Answer:
( x, y ) = ( 4, 1/3)
Step-by-step explanation:
x - 3y = 3
2x +9y = 11
1. substitute the value of x
x= 3 + 3y
2x + 9y = 11
2. solve equation
2 (3 + 3y) +9y = 11
3. substitute the value of y
y = 1/3
4. solve equation
x = 3 + 3 x 1/3
x = 4
5. check solution
(x, y) = ( 4, 1/3 )
check x ----> 4 - 3 x 1/3 = 3
check y ------> 2 x 4 + 9 x 1/3 = 11
for x----> 3=3
for y----> 11=11
Which of the following could be the interpretation of the distance vs time graph shown?
Which of these answers this Question, Is It 1, 2, or 3 that's in parentheses???
( 1.) A biker takes off on a course that begins with a small ramp. The biker bikes up a hill and across a flat portion of the course before heading down a steep descent.
( 2.) A driver leaver her house and slows down to make a stop at her neighbor's house. She then drives at a constant speed and stops at a house further down the street. After visiting with her neighbor, she quickly drives back home.
( 3.) A hiker begins hiking, but shortly after realized he left his water bottle in his car. He turns around to get his water bottle and then starts hiking again at a constant rate. The hiker stops for lunch at the furthest point of his hike and then hikes back at a quicker constant rate.
The slope of the curve is positive between the times t=0\text{ s}t=0 st, equals, 0, start a text, space, s, end text, and t=2 \text{ s}t=2 st, equals, 2, start a text, space, s, end text since the slope is directed upward. This means the acceleration is positive.
The slope of the curve is negative between t=2 \text{ s}t=2 st, equals, 2, start a text, space, s, end text, and t=8 \text{ s}t=8 st, equals, 8, start a text, space, s, end text since the slope is directed downward. This means the acceleration is negative.
At t=2\text{ s}t=2 st, equals, 2, start a text, space, s, end text, the slope is zero since the tangent line is horizontal. This means the acceleration is zero at that moment.
Concept check: Is the object whose motion is described by the graph above speeding up or slowing down at time t=4\text{ s}t=4 st, equals, 4, start a text, space, s, end text?
[Show me the answer.]
What does the area under a velocity graph represent?
The area under a velocity graph represents the displacement of the object. To see why to consider the following graph of motion that shows an object maintaining a constant velocity of 6 meters per second for a time of 5 seconds.
To find the displacement during this time interval, we could use this formula
\Delta x=v\Delta t=(6\text{ m/s})(5\text{ s})=30\text{ m}Δx=vΔt=(6 m/s)(5 s)=30 mdelta, x, equals, v, delta, t, equals, left parenthesis, 6, start text, space, m, slash, s, end text, right parenthesis, left parenthesis, 5, start text, space, s, end text, right parenthesis, equals, 30, start text, space, m, end text
which gives a displacement of 30\text{ m}30 m30, start text, space, m, end text.
Now we're going to show that this was equivalent to finding the area under the curve. Consider the rectangle of the area made by the graph as seen below.
The area of this rectangle can be found by multiplying the height of the rectangle, 6 m/s, times its width, 5 s, which would give
\text{ area}=\text{height} \times \text{width} = 6\text{ m/s} \times 5\text{ s}=30\text{ m} area=height×width=6 m/s×5 s=30 mstart text, space, a, r, e, a, end text, equals, start text, h, e, i, g, h, t, end text, times, start text, w, i, d, t, h, end text, equals, 6, start text, space, m, slash, s, end text, times, 5, start text, space, s, end text, equals, 30, start text, space, m, end text
This is the same answer we got before for the displacement. The area under a velocity curve, regardless of the shape, will equal the displacement during that time interval. [Why is this still true when velocity isn't constant?]
\text{area under curve}=\text{displacement}area under curve=displacementstart text, a, r, e, a, space, u, n, d, e, r, space, c, u, r, v, e, end text, equals, start text, d, i, s, p, l, a, c, e, m, e, n, t, end text
[Wait, aren't areas always positive? What if the curve lies below the time axis?]
What do solved examples involving velocity vs. time graphs look like?
Example 1: Windsurfing speed change
A windsurfer is traveling along a straight line, and her motion is given by the velocity graph below.
Select all of the following statements that are true about the speed and acceleration of the windsurfer.
(A) Speed is increasing.
(B) Acceleration is increasing.
(C) Speed is decreasing.
(D) Acceleration is decreasing.
Options A, speed increasing, and D, acceleration decreasing, are both true.
The slope of a velocity graph is the acceleration. Since the slope of the curve is decreasing and becoming less steep this means that the acceleration is also decreasing.
It might seem counterintuitive, but the windsurfer is speeding up for this entire graph. The value of the graph, which represents the velocity, is increasing for the entire motion shown, but the amount of increase per second is getting smaller. For the first 4.5 seconds, the speed increased from 0 m/s to about 5 m/s, but for the second 4.5 seconds, the speed increased from 5 m/s to only about 7 m/s.
Example 2: Go-kart acceleration
The motion of a go-kart is shown by the velocity vs. time graph below.
A. What was the acceleration of the go-kart at time t=4\text{ s}t=4 st, equals, 4, start a text, space, s, end text?
B. What was the displacement of the go-kart between t=0\text{ s}t=0 st, equals, 0, start text, space, s, end text and t=7\text{ s}t=7 st, equals, 7, start text, space, s, end text?
A. Finding the acceleration of the go-kart at t=4\text{ s}t=4 st, equals, 4, start a text, space, s, end text
We can find the acceleration at t=4\text{ s}t=4 st, equals, 4, start a text, space, s, end text by finding the slope of the velocity graph at t=4\text{ s}t=4 st, equals, 4, start a text, space, s, end text.
\text{slope}=\dfrac{\text{rise}}{\text{run}}slope=
run
pls help ill give brainliest to the PERSON WHO GETS IT RIGHT
Answer:
C) [tex]s\geq 5[/tex]
Step-by-step explanation:
The phrase "at least", represents the greater than or equal to sign. Only Option C shows this sign, so it's correct.
Hope it helps!
Student Council is selling tickets to the Winter
Dance. Tickets cost $5 per person or $8 per
couple. To cover expenses, at least $1200
worth of tickets must be sold. No more than 500
students can fit in the gym where the dance is
being held.
List two combinations of tickets that could be sold, so
that Student Council makes a profit, yet stays under the
room capacity.
Answer:
Two possible combinations are;
1) 200 single and 30 couples
2) 150 single and 57 couples
Step-by-step explanation:
The given parameter in the question are;
The cost of ticket per person = $5
The cost of tickets per couple = $8
The minimum worth of tickets to be sold = $1,200
The maximum number of students that can fit in the gym = 500
Let 'x' represent the number of single persons that attend the dance and let 'y' represent the number of couple that attend, we have;
5·x + 8·y ≥ 1,200
x + y ≤ 500
Making 'y' the subject of both equations gives;
y ≥ 150 - 5·x/8
y ≤ 500 - x
From the graph of the inequalities created with Microsoft Excel, we have;
When x = 200, and y = 30, we get;
5 × 200 + 8 × 30 = 1240 > 1200
200 + 30 × 2 = 460 < 500
We also have;
x = 150, and y = 57, we get
Equating both values of 'y', we get;
5 × 150 + 8 × 57 = 1206 > 1200
150 + 57 × 2 = 264 < 500
Therefore, from the acceptable region in the graph, we have the following two possible combinations
1) 200 single and 30 couples
2) 150 single and 57 couples
HELP ME PLEASE!!!!!ITS DUE TODAY!!
Answer:
T = 11.77
18% Tip = 2.12
Total with tip = $13.89
This should be right :)
Lmk how I did!
If 20% of a number is 60 and 55% of the same number is 165, find 75% of that
number.
(Please be quick :) )
Answer:
300
Step-by-step explanation:
hope this helps!!!!
Answer:
225
Step-by-step explanation:
Hope this helps:)
Marty and Adam want to share 8/10 feet of rope, equally. What amount of rope should each person get?
Answer: 2/5 feet
Step-by-step explanation:
From the question, we are informed that Marty and Adam want to share 8/10 feet of rope, equally.
The amount of rope that each person would get would be calculated by dividing 8/10 by 2. This will be:
= 8/10 ÷ 2
= 8/10 × 1/2
= 8/20
= 2/5
Therefore, each person gets 2/5 feet of rope.
Determine the are of the triangle
Answer:
25m
Step-by-step explanation:
The unit not to be used to find the triangle area is 25 because it is the hypotenuse and to find the area of a triangle you only need base and height. The base would be 24.6 and the height would be 7.3, which would both be needed in the equation.
In a particular lottery, 5 winning numbers are drawn from a set of 37 numbers. What is the probability of picking exactly 2 of the winning numbers in this lottery? Round your answer to the nearest
thousandth (three decimal places).
Since 5 winning numbers are draw and there are exactly 2 winning numbers, the other 3 numbers chosen have to be incorrect.
The 2 numbers picked right, there are 5C2=10 different possibilities.
The other 3 numbers are just picked from the rest of the 32 numbers. Getting there are 32C3=4960 different possibilities.
For each set of 2 correct winning numbers, you could have the 4960 different losing numbers to match up to make a unique set. This meant that there are 4690*10=46900 different total possibilities.
Now the total different outcomes of how you can choose the numbers are 37C5=435897 outcomes.
Now the way to find probabilities is want/total
The want is 46900 and the total is 435897
Doing the division you get the number rounded to the nearest thousandths as 0.107 or in percent form as
10.759% chance of picking exactly 2 winning numbers.
This seems like a competition problem of some sort therefore I assume that you already know what combinations in form nCk and permutation in form nPk means.
Answer this for me please!
The ratio of 6th-grade students to 8th-grade students in a school is 4 to 5. How many 6th grade students are there if a school has 360 8th grade students
Answer: 288
Step-by-step explanation: 360/5 is 72 so multiply the 6th graders times 72 and you get 288
Work out the area of the parallelogram.
Not drawn
accurately
13 cm
799
21 cm
Answer:
273
Step-by-step explanation:
area of parallelogram = b × h
13 × 21
273 cm
i hope its help u ,
Here is a meme for everyone who needs to laugh :)
Answer:
nice
Step-by-step explanation:
Answer: .............
Step-by-step explanation:
AHAHAHAHA-OMGKDKFKSKS
what is the solution of the system of equations 2x-3y=-9 -x+3y=6
Answer:
the answer to the question is (6,10)
Step-by-step explanation:
3y + 7 = x is this a direct proportion
Answer:
no
Step-by-step explanation:
if the ratio (yx) of two variables (x and y) is equal to a constant (k=yx) .in this case y is said to be directly proportional to x with proportionality constant k
ASAP! Please, Thank you.
Answer:
x\left(5-2\right)=4x-x ------> no solutions
14x-17-8x+2=12x+3-x-10 -----> unique solution
6\left(x-2\right)=6x-12 -------> no solutions
\frac{2}{3}x-\frac{7}{4}=\frac{4}{3}x-\frac{2}{3}\left(x+5\right) ------> infinite solutions
Step-by-step explanation:
Plz A total of 41 and 1/3 tons of gravel was split between four dump trucks. How many tons of gravel did each truck hold?
4,6,9, ...
Find the 8th term.
Answer:
39
Step-by-step explanation:
Answer:
39
Step-by-step explanation:
the answer is going up by the numbers 1,2,3,4...
you start with 4 and go up by 2
you then get 6 that's when you count up 3
you get 9 and then count up 4
which is 13 count up 5
18 count up 6
24 count up 7
31 count up 8
39
Three bananas and two pears cost 95p.
Five bananas and three pears cost £1.51
Find the cost of ten bananas and ten pears.
Answer:
Cost of ten bananas and ten pears is £ 3.90
Step-by-step explanation:
As three bananas and two pears cost 95 p and five bananas and three pears cost £ 1.51 or 151 p ,
subtracting former from latter, we get
two bananas and one pear cost 151 p − 95 p = 56 p
and doubling four bananas and two pear cost 56 p × 2 = 112 p
Hence, one banana costs 112 p − 95 p = 17 p .
and two bananas cost 17 p × 2 = 34 p
and hence one pear costs 56 p − 34 p = 22 p
Hence cost of ten bananas and ten pears is
10 × 17 p + 10 × 22 p = 170 p + 220 p = 390 p = £ 3.90
Hope it helps
Please mark me as the brainliest
Thank you
geometry, can u help????
The population of a city is 250,000 and the annual growth rate is 2.2% Write an equation to model the population y after x years.
Answer:
bueno, es 3.70 así que espero que ayude um buena suerte ~ nena ~
Step-by-step explanation:
Find the 11th term of the geometric sequence 6, -18, 54,
Answer:
354294
Step-by-step explanation:
a₁ = 6 = 6 * (-3)⁰
a₂ = -18 = 6 * (-3)¹
a₃ = 54 = -18 * (-3) = 6 * (-3)²
a₁₁ = 6 * (-3)¹⁰ = 354294
Anthony invested $36,000 in an account paying an interest rate of 5.3% compounded
quarterly. Assuming no deposits or withdrawals are made, how long would it take, to
the nearest year, for the value of the account to reach $51,800?
Answer:
3.8 months
Step-by-step explanation:
Question: Anthony invested $36,000 in an account paying an interest rate of 5.3% compounded
quarterly. Assuming no deposits or withdrawals are made, how long would it take, to
the nearest year, for the value of the account to reach $51,800?
First step! What is 5.3% of 36k?
1,908
Second Step! Divide
51,800/1,908= 27.1488469602
Third Step! Round
27.1488469602= 27.1
27.1 weeks.
7 weeks in a month.
12 months in a year.
27.1/7= 3.8
3.8 months
The number of years for the amount of compound interest to reach $51,800 is given by b = 7 years
What is Compound Interest?Compound interest is interest based on the initial principle plus all prior periods' accumulated interest. The power of compound interest is the ability to generate "interest on interest." Interest can be added at any time, from continuously to daily to annually.
The formula for calculating Compound Interest is
A = P ( 1 + r/n )ⁿᵇ
where A = Final Amount
P = Principal
r = rate of interest
n = number of times interest is applied
b = number of time periods elapsed
Given data ,
Let the number years be represented as b
where the amount after b years is = $ 51,800
The initial principal amount P = $ 36,000
The number of times the compound interest is applied = quarterly = 4
Now , the equation is
A = P ( 1 + r/n )ⁿᵇ
On solving for the number of years b , we get
b = ln ( A / P ) / n [ ln ( 1 + r/n ) ]
b = ln ( 51,800.00 / 36,000.00 ) / ( 4 × [ ln ( 1 + 0.053/4 ) ] )
On further simplification , we get
b = ln ( 51,800.00 / 36,000.00 ) / ( 4 × [ ln (1 + 0.01325 ) ] )
b = 6.911 years
On rounding to the nearest year , we get
b = 7 years
Therefore , the value of b is 7 years
Hence , the number of years is 7 years
To learn more about compound interest click :
https://brainly.com/question/21270833
#SPJ2
write the following ratio in its simplest for 64:18
Answer:
32 : 9
Step-by-step explanation:
To write a ratio in its simplest form , the numerator and denominator should be reduced by their common factor(s).
64 = 2 × 2 × 2 × 2 × 2 × 2
18 = 2 × 3 × 3
⇒ Common factor of 64 & 18 is 2.
So , reducing 64 & 18 by 2 gives :-
[tex]\frac{64 \div 2}{18 \div 2} = \frac{32}{9}[/tex]
∴ Hence , the simplest form is 32 : 9.
please help!! ______
Answer: The answer is C.
Step-by-step explanation: The hypotenuse in special case isosceles right triangles is always x√2, x being one of the leg lengths since they are the same.
Expand 3(m + 7).
3(m + 7) =
Find the value of r that makes m
II
n.
m
n
(180 - x) º
xº
Answer:
(180-x)⁰ or it might also be X⁰
An airplane flies 315 km in 1 hour 45 minutes. Calculate the average speed.
Answer:
3 km per minute
Step-by-step explanation:
speed = distance / time
315km/105 minutes
= 3 km per minute
work out the volume of this hemisphere with diameter 9.6 cm
Answer:
Please refer to the attachment
40 people can ride the roller coaster every 15 minutes. How many people can ride the roller coaster every 3 hours?
Answer:
480
Step-by-step explanation:
Answer:
486 people can ride the roller coaster in 3 hours
Step-by-step explanation:
40÷15 = 2.7
2.7 × (60×3)
2.7×180= 486
Can anyone tell me what the answer is for 4097 + 754 + 3188?
Answer:
8,039
Step-by-step explanation:
4097
3188
754
---------
8039
Answer:
4097 + 754 + 3188 = 8039
Step-by-step explanation:
4097 + 754 + 3188
4851 + 3188
8039