Answers
===========================================================
Explanation:
Focus on the endpoints (0,15) and (10,0). They are the y and x intercepts in that order. This is the starting point and ending point of the ball.
The average rate of change is the slope of the line connecting these endpoints. This is when we consider the entire time the ball is in the air.
Let's use the slope formula to get the following:
[tex](x_1,y_1) = (0,15) \text{ and } (x_2,y_2) = (10,0)\\\\m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}\\\\m = \frac{0 - 15}{10 - 0}\\\\m = \frac{-15}{10}\\\\m = -\frac{3}{2}\\\\[/tex]
The slope is -3/2, which is the average rate of change.
It tells us that the height is decreasing by 3/2 = 1.5 meters per second, which is an average speed.
In other words, the ball is going downward at an average speed of 1.5 meters per second.
Keep in mind the instantaneous speed of the ball is changing all the time. The result of -3/2 = -1.5 only applies to the average speed.
------------
Note how the slope formula involves computing the change in y (which was us computing [tex]y_{2} - y_{1} = 0 - 15 = -15[/tex]. It indicates the ball had gone down 15 meters when going from the start point to the ending point. This is the change in distance. The change in time is the [tex]x_{2} - x_{1} = 10-0 = 10[/tex] portion, meaning the duration is 10 seconds.
In short,
slope = rise/run
slope = (change in distance)/(change in time)
slope = (-15)/(10)
slope = -3/2
So this may be a better way to see what's going on rather than rely on a formula in the previous section.
Related Questions
The theater sells two types of tickets: adult
tickets for $17 and child tickets for $10.
Last night, the theater sold a total of 403
tickets for a total of $5563. How many adult
tickets did the theater sell last night?
Show your work here
PLEASE HELP
Answers
Answer:
219
Step-by-step explanation:
adulta 219×17=3723
5563-323=1840
1840÷10=184 kids
219+184=403
For what values of x does 25× - 5ײ-3?
O x = -3, x = 1
O x = -1, x = 3
3
0 X=-²2/₁X-2
Ox
3
O x= -2, x=-2/
Answers
Answer:
X = 3, -1; B
Step-by-step explanation:
Use log properties, log 5 on both sides, log 5 of 25 is 2 that times the exponent, so 2*x = 2x, and on the other side, log 5 and base of 5 cancels. So 2x = x^2 -3, which can be solved using factoring:
x^2 -2x -3 = (x-3)(x+1) = 0, x=3,-1
The value of x in 25ˣ = 5ˣ²⁻³ is x =3 or x = -1.
What is a quadratic function?A polynomial function with one or more variables, where the largest exponent of the variable is two, is referred to as a quadratic function. In other terms, a "polynomial function of degree 2" is a quadratic function.
Given that the equation is 25ˣ = 5ˣ²⁻³.
To solve the equation, take logs on both sides, we get,
x log(25) = (x²- 3)log5
2x log 5 = (x²- 3) log5
2x = x²-3
x²- 2x -3 = 0
Now, factorize the quadratic equation,
we get,
x² - 3x + x - 3 = 0
x(x- 3) + 1(x - 3) = 0
x = 3 or -1.
Therefore, x = 3 or x = -1.
To learn more about the quadratic function;
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2. The letters from the word MATH are placed in a hat. What is the probability that you select an A when you are choosing a letter without looking? A. What is asked in the problem? 8. What are the given numbers? What operation will you use? D What is the mathematical sentence? E What is the answer to the problem? V. A
Answers
The probability of getting M from the word MATH placed in hat is 0.25.
Probability is defined as the ratio of the number of favorable results to the total number of elements of an event.
P= number of favorable outcomes / total number of outcomes of an event
A. The problem is the probability of finding A
B. The given are MATH i.e. {M,A,T,H}
C. the operation used will be selecting a word from hat of word MATH
D. the mathematical statement from the probability of finding M will be
P(getting M from word MATH)
E. the answer to the problem will be calculated as
no. of element in the hat=4 i.e. {M,A,T,H}
no. of favorable outcomes= 1 i.e. {A}
P(getting A from word MATH) = number of favorable outcomes/ number of total outcomes
⇒ P(getting A from word MATH) = 1/4
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Determine whether the given graph is a function or not.
Answers
Answer:
function
Step-by-step explanation:
The graph shows a function since it passes the vertical line test.
c) How long does he travel at 30 km/h, if he travels 1.2 h at 20 km/h?
Answers
Answer:
1.8 hrs
Step-by-step explanation:
1.2 hr = 20 km/hr
A hr = 30 km/hr
(cross multiply)
30 x 1.2 = 20 x A
(30 x 1.2) / 20 = A
on simplifying...
1.8 = A
Therefore, it takes 1.8 hrs to travel 30 km/hr
[this is totally my method]
Drivers pay a toll to pass over a busy bridge, and there are many toll booths that collect money. The city manager counted the total number of cars waiting to pay their tolls at 15-minute intervals during two different days, once on a weekday and once on a weekend. The histograms below show the results.
2 histograms. A histogram titled weekday traffic has number of cars in line on the x-axis, and frequency on the y-axis. 0 to 10, 4; 10 to 20, 13; 20 to 30, 19; 30 to 40, 8; 40 to 50, 5; 50 to 60, 1. A histogram titled weekend traffic has number of cars in line on the x-axis, and frequency on the y-axis. 0 to 10, 12; 10 to 20, 20; 20 to 30, 14; 30 to 40, 3; 40 to 50, 1.
Using the histograms, which of the following is the correct comparison of the distributions?
The 10–20 interval contains the most observations on both days.
The two distributions for number of cars in line are both skewed right.
The median number of cars for both distributions lies in the 20–30 interval.
There were more than 40 cars in line more often on the weekend than the weekday.
Answers
The conclusions are:
The median number of cars for both distributions lies in the 20–30 interval.There were more than 40 cars in line more often on the weekend than the weekday.What is mean and median ?The arithmetic mean is found by adding the numbers and dividing the sum by the number of numbers in the list
The median is the middle value in a list ordered from smallest to largest.
Given:
Data A:
0 - 10 4
10 - 20 13
20 - 30 19
30 - 40 8
40 - 50 5
50 - 60 1
Data B:
0-10 12
10-20 20
20-30 14
30-40 3
40-50 1
The median number of cars for both distributions lies in the 20–30 interval.There were more than 40 cars in line more often on the weekend than the weekday.Learn more about this concept here:
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The median number of cars for both distributions lies in the 20–30 interval and there were more than 40 cars in line more often on the weekend then the weekday.
What is mean and median ?The arithmetic mean is found by adding the numbers and dividing the sum by the number of data in the list.
The median is the middle value in a list ordered from smallest to largest.
Given data:
Data A:
0 - 10 4
10 - 20 13
20 - 30 19
30 - 40 8
40 - 50 5
50 - 60 1
Data B:
0-10 12
10-20 20
20-30 14
30-40 3
40-50 1
Thus, the median number of cars for both distributions lies in the 20–30 interval and there were more than 40 cars in line more often on the weekend then the weekday.
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If a=[-2 -4 2 5 1 5 -1 -3 -4] and b=[2 3 -5 5 -4 2 -1 -1 3] find ba
Answers
The product of A and B matrix will be option D; BA = [tex]\left[\begin{array}{ccc}16&10&39\\-32&-30&-18\\-6&-6&-19\end{array}\right][/tex].
What is the multiplication of matrix?If [tex]A = \left[\begin{array}{ccc}-2&-4&2\\5&1&5\\-1&-3&-4\end{array}\right][/tex]and [tex]B = \left[\begin{array}{ccc}2&3&-5\\5&-4&2\\-1&-1&3\end{array}\right][/tex]
then,
BA = [tex]\left[\begin{array}{ccc}2&3&-5\\5&-4&2\\-1&-1&3\end{array}\right] \left[\begin{array}{ccc}-2&-4&2\\5&1&5\\-1&-3&-4\end{array}\right][/tex]
BA = [tex]\left[\begin{array}{ccc}16&10&39\\-32&-30&-18\\-6&-6&-19\end{array}\right][/tex]
Hence, the product of A and B matrix will be option D; BA = [tex]\left[\begin{array}{ccc}16&10&39\\-32&-30&-18\\-6&-6&-19\end{array}\right][/tex].
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If f(x) = -x-2, what is f¹(x)?
Answers
Answer:
f¯¹(x) =9x+18, for the pictorial(image) question what is the send question is it asking derivative or inverse If it is inverse f¯¹(x)=-x-2 as it isOr if it is derivative f'(x)=-1Step-by-step explanation:
For the image question f(x)=1/9x-2,f¯¹(x)=?f(x)=1/9x-2............giveny=1/9x-2................swapping f(x) by y to Easily writex=1/9y-2................interchanging x and y1/9y-2=x................changeling side of equation 9(1/9y-2)=(x)9.......multiplying both sides by 9 to override the fraction on the right side y-18=9xy=9x-18.................Return to where it weref¯¹(x)=9x+18..........swap back f¯¹(x) in the yFor the question f(x)=-x-2,f¯¹(x)=?following the ☝️ arrangement y=-x-2x=-y-2-y-2=x-y=x+2y=-x-2f¯¹(x)=-x-2the equation of the line in the graph is y = (blank) x+ (blank)
Answers
[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]
[tex]\qquad \tt \rightarrow \: y=-x-1[/tex]
____________________________________
[tex] \large \tt Solution \: : [/tex]
Taking two points : (-1 , 0) and (0 , -1)
[tex] \textsf{Calculate slope (m)} [/tex]
[tex]\qquad \tt \rightarrow \: m = \cfrac{rise}{run} [/tex]
[tex]\qquad \tt \rightarrow \: m = \cfrac{y_2 - y_1}{x_2 - x_1} [/tex]
[tex]\qquad \tt \rightarrow \: m = \cfrac{0 - ( - 1)}{ - 1 - 0} [/tex]
[tex]\qquad \tt \rightarrow \: m = \cfrac{0 + 1}{ - 1}[/tex]
[tex]\qquad \tt \rightarrow \: m = - 1[/tex]
[tex] \textsf{Y - intercept (c) of graph = -1 } [/tex]
Equation of line in slope - intercept form :
[tex]\qquad \tt \rightarrow \: y = mx + c[/tex]
[tex]\qquad \tt \rightarrow \: y = - x - 1[/tex]
Answered by : ❝ AǫᴜᴀWɪᴢ ❞
Age of father is 13 times the age of his son , it will be only five times after four years find the present age of the father
Answers
Answer:26
Step-by-step explanation:
What is the asymptote of the following function: Y = e^x-x
Answers
Answer:
y = -x
Step-by-step explanation:
Breaking down the equation
[tex]y=e^x-x[/tex] can be written as [tex]y=e^x + (-x)[/tex], making it more clear that this function is composed of two functions:
An exponential function, and a linear functionasymptotes of the parts
The regular exponential function normally has an asymptote at y=0, a horizontal line because as "x" gets more and more negative, e^(x) gets closer and closer to zero (see blue graph). This asymptotic behavior perhaps can be more easily understood by recognizing that [tex]e^{-x}[/tex] is equivalent to [tex]\dfrac{1}{e^x}[/tex], so that as the x values get more and more negative, it is effectively dividing 1 by a larger and larger number, thus getting closer and closer to zero.
In this situation, that exponential function is added to "-x", which is a linear function with a slope of negative 1.
As the left end of the exponential function gets closer and closer to zero, the exponential part contributes almost nothing to the sum, whereas as the "x" gets more and more negative, the linear function "-x" gets more and more positive (linearly). Since the exponential piece adds almost nothing to it (when moving to the left), the combined function is essentially "-x" (although it is ever so slightly greater than it, just as it was ever so slightly greater than zero) (see pink graph, with dashed asymptote).
Clarifications
To be clear, on the right side of the graph, the exponential part of the function completely overwhelms the linear piece, and the function behaves much more like an exponential function, nearly completely masking the behavior of the linear piece. Since an exponential function is unbounded, and the domain of both the exponential and linear functions are all real numbers, on the right side of the graph, there is no asymptotic behavior.
Sofia bought $38 worth of video games. She had a coupon that allowed her to save 8% on her purchases.
Answers
Answer:34.96 (answer to what is her purchase price before tax)
Step-by-step explanation:38*(1-.08)
What is the measure of \angle x∠xangle, x?
Angles are not necessarily drawn to scale.
Answers
Answer:
x=135°
Step-by-step explanation:
WZ is 180 degrees. Simply subtract 48 from 180.
180-45=135.
Hope this helps!
If not, I am sorry.
Answer:
The answer is 132
Step-by-step explanation:
For khan academy
What type of relationship is expressed below?
5x = 2x 9
O equation
O function
O inequality
Answers
HELP DUE TODAY WORTH 87 POINTS
Answers
1. Moving at constant, you are at equilibrium and the restorative force of the scale balances your weight. So the scale exerts a force of 490 N and reads 50.0 kg.
2. The elevator is now moving up and slowing down, so its acceleration is pointing opposite the direction of motion, and Newton's second law says the net force is
F - 490 N = (50.0 kg) (-4.9 m/s²)
where F is the magnitude of the force due to the scale. Solve for F to get
F = 490 N - (50.0 kg) (4.9 m/s²) = 245 N
and the scale would read (245 N)/g = 25 kg. This should make sense; your inertia will cause your body to "want" to continue moving up at the same speed while the elevator slows down, and this relieves some of the upward force needed to keep your body moving with the elevator.
3. With the elevator in free fall, Newton's second law gives
F - 490 N = (50.0 kg) (-9.8 m/s²) ⇒ F = 0 N
and the scale would read 0 kg. Now you're falling with the elevator; the scale doesn't have to counteract your weight anymore.
can someone help meeee
Answers
Answer:
1. 0
2. undefined
3. -3/2
Step-by-step explanation:
y=-3/2. This value is constant and the x does not change the value at all. so the coordinate are going to be (x, -3/2) so if we take any 2 values you're going to get (-3/2 - (-3/2)) / (x2 - x1) = (-3/2 + 3/2) / (x2 - x1) = (0) / (x2 - x1) which is always going to be 0.
x=-3/2. This value is also constant except the x-value does not vary at all so x2 and x1 are always going to be equal which will result in a 0 as the denominator thus making the slope undefined
y=-3/2x. it's just -3/2 given the slope-intercept form y=mx+b where m is the slope
Answer:
0 underfined 3
—
2
Step-by-step explanation:
SOLVING STEP.
the line y= 3 is parallel to the x-axis,
—
— 2
so the slope is 0
the line x= 3 is perpendicular to the x-axis,
—
— 2
so the slope is underfined
the slope of the line y= 3 x 3
—
— — 2.
2
thank me later
please help fr , like i acc need help
Answers
Step-by-step explanation:
first a little help, how they got the equations :
in total they need 15 liters.
so, whatever x and y are, but together they must be 15 L.
x + y = 15
then, we are mixing x liters of 20% alcohol with y liters of 100% alcohol, that have to result in a 40% solution of (x+y) liters :
0.2x + y = 0.4(x+y)
we know from the first equation that x+y = 15, so the second equation is actually
0.2x + y = 0.4 × 15 = 6
so, we have
x + y = 15
0.2x + y = 6
do you notice something ? there is a "+ y" in both equations.
so we can actually subtract the second equation from the first, eliminate y and solve for the remaining x. and then use one of the original equating to get also y :
x + y = 15
- 0.2x + y = 6
---------------------
0.8x 0 = 9
0.8x = 9
x = 9/0.8 = 11.25 liters
x + y = 15
11.25 + y = 15
y = 15 - 11.25 = 3.75 liters
Someone help asap pls!! Ill mark you brainliest
Answers
Answer:
d.
Step-by-step explanation:
The parent graph is shifted right 2 and down 2
type an equation for the line shown on the graph
(0,2)
Answers
Answer: Hope this helps you.
Y = MX + 2
Step-by-step explanation:
Since you don't have a picture of the line I cant find the slope but with the info I know the equation is.
Y = MX + 2
(Replace M with the slope or post the graph so I can identify the slope)
A girl get n cedis pocket money each week. she saves her money for five weeks and buys a present for her mother which costs ghc7900.00.
i) write an expression for the amount of money left.
ii) what is the minimum amount she needs to save each week to be able to afford the gift
Answers
Answer:
1) n = 5n - 7900
2) 1580
Step-by-step explanation:
first one you just set up an equation and second one you set up a different equation and solve for N ( I divided n by 5 to get the answer)
complete the square to solve the equation below. check all that apply.
x^2 + 8x - 1 = 19
Answers
Answer:
B and D
Step-by-step explanation:
First take the equation and subtract 19 on both sides. You get x^2+8x-20=0
using the quadratic formula you get x= (-8 + or - root (8^2 -4(1)(-20)))/ 2(1)
simplify it and you get x= (-8 +or- 12) / 2
Separate the equation into two and you get (-8 + 12) / 2 and (-8 - 12) / 2
first one gives: 4/2=2
second gives -20/2=-10
answer x=-10,2
Can someone help me please?
Answers
Answer:
B. <TSN and <ISW
C. <KSW and <NST
Answer:
D. ∠ISN and ∠TSW
Step-by-step explanation:
The meaning of vertical angles is each of the pairs of opposite angles made by two intersecting lines.
The angles ∠ISN and ∠TSW are made by two intersecting lines. This means that these angles are vertical angles.
Hope this helps!
If not, I am sorry.
Graph g(x)=|x−4|+3.\
Answers
I insert an image graphing the function.
Function:[tex] \boxed{ \boxed{g(x) \: = \: |x \: - \: 4| \: + \: 3}}[/tex]
MissSpanishI'm just confused. I know we've learnt this before but I just forget. I'm doing one of the review sheets before our exam tomorrow. If you could help me out that would be great
Answers
Answer:
b. y= 4x-34.
Step-by-step explanation:
We can use the information in the problem to make an equation in slope-intercept form (y=mx+b).
Steepness typically means the slope of the graph, thus m=4.
This means we can automatically cross out "a" and "c", which leaves us with "b" and "d" as possible answers.
Next, I will plug in the given point (8, -2) into "b" and "d".
b. y=4x-34
-2=4(8)-34
-2=32-34
d. y=4x+34
-2=4(8)+34
-2 does not equal 66
Thus, the answer is b. y= 4x-34.
a town B is 12km from another town A on a bearing of 47degree and another C is 8km from town B on a bearing of 124degree.how far is town A from town C?what is the bearing of A from C
Answers
Answer:
Distance between A and C = 16km
Bearing of A from C = 257°
Step-by-step explanation:
please see photo for detailed analysis
Exercise 1.2 1 Round each of these numbers to the degree of accuracy shown in brackets. a) 7765 (nearest hundred). b) 1099 (nearest thousand). c) 487 (nearest ten) d) 34 766 (nearest hundred) e) 45620000 (nearest million please help me
Answers
Answer:
a. 700
b. 1000
c. 80
d. 700
e.
Which of the following are solutions to the equation below?
Check all that apply.
(3x - 5)^2 = 19
Answers
Answer:
To solve the answer, you can do it in 2 ways:
1) you could take the square root on both sides and solve for x
OR
2)you could multiply 3x-5 times itself and subtract 19 on both sides and use the grouping or quadratic formula method to find x.
Hope it helps.
Remove the perfect root factor
under the radical to solve
The complete solution is the result of both the positive and negative portions of the solution.
The result can be shown in multiple forms.
The volume of a cylinder with a height of 4 feet is 144n cubic feet what is the radius of the base of the cylinder V=nr2h
Answers
Answer: 6 ft
Step-by-step explanation:
[tex]144\pi =\pi(r^{2})(4)\\\\144\pi=4\pi r^{2}\\\\36=r^{2}\\\\r=\boxed{6 \text{ ft}}[/tex]
What’s the value of x?
Answers
Answer:
the two angles equal 180 degree
so 2x+2+5x+3=180
2x+5x+3+2=180
7x=180-5
7x/7=175/7
x=25
Step-by-step explanation:
hope I helped
please mark me as brainlyst
HELP PLEASE
which choice is equivalent to the quotient below? √15/3√3
A. √5/3
B. √5/9
C. √5/√3
D. √4
Answers
Answer:
A - [tex]\sqrt{5}[/tex]
Step-by-step explanation:
[tex]\sqrt{15} = \sqrt{5} *\sqrt{3} \\\frac{\sqrt{5} *\sqrt{3}}{3*\sqrt{3}} = \frac{\sqrt{5}}{3}[/tex]
Answer: √5/3
Step-by-step explanation:
