Using the function concept, we have that:
Items, a, and d are functions.Item b and c are not functions.When does a relation represents a function?A relation represents a function when each value of the input is mapped to only one value of the output.
On a graph, it means that each value of x is mapped to only one value of y, that is, there are no vertically aligned points on the graph.
For this problem, relation c does not represent a function, as there are multiple values of x are related to two values of y, and there are vertically aligned points on the graph.
In item b, when x = 6, there are two values of y, hence this is also not a function. For items a and d, each value of x is mapped to only one value of y, hence they are functions.
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Use the Ratio Test to determine whether the series is convergent or divergent. [infinity]
∑ 9^n / (n+1)7^2n + 1 n=1
Identify an ___________
Evaluate the following limit.
lim n -> [infinity] |an + 1 / an |
The series has an alternating sign since every term is positive, and |(an + 1 / an)| is decreasing to 9/49. Therefore, we can use the Alternating Series Test to conclude that the series converges.
Using the Ratio Test:
lim n -> [infinity] |(9^(n+1) / ((n+1)+1)7^(2(n+1) + 1)) / (9^n / (n+1)7^(2n + 1))|
= lim n -> [infinity] |(9^(n+1) / 7^(2n+3)) * ((n+1)7^(2n+1) / (n+2)7^(2n+3))|
= lim n -> [infinity] |(9 / 49) * (n+1) / (n+2)|
= 9/49
Since the limit is less than 1, the series converges.
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A vase has 3 red roses, 4 pink roses, and 5 white roses. Another vase has 2 red roses, 2 pink roses, and 2 white roses. If one rose is to be selected at random from each vase, what is the probability that both roses will be the same color
Answer:
The probability that both roses are red 1/12.
The probability that both roses are pink is 1/9.
The probability that both roses are white is 5/36.
Adding these probabilities together, we get 11/36.
So the probability that both roses will be the same color is 11/36.
Step-by-step explanation:
URGENT!!!!! LAST TWO QUESTIONS!!!!!!! WILL GIVE BRANLIEST!!!AT LEAST TAKE A LOOK!!!!!! PLS HELP!!! 1. A cartographer wants to create a map of Seattle. He has designed a key/legend for the map indicating that 1 cm equals 2 miles. If the distance between Woodland Park Zoo and the Seattle Aquarium is 5.2 miles, how long is the distance going to be on the map? A) 2.6 cm B) 8.2 cm C) 6 cm D) 10.4 cm 5. What similarity property, if any, can be used to show that the following two triangles are similar. A) SAS B) SSS C) AA D) Not enough information given
Answer:
1. 5.2 / 2 = 2.6 cm
2. Since 2 angles are congruent the answer is AA.
chapter 2 of volume ii ends with victor saying, "for the first time i felt what the duties of a creator towards his creature were" (85). what does this mean, and why does he say it?]\
In Chapter 2 of Volume II of Frankenstein, Victor Frankenstein concludes by stating, "for the first time I felt what the duties of a creator towards his creature were" (85). Victor's remark implies that he has finally realized that he has a responsibility towards the creature he has created, and that he must accept the consequences of his creation.
Victor recognizes that as the creator of the creature, he is morally obliged to ensure that the creature is well-treated and cared for. Victor expresses remorse for creating the monster and for failing to take responsibility for his actions as the creature's creator. He finally acknowledges his role in the creature's life and feels a sense of obligation to be there for him as his creator.
Victor understands the importance of having a sense of responsibility and accountability as a creator towards his creation. This demonstrates the theme of the novel, which is the dangers of playing God and the consequences that come with taking on a task that is beyond one's capabilities.
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Graph the line with slope 3/4 passing through the point (-2,3)
The slope of the line is:
rise/run = 3/4
The line passes through (-2, 3), we start at this point and use the rise and run to find the second point on the line.
The run is 4, so we add 4 to the x-coordinate.
The rise is 3, so we add 3 to the y-coordinate.
We have:
(-2 + 4, 3 + 3) = (2, 6)
We use (-2, 3) and (2, 6) to graph the line.
This is shown below
Answer: wockhardt is good rap
Given the polar coordinates (−10,135∘), convert to exact rectangular coordinates. Answer
The exact rectangular coordinates for the polar coordinates (-10, 135°) are (5\(\sqrt{2}\), -5\(\sqrt{2}\)).
To convert polar coordinates to rectangular coordinates, we can use the following formulas:
x = r * cos(θ)
y = r * sin(θ)
Given the polar coordinates (-10, 135°), where r is the distance from the origin (radius) and θ is the angle in degrees, we can apply these formulas.
x = (-10) * cos(135°)
y = (-10) * sin(135°)
To evaluate the trigonometric functions, we'll use the corresponding values from the unit circle:
cos(135°) = -\(\sqrt{2}\)/2
sin(135°) = \(\sqrt{2}\)/2
Substituting these values into the formulas, we have:
x = (-10) * (-\(\sqrt{2}\)/2)
y = (-10) * (\(\sqrt{2}\)/2)
Simplifying, we get:
x = 5\(\sqrt{2}\)
y = -5\(\sqrt{2}\)
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Find the missing length indicated.
Answer:
I think the answer is 8 you should search it up to make sure
2) Byron made a scale model of his
favorite car. The car is 14 feet long.
Byron's model is 3.5 inches long. What
is the scale Byron used to make his
model car?
9514 1404 393
Answer:
1 : 48
Step-by-step explanation:
The scale is ...
3.5 in : 14 ft = 3.5 in : 168 in = 1 : 48
Answer:
Solution :-At first we need to convert ft into in
1 ft = 12 in
14 × 12 = 168 inches
Ratio = 3.5 : 168
Ratio = 1:48
\( \\ \)
Consider a continuous random variable x, which is uniformly distributed between 65 and 85. The probability of x taking on a value between 75 to 90 is ________. 0.50 0.075 0.75 1.00
The probability of x taking on a value between 75 to 90 is 0.25.
Given that x is a continuous random variable uniformly distributed between 65 and 85.To find the probability that x lies between 75 and 90, we need to find the area under the curve between the values 75 and 85, and add to that the area under the curve between 85 and 90.
The curve represents a rectangular shape, the height of which is the maximum probability. So, the height is given by the formula height of the curve = 1/ (b-a) = 1/ (85-65) = 1/20.Area under the curve between 75 and 85 is = (85-75) * (1/20) = (10/20) = 0.5Area under the curve between 85 and 90 is = (90-85) * (1/20) = (5/20) = 0.25.
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PLSSSS HELP IF YOU TRULY KNOW THISSS
Answer:
x = 2
Step-by-step explanation:
14 + 3x = 2 + 9x
Collect like terms so when positive 2 crosses the equals to sign, it becomes negative 2 and when positive 3x crosses the equals to sign, it becomes negative 3x.
14 - 2 = 9x - 3x
12 = 6x
Divide both sides by the co efficient of x which is 6 so,
12/6 = 6x/6
2 = x
Hope this helps you <3
Pls rate as brainliest answer!
Mario tracks his heart rate after throwing warm-up pitches before a game. In 1/4 minutes, Mario's heart beats 28 times
Answer:112
Step-by-step explanation: 1/4 divided by 28/1 = 1/112
Answer:
112 and very light
Step-by-step explanation:
A small publishing company is planning to publish a new book. The production costs will include one-time fixed costs (such as editing) and variable costs (suchas printing). The one-time fixed costs will total $30456. The variable costs will be $10 per book. The publisher will sell the finished product to bookstores at aprice of $21.75 per book. How many books must the publisher produce and sell so that the production costs will equal the money from sales?
Let x be the number of books that need to be sold, then for the cost of the production and the profit to be the same we can set the following equation:
\(30456+10x=21.75x\text{.}\)Subtracting 10x from both sides of the equation we get:
\(30456=21.75x-10x,\)adding like terms we get:
\(30456=11.75x\text{.}\)Dividing by 11.75 we get:
\(x=2592.\)Then the producer must sell 2592 books.
Answer: 2592.
In whitch number dose one digit 6 have a value that is 1,100 of value of the other difit 6?
6,702 = 6 thousands and 7 hundreds and 0 tens and 2 ones
\(= 6 \times 1000 + 7 \times 100 + 0 \times 10 + 2 \times 1\)
\(= 6000 + 700 + 2\).
Above, we have written the number 6,702 in expanded form, or as a SUM of its different parts according to place value. The digit 6 in the number 6,702 actually has the value 6,000 and the digit 7 actually signifies the value 700. This is why our number system is also called a place value system, because the value of a digit (like 6 or 7 in our example) depends on its placement within the number. In other words, the digit 6 in 6702 does not mean six but six thousand, because the six is placed in the thousands' place. The place of a digit determines its value. I'll go for 66.04 that's the closest.
Complete Question-
In which number does one digit 6 have the value of 1/100 of the other digit 6? The answers given are 66.04, 56.60, 46.06, and 40.66, which is the correct answer?
Identify the slope of each of the following equations.
(a) y = 4/5x + 3
(b) y = -x + 1
(c) y = 2x
And what is the y-intercept of equation (c)?
Answer:
Please see the explanation.
Step-by-step explanation:
As we know that the slope-intercept form of the equation is
\(y=mx+b\)
where m is the slopeb is the y-interceptNow, comparing the given equations with the slope-intercept form
a) y = 4/5x + 3
Here:
m = 4/5
Therefore, the slope of the equation y = 4/5x + 3 is: m = 4/5
b) y = -x + 1
Here:
m = -1
Therefore, the slope of the equation y = -x + 1 is: m = -1
b) y = 2x
Here:
m = 2
y-intercept = b = 0 ∵ y = mx+b here b is the y-intercept
Therefore, the slope of the equation y = 2x is:
m = 2 and
y-intercept = b = 0
3. What is the current price of a common stock that just paid a $4 dividend if it grows 5% annually and investors want a 15% return? (5) ch.7
4(1,05)_4:20 - $42 715-.05 110
4. Redo the preceding problem assuming that the company quits business after 25 years. (5) ch.7
42x 7.05 5. Redo Problem #3 assuming that dividends are constant. (5) 2
Ch.7
=$37,68
4 15 #26.67
6. Redo Problem #3 assuming that dividends are constant and the company quits business after 25 years. (5)
4 x 6.4641 = $25.88
3. The current price of the common stock is $40.
4. The stock price considering the company quitting business after 25 years is $46.81.
5. The stock price assuming constant dividends is $26.67.
6. The stock price assuming constant dividends and the company quitting business after 25 years is $25.88.
3. The current price of the common stock can be calculated using the dividend discount model. The formula for the stock price is P = D / (r - g), where P is the stock price, D is the dividend, r is the required return, and g is the growth rate. In this case, the dividend is $4, the required return is 15% (0.15), and the growth rate is 5% (0.05). Plugging these values into the formula, we get P = 4 / (0.15 - 0.05) = $40.
4. If the company quits business after 25 years, we need to calculate the present value of the dividends for those 25 years and add it to the final liquidation value. The present value of the dividends can be calculated using the formula PV = D / (r - g) * (1 - (1 + g)^-n), where PV is the present value, D is the dividend, r is the required return, g is the growth rate, and n is the number of years. In this case, D = $4, r = 15% (0.15), g = 5% (0.05), and n = 25. Plugging these values into the formula, we get PV = 4 / (0.15 - 0.05) * (1 - (1 + 0.05)^-25) = $46.81. Adding the final liquidation value, which is the future value of the stock price after 25 years, we get $46.81 + $0 = $46.81.
5. Assuming constant dividends, the stock price can be calculated using the formula P = D / r, where P is the stock price, D is the dividend, and r is the required return. In this case, the dividend is $4 and the required return is 15% (0.15). Plugging these values into the formula, we get P = 4 / 0.15 = $26.67.
6. If the company quits business after 25 years and assuming constant dividends, we need to calculate the present value of the dividends for those 25 years and add it to the final liquidation value. The present value of the dividends can be calculated using the formula PV = D / r * (1 - (1 + r)^-n), where PV is the present value, D is the dividend, r is the required return, and n is the number of years. In this case, D = $4, r = 15% (0.15), and n = 25. Plugging these values into the formula, we get PV = 4 / 0.15 * (1 - (1 + 0.15)^-25) = $25.88. Adding the final liquidation value, which is the future value of the stock price after 25 years, we get $25.88 + $0 = $25.88.
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hi!
can you guys please help me I don’t understand this :)
Answer:
b) Mood
Step-by-step explanation:
The mood is created by a writer by describing the setting and other objects.
12. What is the Product of 0.04 x 0.08? A. 32 B. 0.32 C. 0.032 D. 0.0032
Answer: The answer is D 0.0032
Step-by-step explanation:
what are the ordered pairs of the solutions for this system of equations?
f(x)=x^(2)-2x+3; f(x)=-2x+12
The ordered pairs for the system of equations f(x) = x^2 -2x + 3 and f(x) = -2x + 12 are (3, 6) and (-3, 18)
What is a quadratic equation?A quadratic equation is an algebraic equation of the second degree in x. The quadratic equation in its standard form is ax2 + bx + c = 0, where a and b are the coefficients, x is the variable, and c is the constant term. The first condition for an equation to be a quadratic equation is the coefficient of x2 is a non-zero term(a ≠ 0)
f(x) = x^2 -2x +3 and f(x) = -2x + 12
which means
x^2 -2x +3 = -2x + 12
x^2 -2x +3 + 2x - 12 = 0
x^2 -9 = 0
by factorizing we have
(x-3)(x+3) = 0
x = 3 or -3
when x = 3
f(x) = -2x + 12
f(3) = -2(3) + 12 which is 6
when x = -3
f(-3) = -2(-3) + 12 which is 18
ordered pairs are (3, 6) and (-3, 18)
In conclusion, (3, 6) and (-3, 18) are the ordered pairs
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*HELP*
You ask your friend to pick a number 1-10. If he picks a number larger than 5, what are the odds it is an 8?
A) 1/10
B) 5/8
C) 1/8
D) 1/5
If your friend picks a number larger than 5, the possible choices are 6, 7, 8, 9, and 10. The correct answer is C) 1/8.
There are 5 numbers from 6 to 10. Out of these 5 numbers, only one of them is an 8. Therefore, the probability of picking an 8 if the number is larger than 5 is 1/5. However, the question specifically asks for the odds of picking an 8, which is different from probability.
Odds are calculated by dividing the probability of the event occurring by the probability of the event not occurring. The probability of not picking an 8 is 4/5, since there are 4 numbers from 6 to 10 that are not 8. So the odds of picking an 8 are 1/5 divided by 4/5, which simplifies to 1/8.
If your friend picks a number larger than 5, the possible choices are 6, 7, 8, 9, and 10. There is only one instance of the number 8 within these options. Therefore, the odds of your friend picking an 8 are: 1 (instance of 8) / 5 (total possible choices) = 1/5
Probability is the branch of mathematics concerned with measuring the likelihood or chance of events occurring. It is a way to quantify uncertainty and can be applied to a wide range of fields, including statistics, finance, and science.
The probability of an event is a number between 0 and 1, with 0 indicating that the event is impossible and 1 indicating that the event is certain. If the probability of an event is 0.5, for example, it means that the event has an equal chance of occurring or not occurring.
There are two main types of probability: theoretical and experimental. Theoretical probability is based on mathematical models and calculations, while experimental probability is based on observations and experiments.
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what is the slope of a horizontial line
Answer: The slope of a horizontal line is equal to 0.
Step-by-step explanation:
Brainliest plz
Answer:
zero
Step-by-step explanation:
The slope of a horizontal line is zero, while the slope of a vertical line is undefined. Slopes represent a line's ratio of its vertical change to its horizontal change. Horizontal lines have no steepness at all and they remain constant, so the slope is always zero.
What is 8(3+a)? Please answer
The Answer is
24 + 8aor, 8a + 24
To get the answer we have to distribute the 8, which means we have to multiply both terms in the parentheses by 8.
8 x 3 = 24
8 x a = 8a
So the answer is 24 + 8a
Answer:
24+8a
Step-by-step explanation:
8(3+a)
= 8 x 3 + 8 x a
=24+8a
find the coordinate of the points on the cardioid r 1 cos at which there is a horizontal tangent line, a vertical tangent line, or a singular point.
A cardioid is a mathematical curve that is commonly studied in geometry and calculus. It is defined by the equation r = 1 + cos(θ), where r is the radial distance from the origin and θ is the polar angle. The cardioid has a distinctive heart-shaped form, and it is a smooth curve that can have tangent lines at certain points.
Horizontal Tangent Line:
A horizontal tangent line is a tangent line that is parallel to the x-axis. To find the points on the cardioid at which there is a horizontal tangent line, we need to find the points where the derivative of the curve is equal to zero in the x direction. The derivative of r = 1 + cos(θ) with respect to θ is -sin(θ), and the derivative of r with respect to x is cos(θ). Setting these two derivatives equal to zero, we have:
-sin(θ) = 0
cos(θ) = 0
The first equation has a solution when θ = n * π, where n is an integer. The second equation has solutions when θ = (2n + 1) * π/2, where n is an integer. When θ = n * π, the cardioid is at its maximum value, and when θ = (2n + 1) * π/2, the cardioid is at its minimum value. These points correspond to horizontal tangent lines on the cardioid.
Vertical Tangent Line:
A vertical tangent line is a tangent line that is perpendicular to the x-axis. To find the points on the cardioid at which there is a vertical tangent line, we need to find the points where the derivative of the curve is equal to zero in the y direction. The derivative of r with respect to y is sin(θ), and setting this derivative equal to zero, we have:
sin(θ) = 0
This equation has solutions when θ = (2n) * π/2, where n is an integer. These points correspond to vertical tangent lines on the cardioid.
Singular Point:
A singular point is a point on the curve at which the curve is not smooth and its tangent line is undefined. To find the singular points on the cardioid, we need to find the points where the second derivative of the curve is equal to zero. The second derivative of r = 1 + cos(θ) with respect to θ is -cos(θ), and setting this derivative equal to zero, we have:
-cos(θ) = 0
This equation has solutions when θ = n * π, where n is an integer. These points correspond to singular points on the cardioid.
In conclusion, the points on the cardioid at which there is a horizontal tangent line are given by θ = n * π and θ = (2n + 1) * π/2. The points at which there is a vertical tangent line are given by θ = (2n) * π/2. The singular points are given by θ = n * π. These points can be used to study the properties and behavior of the cardioid in more detail.
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a high school student wants to select a career that makes a lot of money. so, he decides to study the relationship between how much education people get and their starting salaries. which statistical method would be best to use in this situation? g
Answer:
He would have to use the method of polling
Step-by-step explanation:
Polliong would be the method used to solve hope this help
Three rays have a common vertex on a line. Show all of your work and explain, using math evidence, the measures of m and n. (Make sure to use the C-E-R strategy to respond: Make your CLAIM; use words from the question to answer the question being asked; state what you discovered from your math EVIDENCE and facts; and REASONING. 221 62 27"
Answer:
m° = 63°n° = 28°Step-by-step explanation:
You want the measures of the angles marked m° and n° in the given figure.
CER modelThe Claim, Evidence, Reasoning (CER) model tells us an explanation consists of:
A claim that answers the question. Evidence from given data. Reasoning that describes why the evidence supports the claimAngle mClaim: The measure of m° is 63°.
Evidence: Angle m° is one of three angles in the figure that form a straight angle.
Reasoning: The measure of a straight angle is 180° (definition). The sum of the angles is equal to the whole (angle addition theorem).
m° +90° +27° = 180°
m° = 63° . . . . add -117° to both sides (addition property of equality)
Angle nClaim: The measure of n° is 28°.
Evidence: Angle n° is one of two angles in the figure that form a right angle.
Reasoning: The square corner signifies a right angle, whose measure is 90°. The angle addition theorem tells us that angle is the sum of the two angles into which it is divided:
90° = 62° + n°
28° = n° . . . . . . . add -62° to both sides (addition property of equality)
pls answer this simple
Answer:
Step-by-step explanation:
a) 4.5m = 4.5×100 = 450 cm
b) 7.6km = 7.6×1000 = 7600 m
c) 68mm = 68÷10 = 6.8 cm
d) 190cm = 190÷100 = 1.9 m
...
physically Stephanie bought a used one for 1500naira and sold it to her friend at profit of 4%
The amount by which Stephanie sold the item is given as follows:
1560 naira.
How to obtain the amount?The amount by which Stephanie sold the item is obtained applying the proportions in the context of the problem.
The amount at which the item was purchased is given as follows:
1500 naira.
Hence the amount at which the item was sold is given as follows:
1.04 x 1500 = 1560 naira.
Missing InformationThe problem asks for the amount by which Stephanie sold the item.
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An urn holds 9 identical balls except that 1 is white, 3 are black, and 5 are red. An exp How many outcomes are in the sample space for this experiment? How many outcomes are in the event "no ball is
Answer c
Step-by-step explanation:
In a county containing a large number of rural homes, 60% of the homes are insured against fire. Four rural homeowners are chosen at random from this county, and x are found to be insured against fire. Find the probability distribution for x.
Answer:
\(\begin{array}{cccccc}x & {0} & {1} & {2} & {3} & {4} \ \\ P(x) & {0.0256} & {0.1536} & {0.3456} & {0.3456} & {0.1296} \ \end{array}\)
Step-by-step explanation:
Given
\(p = 60\%\)
\(n = 4\)
Required
The distribution of x
The above is an illustration of binomial theorem where:
\(P(x) = ^nC_x * p^x *(1 - p)^{n-x}\)
This gives:
\(P(x) = ^4C_x * (60\%)^x *(1 - 60\%)^{n-x}\)
Express percentage as decimal
\(P(x) = ^4C_x * (0.60)^x *(1 - 0.60)^{n-x}\)
\(P(x) = ^4C_x * (0.60)^x *(0.40)^{4-x}\)
When x = 0, we have:
\(P(x=0) = ^4C_0 * (0.60)^0 *(0.40)^{4-0}\)
\(P(x=0) = 1 * 1 *(0.40)^4\)
\(P(x=0) = 0.0256\)
When x = 1
\(P(x=1) = ^4C_1 * (0.60)^1 *(0.40)^{4-1}\)
\(P(x=1) = 4 * (0.60) *(0.40)^3\)
\(P(x=1) = 0.1536\)
When x = 2
\(P(x=2) = ^4C_2 * (0.60)^2 *(0.40)^{4-2}\)
\(P(x=2) = 6 * (0.60)^2 *(0.40)^2\)
\(P(x=2) = 0.3456\)
When x = 3
\(P(x=3) = ^4C_3 * (0.60)^3 *(0.40)^{4-3}\)
\(P(x=3) = 4 * (0.60)^3 *(0.40)\)
\(P(x=3) = 0.3456\)
When x = 4
\(P(x=4) = ^4C_4 * (0.60)^4 *(0.40)^{4-4}\)
\(P(x=4) = 1 * (0.60)^4 *(0.40)^0\)
\(P(x=4) = 0.1296\)
So, the probability distribution is:
\(\begin{array}{cccccc}x & {0} & {1} & {2} & {3} & {4} \ \\ P(x) & {0.0256} & {0.1536} & {0.3456} & {0.3456} & {0.1296} \ \end{array}\)
state the sample space. list outcomes separated by commas. use notation like 1h to mean you rolled a 1 on the die and flipped heads on the coin.
The sample space consists of the following outcomes: 1H, 1T, 2H, 2T, 3H, 3T, 4H, 4T, 5H, 5T, 6H, 6T
To state the sample space, we'll consider all the possible outcomes of rolling a die and flipping a coin. There are 6 possible outcomes for the die (1-6) and 2 possible outcomes for the coin (heads or tails).
We'll use notation like 1h means rolling a 1 on the die and flipping heads on the coin, 1t means rolling a 1 on the die and flipping tails on the coin, 2h means rolling a 2 on the die and flipping heads on the coin, and so on.
The sample space consists of the following outcomes: 1H, 1T, 2H, 2T, 3H, 3T, 4H, 4T, 5H, 5T, 6H, 6T
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What is the equation of the straight line with gradient 3 that passes through (0,2)? Give your answer in the form y=mx+c where m and c are integers or fractions in their simplest forms.
The equation of the straight line with gradient 3 that passes through (0, 2) is y = 3x + 2.
What is the equation of the straight line?The formula for equation of line is expressed as;
y = mx + b
Where m is slope and b is y-intercept.
Given that:
Point ( 0,2 )
x = 0y = 2Gradient / Slope m = 3Substituting these values into the point-slope form, we get:
y - y1 = m(x - x1)
where m is the slope of the line and (x1, y1) is a point on the line.
y - 2 = 3(x - 0)
Simplifying, we get:
y - 2 = 3x
Adding 2 to both sides, we get the final equation:
y = 3x + 2
Therefore, the equation of the straight line is y = 3x + 2.
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