Find the linear function y, where y depends on t, the number of years since 1980. Helppp due Sunday
Answers
===================================================
Explanation:
For now I'll use x in place of t.
Two points on that line segment are: (15,190) and (25,170)
Use the slope formula to get the following
\((x_1,y_1) = (15,190) \text{ and } (x_2,y_2) = (25,170)\\\\m = \text{slope} = \frac{\text{rise}}{\text{run}} = \frac{\text{change in y}}{\text{change in x}}\\\\m = \frac{\text{y}_{2} - \text{y}_{1}}{\text{x}_{2} - \text{x}_{1}}\\\\m = \frac{170 - 190}{25 - 15}\\\\m = \frac{-20}{10}\\\\m = -2\\\\\)
The slope is -2.
A slope of -2 means we go down 2 each time we move to the right 1.
In short: "down 2, right 1".
Now use point-slope form to determine the equation
\(y - y_1 = m(x - x_1)\\\\y - 190 = -2(x - 15)\\\\y - 190 = -2x + 30\\\\y = -2x + 30 + 190\\\\y = -2x + 220\\\\\)
The last step to do is replace x with t and we get y = -2t+220 which is the final answer.
---------
Check:
Plugging in t = 15 should lead to y = 190.
y = -2t + 220
y = -2(15) + 220
y = -30 + 220
y = 190
So far so good.
Now we need to check if t = 25 leads to y = 170.
y = -2t + 220
y = -2(25) + 220
y = -50 + 220
y = 170
That works as well.
We have confirmed the points (15,190) and (25,170) are on this equation. The answer is confirmed.
Related Questions
A group of 10 people is choosing a chairperson and vice-chairperson. They put all 10 people's names into a hat. The first name drawn becomes chair. The second name drawn becomes vice-chair. How many possible combinations of chair and vice-chair are there?
Answers
Answer:
45
Step-by-step explanation:
\(_{10} C_{2}\) = (10!) ÷(8!) (10-8)!
(10 × 9)÷2 = 45
Answer: 100
Step-by-step explanation:
10 people
2 chairs 1 chair 1 vice chair
10*10=100 different combinations
Find the 12th term of the geometric sequence 10, -20, 40,
Answers
Answer:
10-20-40-50-80-110-140-140-180-220+260-300
Step-by-step explanation:
30
A restaurant used 231 eggs last week. Of these, 46 were brown in color. The remaining
eggs were white in color. Which equation can be used to solve for w, the number
of white eggs used last week?
A 231 +46w=0
B 46+ w = 231
C w = 231 +46
D 231 = 46w
Answers
D 231 = 46w can be used to solve for w, the number of white eggs used last week.
Question 2 (3 points)
Find the perimeter of the trapezoid.
Hint: you will need to use the Pythagorean
formula to find the missing side. Then find the
perimeter.
162.68
176.68
182.51
175.26
16
56
80
14
21.26
Answers
The perimeter of the trapezoid is given as follows:
44 cm.
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.
The missing side is a side of a right triangle, in which the other side is of 18 - 10 = 8 cm, while the hypotenuse is of 10 cm, hence:
8² + h² = 10²
64 + h² = 100
h² = 36
h = 6.
Hence the perimeter is given as follows:
P = 18 + 10 + 10 + 6 = 44 cm.
Missing InformationThe trapezoid is given by the image presented at the end of the answer.
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For males in a certain town, the systolic blood pressure is normally distributed with a
mean of 120 and a standard deviation of 8. What is the probability that a randomly
selected male's systolic blood pressure will be less than 108, to the nearest
thousandth?
Answers
Answer:
0.89
Step-by-step explanation:
The probability that a randomly selected male's systolic blood pressure will be less than 108 is 0.25.
What is Probability?
Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event. The value is expressed from zero to one.
Here, mean = 110, standard deviation = 8
P = \(\frac{x_{mean}-x }{SD}\)
P = (110 - 108)/8
P = 2/8 = 0.25
P(Z<0.25) = 0.5 - 0.25 = 0.25
Thus, The probability that a randomly selected male's systolic blood pressure will be less than 108 is 0.25.
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A table is being sold for 67% off the regular price the sale price is $536 what is the regular price
Answers
Answer:
Step-by-step explanation:
Use a simple Equation
Price = Number x Price
So Price = 536.
Since it was 67% off we multiple the price of the original by .67.
So
536 = .67x
Solve for x = 536/.67 = 800
The original Price is $800.
check by multiplying by the sale %.
Cost of a sled = $99.50, markup = 95%
Answers
Answer:
take wholesale cost and multiply it by 95%, then add to the original value
another way, just multiply by 1.95
Retail cost: 1.95*($99.50) = $194.03
Step-by-step explanation:
Answer:
Below
Step-by-step explanation:
So the sales price of the sled is 100% + 95 % = 195 % of the cost
= 1.95 * cost = 1.95 * 99.50 = 194.03 dollars
The function f(x) = 1.85x2 models the cost of a square carpet, where x is the length in feet. Find the average rate of change for f, to the nearest tenth, over the interval 10 ≤ x ≤ 20.
Answers
To find the average rate of change of the function f(x) = 1.85x^2 over the interval 10 ≤ x ≤ 20, we need to find the difference in the function values at the endpoints of the interval and divide by the length of the interval.
The function value at x = 10 is:
f(10) = 1.85(10)^2 = 185
The function value at x = 20 is:
f(20) = 1.85(20)^2 = 740
The length of the interval is:
20 - 10 = 10
So the average rate of change of the function over the interval 10 ≤ x ≤ 20 is:
(f(20) - f(10)) / (20 - 10) = (740 - 185) / 10 = 55.5
Rounding to the nearest tenth, the average rate of change of the function over the interval 10 ≤ x ≤ 20 is approximately 55.5.
How to solve adjacent angles?
Answers
Answer:
D
Step-by-step explanation:
1 + 4x and 57° are corresponding angles and are congruent , so
1 + 4x = 57 ( subtract 1 from both sides )
4x = 56 ( divide both sides by 4 )
x = 14
When she first purchased it, Soledad's computer had 500 GB of hard drive space. After six months, there
were only 407 GB available. Enter and solve an equation to find the amount of hard drive space that
Soledad used in the first six months. Uses as your variable.
- 500
The equation is
She has used
GB of memory
Answers
Answer:
I think 500-407=93
Please answer quick
Taylor is playing a board game with two friends. Using a single dice, one friend rolled a one, and the other friend rolled a three. Taylor need to roll a number higher than both friends in order to win the game, and she wants to calculate her probability of winning m. What is the probability that Taylor will win the game?
A. P(winning)= 4/6=66%
B.P(winning)= 3/6=50%
C. P(winning)= 5/6=83%
D. P(winning)= 2/6=33%
Answers
Answer:
It would be 2/6.
Step-by-step explanation:
2/6 simplified is 1/3 and she is going against two of her friends in which makes three.
The probability that Taylor will win the game is 3/6 or 50% option (B) is correct.
What is probability?It is defined as the ratio of the number of favorable outcomes to the total number of outcomes, in other words, the probability is the number that shows the happening of the event.
We have:
Taylor is playing a board game with two friends. Using a single dice, one friend rolled a one, and the other friend rolled a three.
To win, Taylor needs to roll a 4, a 5, or a 6.
Total number in a standard roll = 6
Favorable outcomes = 3
Probability = 3/6 or
= (3/6)×100
= 50 %
Thus, the probability that Taylor will win the game is 3/6 or 50% option (B) is correct.
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A verbal description of a linear function f is given. Express the function f in the form
f(x) = ax + b.
The linear function g has rate of change −16 and initial value 600.
Answers
The linear function g which has a rate of change of -16 and initial value 600 is; g = -16x + 600.
What is the linear function which is as described?It follows from the task content that the linear expression which is as described by the given verbal description is to be determined.
Since the standard slope-intercept form of a linear function is as given; f(x) = ax + b.
Where, a = slope (rate of change) and b = y-intercept (initial value).
Therefore, the required linear function which is as described is;
g = -16x + 600
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is this graph a function???
Answers
Answer:
No
Step-by-step explanation:
Hope this helps!
andrea ran 1.04 kilometers more on Wednsday than thursday. how far did andrea run on thursday
Answers
Answer: She ran about 4.88 km answer B
Step-by-step explanation:
Answer:
bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb
Step-by-step explanation:
f(x) = 4* g(x)=?
Which of the following is equal to g(x)?
OA. 4(x-2)
OB. 4* + 2
OC. 4(x+2)
D. 4*-2
g(x) = ?
Answers
Since x - 2 in the exponent would move the graph to the right, B is the right response.
What in math is changing?
a transformation when a graph or geometric figure is picked up and placed somewhere else without changing its shape or size.
What is an example of a vertical shift?
By altering the constant, or the number that follows the x-value alone, an equation can be moved vertically. For instance, you can add or subtract from the "-2" in the linear equation y = x - 2 to move it vertically. The graph will go up three units if a positive adjustment is made by adding 3 to the constant -2.
What does a horizontal shift look like in practice?
The function f(x)=3x is shifted horizontally. Take note of how the graph is shifted to the left, or towards negative x values, when h=1. For instance, g(x)=(x2)2 is a new function if f(x)=x2. Each input is decreased by two before the function is squared.
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If I have 25 dollars and want to buy something for 14 dollars and 99 cents how much money will I have left
Answers
- 14.99
————
10.01
Your answer is 10.01
9) Write the equation of the given line in slope-intercept form:
Answers
Answer:
\(y = - 3x - 1\)
Step-by-step explanation:
shown in attachment
I need help with this
Answers
Answer:
A
Step-by-step explanation:
process of elimination... :D
The blue object (D) has been rotated 270° clockwise about the point (1, 2). Which is the correct image?
Answers
The correct image include the following: B. Green: image A.
What is a rotation?In Mathematics and Geometry, a rotation is a type of transformation which moves every point of the object through a number of degrees around a given point, which can either be clockwise or counterclockwise (anticlockwise) direction.
By applying a rotation of 270° clockwise about the point (1, 2) to the coordinate of the vertices of blue block D, the coordinate the vertices of of its image would be located at the position of the Green: image A.
In this context, we can reasonably infer and logically deduce that Green: image A is the correct transformed shape.
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What is the image of (2, 4) after a reflection over the x-axis?
Answers
Patricia can buy individual songs for $1.00 to download. Also, an entire album costs $10.00 to download. She can spend no more than a total of $80. She wants to buy no more than four albums, and at least 30 individual songs. The following system of inequalities represents this situation, where x is the number of individual songs and y is the number of albums.
Answers
Answer:
The system of inequalities is:
\(x\geq30\\\\y\leq4\\\\10x+1y\leq80\)
Step-by-step explanation:
We will write each of the conditions stated in this problem
Patricia wants to buy at least 30 individual songs.
\(x\geq30\)
She wants to buy 4 albums at most.
\(y\leq4\)
The total expenditure has to be equal or less than $80, when each album cost $10 and each individual song cost $1.
\(10x+1y\leq80\)
The system of inequalities is:
\(x\geq30\\\\y\leq4\\\\10x+1y\leq80\)
28 points. I need help ASAP please
Answers
Answer:
1) Thousands
2) 5
3) ten million
4) 3,000,000
Step-by-step explanation:
Answer:
1. hundred thousands
2. 5
3. ten millions
4. 3,000,000
Step-by-step explanation:
A real estate agent has 8 master keys to open several new homes. Only 1 master key will open any given house. If 40% of these homes are usually left unlocked, what is the probability that the real estate agent can get into a specific home if the agent selects 3 master keys at random before leaving the office?
Answers
Answer:
Step-by-step explanation:
Suppose F represents the value that a room is unlocked.
Then, we can assume that the probability of unlocked homes is:
P(unlocked homes) = P(U)
P(unlocked homes) = 40%
P(unlocked homes) = 0.40
Also, let us represent the value of the locked room with G.
P(locked homes) = P(G)
P(locked homes) = (1 - 0.40)
P(locked homes) = 0.60
Let the probability of selecting a correct key be P(S)
It implies that for the agent to use 3 keys, we have a combination of \(^8C_3\) possible ways for the set of keys.
Now; since only one will open the house, then:
P(select correct key) = P(S)
\(P(S) = \dfrac{ (^1_1) (^7_2) }{ ^8_3 }\)
\(P(S) = \dfrac{21}{56}\)
P(S) = 0.375
Finally, for the real estate agent to have access to specific homes supposing the agent select three master keys at random prior to the time he left his office, Then:
P(F ∪ (G∩S) = P(F) + P(G∩S)
P(F ∪ (G∩S) = P(F) + P(G) × P(S)
P(F ∪ (G∩S) = 0.40 + (0.60×0.375)
P(F ∪ (G∩S) = 0.40 + 0.225
P(F ∪ (G∩S) =0.625
Ali used 2/7 of a foot of ribbon to attach a decoration to his rearview mirror. Now, he has 10/21 of a foot of ribbon left.
QUESTION: How much ribbon did Ali start with?
Answers
The quantity of ribbon that Ali started with was 16/21 feet, based on the mathematical operation of addition.
What are mathematical operations?The basic mathematical operations include addition, subtraction, division, and multiplication.
In the addition operation, two or more addends are added to obtain a result called the sum or total using the equation symbol (=) and the addition operand (+).
The quantity of ribbon attached to the rearview mirror = 2/7
The remaining quantity of ribbon after the attachment = 10/21
The quantity of ribbon Ali started with = 16/21 (2/7 + 10/21)
Thus, using the addition operation, we can conclude that Ali started with 16/21 feet of ribbon.
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4x + 3x + 5 = 7x + 5
True or False?
Answers
Answer:
True.
Step-by-step explanation:
Combine like terms (terms with like variables and the same amount of them):
(4x + 3x) = 7x
7x + 5 = 7x + 5 (True) , ∴ 4x + 3x + 5 = 7x + 5
Which number line represents the solutions to |–2x| = 4?
(I want a clear explanation)
Answers
Answer:
third option
Step-by-step explanation:
| - 2x | = 4
the absolute value function always gives a positive value, however, the expression inside can be positive or negative , that is
- 2x = 4 ( divide both sides by - 2 )
x = - 2
or
- (- 2x) = 4
2x = 4 ( divide both sides by 2 )
x = 2
solutions are x = - 2 , x = 2
these are illustrated on the number line by solid circles at - 2 and 2
this is indicated on the third number line
Number line represents the solutions to |–2x| = 4 is third number line (x1 = -2, x2= 2).
Solving steps :
1. Calculate
Calculate the absolute value.
|-2x| = 4
Use |ab| = |a| * |b| to transform the expression.
|-2x|
|-2| * |x|
The absolute value of any number is always positive.
2 * |x|
We did it!
|-2x| = 4
2 * |x| = 4
2. Divide both sides
Divide both sides of the equation by 2.
2 * |x| = 4
2 * |x| ÷ 2 = 4 ÷ 2
Any expression divided by itself equals 1.
|x| = 4 ÷ 2
Calculate the quotient.
|x| = 2
3. Separate into possible cases
Use the absolute value definition to rewrite the absolute value equation as two separate equations.
|x| = 2
x = 2
x = -2
4. The equation has 2 solutions.
x1 = -2, x2= 2
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Plz help I don’t know what to do it and I need a explanation for it
Answers
Answer:
A function is defined as an equation in which no x value has two y values. You can find the answer to this via the vertical line test. If you move a pencil across a graph and it does not touch the graph at two points, then it is a function. Utilizing this logic, the correct answer is yes, this is a function.
Step-by-step explanation:
Plz help I’ll give 20 points
Answers
Answer: D
Step-by-step explanation: y=2 so 2+2=4+1=5
If f(x)= x^3+x^2-x what is f(4)?
Answers
Answer:
that would be 76
Step-by-step explanation:
Answer:
f(4) = 76
Step-by-step explanation:
To evaluate f(4), substitute x = 4 into f(x), that is
f(4) = 4³ + 4² - 4 = 64 + 16 - 4 = 80 - 4 = 76
Now you try on your own.
Kelly wants to build a new wardrobe for herself with only clothing pieces she loves, fit her well, and coordinate together. She already has most of the pieces she will use, but needs to save up to go shopping for the remaining items. She has already saved some money from her job, and she decides to set aside money weekly from her tips. The expression $25w+$65
represents the amount of money Kelly will have saved after some amount of weeks. What does each part of this expression represent?
$25=
Answer
w=
Answer
$65=
Answer
For this specific expression, would it make sense to plug in a negative number for w
? Answer
For this specific expression, would you ever expect to get a number less than 65
for your total amount saved?
Answers
The Interpretatiom of the equation is that;
w represents number of weeks she will have saved for the remaining items
$25 represents the amount she saves per week
$65 represents the amount she has already saved
How to solve algebra word problems?The algebra word problem can be solved by using variables to denote certain parameters I'm the question.
The general form of equation of a line in slope intercept form is;
y = mx + c
Where;
m is slope
c is y-intercept
We are given the equation:
$25w + $65
This equation represents the amount of money Kelly will have saved after some amount of weeks.
Thus;
w represents number of weeks she will have saved for the remaining items
$25 represents the amount she saves per week
$65 represents the amount she has already saved
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