angle in degr}ees \end{gathered}[/tex]then
Step 1
Let
[tex]\begin{gathered} \text{radius}=\text{ 60 ft} \\ \text{angle}=33\text{ \degree} \end{gathered}[/tex]now, replace in the formula
[tex]\begin{gathered} \text{Area}_{sc}=\frac{\theta}{360}\pi r^2 \\ \text{Area}_{sc}=\frac{33}{360}\pi(60ft)^2 \\ \text{Area}_{sc}=1036.72ft^2 \\ \text{rounded} \\ \text{Area}_{sc}=1036.72ft^2 \end{gathered}[/tex]Step 2
if shrubs are planted every 2 ft along the outer border of the garden, how many shrubs
are needed?
to figure out this, we need to take the perimeter of the circular sector and divide by 2 ft, to get the total number of shrubs in the border
so,
[tex]\text{perimeter}=(2\cdot\text{radius)}+length\text{ of arc}[/tex]so, we need to find the length of the arc
the length of the arc is given by
[tex]l=\frac{2\pi r}{360}\cdot\theta[/tex]replace.
[tex]\begin{gathered} l=\frac{2\pi r}{360}\cdot\theta \\ l=\frac{2\pi\cdot60}{360}\cdot33 \\ l=34.55 \end{gathered}[/tex]finally, replace in the perimeter formula
[tex]\begin{gathered} \text{perimeter}=(2\cdot\text{radius)}+length\text{ of arc} \\ \text{perimeter}=(2\cdot60ft\text{)}+34.55 \\ \text{perimeter}=120\text{ ft+34.55 ft} \\ \text{Perimeter}=154.55\text{ ft} \end{gathered}[/tex]divde by 2 to know the numbers of shrubs
[tex]\begin{gathered} Numbver\text{ of shrubs=}\frac{\text{ perimeter}}{2})=\frac{154.55\text{ ft}}{2} \\ Numbver\text{ of shrubs=}77.275\text{ ft} \\ Numbver\text{ of shrubs=}78 \end{gathered}[/tex]
HelpWhich equation can be used to solve for x in the following diagram?
Answers
The sum of the angles is 90° because is a right angle because the square on the angle means it
then if we sum the angles 30° and 2x° we have 90°
[tex]30+2x=90[/tex]or
[tex]2x+30=90[/tex]then right option is A
An electronics store sends an email survey to all customers who bought tablets. The previous month, 570 people bought tablets. Surveys were sent to 300 of these people, chosen at random, and 138 people responded to the survey. Identify the population and the sample. (4 points)The population is 570. The sample is 138.The population is 570. The sample is 300.The population is 300. The sample is 138.The population is 138. The sample is 570.The population is 138. The sample is 300.
Answers
Answer:
The population is 300. The sample is 138.
Explanation:
In statistics, population refers to the entire group of persons or things that a study is to be carried out on. Looking at the given question, we can see that, even though there were 570 people that bought tablets, the surveys were only sent to 300 people chosen at random. It shows that only 300 of the 570 people are to be surveyed, therefore, the population is 300.
A sample is the particular/specific group of persons or things that data is to be received from.
Looking at the given question, we can see that, out of the 300 people that the surveys were sent to, only 138 people responded to the survey. So the sample is 138.
How much higher is the summit of Mt. McKinley than the summit of Mt. Kosciuszko?
Answers
Based on the heights of the summits of Mt. McKinley and Mt. Kosciuszko, we find that Mt. McKinley is higher than Mt. Kosciuszko by 13,000 ft
What are the heights of Mt. Kosciuszko and Mt. McKinley?Mt. McKinley is reputed to be the tallest mountain in the North American continent which makes sense considering it has a summit with the height of 20,310 feet.
Mt. Kosciuszko on the other hand, is not that tall and stands at a height of 7,310 ft and is located in Australia.
The difference between both summits is:
= 20,310 - 7,310
= 13,000 ft
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if a certain number is added to both the numerator and denominator of the fraction 8/9, the result is 6/7. Find the numer.
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3. The function f(x) has the coordinates below. State the changes made to f(x) which result in the function g(x). Write the (x,y) rule that would transform the coordinates of f(x) to the coordinates of g(x). g(x) = -2f(x + 1) - 4
Answers
Problem
The function f(x) has the coordinates below. State the changes made to f(x) which result in the function g(x). Write the (x,y) rule that would transform the coordinates of f(x) to the coordinates of g(x). g(x) = -2f(x + 1) - 4
Solution
From this table we know that
f(-1) = 5, f(2) = 1, f(6)=0
The rule for this case would be:
y= 13/84x^2 -125/84x +47/14
We also know that we have the following transformation
g(x) = -2f(x + 1) - 4
The corresponding coordinates of x on g(x) are:
0, 3, 7
So we have this:
f(0) = 47/14
f(3)= 2/7
f(7) = 11/21
And the corresponding y coordinates are:
-2(47/14) -4=-75/7
-2(2/7) -4=-3277
-2(11/21) -4=-106/21
ANSWER ASAP!! Raise the monomial to a power: -2m^3n^2t to the power of 4
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In the diagram below , ^PQR = ^STR . Complete the statement
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Given:
[tex]\Delta\text{PQR}\cong\Delta\text{STR}[/tex]Since it is given that triangles PQR and STR are congruent, the corresponding angles of the triangles are equal.
Hence,
Therefore, option D is correct.
Solve the system of equations below using any method you learned in this unit. Show all work (even if you are using your calculator).
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Given the system of equations
[tex]\begin{gathered} x+4y-z=20-----1 \\ 3x+2y+z=8-----2 \\ 2x-3y+2z=-16-----3 \end{gathered}[/tex]We can solve for x, y and z below.
Explanation
Step 1: Find the value of z using the substitution method
[tex]\begin{gathered} \begin{bmatrix}x+4y-z=20\\ 3x+2y+z=8\\ 2x-3y+2z=-16\end{bmatrix} \\ Isolate\text{ for x in equation 1} \\ x=20-4y+z \\ \mathrm{Substitute\:}x=20-4y+z\text{ in equation 2 and 3} \\ \begin{bmatrix}3\left(20-4y+z\right)+2y+z=8\\ 2\left(20-4y+z\right)-3y+2z=-16\end{bmatrix} \\ sinplify \\ \begin{bmatrix}-10y+4z+60=8 \\ -11y+4z+40=-16\end{bmatrix} \\ Isolate\text{ for y in}-10y+4z+60=8 \\ -10y=8-4z-60 \\ y=\frac{8-4z-60}{-10} \\ y=\frac{-4z-52}{-10} \\ y=\frac{2\left(z+13\right)}{5} \\ \mathrm{Substitute\:}y=\frac{2\left(z+13\right)}{5}\text{ in }-11y+4z+40=-16 \\ \begin{bmatrix}-11\cdot \frac{2\left(z+13\right)}{5}+4z+40=-16\end{bmatrix} \\ simplify \\ \begin{bmatrix}\frac{-2z-286}{5}+40=-16\end{bmatrix} \\ multiply\text{ through by 5} \\ -2z-286+200=-80 \\ isolate\text{ for z} \\ -2z=-80-200+286 \\ -2z=6 \\ z=\frac{6}{-2} \\ z=-3 \end{gathered}[/tex]Step 2: Find y
[tex]\begin{gathered} \mathrm{Substitute\:}z=-3\text{ in}\mathrm{\:}y=\frac{2\left(z+13\right)}{5} \\ y=\frac{2(-3+13)}{5} \\ y=\frac{2(10)}{5} \\ y=4 \end{gathered}[/tex]Step 3: Find z
[tex]\begin{gathered} \mathrm{Substitute\:}z=-3,\:y=4\text{ in }x=20-4y+z \\ x=20-4\cdot \:4-3 \\ x=1 \end{gathered}[/tex]Answer: The solutions to the system of equations are
[tex]x=1,\:z=-3,\:y=4[/tex]7. Principal = $39,300, Rate = 4.5%, Time = 6 months. What will that total principal + interest payment be rounded to the nearest dollar? o Lidhe total amount of
Answers
Given :
Principal = $39,300,
Rate = 4.5% = 0.045
Time = 6 months = 6/12 year = 0.5 year
Assume simple interest
So,
interest = Principal * rate * time = 39,300 * 0.045 * 0.5 = 884.25
So, the total = Principal + interest = 39,300 + 884.25 = 40,184.25
Rounding the answer to the nearest dollar
So, the total = $40,184
Sara is 33 years younger than Rolando. The sum of their ages is 105. Select the system of equations if Sara’s age is represented by S and Rolando’s age is represented by R.
Answers
Given:
Sara's age is represented by S and Ronaldo's age is represented by R.
Since,
Sara is 33 years younger than Ronaldo, then;
S= R - 33
Now, the sum of ages of Sara and Ronaldo is 105 then
[tex]R+S=105[/tex]Hence, from above,
[tex]\begin{gathered} S+R=105 \\ S=R-33 \end{gathered}[/tex]Therefore, second option is correct.
Sarah wants to take a vacation that will cost 2,562 if sarah plans to save for 9 months, then how much needs to be saved per month
Answers
Let:
x = Number of months
y = Total savings
a = Savings per month
so:
[tex]\begin{gathered} y=ax \\ where \\ y=2562 \\ x=9 \\ so\colon \\ 2562=9a \\ solve_{\text{ }}for_{\text{ }}a\colon \\ a=\frac{2562}{9} \\ a\approx284.67 \end{gathered}[/tex]She needs to save approximately $284.67 per month
Note:enter your answer and show all steps that you use to solve this problem3.jaoquin buys 3 dozen lightbulbs.after changing the lightbulbs in his house, he has 15 lightbulbs left how many lightbulbs did he use?*btw the not is the same thing to my question I have for number 6*6. the empire state building in new York City is 1,250 feet tall. it has 103 floors. rounded to the nearest whole, what is the height of each floor?
Answers
Answer: Number of lightbulbs that he used = 21 lightbulbs
1 dozen of light bulbs = 12 light bulbs
Jaoquin buys 3 dozens
3 dozens of lightbulbs = 3 * 12 lightbulbs
3 dozens of lightbulbs = 36 lightbulbs
This means that :
The number of light bulbs Jaoquin bought = 36
The number of lightbulbs that remain = 15
The number of lightbulbs that he used = (Number of lightbulbs that he buys) - (Number of lightbulbs that remains)
Number of lightbulbs that he used = 36 - 15
Number of lightbulbs that he used = 21 lightbulbs
Henry has 3 3/5 metres of rope, and Sam has a piece of rope that is 1 1/2 metres
shorter. What is the total amount of rope that the boys have together?
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A rational number is one that can be stated mathematically as the ratio or fraction p/q of two numbers, where p and q are the numerator and denominator, respectively. For instance, every integer and 3/7 are rational numbers.
The answer to the puzzle is 21 divided by ten.
What factors make a number rational?
It is possible to express rational numbers in the form pq, where p and q are integers and q0. Fractions cannot have a negative numerator or denominator, which is what distinguishes them from rational numbers.
Rates and ratios compare two different numbers. Simply put, a rate is a particular kind of ratio. The distinction is that a rate involves comparing two numbers.
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4) At a fundraising event, there is a raffle. A total of 165people bought a raffle ticket. The ratio of losing ticketsto winning tickets is 12:3. How many people wonsomething in the raffle?
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In order to determine the number of people which won something, it is necessary to write the following system of equations:
x + y = 165
y/x = 12/3
x is the people won and y the people lost.
The first equation represents tha total number of people in the event.
The second equation represents the ratio of losing tickets to winning people.
First, solve the second equation for y, and then replace the expression for y into the first equation:
y = 12/3 x
x + 12/3 x = 165
next, solve the last equation for x:
(3+12)/3 x = 165
15/3 x = 165
5x = 165
x = 165/5
x = 33
x is the number of people who won something in the event.
Hence, the number of people was 33
number serieswhat number comes next in the following series 27, 28, 32, 41, 57, 82, ?
Answers
Answer:
The number that comes next is;
[tex]118[/tex]Explanation:
Given the series;
[tex]27,28,32,41,57,82[/tex]From the series, if we observe the series closely we can see a relationship between the difference between consecutive terms.
[tex]\begin{gathered} 28-27=1=1^2 \\ 32-28=4=2^2 \\ 41-32=9=3^2 \\ 57-41=16=4^2 \\ 82-57=25=5^2 \end{gathered}[/tex]We can see that the difference follows the same pattern.
So, the next term would be the sum of the last term and the square of 6;
[tex]\begin{gathered} 82+6^2 \\ =82+36 \\ =118 \end{gathered}[/tex]Therefore, the number that comes next is;
[tex]118[/tex]find the volume or missing value 3ft, 2.5ft, 6ft
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The formula to find the volume of a rectangular prism is
[tex]\begin{gathered} V=l\cdot w\cdot h \\ \text{ Where V is the volume}, \\ l\text{ is the length,} \\ w\text{ is the width and} \\ \text{h is the height of the rectangular prism} \end{gathered}[/tex]Graphically,
So, in this case, you have
[tex]\begin{gathered} l=3ft \\ w=2.5ft \\ h=6ft \\ V=l\cdot w\cdot h \\ V=3ft\cdot2.5ft\cdot6ft \\ V=45ft^3 \end{gathered}[/tex]Therefore, the volume of the rectangular prism is 45 cubic feet.
You live 3 miles from collage and 2 miles from the business where you work.Let d represent the distance between your work and the collage write an inequality involving d.
Answers
The inequality involving the distance is 3 > d > 2.
What is an inequality?An inequality is simply used to illustrate the expressions that aren't equal. This can be illustrated through the use of greater than, less than, etc.
When you live live 3 miles from collage and 2 miles from the business where you work. This will be expressed thus
Let d represent the distance between your work and the collage and the inequality is 3 > d > 2.
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= The number of counties in state A and the number of counties in state B are consecutive even integers whose sum is 82. If state A has more counties than state B, how many counties does each state have? State A has counties.
Answers
State A have 42 counties and State B have 40 counties.
Define Linear equation
An equation is said to be linear if the maximum power of the variable is consistently 1. Another name for it is a one-degree equation. The standard form of a linear equation in one variable is of the form Ax + B = 0. Here, x is a variable, A is a coefficient and B is constant
Let,
x = The number of counties of state B
x + 2 = The number of counties of State A
It's given, The sum of counties of state A and state B is 82
so, the equation become is linear.
The linear equation will be,
x + (x + 2) = 82
solve for x,
2x + 2 = 82
2x = 82 - 2
2x = 80
x = 80/2
x = 40 (counties of State B)
put the value in x in x + 2,
40 + 2 = 42 (counties of State A)
Therefore, State A have 42 counties and State B have 40 counties.
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if the probability of drawing an A or B is 9/25, what is the probability of the complementary event?
Answers
If an event has a probability of "A", then the complementary event will have a probability of "1 - A".
Given, the probability of an event is 9/25, we can easily find the probability of the complementary event. Shown below:
[tex]\begin{gathered} 1-\frac{9}{25} \\ =\frac{25}{25}-\frac{9}{25} \\ =\frac{16}{25} \end{gathered}[/tex]The correct answer is:
[tex]\frac{16}{25}[/tex]What is the equation in slope-intercept form of the line that passes through the point (1,5) and is parallel to the line represented by 3x-y=4?
Answers
Answer:
[tex]3x - 14[/tex]
Step-by-step explanation:
-y= -3x+4
-1 because de y no have a number in front
-1y÷-1= -3x÷-1 4÷-1
if angle 2 = 106 degrees, what is the measurement of angle 6 ? ( better explanation in picture )
Answers
angle 2 and angle 6 are corresponding angles.
Since the lines crossed by the trnasversal are parallel, corresponding angles are congruent. (equal)
angle 6 = 106°
I need some help with this
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The product is:
(7*10⁵)*(3*10²) = 2.1*10⁸
So the correct option is D
The quotient is:
(2*10⁵)/(4*10²) = 5*10²
So the correct option is B.
How to get the products?
Here we want to get the product between numbers in scientific notation, the first one is:
a) (7*10⁵)*(3*10²)
We can rewrite this as:
(7*10⁵)*(3*10²) = (7*3)*(10⁵*10²) = (21)*(10⁵⁺²) = 21*10⁷
In scientific notation we can have only one digit at the left of the decimal point, so we can rewrite:
21*10⁷ = 2.1*10⁸
So the correct option is D.
b) Now the quotient is:
(2*10⁵)/(4*10²) = (2/4)*(10⁵*10²) = 0.5*10⁵⁻² = 0.5*10³
Again, we need to have a single digit in the left of the decimal point:
0.5*10³ = 5*10²
The correct option is B.
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Approximate when the function is positive, negative, increasing, or decreasing.
Describe the end behavior of the function.
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The function y = - | x | + 1 is increasing on ( - ∞, 0 ) and decreases on ( 0, ∞ ).
A relationship between a group of inputs with each output is referred to as a function. In plain English, a function is an association between inputs in which each input is connected to precisely one output. A domain, codomain, or range exists for every function. Typically, f(x), where x is the input, is used to represent a function.
Consider the function,
y = - | x | + 1
The non-negative value of a real number x, represented by the symbol |x|, is the absolute value or modulus of x, regardless of its sign.
From the graph, we can approximate that the function is increasing from negative infinity to zero and the function decreases from zero to infinity.
Increasing on: ( - ∞, 0 )
Decreasing on: ( 0, ∞ )
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The distance to your brother's house is 481 miles, and the distance to Disneyland is 518 miles. If it took 13 hours to drive to your brother's house, how long would you estimate the drive to Disneyland to take?
Answers
Answer:
364/7 = 260/d
Cross multiply.
364d = 1820
d = 5 hours
Miles per hour, mph = miles/hour
364 miles/7 hours = 52 mph
260 miles/52 mph = 5 hours
Meaning 1 hour = 37 miles
Difference between brothers house and Disneyland = 37 miles
37 miles = 1 hour
Disneyland = 13 from brothers house + 1 hour from 37 extra miles =14 hours
It would take 14 hours to drive to Disneyland.