Answer:
Y=3 is a horizontal line. So, a line perpendicular to y=3 must be vertical. The only vertical line among the choices is x=-3, so C must be the answer.
Step-by-step explanation:
Can someone please help me with this question?!?
Answer:
(3, 10, 17, 24....)
Step-by-step explanation:
f(x) = 7x - 4
x = 1:
f(1) = 7*1 - 4 = 7 - 4 = 3
x = 2:
f(2) = 7*2 - 4 = 14 - 4 = 10
x = 3
f(3) = 7*3 - 4 = 21 - 4 = 17
then the sequence is:
(3, 10, 17, 24.....)
Please help I will be very grateful for this
Answer:
____________
the answer is B
___________
explanation
Factor out the greatest common factor from each group.
Group the first two terms and the last two terms.
(x^2 - 2x) - 3xy + 6y
Factor out the greatest common factor (GCF) from each group.
x(x - 2) - 3y (x - 2)
Factor the polynomial by factoring out the greatest common factor, x - 2
(x - 2) (x - 3y)
Answer:
Step-by-step explanation:
your answer would be B.
add and subtract the second turn to the expression and Factor by grouping
#16 i
MODELING REAL LIFE A public university charged $9200 for tuition and fees in the 2014-2015 academic year. This cost
increased at a constant rate and reached $10,900 in the 2019-2020 academic year. Estimate the cost of tuition and fees in the
2023-2024 academic year.
The tuition is an illustration of a linear function.
The cost of tuition and fees in the academic year 2023-2024, is $12260
Let the number of academic years after 2014-2015 academic year be x.
So, we have:
\(\mathbf{(x,y) \to (0,9200)(5,10900)}\)
A linear function is represented as:
\(\mathbf{y = mx + b}\)
Where m represents the slope (i.e. constant rate), and b represents the y-intercept (i.e. the value of y when x = 0)
So, we have:
\(\mathbf{10900 = 5m + 9200}\)
Subtract 9200 from both sides
\(\mathbf{1700 = 5m}\)
Divide both sides by 5
\(\mathbf{340 = m}\)
So, we have:
\(\mathbf{m =340 }\)
The function becomes
\(\mathbf{y = mx + b}\)
\(\mathbf{y = 340x + 9200}\)
In the academic year 2023-2024, x = 9.
So, we have:
\(\mathbf{y = 340x + 9200}\)
\(\mathbf{y = 340 \times 9 + 9200}\)
\(\mathbf{y = 3060 + 9200}\)
\(\mathbf{y = 12260}\)
Hence, the cost of tuition and fees is $12260
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find the measurement indicated in the parallelogram
Answer:
m(∠W) = 114°
Step-by-step explanation:
By the property of a parallelogram,
"Opposite angles of a parallelogram are equal in measure"
By this property,
m(∠W) = m(∠U)
9x + 15 = 4 + 10x
15 - 4 = 10x - 9x
x = 11
Therefore, m(∠W) = 9x + 15
= 9(11) + 15
= 99 + 15
= 114°
Measure of angle W is 114°.
Factorize a² +3ab - 5ab - 15b².
Answer:
\(a^2+3\,a\,b-5\,a\,b-15\,b^2=(a-5\,b)\,(a+3\,b)\)
Step-by-step explanation:
Work via factoring by groups:
!) re arrange the terms as follows:
\(a^2-5ab+3ab-15b^2\)
then extract the common factor for the first two terms (a), and separately the common factors for the last two terms (3 b):
\(a^2-5ab+3ab-15b^2\\a\,(a-5\,b)+3\,b\,(a-5\,b)\)
Now notice that the binomial factor (a-5 b) is in both expressions, so extract it:
\(a\,(a-5\,b)+3\,b\,(a-5\,b)\\(a-5\,b)\,(a+3\,b)\)
which is the final factorization.
Answer:
\( \boxed{\sf (a + 3b)(a - 5b)} \)
Step-by-step explanation:
\( \sf Factor \: the \: following: \\ \sf \implies {a}^{2} + 3ab - 5ab - 15 {b}^{2} \\ \\ \sf Grouping \: like \: terms, \\ \sf {a}^{2} + 3ab - 5ab - 15 {b}^{2} = {a}^{2} + (3ab - 5ab) - 15 {b}^{2} : \\ \sf \implies {a}^{2} + (3ab - 5ab) - 15 {b}^{2} \\ \\ \sf 3ab - 5ab = - 2ab : \\ \sf \implies {a}^{2} - 2ab - 15 {b}^{2} \\ \\ \sf The \: factors \: of \: - 15 \: that \: sum \: to \: - 2 \: are \: 3 \: and \: - 5. \\ \\ \sf So, \\ \sf \implies {a}^{2} + (3 - 5)ab - 15 {b}^{2} \\ \\ \sf \implies {a}^{2} + 3ab - 5ab - 15 {b}^{2} \\ \\ \sf \implies a(a + 3b) - 5b(a + 3b) \\ \\ \sf \implies (a + 3b)(a - 5b)\)
A red candle is 8 inches tall and burns at a rate of 7
10 inch per hour.
A blue candle is 6 inches tall and burns at a rate of 1
5 inch per hour.
After how many hours will both candles be the same height?
After four hours, the height of the candles will be the same.
What is a linear equation?A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.
The linear equation is given as,
y = mx + c
Where m is the slope of the line and c is the y-intercept of the line.
A red candle has an 8-inch height and burns at a 7/10-inch per hour rate. A 6-inch tall blue candle burns at a rate of 1/5 inch per hour.
Let x be the number of hours and y be the height.
y = -0.70x + 8 ...1
y = -0.20x + 6 ...2
From equations 1 and 2, then we have
- 0.20x + 6 = - 0.70x + 8
(0.70 - 0.20)x = 8 - 6
0.50x = 2
x = 4 hours
After four hours, the height of the candles will be the same.
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Please help ASAP!!!!
Answer:
It'll have an open circle on both 7 and 21, with a line connecting.
Which is none of the options, unless one isn't shown?
Step-by-step explanation:
-23 > -4x + 5 > -79
So:
-23 > -4x + 5
-23 - 5 > -4x
-4x < -28
x > -28 / -4
x > 7
-4x + 5 > -79
-4x > - 79 - 5
-4x > -84
x < -84 / -4
x < 21
Which statement is FALSE about the Cell Cycle?
1: The stages of the cell cycle repeat themselves.
2: During Prophase, the cell fully splits into a parent and a daughter cell.
3: Most of the cell's life is spent in Interphase, growing larger.
4: The cytoplasm divides during the process called cytokinesis.
PLEASE HELP I NEED HELP ASAP
Answer:2
Step-by-step explanation:
Prophase is the first stage of cell division in both mitosis and meiosis. Beginning after interphase, DNA has already been replicated when the cell enters prophase. The main occurrences in prophase are the condensation of the chromatin reticulum and the disappearance of the nucleolus.
Answer:
B
Step-by-step explanation:
Problem 2 (15 pts.) (a) (8pte ) Recall that for sets A and B,A⊆B is equivalent to the statement If x∈A then x∈B. What is the contrapocitive of this statement (written as an if-then statement)? Hint. We discuss the contrapositive both in Weck 3's videus on propositional logic and on prools by contrapositive. Grading Notes. For thls problem you get 2 points if yois currectly state the contrapoeltive in the requested format. (b) (13 pta) Let S,T and W be sets such that S∩T⊂W, and suppose that t∈T. Use a proof by contradiction to show that t∈S(W. Hint. Since this claim tnvolves relationships amongit sets, I recotnmend drawing a Venu diagram to help visualize the elaim. Hint. As with the prevhous problem, double doek that voit corrertly nesenter the neconary proponitions before you attempt the proch, and enatre sois ary doing is proof to contradiction. You con ses exauples in Week 3 s loctures and Titorial 3 .
a. If an element is not in set B, then it is not in set A.
b. Since we are assuming t∈T, if we can show that t∉W, then we have a contradiction.
(a) The contrapositive of the statement "If x∈A then x∈B" can be written as "If x∉B then x∉A."
(b) To prove that t∈S, we can assume the opposite, which is t∉S. Since S∩T⊂W, this means that if an element is in both sets S and T, then it is also in set W.
Using a proof by contradiction, we assume that t∉W. Since t∈T and S∩T⊂W, this means that t∈S. But this contradicts our initial assumption that t∉S. Therefore, our assumption that t∉W must be incorrect.
Hence, we can conclude that t∈S.
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Determine the equation of the line in slope-intercept form in the graph shown
Answer:
y = (7/6)x + 5 +1/3
Step-by-step explanation:
yeah-ya.....
Ronnie wants to lower his utility bills to save money on his monthly expenses. he discovers that if he replaces his water heater with a solar water heater his monthly utility bills can decrease around 50% to 85%. at the end of the year ronnie wants to calculate the percentage his new solar water heater saved him in the utility bills compared to last year. ronnie's total utility expenses for this year are $862.40 and last year the utility expenses were $1935.67. what percentage did ronnie save on his utlility bills by switching to a solar water heater? a. 44.5% b. 97.8% c. 55.4% d. 67.5% please select the best answer from the choices provided a b c d
Answer:
c. 55.4%
Step-by-step explanation:
We calculate what percentage this year's bill of $862.40 is compared to last year's bill of $1935.67.
862.4/1935.67 × 100% = 44.55304%
Since this year's bill is 44.6% of last year's bill, the percent saved is
100% - 44.6% = 55.4%
Answer: c. 55.4%
Determine whether the variable is qualitative or quantitative. Hair color Is the variable qualitative or quantitative? O A. The variable is quantitative because it is a numerical measure. O B. The variable is quantitative because it is an attribute characteristic. O C. The variable is qualitative because it is a numerical measure. OD. The variable is qualitative because it is an attribute characteristic. Determine whether the quantitative variable is discrete or continuous. Number of members present at a meeting Is the variable discrete or continuous ? O A. The variable is continuous because it is countable. O B. The variable is continuous because it is not countable. C. The variable is discrete because it is not countable. D. The variable is discrete because it is countable.
1. The variable is qualitative or quantitative is the variable is qualitative because it is an attribute characteristic (option d). 2. The quantitative variable is discrete or continuous is the variable is discrete because it is countable (option d).
The variable "Hair color" is qualitative because it represents an attribute characteristic rather than a numerical measure. It refers to the different categories or qualities of hair color, such as blonde, brown, black, or red. It is not based on a numerical scale or measurement. Therefore, the correct answer is D) The variable is qualitative because it is an attribute characteristic.
The variable "Number of members present at a meeting" is discrete because it is countable and takes on distinct, separate values. It cannot take on any value between the integers, and there are no fractions or decimals involved. The number of members present can only be whole numbers, such as 0, 1, 2, 3, and so on. Therefore, the correct answer is D) The variable is discrete because it is countable.
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What is the value of the expression? Show your work.
\(\dfrac{7^{12} \cdot 7^9}{\left(7^6 \right)^3}\\\\\\=\dfrac{7^{12+9}}{7^{18}}\\\\\\=\dfrac{7^{21}}{7^{18}}\\\\\\=7^{21-18}\\\\\\=7^3\\\\\\=343\)
Answer:
342.9385905398
I’m too lazy to put in any more so ya
Step-by-step explanation:
We solve the top first.
7^12 x 7^9
13,841,287,201 x 40,353,607
558,545,864,083,284,007
The bottom is (7^6)^3
(7^6)^3
(7^18)
1,628,413,597,910,449
558,445,864,083,284,007 divided by 1,628,413,597,910,449
342.9385905398
I’m too lazy to put in any more so ya
two cards are selected in a sequence from a standard deck. what is the probability that the second card is a jack given that the first card was a 2. (assume the 2 was not replaced.)
The probability that the second card is a jack given that the first card was a 2 is 52/51.
To calculate the probability that the second card is a jack given that the first card was a 2, we need to consider the remaining cards in the deck after the first card is drawn.
When the first card is drawn and it is a 2, there are 51 cards remaining in the deck, out of which there are 4 jacks.
The probability of drawing a jack as the second card, given that the first card was a 2, can be calculated using conditional probability:
P(Second card is a jack | First card is a 2) = P(Second card is a jack and First card is a 2) / P(First card is a 2)
Since the first card is already known to be a 2, the probability of the second card being a jack and the first card being a 2 is simply the probability of drawing a jack from the remaining 51 cards, which is 4/51.
The probability of the first card being a 2 is simply the probability of drawing a 2 from the initial deck, which is 4/52.
P(Second card is a jack | First card is a 2) = (4/51) / (4/52)
Simplifying the expression:
P(Second card is a jack | First card is a 2) = (4/51) * (52/4)
P(Second card is a jack | First card is a 2) = 52/51
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ASNWER THIS AND ILL HUG YOU
Kim Invested $5,000 in a 3-year Certificate Of Deposit (CD) that pays 2.3% interest compounded annually. How much interest will she earn on the CD at the end of 3 years?
She earns 345$ for the whole 3 years.
Drag and drop the missing terms in the boxes.
6x²-14x-4/2x³ - 2x=A/2x + B/____+C/_____
2x - 1
x - 1
x+1
2x + 1
(i) A = 3, B = 2, C = -1. (ii) The missing terms in the boxes are B/(x - 1) and C/(x + 1), respectively. To determine the values of A, B, and C, we need to perform partial fraction decomposition on the rational expression.
The given expression is (6x² - 14x - 4) / (2x³ - 2x). We can start by factoring the denominator, which gives us 2x(x - 1)(x + 1). Using partial fraction decomposition, we assume that the expression can be written as A/(x) + B/(x - 1) + C/(x + 1), where A, B, and C are constants. Now we can find the values of A, B, and C by equating the numerator of the original expression to the sum of the numerators in the partial fraction decomposition. This gives us 6x² - 14x - 4 = A(x - 1)(x + 1) + B(x)(x + 1) + C(x)(x - 1).
To solve for A, we let x = 0 and simplify the equation to get -4 = -A. Therefore, A = 4. For B, we let x = 1 and simplify the equation to get -12 = 2B. Thus, B = -6. Finally, for C, we let x = -1 and simplify the equation to get -16 = 2C. Hence, C = -8.
Therefore, the missing terms in the boxes are B/(x - 1) = -6/(x - 1) and C/(x + 1) = -8/(x + 1), respectively.
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a woman you know has five children - all of whom are boys. what is the probability for a woman to have five boys out of five children?
A woman you know has five children among which all five are boys. probability for a woman that she will have all five boy as a five children is 0.5.
The probability or the outcome in which a women with five children have all the girls and none of them as boys is :-
0.5x0.5=0.25.
So for the first child there is a a 50% chance that is will be of a male. And same for the second child being male there will be equal probability that it can be boy so it also will have a probability .
So the probability of having five females is 0.55=0.03125
Except the above define value all the other outcome or choices means that the women have a least one son in the five children and the total probability of an event is 1.
.The theoretical probability is mainly reasoning bases which is behind probability. For example, if a coin is tossed then the theoretical probability or the outcome of getting a head will be ½.
Probability provides information about the happening of something which might happen and might not depending upon the outcome demand happen. Meteorologists, also take the help of probability to predict whether the rain may happen or not for instance In epidemiology, also probability theory is used to understand about various risk related to life an to demonstrate various relation .
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Which is an equation of the line that passes through the points (2, 3), (6, 7), and (8, 9)?
Answer:
y=x+1
hope this helps
A parallelogram 756 has vertices A(-1,2, -1), B(3,-2,-4), D(-3,0,-2). Determine (a) the coordinates of vertex C (b) the area of parallelogram 756
The coordinates of vertex C are (1, -4, -5) and the area of the parallelogram 756 is 8.71 square units.
(a) We need to find the coordinates of vertex C. Use the fact that opposite sides of a parallelogram are parallel and equal in length. We can obtain the coordinates of vertex C. It will be obtained by adding the displacement vectors of AB and AD to the coordinates of vertex A.
Displacement vector AB = = (3 - (- 1), - 2 - 2, - 4 - (- 1))
= (4, - 4, - 3)
Displacement vector AD = (- 3 - (- 1), 0 - 2, - 2 - (- 1))
= (- 2, - 2, - 1)
Coordinates of vertex C = Coordinates of vertex A + Displacement vector AB + Displacement vector AD,
= (-1, 2, -1) + (4, -4, -3) + (-2, -2, -1)
= (-1 + 4 - 2, 2 - 4 - 2, -1 - 3- 1)
= (1, -4, -5)
Coordinates of vertex C are (1, -4, -5).
(b) We have to find the area of the parallelogram. We can calculate the magnitude of the cross product of vectors AB and AD.
Cross product AB x AD = |i j k|
|4 -4 -3|
|-2 -2 -1|
= (-8i - 6j + 8k) - (-6i - 8j - 4k) + (-8i - 6j + 2k)
= -2i - 6j + 6k
Magnitude of this cross product.
|AB x AD| = √(4 + 36 + 36)
= √(4 + 36 + 36)
= √(76)
= 2 × √(19)
= 8.71 square units.
So area of parallelogram ABCD is 8.71 square units.
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Study the food web below and answer the following :
i. In the pyramid of numbers there is an increase in numbers towards the base. Mention a pyramid where the base will be smaller.
ii. Predict the impact of removing snakes from this food web
Answer:
predict the impact of removing snakes from this food web
a new car is purchased for 18500 dollars. the value of the car depreciates at 8% per year. to the nearest tenth of a year, how long will it be until the value of the car is 9100 dollars?
Answer:
8.5 years
Step-by-step explanation:
You want to know the number of years until 18500 depreciates to 9100 at the rate of 8% per year.
ValueThe depreciation rate given as a percentage of current value tells you the depreciation is exponential. The formula will be ...
value = (initial value) × (1 - (depreciation rate))^t
where the rate is "per year" and t is in years.
Applicationvalue = 18500·(1 -0.08)^t
9100 = 18500·0.92^t . . . . fill in the value of interest
9100/18500 = 0.92^t . . . . divide by 18500
log(91/185) = t·log(0.92) . . . . take logarithms
t = log(91/185)/log(0.92) ≈ -0.3081/-0.03621 ≈ 8.509
It will be about 8.5 years until the value is $9100.
__
Additional comment
The graph shows the solution to ...
18500·0.92^t -9100 = 0
We find it fairly easy to locate an x-intercept, so we wrote the equation in the forms that makes the x-intercept the solution.
a rectangular room is 3 3 times as long as it is wide, and its perimeter is 56 56 meters. find the dimension of the room.
Consequently, the room has a 7 meter width. The room's length is
\(= 7 * 3 meters = 21 meters\)
What is rectangle?
A rectangle in Euclidean plane geometry is a quadrilateral with four right angles. You might also describe it as follows: a quadrilateral that is equiangular, which indicates that all of its angles are equal. The parallelogram might also have a straight angle. Squares are rectangles with four equally sized sides. A quadrilateral of the shape of a rectangle has four 90-degree vertices and equal parallel sides. As a result, it is sometimes referred to as an equirectangular rectangle. Because its opposite sides are equal and parallel, a rectangle is also known as a parallelogram.
Given that the length of the rectangular space is three times its breadth
The chamber has a 56-meter perimeter.
Assume that the room's width is x.
As a result, the room is three times as long.
The room's perimeter is now equal to 2(3x + x).
\(Here, 2(3x + x) = 56\\ 2 * 4x = 56\\ 8x = 56\\ x = 7.\)
Consequently, the room has a 7 meter width.
The room's length is
\(= 7 * 3 meters\\= 21 meters\)
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Find an equation of a square root curve of the form
= √ + that approximately contains the points
(3,7) and (6, 8)
Answer:
y = √(5x+34)
Step-by-step explanation:
The regression formula that matches a square root function to these points can be worked out by a suitable calculator. The attachments shows the points are matched exactly by the function ...
y = √(5x+34)
__
If you would like to work this by hand, you can put the (x, y) point values into the proposed equation and see what the coefficients need to be:
y = √(ax +b)
7 = √(3a +b) ⇒ 49 = 3a +b
8 = √(6a +b) ⇒ 64 = 6a +b
Subtracting the first equation from the second, gives ...
(64) -(49) = (6a +b) -(3a +b)
15 = 3a ⇒ a = 5
49 = 3(5) +b ⇒ b = 34
What is fh perpendicular
Answer:
At an angle of 90° to a given line, plane, or surface.
Step-by-step explanation:
;)
Solve the system of equations.
−5x+2y=9
y=7x
Answer:
x=1 y=7
Step-by-step explanation:
−5x+2y=9
y=7x
Substitute the second equation into the first
-5x +2(7x) = 9
Distribute
-5x +14x = 9
Combine like terms
9x=9
Divide by 9
9x/9 =9/9
x= 1
Now find y
y = 7(1)
y = 7
Answer:
\(x=1\\y=7\)
Step-by-step explanation:
\(-5x+2y=9\\y=7x\)
Replace y in the first equation.
\(-5x+2(7x)=9\)
Distribute the 2 and combine like terms;
\(-5x+14x=9\\9x=9\)
Divide by 9
\(x=\frac{9}{9}\\ x=1\)
-----------------------------------------------
After having found x, you can replace it in any of the equations to find y. I'll use the second equation.
\(y=7x\\y=7(1)\\y=7\)
If h(x) = 2x² - 5 find h(4x²)
Answer:
8x^4-5
Step-by-step explanation:
8x^4-5
Just substitute 4x^2 into x
Answer:
= 32x^4-5
Step-by-step explanation:
Anna and Brian participate in a 2-player simultaneous sealed-bid auc- tion with the rules below: bid can be 100 or 200 only highest bidder wins (fair coin is tossed in case of a tie) winner pays own bid. Annas valuation is known by everyone to be 300 Yuan, while only Brian knows his own valuation. What everyone does know is that Brians valuation is drawn from the set {150,250} with equal probability a Write down the normal form of the game (b) Find all pure BNE,if any, of this game.
In this game, the pure best response equilibria (BNE) are when Anna bids 200 and Brian bids 100, or when Anna bids 100 and Brian bids 200. These equilibria occur because both players are playing their best response to the other player's strategy, resulting in a Nash equilibrium.
(a) The normal form of the game can be represented in a payoff matrix where the rows represent Anna's strategies (bids) and the columns represent Brian's strategies (bids):
scss
Copy code
Brian
| 100 | 200 |
-------------------------------
100 | (300, 0) | (300, 0) |
-------------------------------
200 | (0, 100) | (0, 200) |
-------------------------------
In each cell, the first number represents Anna's payoff, and the second number represents Brian's payoff.
(b) To find all pure best response equilibria (BNE), we need to examine each player's strategy and determine if they have a best response to the other player's strategy.
For Anna:
If Brian bids 100, Anna's best response is to bid 200, as this guarantees a higher payoff of 300.
If Brian bids 200, Anna's best response is to bid 100, as this guarantees a higher payoff of 300.
For Brian:
If Anna bids 100, Brian's best response is to bid 200, as this guarantees a higher payoff of 0.
If Anna bids 200, Brian's best response is to bid 100, as this guarantees a higher payoff of 0.
Therefore, the pure best response equilibria (BNE) of this game are:
(Anna: 200, Brian: 100)
(Anna: 100, Brian: 200)
In both cases, both players are playing their best response to the other player's strategy, resulting in a Nash equilibrium.
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In terms of relative growth rate, what is the defining property of exponential growth?
In terms of relative growth rate Exponential growth is characterized by a constant relative growth rate.
Exponential growth is the process of increasing quantity over time. Occurs when the instantaneous rate of change of a quantity over time is proportional to the quantity itself. The exponential growth model has the form
y (t) = C eᵏᵗ, where k is the rate constant.
Relative Growth Rate:Relative growth rate (RGR) is the rate of growth relative to size. That is, the rate of growth per unit time relative to the size at that point in time and y'(t)/y(t) is the relative growth rate of a function y at time t.
1/y dy/dt = 1/y d(C eᵏᵗ)/dt
= 1/y(kC eᵏᵗ)
= 1/y ( ky) ( since, y (t) = C eᵏᵗ)
= k
Therefore a constant relative growth rate.
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Complete question:
In terms of relative growth rate, what is the defining property of exponential growth? Choose the correct answer below.
A. The relative growth rate at time t is the slope of the exponential function at time t.
B. dy dt If y represents a population, then the relative growth rate can be represented by dy/dt
C. The relative growth rate is proportional to the size of the population
D. The relative growth rate is constant.
AGAIN HELP!!!!!!!!!!!!!!!STILL TRYING TO TEACH MYSELF LOL
What is the equation of the line that is parallel
to the line y = 2x - 1 and passes through the
point (2, 7)?
Answer:
y= 2x + 3
Step-by-step explanation:
To have a parallel line they need to have the same slope.
Then you need to plot the point (2,7).
A slope of 2x means that it goes up 2 y values for every x value it goes up by. So to find the y-intercept, you need to go down 2 x values. Meaning you need to subtract 4 y values. (0,3).
y= (slope) + y-intercept
Answer:
y = 2x + 3
Step-by-step explanation:
1. Approach
The line y = 2x -1 is written in slope-intercept form, essentially; y = mx + b, where "m" is the slope, and "b" is the y-intercept. If two lines are parallel, then they both have the same slope. So one simply has to substitute in a point on the line to find out what the y-intercept is, and assemble the equation.
2. Slope
As mentioned above, two parallel lines have the same slope. Hence the slope of the line that one is trying to find the equations of is 2.
3. y-intercpet
Substitute in the point that is given, and solve for the y-intercept.
y = mx + b
y = 2x + b
7 = 2(2) + b
7 = 4 + b
3 = b
4. Assembling what one knows
The equation of the line is;
y = 2x + 3
Were 2 is the slope, and 3 is the y-intercept.