What is the function rule for the line?
f(x)=2/3x−2
f(x)=3/2x−2
f(x)=−2/3x−2
f(x)=3/2x+2
The function rule of the line is, f(x)=2/3x-2
What is a straight line?
A straight line is an endless one-dimensional figure that has no width. It is a combination of endless points joined both sides of a point and has no curve.
Here, we have to points (0,-2) and, (3,0)
So, by using the formula of equation of straight line of two-point form, we get,
(y-y_1)/(x-x_1 )=(y_2-y_1)/(x_2-x_1 )
=>(y+2)/(x-0)=(0+2)/(3-0)
=>3y+6=2x
=>y=2/3x-2
Let, y= f(x)
So, the required function rule of the line is f(x)=2/3x-2
Hence, the required function rule of the line is, f(x)=2/3x-2
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A retiree invests $8,000 in a savings plan that pays 7% per year. What will the account balance be at the end of the first year?
Final answer:
To calculate the account balance at the end of the first year for an investment of $8,000 at 7% per year, the formula for simple interest is used. After applying the formula, the final account balance is determined to be $8,560.
Explanation:
The retiree invests $8,000 in a savings plan that pays 7% per year. To find out what the account balance will be at the end of the first year, we can use the formula for simple interest because it is only for one year. The formula is:
Final amount = Principal amount (1 + (Interest rate * Time))
Let's calculate:
Principal amount (P) = $8,000Interest rate (r) = 7% or 0.07Time (t) = 1 yearNow, substituting the values into the formula:
Final amount = $8,000 (1 + (0.07 * 1))
Final amount = $8,000 (1 + 0.07)
Final amount = $8,000 (1.07)
Final amount = $8,560
So, the account balance at the end of the first year will be $8,560.
Use volume and meniscus in the same sentence
Line segment JL is an altitude in triangle JKM. Which statement explains whether JKM is a right triangle? Round measures to the nearest tenth.
A) JKM is a right triangle because KM = 15.3.
B) JKM is a right triangle because KM = 18.2.
C) JKM is not a right triangle because KM ≠ 15.3.
D) JKM is not a right triangle because KM ≠ 18.2.
Answer:
C. JKM is not a right triangle because KM ≠ 15.3.
Step-by-step explanation:
We can see from our diagram that triangle JKM is divided into right triangles JLM and JLK.
In order to triangle JKM be a right triangle [tex]KM^{2}=JK^{2}+JM^{2}[/tex].
We will find length of side KM using our right triangles JLM and JLK as [tex]KM=KL+LM[/tex].
Using Pythagorean theorem in triangle JLM we will get,
[tex]LM=\sqrt{JM^{2}-JL^{2}}[/tex]
[tex]LM=\sqrt{8^{2}-5^{2}}[/tex]
[tex]LM=\sqrt{64-25}[/tex]
[tex]LM=\sqrt{39}=6.244997998\approx 6.24[/tex]
Now let us find length of side KL.
[tex]KL=\sqrt{JK^{2}-JL^{2}}[/tex]
[tex]KL=\sqrt{13^{2}-5^{2}}[/tex]
[tex]KL=\sqrt{169-25}[/tex]
[tex]KL=\sqrt{144}=12[/tex]
Now let us find length of KM by adding lengths of KL and LM.
[tex]KM=12+6.24=18.24[/tex]
Now let us find whether JKM is right triangle or not using Pythagorean theorem.
[tex]KM^{2}=JK^{2}+JM^{2}[/tex]
[tex]18.24^{2}=13^{2}+8^{2}[/tex]
[tex]18.24^{2}=169+64[/tex]
[tex]18.24^{2}=233[/tex]
Upon taking square root of both sides of equation we will get,
[tex]18.24\neq 15.264337522473748[/tex]
[tex]18.2\neq 15.3[/tex]
We have seen that KM equals 18.2 and in order to JKM be a right triangle KM must be equal to 15.3, therefore, JKM is not a right triangle and option C is the correct choice.
Answer:
I just took the test it is C
What is the product of 1/2 times 2/3 times 3/4 .... times 1999/2000?
Factor this expression completely 9a4 - b2
The outdoor furniture buys wooden benches for $50 each. The furniture store owner adds 200% markup to the cost of the bench. After hearing from the costumers the selling cost of the bench is too high, the owner changes the markup to 120%. How much less per bench does the store owner make with the lower markup
50 42 32 35 41 44 24 46 31 47 36 32 30 44 22 47 31 56 28 37 49 28 42 38 45 mean and median
Patrick has seen 10 movies this year.what is the ratio of comedies to the toatal. 4 actions,1 animated,3 comedys,and 2 dramas
Alexia and Haley start out together to bike from Apple Valley to Hesperia, a distance of 15 miles.
Alexia bikes at 5 miles per hour.
Haley bikes at 7.5 miles per hour.
Which statement is true?
They arrive at the same time.
Alexia arrives 1 hour later than Haley.
Alexia arrives 2.5 hours later than Haley.
Haley arrives 37.5 hours earlier than Alexia.
Please help me
6 (d+1) - 2d = 54
6(d+1) -2d=54
distribute the 6
6d+6 -2d=54
subtract 2d from 6d
4d+6 =54
subtract 6 from each side
4d=48
divide both sides by 4 to get d
d=48/4
d=12
Please help thanks very much!
A club treasurer has $28.45 consisting of nickels, dimes, and quarters. she has 9 more nickels than dimes and three times as many dimes as quarters. how many does she have of each coin?
The equation y=0.25x+50 models the cost y of renting a car if the car is driven x miles according to the model what is the best estimate of the cost for renting a car if you plan to drive 250 miles
Answer: $112.5
Step-by-step explanation:
Given : The equation [tex]y=0.25x+50[/tex] models the cost y of renting a car if the car is driven x miles according to the model .
To find the cost for renting a car if you plan to drive 250 miles, we substitute x= 250 in the given equation , we get
[tex]y=0.25(250)+50\\\\\Rightarrow\ y=62.5+50\\\\\Rightarrow\ y=112.5[/tex]
Hence, the cost for renting a car if you plan to drive 250 miles = $112.5
Thus , the best estimate of the cost for renting a car if you plan to drive 250 miles = $112.5
range of 89,82,73,86,89,68,94
In a proportional relationship, how can you determine the unit rate while looking at the graph?
Polly brennan earns $8.32 per hour for playing fuitar at kaldi's coffee shop. she works 12.5 hours a week. what is the musician's stright- time pay?
Armando likes to watch sports on television. He recorded the following statistics about four games he watched. (Note: The times below include television commercials and commentary.) SportTime WatchedAmount of Game Watched basketball1 hr 27 min1 of 2 halves football48 min1 of 4 quarters soccer50 min1 of 2 halves baseball1 hr 24 min4 of 9 innings Order the sports by their unit rates in hours per game from least to greatest.
Cheryl Assembled 128 chairs in 16 hours. How many chairs per hour?
How much money will be in a bank account after 4 years if $8 is deposited at an interest rate of 5%?
What is the answer to in a science class the girl to boy ratio is 3 to 7 out of 50 student how many are boys?
A truck is moving at a rate of 105 kilometers per hour and the diameter of its wheels is 1 meter find the angular speed of the wheels in radians per minute
The angular speed of the truck's wheels is 3500 radians per minute, calculated by dividing the linear speed in meters per minute by the wheel's radius in meters.
Explanation:To calculate the angular speed of the truck's wheels in radians per minute, we first need to understand the relationship between linear speed and angular speed. Angular speed (
adians) is given by the formula
adians = linear speed (v) divided by the radius of the wheel (r).
First, we convert the truck's speed from kilometers per hour to meters per minute:
105 km/hr = (105 * 1000 meters) / (60 minutes) = 1750 meters/minute.
Since the diameter of the wheel is 1 meter, the radius (r) is half of that, which is 0.5 meters.
Now we can calculate the angular speed:
adians = v / r = 1750 m/min / 0.5 m which gives us 3500 rad/min.
Therefore, the angular speed of the wheels is 3500 radians per minute.
what is the slope intercept form of 2x+y=8
The points ( - 6, - 2) and ( - 4,6) fall on a particular line. what is its equation in point-slope form?
A line passes through (2, −1) and (4, 5).
Which answer is the equation of the line?
−3x+5y=−13
−3x+y=−7
−3x+y=17
−3x+5y=13
What is the solution of the system?
Use the elimination method.
4x + 2y = 18
2x + 3y = 15
Enter the answer in the boxes.
(__,__)
To solve this system of equations using the elimination method, we multiply one or both equations so that the coefficients of either x or y are the same or additive inverses. Then, we subtract one equation from the other to eliminate one variable. Finally, we solve for the remaining variable by substituting the value of the other variable.
Explanation:To solve the system of equations using the elimination method, we need to eliminate one variable by multiplying one or both equations so that the coefficients of either x or y are the same or additive inverses. In this case, we can multiply the first equation by 3 and the second equation by 2:
12x + 6y = 54
4x + 6y = 30
Next, we subtract the second equation from the first:
(12x + 6y) - (4x + 6y) = 54 - 30
8x = 24
Divide both sides by 8 to solve for x:
x = 3
To find the value of y, substitute the value of x into either of the original equations:
4(3) + 2y = 18
12 + 2y = 18
2y = 18 - 12
2y = 6
y = 6/2
y = 3
The image shows a geometric representation of the function f(x) = x2 – 2x – 6 written in standard form.
What is this function written in vertex form?
A) f(x) = (x –1)2 – 7
B) f(x) = (x +1)2 – 7
C) f(x) = (x –1)2 – 5
D) f(x) = (x +1)2 – 5
It has to be A, B, C, Or D someone has asked this question before but whoever answered it just copied and pasted the question that was asked as the answer so please help the answer has to be one of the above.
Where does the function f have a zero? (more than one can apply)
A bathtub that holds 32 gallons of water contains 12 gallons of water. begin filling it, and after 5 minutes the tub is filled. write a standard equation
Answer:
In standard equation format, the condition can be written as [tex]V=5x+12[/tex].
Step-by-step explanation:
The capacity of the bathtub is 32 gallons.
The water already in the tub is 12 gallon.
It takes 5 minutes for the tub to be filled.
Let x be the flow rate of water through tap, in gallon per minutes.
Now, the water filled in the tank in 5 minutes will be [tex]5x[/tex] gallons.
So, in equation, the given condition can be written as,
[tex]V=5x+12\\32=5x+12[/tex]
here V represents the volume of the bathtub.
Therefore, in standard equation format, the condition can be written as [tex]V=5x+12[/tex].
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The standard equation for the volume of water in the bathtub at time t is V(t) = 12 + 4t, indicating the tub starts with 12 gallons and fills at a rate of 4 gallons per minute.
Explanation:To write a standard equation for filling a bathtub, we need to find the rate at which the tub fills. Since the tub starts with 12 gallons and ends up holding 32 gallons, it needs an additional 20 gallons to be filled. If it takes 5 minutes to fill these 20 gallons, then the fill rate is 20 gallons per 5 minutes.
The equation for the volume V of water in the tub at any given time t (in minutes) is:
V(t) = 12 + r × t
where r is the rate of filling the tub. We already calculated r to be 4 gallons per minute (20 gallons/5 minutes). Therefore, the equation becomes:
V(t) = 12 + 4t
This equation represents the amount of water in the bathtub at any given time t, assuming it starts with 12 gallons and fills at a rate of 4 gallons a minute.
determine the equation of the graph and select the correct answer below
Answer:
slef
Step-by-step explanation: