The correct Option is D. 45÷3= 15 . The equation that best shows that 45 is a multiple of 15 is 45 ÷ 3 = 15.
A multiple is a product that results from multiplying two or more numbers.
A common multiple is a multiple that is common to two or more numbers.
A multiple of a number can be expressed as an integer multiple of the number.
If the result is a whole number, the first number is a multiple of the second.
An equation that shows 45 is a multiple of 15 is as follows: 45 ÷ 3 = 15.
A multiple is a number that can be divided by another number without leaving a remainder.
As a result, we divide 45 by 3 to find out whether 45 is a multiple of 15.
If the result is a whole number, 45 is a multiple of 15.
Here is the equation that shows this: 45 ÷ 3 = 15
Thus, we can conclude that the equation that best shows that 45 is a multiple of 15 is 45 ÷ 3 = 15.
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In ΔBCD,
B
D
‾
BD
is extended through point D to point E,
m
∠
C
D
E
=
(
9
x
−
12
)
∘
m∠CDE=(9x−12)
∘
,
m
∠
B
C
D
=
(
2
x
+
3
)
∘
m∠BCD=(2x+3)
∘
, and
m
∠
D
B
C
=
(
3
x
+
5
)
∘
m∠DBC=(3x+5)
∘
. Find
m
∠
B
C
D
.
m∠BCD.
m∠BCD = 31.57° (approx). Hence, the answer of the angle is 31.57 degrees.
In the given diagram, BD is extended through point D to point E, m∠CDE = (9x - 12)°, m∠BCD = (2x + 3)°, and m∠DBC = (3x + 5)°. We need to find m∠BCD.
Use the Angle Sum Property of a Triangle.The Angle Sum Property of a Triangle states that the sum of all the angles in a triangle is equal to 180°.The angle sum of ΔBCD is:m∠BCD + m∠DBC + m∠CDE = 180°Substituting the given angles, we get:(2x + 3)° + (3x + 5)° + (9x - 12)° = 180°Simplifying the above expression, we get:14x - 4 = 180°14x = 180° + 4x = 184/14x = 92/7Find m∠BCDWe know that m∠BCD = (2x + 3)°
Substituting x = 92/7, we get:
m∠BCD = (2 × 92/7 + 3)° = (184/7 + 3)° = 221/7°
Therefore, m∠BCD = 31.57° (approx). Hence, the answer is 31.57.
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determine the value of x
The hypotenuse (x) of the right triangle is 10 units
Finding the hypotenuse of the right triangleFrom the question, we have the following parameters that can be used in our computation:
The right triangle
The hypotenuse (x) of the right triangle can be calculated using the following sine equation
sin(30) = 5/x
Using the above as a guide, we have the following:
x = 5/sin(30)
Evaluate
x = 10
Hence, the hypotenuse of the right triangle is 10
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Please answer ASAP I will brainlist
Answer:
Step-by-step explanation:
The given augmented matrix is already in reduced row echelon form. We can interpret it as a system of equations as follows:
1x + 0y + 0z + (4/5)w = 0
0x + 1y + 0z + 5w = 0
0x + 0y + 1z - 4w = 0
0x + 0y + 0z + w = -4
From the last row, we can see that w = -4. Substituting this value back into the previous rows, we get:
1x + 0y + 0z + (4/5)(-4) = 0
0x + 1y + 0z + 5(-4) = 0
0x + 0y + 1z - 4(-4) = 0
Simplifying these equations, we have:
x - (16/5) = 0
y - 20 = 0
z + 16 = 0
From the second equation, y = 20. From the third equation, z = -16. Substituting these values into the first equation, we get x - (16/5) = 0, which implies x = 16/5.
Therefore, the solution of the system is (16/5, 20, -16, -4).
So, the correct choice is:
A. The system has exactly one solution. The solution is
(16/5, 20, -16, -4)
A box contains 240 lumps of sugar. Five lumps are fitted across the box and there were three layers. How many lumps are fitted along the box?
Which expression is equivalent to 3(x+4)
The answer is:
3x + 12
Work/explanation:
To simplify this expression, we will use the distributive property:
[tex]\sf{3(x+4)}[/tex]
Distribute the 3:
[tex]\sf{3\cdot x + 3 \cdot 4}[/tex]
[tex]\sf{3x+12}[/tex]
Therefore, the answer is 3x + 12.The new corporate logo created by the design engineers at Magic Motors is shown in the accompanying diagram. If the measure of arc AC = 80°, what is the mLB?
The measure of angle LB is 40°.
To find the measure of angle LB, we can use the fact that the measure of an inscribed angle is half the measure of its intercepted arc.
In this case, we are given that the measure of arc AC is 80°, so we can conclude that the measure of angle LB is half of that.
Since angle LB is an inscribed angle that intercepts arc AC, we can write the equation:
mLB = 1/2 [tex]\times[/tex] mAC
Substituting the given value, we have:
mLB = 1/2 [tex]\times[/tex] 80°
mLB = 40°
Therefore, the measure of angle LB is 40°.
In the context of the corporate logo, angle LB represents a portion of the circular shape of the logo.
By knowing the measure of arc AC, we can determine the measure of angle LB, which helps in accurately representing the logo in terms of angles and proportions.
This information is crucial for design and branding purposes, as it ensures consistency and precision in the presentation of the logo across various media and materials.
Overall, understanding the measures of angles and arcs in the logo design allows for effective communication and replication of the logo's visual elements, ensuring brand recognition and consistency in its representation.
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The height of a rectangular box is 7 ft. The length is 1 ft longer than thrice the width x. The volume is 798 ft³.
(a) Write an equation in terms of x that represents the given relationship.
The equation is
The equation in terms of x that represents the given relationship is 114 = (1 + 3x) * (Width)
Let's break down the information given:
Height of the rectangular box = 7 ft
Length of the rectangular box = 1 ft longer than thrice the width (x)
Volume of the rectangular box = 798 ft³
To write an equation that represents the given relationship, we need to relate the length, width, and height to the volume.
The volume of a rectangular box is given by the formula: Volume = Length * Width * Height.
Given that the height is 7 ft, we can substitute this value into the equation.
Volume = (Length) * (Width) * (7)
Now, let's focus on the length. It is described as 1 ft longer than thrice the width.
Length = 1 + (3x)
Substituting this value into the equation, we have:
Volume = (1 + (3x)) * (Width) * (7)
Since the volume is given as 798 ft³, we can set up the equation as follows:
798 = (1 + (3x)) * (Width) * 7
Simplifying further, we get:
798 = 7 * (1 + 3x) * (Width)
Dividing both sides of the equation by 7, we have:
114 = (1 + 3x) * (Width)
Therefore, the equation in terms of x that represents the given relationship is:
114 = (1 + 3x) * (Width)
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The solution to the system is (a) (4/5, 5, -4, -4)
How to determine the solution to the systemFrom the question, we have the following parameters that can be used in our computation:
The augmented matrix
Where, we have
[tex]\left[\begin{array}{cccc|c}1&0&0&0&4/5\\0&1&0&0&5\\0&0&1&0&-4\\0&0&0&1&-4\end{array}\right][/tex]
From the above, we have the diagonals to be 1
And other elements to be 0
This means that the equation has been solved
So, we have
a = 4/5, b = 5, c = -4 and d =-4
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Question #3
Solve for x
OOO
O 10
07
5
8
6x+8
N
p
U
K
122°
L
M
194°
The calculated value o x in the circle is 7
How to determine the solution for xFrom the question, we have the following parameters that can be used in our computation:
The circle
The value of x can be calculated using teh equation of the intersection of chords
So, we have
122 = 1/2(6x + 8 + 194)
Evaluate
244 = 6x + 202
So, we have
6x = 42
Divide by 6
x = 7
Hence, the solution for x is 7
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Solve the proportion for the missing values 5/12 = x/20
Answer:
x = 5
Step-by-step explanation:
We can solve for x in this proportion, or an equation of ratios, by multiplying both sides by 20.
[tex]{/}\!\!\!\!\!{20}\cdot \dfrac{5}{{/}\!\!\!\!\!20}=\dfrac{x}{{/}\!\!\!\!\!20} \cdot {/}\!\!\!\!\!20[/tex]
We can see that the 20s cancel in the numerator and denominator in both sides, and the equation is solved for x:
[tex]x = 5[/tex]
What are the values of x and y?
A) x = 18√3; y = 9√3
B) x = 9; y = 9√3
C) x = 9√3; y = 9
D) x = 9√2; y = 9
The values of x and y are 9√3 and 9. Thus, option C is the answer.
From the figure, we know that angle A = 60°, angle C = 30° and side AC =18 units.
We have to use trigonometric ratios to find the values of x and y.
sin30° = Opposite side/Hypotenuse
But, we also know that sin30° = 1/2
Substituting the value in the above equation, we get
1/2 = y/18
Thus, the value of y = 18/2 = 9.
Now, sin60° = Opposite Side/ Hypotenuse
sin60° = √3/2
Substituting the value, we get
√3/2 = x/18
Thus, x = 9√3.
Therefore, the values of x and y in the given triangle are 9√3 and 9.
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find the inverse of each function
Answer:
c
Step-by-step explanation:
assume base 10
-logy = x
[tex] \frac{1}{ log(y) } = x[/tex]
log base x y = 5 turns into the format x^ 5 = y
implement that to get c
Find the measure of the indicated arc:
55°
110°
O 250°
220°
?
Q
110 °
R
S
Answer:
? = 220°
Step-by-step explanation:
the measure of the inscribed angle QRS is half the measure of its intercepted arc QS , then
QS = ? = 2 × QRS = 2 × 110° = 220°
A ship X sailing with a velocity (21 kmh 052⁰) observes a light fron a lighthuse due North. The bearing of the liglhthouse from the ship 20 minutes later is found to be 312. calcuate correct to thre sigificant figures
i) the orignal distance when the lighthoues is due West of the ship from the time when it is due North of the ship.
ii) the time in minutes, when the lighthouse is due West of the ship from the time when it is due North of the ship.
iii) the distance in km of the ship from the lighthoue when the light.hose is due West of the ship
i) the original distance when the lighthouse is due West of the ship is 7 km
ii) The time in minutes when the lighthouse is due West of the ship is 21 minutes
iii) The distance in km of the ship from the lighthouse when the lighthouse is due West of the ship is 29.97 km
To solve this problem, we'll use the concepts of relative velocity and trigonometry. Let's break down the problem into three parts:
i) Finding the original distance when the lighthouse is due West of the ship:
The ship's velocity is given as 21 km/h at a bearing of 052°. Since the ship observed the lighthouse due North, we know that the angle between the ship's initial heading and the lighthouse is 90°.
To find the distance, we'll consider the ship's velocity in the North direction only. Using trigonometry, we can determine the distance as follows:
Distance = Velocity * Time = 21 km/h * (20 min / 60 min/h) = 7 km (to three significant figures).
ii) Finding the time in minutes when the lighthouse is due West of the ship:
To find the time, we need to consider the change in angle from 052° to 312°. The difference is 260° (312° - 052°), but we need to convert it to radians for calculations. 260° is equal to 260 * π / 180 radians. The ship's velocity in the West direction can be calculated as:
Velocity in West direction = Velocity * cos(angle) = 21 km/h * cos(260 * π / 180) ≈ -19.98 km/h (negative because it's in the opposite direction).
To find the time, we can use the formula:
Time = Distance / Velocity = 7 km / (19.98 km/h) = 0.35 h = 0.35 * 60 min = 21 minutes (to three significant figures).
iii) Finding the distance in km of the ship from the lighthouse when the lighthouse is due West of the ship:
We can use the formula for relative velocity to find the distance:
Relative Velocity = sqrt((Velocity in North direction)² + (Velocity in West direction)²)
Using the values we calculated earlier, we have:
Relative Velocity = sqrt((21 km/h)² + (-19.98 km/h)²) ≈ 29.97 km/h (to three significant figures).
Therefore, the ship is approximately 29.97 km away from the lighthouse when the lighthouse is due West of the ship.
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williams has 32 coins that are all either quarter or dimes the coins have a value of $5 how many dimes does williams have
Answer:
20 dimes
Step-by-step explanation:
1 dime = $0.1
1 quarter = $0.25
Let there be x dimes
Then the number of quarters is 32-x
Also, $5 = 0.1x + 0.25(32-x)
⇒ 5 = 0.1x + 8 - 0.25x
⇒ 0.25x - 0.1x = 8 - 5
⇒ 0.15x = 3
⇒ x = 3/0.15
⇒ x = 20
witch of the following would be a good name for the function that takes the length of a race and returns the time needed to complete it
a. length(time)
b.Time(race)
c.time(length)
d.cost(time)
The most appropriate name for the function that takes the length of a race and returns the time needed to complete it would be "time(length)".
When choosing a name for a function, it is important to consider clarity and readability. The name should accurately describe the purpose of the function and provide a clear indication of what it does.
In this case, the function is expected to take the length of a race as input and return the time needed to complete it as output. Among the given options, "time(length)" is the most suitable choice.
a. length(time): This name suggests that the function takes time as input and returns the length. However, in this scenario, we are interested in finding the time needed to complete the race based on its length, so this option is not the best fit.
b. Time(race): This name implies that the function takes a race as input and returns the time. While it conveys the idea of finding the time, it doesn't explicitly mention that the input is the length of the race, making it less clear.
c. time(length): This option accurately describes the purpose of the function, indicating that it takes the length of the race as input and returns the corresponding time. It is concise, clear, and aligns with the conventional naming conventions for functions.
d. cost(time): This name suggests that the function calculates the cost based on time, which is not relevant to the scenario of finding the time needed to complete a race.
Therefore, "time(length)" is the most suitable and appropriate name for the function.
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CAN SOMEONE HELPPPPPP
Answer:
∠1 = 100
∠2 = 110
Step-by-step explanation:
∠1 + 80 = 180(angles on a straight line add to 180)
∠1 = 180 - 80
∠1 = 100
∠2 = 110 (vertically opposite angles are equal)
Pamela bought a cat carrier to take her new kitten, Muffinnette, to the vet. The carrier is shaped like a rectangular prism that is 15 inches long, 9 1/2
inches wide, and 10 inches tall.
Which equation can you use to find the volume of the cat carrier, V?
What is the volume of the cat carrier?
Select the correct answer. What is the solution to this equation? 9^x - 1 = 2 O A. - 1/1/20 OB. 2 O C. OD. 1/1/20 1 23 Edmentum. All rights reserved. Reset Next
Answer:
D. 1/2
Step-by-step explanation:
9^x - 1 = 2
9^x = 3
x = log{sub}9 (3)
x = 1/2 (9^(1/2)=3)
The area of the figure is square units.
3 units, 8 units, 3 units, 9 units, 3 units, 21 units
The area of the figure is 114 square units.
To determine the area of the figure, we need to identify its shape.
From the given dimensions, it appears that we have three rectangular sections.
The first section has a length of 3 units and a width of 8 units, giving us an area of 3 [tex]\times[/tex] 8 = 24 square units.
The second section has a length of 3 units and a width of 9 units, resulting in an area of 3 [tex]\times[/tex] 9 = 27 square units
The third section has a length of 3 units and a width of 21 units, yielding an area of 3 [tex]\times[/tex] 21 = 63 square units.
To find the total area of the figure, we need to sum up the areas of the individual sections:
Total area = 24 + 27 + 63 = 114 square units.
Therefore, the area of the figure is 114 square units.
It's important to note that without a clear description or diagram of the figure, it's challenging to provide an accurate interpretation.
The given dimensions could represent various arrangements, and the resulting area would vary accordingly.
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Pls help I am stuck thank you so much
The perimeter of shape C is 30 cm shorter than the total perimeter of A and B.
What is the perimeter of a polygon?The perimeter of a polygon is given by the sum of all the lengths of the outer edges of the figure, that is, we must find the length of all the edges of the polygon, and then add these lengths to obtain the perimeter.
Hence the perimeter of each shape is given as follows:
A = 2 x (5 + 12) = 34 cm.B = 2 x (4 + 9) = 26 cm.C = 12 + 5 + 9 + 4 = 30 cm.Then the difference is given as follows:
34 + 26 - 30 = 30 cm.
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When parallel lines are intersected by a transversal, which of the following angle pairs are supplementary?
Answer:
if two parallel lines are cut by a transversal,then, exterior angles on the same side of the transversal are supplementary!
Step-by-step explanation:
I don't really know how to explain it but I hope this helped!
Polygon s is a scaled copy of polygon R.
What is the value of t
Using the concept of scale factor, the value of t in polygon s is: 7.2
How to use the scale factor?The amount by which the shape is expanded or contracted is referred to as the scale factor. This is usually utilized when 2D shapes such as circles, triangles, squares and rectangles need to be enlarged. If y = Kx is an equation, K is the scaling factor for x.
From the given image, since Polygon s is a scaled copy of polygon R, then we can say that using the concept of scale factor, we have:
9/t = 12/9.6
t = (9 * 9.6)/12
t = 7.2
Thus, we can be sure that is the value of t of the polygon S using the concept of scale factor
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On a number line, a number, b, is located the same distance from 0 as another number, a, but in the opposite direction.
The number b varies directly with the number a. For example b = 22 when a = -22. Which equation represents this
direct variation between a and b?
b=-a
0-b=-a
O b-a=0
Ob(-a)=0
Let theta be an angle in quadrant two such that cos theta=-3/4. find the exact values of csc theta and cot theta
The exact values of csc(theta) and cot(theta) are: csc(theta) = 4√7/7
cot(theta) = -3√7/7.
To find the exact values of csc(theta) and cot(theta), given that cos(theta) = -3/4 and theta is an angle in quadrant two, we can use the trigonometric identities and the Pythagorean identity.
We know that cos(theta) = adjacent/hypotenuse, and in quadrant two, the adjacent side is negative. Let's assume the adjacent side is -3 and the hypotenuse is 4. Using the Pythagorean identity, we can find the opposite side:
[tex]opposite^2 = hypotenuse^2 - adjacent^2opposite^2 = 4^2 - (-3)^2opposite^2 = 16 - 9opposite^2 = 7[/tex]
opposite = √7
Now we have the values for the adjacent side, opposite side, and hypotenuse. We can use these values to find the values of the other trigonometric functions:
csc(theta) = hypotenuse/opposite
csc(theta) = 4/√7
To rationalize the denominator, we multiply the numerator and denominator by √7:
csc(theta) = (4/√7) * (√7/√7)
csc(theta) = 4√7/7
cot(theta) = adjacent/opposite
cot(theta) = -3/√7
To rationalize the denominator, we multiply the numerator and denominator by √7:
cot(theta) = (-3/√7) * (√7/√7)
cot(theta) = -3√7/7
Therefore, the exact values of csc(theta) and cot(theta) are:
csc(theta) = 4√7/7
cot(theta) = -3√7/7
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1. Brandon went to a Formula One car race and used his stopwatch to time how fast his favorite driver, Fernando Alonso, went around the 4.7-kilometer track. Brandon started the timer at the beginning of the second lap, when the cars were already going fast. When he stopped the timer at the beginning of the third lap, one minute and three seconds had passed.
b. If you graphed the distance Fernando had traveled at the beginning of the lap and at the end of the lap, what would the coordinates of these points be? What would the
- and
-axes on this graph represent?
c. Find the equation of the line between these two points. What does this line represent?
d. If Fernando continues to average this speed, about how long do you think it would take him to finish the entire race? The race is 500 km.
Step-by-step explanation:
b. To determine the coordinates of the points on the graph, we need to consider the information given.
At the beginning of the second lap, one minute and three seconds had passed. Since each lap is 4.7 kilometers long, we can calculate the distance traveled at the beginning of the lap using the formula:
Distance = (Number of laps - 1) × Length of each lap
For the beginning of the second lap:
Distance = (2 - 1) × 4.7 km = 4.7 km
At the beginning of the third lap, one minute and three seconds had passed. Therefore, the distance traveled at the beginning of the third lap is:
Distance = (3 - 1) × 4.7 km = 9.4 km
The coordinates of the points on the graph would be:
Point A: (4.7 km, 4.7 km)
Point B: (9.4 km, 9.4 km)
On the graph, the x-axis would represent the distance traveled at the beginning of the lap, and the y-axis would represent the distance traveled at the end of the lap.
c. To find the equation of the line between the two points, we can use the slope-intercept form of a linear equation:
y = mx + b
where m is the slope and b is the y-intercept.
Using the coordinates of the two points (4.7 km, 4.7 km) and (9.4 km, 9.4 km), we can calculate the slope:
m = (y2 - y1) / (x2 - x1)
= (9.4 km - 4.7 km) / (9.4 km - 4.7 km)
= 4.7 km / 4.7 km
= 1
The slope of the line is 1.
Since the line passes through the origin (0, 0), the y-intercept (b) is 0.
Therefore, the equation of the line is:
y = 1x + 0
y = x
This line represents a one-to-one relationship between the distance traveled at the beginning of the lap and the distance traveled at the end of the lap.
d. To estimate how long it would take Fernando to finish the entire race if he continues to average the same speed, we need to find the time it takes for one lap.
In the given scenario, Brandon timed Fernando's lap for one minute and three seconds. Since there are 3 laps in total, we can divide the total time by the number of laps to find the average time per lap:
Average time per lap = Total time / Number of laps
= 1 minute and 3 seconds / 3
= 21 seconds
Since each lap is 4.7 kilometers long, we can calculate the speed:
Speed = Distance / Time
= 4.7 km / (1 minute + 21 seconds)
To estimate the time it would take Fernando to finish the entire race, we divide the total race distance by the speed:
Total race time = Total race distance / Speed
= 500 km / (4.7 km / (1 minute + 21 seconds))
To calculate the time, we need to convert 1 minute and 21 seconds to a decimal form:
1 minute + 21 seconds = 1 minute + (21 seconds / 60 seconds)
= 1 minute + 0.35 minutes
= 1.35 minutes
Substituting the values:
Total race time = 500 km / (4.7 km / 1.35 minutes)
= 500 km × (
1.35 minutes / 4.7 km)
= 500 km × 0.28723...
≈ 143.615 minutes
Therefore, it would take approximately 143.615 minutes for Fernando to finish the entire race if he continues to average the same speed.
A bag of marbles contains 2 blue marbles, 4 red marbles 6 green marbles
Answer:
We start with 17 marbles, 4 of which are red. So P(first marble is red) = 4/17. Since the red marble is not replaced, there are now 16 marbles, 3 of which are red. So P(second marble is red) = 3/16.
The correct calculation is
P(red, then red) = 4/17 × 3/16
A charged particle produces an electric field with a magnitude of 2.0 N/C at a point that is 50 cm away from the particle. a) Without finding the charge of the particle, determine the electric field produced by this charge at a point 25 cm away from it. b) What will happen to the Electric field at the distance 50 cm, if you double the charge? c) What is the magnitude of the particle’s charge?
To solve these problems, we can use Coulomb's Law, which states that the magnitude of the electric field produced by a charged particle is directly proportional to the charge and inversely proportional to the square of the distance from the particle.
a) Without finding the charge of the particle, we can use the inverse square relationship. If the electric field magnitude is 2.0 N/C at a distance of 50 cm, then at half the distance (25 cm), the electric field would be four times stronger. Therefore, the electric field at 25 cm would be 4 * 2.0 N/C = 8.0 N/C.
b) Doubling the charge would result in doubling the electric field magnitude. So, if the electric field at a distance of 50 cm was initially 2.0 N/C, it would become 4.0 N/C after doubling the charge.
c) To determine the magnitude of the particle's charge, we need to use the equation for the electric field:
E = k * (|q| / r^2)
where E is the electric field magnitude, k is the electrostatic constant, |q| is the magnitude of the charge, and r is the distance from the particle.
Using the known values of E = 2.0 N/C and r = 50 cm (or 0.5 m), we can rearrange the equation to solve for |q|:
|q| = E * r^2 / k
Substituting the values and the known value of k, we can calculate the magnitude of the charge.
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The following pie chart shows the number of rabbits, sheep, cattle, pigs on a farm
sheep
700
cattle
300
Pig
500
a. How many animals are on the farm? b.What represents the number of sheep on the farm
c. what percentage of the total number of animals are rabbits
d. Calculate the angle that represents number of pigs
Roger can run one mile in 9 minutes. Jeff can run one mile in 6 minutes. If Jeff gives Roger a 1 minute head start, how
long will it take before Jeff catches up to Roger? How far will each have run?
They each will have run of a mile.
Both Roger and Jeff will have run a distance of 1/3 mile when Jeff catches up to Roger after 2 minutes.
To solve this problem, we can determine the relative speeds of Roger and Jeff.
Since Roger runs one mile in 9 minutes, his speed is 1/9 miles per minute.
Similarly, Jeff runs one mile in 6 minutes, so his speed is 1/6 miles per minutes.
Let's assume that Jeff catches up to Roger after t minutes.
In that time, Roger would have run (1/9) [tex]\times[/tex] t miles, and Jeff would have run (1/6) [tex]\times[/tex] t miles.
Since Jeff gives Roger a 1-minute head start, we can express their distances covered as:
Distance covered by Roger = (1/9) [tex]\times[/tex] (t+1) miles
Distance covered by Jeff = (1/6) [tex]\times[/tex] t miles
For Jeff to catch up to Roger, their distances covered must be equal. So we can set up the equation:
(1/9) [tex]\times[/tex] (t+1) = (1/6) [tex]\times[/tex] t
To solve for t, we can cross-multiply and simplify:
6(t+1) = 9t
6t + 6 = 9t
6 = 9t - 6t
6 = 3t
t = 2
Therefore, it will take 2 minutes for Jeff to catch up to Roger.
Substituting t = 2 back into the equations, we can find the distances covered by each:
Distance covered by Roger = (1/9) [tex]\times[/tex] (2+1) = 1/3 mile
Distance covered by Jeff = (1/6) [tex]\times[/tex] 2 = 1/3 mile
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