the train travels at 45 meters per each second
this question can be rewritten into the equation d = 45t, where d represents the distance traveled and t represents the time elapsed.
we are given two seperate times, so we can replace the variable t with each respective time. this leaves us with only one missing variable, so we can successfully isolate to find the other.
for i), we substitute t for 30 seconds, shown as follows
d = 45t
d = 45(30)
d = 1350m
for ii), we know that there are 60 seconds in every minute, so in multiplying 60 seconds by two we get the total amount of seconds in two minutes, which is 120.
we can now use 120 to substitute t in our equation
d = 45t
d = 45(120)
d = 5400m
hope this helps!!
Answer:
i) 1350 m
ii) 5400 m
Step-by-step explanation:
To calculate the distance traveled by the train, we can use the formula:
[tex]\large\boxed{\sf Distance=Speed \times Time}[/tex]
[tex]\hrulefill[/tex]
Question (i)Given values:
Speed = 45 m/s (meters per second)Time = 30 secondsSubstitute the given values into the formula for distance:
[tex]\begin{aligned}\sf Distance&= \sf 45\; m/s \times 30\;s\\& = \sf 1350\:m\end{aligned}[/tex]
Therefore, the train travelled a distance of 1350 meters in 30 seconds.
[tex]\hrulefill[/tex]
Question (ii)Given values:
Speed = 45 m/s (meters per second)Time = 2 minutesAs the time is given in a different unit of time than the speed, we must first convert the time into seconds. As 1 minute = 60 seconds, then:
[tex]\sf 2\; minutes = 60 \;s \times 2 = 120 \;s[/tex]
Substitute the given values into the formula for distance:
[tex]\begin{aligned}\sf Distance&= \sf 45\; m/s \times 120\;s\\& = \sf 5400\:m\end{aligned}[/tex]
Therefore, the train travelled a distance of 5400 meters in 2 minutes.
In the graph above, which vertical line (V) and horizontal line (H) can be used to graph point D?
Question 5 options:
A)
V: x = –4; H: y = 4
B)
V: y = –4; H: x = –4
C)
V: y = 4; H: x = –4
D)
V: x = 4; H: y = 4
Answer: A. V: x = –4; H: y = 4
Step-by-step explanation:
Write the equation of straight line passing through (3,4). Does the point (4,3) lie on
your line
Answer:
Is there more information? There is not enough to find the slope of a line. I'll answer with an equation that works, but I suspect it won't be correct.
Step-by-step explanation:
If the only requirement is to have a line that goes through (4,3). Then one could simply say:
y = 4
This is a horizonal line that goes through (3,4), and will always produce a y value of 4 regardless of x. No, it will not pass through (4,3) since y is aleways 4, regardless of x.
If you wanted to get fancier, we could write a needlessly more complex equation:
y = (4/3)x
When x = 3, y = 4, so (3,4) is on this line. But (4,3) is not. y = (4/3)(4) means y = (16/3), not 4.
What is the equation in slope-intercept form for the line that passes through the points (-2, -1) and (1, 5)?
Answer:
Step-by-step explanatio
13. In A ABC, if m
BF is an angle bisector, find
m
If in the triangle ABC , BF is an angle bisector and ∠ABF=41° then angle m∠BCE=8°.
Given that m∠ABF=41° and BF is an angle bisector.
We are required to find the angle m∠BCE if BF is an angle bisector.
Angle bisector basically divides an angle into two parts.
If BF is an angle bisector then ∠ABF=∠FBC by assuming that the angle is divided into two parts.
In this way ∠ABC=2*∠ABF
∠ABC=2*41
=82°
In ΔECB we got that ∠CEB=90° and ∠ABC=82° and we have to find ∠BCE.
∠BCE+∠CEB+EBC=180 (Sum of all the angles in a triangle is 180°)
∠BCE+90+82=180
∠BCE=180-172
∠BCE=8°
Hence if BF is an angle bisector then angle m∠BCE=8°.
Learn more about angles at https://brainly.com/question/25716982
#SPJ1
Solve the inequality for w .
−9>6+5w
Hi :)
Let's use some Algebra skills to find w ^•^
————————————First off, let's subtract both sides by 6
[tex]\longrightarrow\darkblue\sf{-9-6 > 5w}[/tex]
[tex]\longrightarrow\darkblue\sf{-15 < 5w}[/tex]
Divide both sides by 5
[tex]\longrightarrow\sf{-3 < w}[/tex]
Or
[tex]\longrightarrow\sf{w > -3}[/tex]
[tex]\tt{Learn\:More;Work\:Harder}[/tex]
:)
Quick algebra 1 question for 10 points!
Only answer if you know the answer, quick shout-out to tariqareesha2 and MrBrainly, tysm for the help!
[tex]y = 2x {}^{2} - 4x - 16 \\ \delta = b {}^{2} - 4ac \\ \delta = ( - 4) {}^{2} - 4(2)( - 16) \\ \delta = 16 + 128 \\ \delta = 144 > 0 [/tex]
[tex]x = \frac{ - b + \sqrt{ \delta} }{2a} = \frac{4 + 12}{2 \times 2} = \frac{16}{4} = 4[/tex]
[tex]x = \frac{ - b - \sqrt{ \delta} }{2a} = \frac{4 - 12}{2 \times 2} \frac{ - 8}{4} = - 2[/tex]
[tex]x = 4 \: \: \: \: \: or \: \: \: \: x = - 2 \\ (x - 4) = 0 \: \: \: \: \: or \: \: \: \: \: (x + 2) = 0[/tex]
[tex]f(x) = \alpha (x - 4)(x + 2) \\ f(x) = \alpha x { }^{2} + 2 \alpha x - 4 \alpha x - 8 \alpha \\ f(x) = \alpha x {}^{2} - 2 \alpha x - 8 \alpha \\ by \: comparison \\ \alpha = 2[/tex]Factors are:1) 22) x - 43) x + 2The scores of students on a standardized test are normally distributed with a mean of 300 and a standard deviation of 40. (a) what proportion of scores lie between 220 and 380 points?
0.9544 = 95.44% of scores lie between 220 and 380 points.
Normal distribution problems can be solved using the Z-score formula.
With a set of means and standard deviations, the Z-score for measure X is given by: After finding the Z-score, look at the Z-score table to find the p-value associated with that Z-score. This p-value is the probability that the value of the measure is less than X. H. Percentile of X. Subtract 1 from the p-value to get the probability that the value of the measure is greater than X.
[tex]z = \frac{x - \mu}{\sigma} \,[/tex]
We are given mean 300, standard deviation 40.
This means that µ= 300, σ = 40
What proportion of scores lie between 220 and 380 points?
This is the p-value of Z when X = 380 subtracted by the p-value of Z when X = 220.
X = 380
[tex]z = \frac{x - \mu}{\sigma} \,[/tex]
Z= (380-300)/40
Z= 2
Z=2 has a p-value of 0.9772.
X=300
[tex]z = \frac{x - \mu}{\sigma} \,[/tex]
Z= (220-380)/40
Z=-2
Z=-2 has a p-value of 0.9772.
0,9772 - 0,0228 = 0,9544
0.9544 = 95.44% of scores lie between 220 and 380 points.
For more information about normal distribution, visit https://brainly.com/question/4079902
#SPJ1
PLEASE HELP IK ITS SO HARD TO UNDERSTAND FOR MEEE
Answer: 15
Step-by-step explanation:
First step is to find the slope of the line given
y = -x - 2
y = mx + c where m is the slope of the line so the slope of the line is -1
If 2 lines are perpendicular to one another, the product of the slopes is -1 so the slope of the perpendicular line is -1/-1 = 1
y = 1x + c or y = x + c
As the line passes through the coordinate (-5,10), we can substitute the x and y value of the coordinates into the equation
10 = -5 + c
c = 15
So the equation of the line is y = x + 15
Given MTS and SQP, find sq
From the given similar triangles we can conclude that the length of Side SQ is; 4
How to solve similar triangles?
We are given that;
PQ is parallel and congruent to MT.
Now, from the concept of similar triangles , we can say that;
PS/TS = QS/MS
From the given triangle we see that;
PS = 3 - 2x
QS = 6x - 1
MS = 30
TS = 10
Thus;
(3 - 2x)/10 = (6x - 1)/30
Cross multiply to get;
3(3 - 2x) = 6x - 1
9 - 6x = 6x - 1
Rearranging gives;
6x + 6x = 9 + 1
12x = 10
x = 10/12
x = 5/6
Thus;
SQ = 6(5/6) - 1
SQ = 4
Read more about Similar Triangles at; https://brainly.com/question/11920446
#SPJ1
Which construction requires both endpoints of the diameter and the points where the arcs intersect the circle to be connected, in order, by line segments? an equilateral triangle inscribed in a circle a square inscribed in a circle a similar circle inscribed in a circle a regular hexagon inscribed in a circle
A regular hexagon inscribed in a circle is the construction that requires both endpoints of the diameter and the points where the arcs intersect the circle to be connected, in order, by line segments. Option D. This is further explained below.
What is a segment?Generally, any of the pieces into which something may be separated or which naturally separates over time. a section that is removed from a figure (such as a circle) using a line or plane as the cutting tool. a segment of a straight line that includes the territory between two points.
In conclusion, For the construction of a regular hexagon that is inscribed inside a circle, it is necessary for the ends of the diameter as well as the locations at which the arcs meet the circle to be linked, in the correct sequence, by line segments.
Read more about segments
https://brainly.com/question/17430860
#SPJ1
Complete Question
Which construction requires both endpoints of the diameter and the points where the arcs intersect the circle to be connected, in order, by line segments?
an equilateral triangle inscribed in a circle a square inscribed in a circle a similar circle inscribed in a circle a regular hexagon inscribed in a circleP= ().()
Q=(),()
Please help thanks so much
The coordinates for P and Q are as follows,
P = (a, a)
Q = (0, a)
Finding the Missing Coordinates:
Triangle OPQ is an isosceles triangle, hence two of its legs are equal.
Since the coordinates of the end point of the leg OQ lies on the y-axis, and OP is parallel to x-axis, OQ ⊥ QP ............ (1)
Also, it indicates that the x- coordinate of point Q is 0.
⇒ The coordinates of point Q are (0, a)
From (1), we can infer that,
OP = OQ [∵ OP is the hypotenuse]
⇒ The distance of point P from x-axis = a
The distance of point P from y-axis =a
Hence, the coordinates of point P are given as (a, a).
Learn more about coordinates here:
https://brainly.com/question/16679833
#SPJ1
Select the correct answer. emily wants to find the number that appears in the middle of a set of 25 numbers arranged in ascending order, in a spreadsheet. which statistical function will help her do so? a. mode b. rank c. median d. average
The correct answer is option (C) median.
The median will help Emily to find the number that appears in the middle of the 25 numbers that are arranged in ascending order.
What is the mean, median and mode?The mean, median, and mode are the three most commonly used measures of central tendency for populations that do not have much data, that is, they do not need to be grouped.
The mean, also known as average, is the value obtained by dividing the sum of a cluster of numbers by the number of them.
When arranging the numbers from least to largest, the median sits exactly in the middle of the values that are above. The median is a set that is a value that is in the middle of the other values.
The number that appears most frequently in a set of numbers is called the mode.
So, The median will help Emily to find the number that appears in the middle of the 25 numbers that are arranged in ascending order.
To learn more about central tendency, visit: https://brainly.com/question/28101345
#SPJ4
2. Solve the system of equations. Type in all points of intersection for the two functions and round to the nearest tenth if necessary
f(x)=-0.5x+2
g(x)=x³-5x² + 3
The points of intersection for the two functions and round to the nearest tenth exists (0.5, 1.4) and (4.85, -0.3).
How to solve the system of equations?Given:
f(x) = -0.5x+2
g(x) = x³ - 5x² + 3
The point of intersection exists the point where f(x) = g(x)
x³ - 5x² + 3 = - 0.5x + 2
x³ - 5x² + 3 + 0.5x - 2 = 0
x³ - 5x² + 0.5x + 1 = 0
Factorize and estimate the value of x
Let x = 0.53 and 4.85
substitute the value of x = 0.53
f(0.53) = -0.5(0.53) + 2
f(0.53) = -0.265 + 2
f(0.53) = 1.375
If x = 4.85
f(4.85) = -0.5(4.85) + 2
f(4.85) = -2.425 + 2
f(4.85) = -0.245
Therefore, the points of intersection for the two functions and round to the nearest tenth exists (0.5, 1.4) and (4.85, -0.3).
To learn more about functions refer to:
brainly.com/question/10439235
#SPJ9
A realtor is decorating some homes for sale, putting a certain number of decorative pillows on each twin bed and a certain number on
each queen bed. In one house, she decorated 1 twin bed and 1 queen beds and used a total of 15 pillows. At another house, she used
21 pillows to spruce up 2 twin beds and 1
queen beds. How many decorative pillows did the realtor arrange on each bed?
The number of decorative pillows did the realtor arrange on each twin bed and queen bed is 6 and 9 respectively.
Simultaneous equationlet
Number of decorative pillows for twin bed = xNumber of decorative pillows for queen bed = yx + y = 15
2x + y = 21
From equation (1)
x = 15 - y
Substitute x = 15 - y into (2)2x + y = 21
2(15 - y) + y = 21
30 - 2y + y = 21
- 2y + y = 21 - 30
-y = -9
y = 9
Substitute y = 9 into
x + y = 15
x + 9 = 15
x = 15 - 9
x = 6
Learn more about simultaneous equation:
https://brainly.com/question/16863577
#SPJ1
Coach Bennet’s high school basketball team has 14 players, consisting of six juniors and eight seniors. Coach Bennet must select three players from the team to participate in a summer basketball clinic.
Using the permutation formula, the number of different options for the top three finishers is given as follows:
[tex]P_{14,3} = \frac{14!}{11!} = 2184[/tex]
The order in which the players are chosen is important, as A, B, C is a different outcome than C,B,A for example, hence the permutation formula is used to solve this question.
What is the permutation formula?The number of possible permutations of x elements from a set of n elements is given by:
[tex]P_{(n,x)} = \frac{n!}{(n-x)!}[/tex]
In this problem, 3 students will be chosen from a set of 14, hence the number of ways is:
[tex]P_{14,3} = \frac{14!}{11!} = 2184[/tex]
More can be learned about the permutation formula at https://brainly.com/question/25925367
#SPJ1
Ask your teacher find the limit. use l'hospital's rule where appropriate. if there is a more elementary method, consider using it. lim x→1 [ln(x5 − 1) − ln(x3 − 1)]
Answer:
ln(5/3)
Step-by-step explanation:
The desired limit represents the logarithm of an indeterminate form, so L'Hopital's rule could be applied. However, the logarithm can be simplified to a form that is not indeterminate.
LimitWe can cancel factors of (x-1), which are what make the expression indeterminate at x=1. Then the limit can be evaluated directly by substituting x=1.
[tex]\diplaystyle \lim\limits_{x\to1}{(\ln(x^5-1)-\ln(x^3-1))}=\lim\limits_{x\to1}\ln{\left(\dfrac{x^5-1}{x^3-1}\right)}\\\\=\lim\limits_{x\to1}\ln\left(\dfrac{x^4+x^3+x^2+x+1}{x^2+x+1}\right)=\ln{\dfrac{5}{3}}[/tex]
-0.8662866239 . . . is:
rational
irrational
Answer:
irrational, it can't be written as a fraction
Step-by-step explanation:
I need the answers with the explanation!
Answer:
you need all of them?
Step-by-step explanation:
Using Euler's formula, how many
edges does a polyhedron with 9
faces and 14 vertices have?
[?] edges
Euler's Formula: F+ V=E+2
Answer:
Euler's Formula = F+V=E+2
F=9
V=14
So, 9+14=E+2
23=E+2
23-2=E
21=E
Hence, E (edges) = 21
Step-by-step explanation:
Finding the area of a regular polygon
360° ÷ 10 ÷ 2 = 18°
So the length of the decagon side is:
10 × tan18° × 2 = 20 × tan18°
The area is: ½ × 20 × tan18° × 10 × 10 = 1000 × tan18°
≈ 324.9
.: 324.9 is the final answer.
I hope this helps.
grade 9 math
useing frist diff is this a linear relation yes or no show your work
Answer:
not linear since all first differences are not equal
Step-by-step explanation:
To find the first differences, subtract each y value from the next y value.
Use only y values.
here are the 4 first differences you need to calculate.
1 - 0 = 1
4 - 1 = 3
9 - 4 = 5
16 - 9 = 7
Now you place them in the appropriate column in the table.
x y first difference
0 0 1
1 1 3
2 4 5
3 9 7
4 16
If the first differences were all equal, the function would be a linear function.
In this case, the first differences are all different, 1, 3, 5, 7, so the function is not linear.
triangle ABC is reflected across the y-axis and then dilated by a factor of 1/2 centered at the origin. which statement correctly describes the resulting image
Answer:
Step-by-step explanation:
The reflection preserves the side lengths and angles of triangle ABC. The dilation preserves angles but not side lengths.
When Kenny's electricity went out one night, his clock stopped at 8:39 p.m. when Kenny woke up the next morning his power was back on and his clock read 5:34 a.m. When he called the time services, the time was actually 7:11 a.m. How long was his electricity off?
Answer:
Step-by-step explanation:
Let's look at this in this perspective. There are 60 minutes in 1 hour. What I would do first is get rid of the 39 minutes at the end of 8:39. Now you have 8:00. Count until you get to 7 AM. 9, 10, 11, 12, 1, 2, 3, 4, 5, 6, 7. That's 11 hours from 8 PM to 7 AM. 60 x 11 = 660. Now, there are 11 minutes more on that 7-o clock and the 39 minutes we got rid of in the beginning. 11 + 39 = 40. 660 + 40 = 700.
Answer: Kenny's energy was off for 700 minutes, or 11 hours and 40 minutes.
Based on the scatterplot, which equation BEST represents the relationship between velocity and time?
The line of best-fit that represents the relationship between velocity and time is:
v = 2.19t + 6.7.
How to find the equation of linear regression using a calculator?To find the equation, we need to insert the points (x,y) in the calculator.
For this problem, the points (t,v) are given as follows:
(0, 6.1), (2.1, 12.2), (5.3, 17.4), (8.2, 26.4), (10, 28.1), (12.1, 32.8).
Hence, inserting these points into a calculator, the equation is given by:
v = 2.19t + 6.7.
More can be learned about a line of best-fit at https://brainly.com/question/22992800
#SPJ1
Which function has a domain of x>5 and a range of y≤3?
Oy=√x-5+3
Oy=√x+5-3
O y=-√x-5+3
O y = -√x+5-3
The correct option is the third one.
y = -√(x - 5) + 3
Which function has a domain of x>5 and a range of y≤3?Remember that a square root can only be evaluated in values equal or larger than zero.
So, if we want the domain to be x > 5, then we must have:
√(x - 5)
Now we also want the range to be equal or smaller than 3, then we should have a constant term equal to 3, and a negative coefficient before the square root, then we get:
y = -√(x - 5) + 3
So the correct option is the third one.
If you want to learn more about domains:
https://brainly.com/question/1770447
#SPJ1
PLSSSS HELPPPP THANK YOUU IF YOU DOOO
Answer:
B
Step-by-step explanation:
This is a really hard question- Help
Answer:
680
Step-by-step explanation:
x = total number
.6x = bus riders = 408 (.6 is decimal for 60%)
.6x = 408
x = 408/.6 = 680
Which situation will likely have no correlation?
Answer:
The third one as they have no links really
The following are the distances (in miles) to the nearest airport for 11 families. 9, 11, 11, 16, 16, 24, 28, 30, 34, 42, 45 Notice that the numbers are ordered from least to greatest. Give the five-number summary and the interquartile range for the data set.
Here is the five-number summary, range and interquartile range:
Minimum: 9
Lower quartile: 11
Median: 24
Upper quartile: 34
Maximum: 45
Interquartile range: 23
What is the five-number summary?The minimum number is the smallest number in the data. The minimum number is 9. The maximum number is the biggest number in the dataset. The maximum number is 45.
The first quartile, third quartile and the interquartile range are used to measure dispersion.
The first quartile : 1/4(n + 1)
1/4 x (12) = 3rd term = 11
The third quartile : 3/4 x (n + 1)
3/4 x (12) = 9th term = 34
Interquartile range = third quartile - first quartile
34 - 11 = 23
Median can be described as the number that is at the center of the dataset when the number is arranged in either ascending or descending order.
Median = 25
To learn more about median, please check: https://brainly.com/question/14746682
#SPJ1
Given that xy=3/2 and both x and y are nonnegative real numbers, find the minimum value of 10x (3y/5)
The munimum value is, at x = 3/10, y = 5 and 10x+3y/5 = 6.
What are nonnegative real numbers?Non-negative real numbers are the set of positive real numbers that are bigger than 0 (zero). That is, the true values are either positive or negative. The collection will include numbers such as 0, 1, 2, 3, 4, 5, and so on.To find the minimum value of 10x (3y/5):
Given - y = 3/(2x)
So, we want the bare minimum of,
= 10x + 3/5 × 3/(2x)= 10x + 9/(10x)Take the derivative to obtain:
= 10 - 9/(10x^2)When you set it to zero, you get:
= 100x^2 - 9 = 0= (10x-3)(10x+3) = 0= x = ± 3/10So, at x = 3/10, y = 5 and 10x + 3y/5 = 3 + 3 = 6.
Therefore, the munimum value is, at x = 3/10, y = 5 and 10x+3y/5 = 6.
Know more about nonnegative real numbers here:
https://brainly.com/question/26606859
#SPJ4
