How can I factor the following trinomial?
a) x^2+7x+10
Answer:
x² + 7x + 10 = (x + 5)(x + 2)
Step-by-step explanation:
***********************************************************
Rule:
To factor a trinomial of the form
x² + ax + b,
find two numbers whose product is b and whose sum is a.
Call these numbers, if they exist, p and q.
Then the factorization is
(x + p)(x + q).
***********************************************************
Let's apply the rule to this problem.
To factor
x² + 7x + 10.
Here, a = 7, and b = 10, so we need to find two numbers that multiply to 10 and add to 7.
The numbers are 5 and 2 since 5 × 2 = 10, and 5 + 2 = 7.
The factorization is
(x + 5)(x + 2)
Answer: x² + 7x + 10 = (x + 5)(x + 2)
What is the percentage strength of a w/w ointment containing 1 g of medication in 100 g of total ointment?
000
The percentage strength of the ointment containing 1 g of medication in 100 g of total ointment is 1%.
The percentage strength of a w/w (weight/weight) ointment is calculated by dividing the weight of the active ingredient by the weight of the total ointment and multiplying by 100.
In this case, you have 1 gram of medication in 100 grams of total ointment. To calculate the percentage strength, you can use the following formula:
Percentage strength = (weight of medication / weight of total ointment) × 100
Substituting the values, we get:
Percentage strength = (1 g / 100 g) × 100
Simplifying this equation:
Percentage strength = 0.01 × 100
Therefore, the percentage strength of the ointment containing 1 g of medication in 100 g of total ointment is 1%.
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According to a study, the probability that an individual will cover his or her mouth when sneezing is 0.29. If 10 randomly
selected individuals are observed, compute the following probabilites.
Your answers should be rounded to four decimal places.
The probability that more than seven individuals will cover their mouth when sneezing is
The probability that less than four individuals will cover their mouth when sneezing is
Answer:
The probability that more than seven individuals will cover their mouth when sneezing is approximately 0.0012 when rounded to four decimal places.
The probability that less than four individuals will cover their mouth when sneezing is approximately 0.6761 when rounded to four decimal places.
Step-by-step explanation:
1. Identify the parameters of the binomial experiment. In this case, we have:
- [tex]\(n = 10\)[/tex], the number of trials (individuals observed)
- [tex]\(p = 0.29\)[/tex], the probability of success on each trial (an individual covering their mouth when sneezing)
2. Use the cumulative distribution function (CDF) of a binomial distribution. The CDF gives the probability of getting a certain number of successes or fewer in [tex]\(n\)[/tex] trials. We can use it to calculate the probability of getting more than a certain number of successes, or less than a certain number of successes.
3. To calculate the probability of more than seven successes:
- We first calculate the probability of seven or fewer successes using the CDF: [tex]\(P(X \leq 7)\)[/tex].
- Since the total probability is 1, the probability of more than seven successes is [tex]\(1 - P(X \leq 7)\)[/tex].
- In the Wolfram Language, this is calculated as `Probability[x > 7, x \[Distributed] BinomialDistribution[n, p]]`.
4. To calculate the probability of less than four successes:
- We can directly use the CDF to calculate the probability of three or fewer successes: [tex]\(P(X \leq 3)\)[/tex].
- This is calculated as `Probability[x < 4, x \[Distributed] BinomialDistribution[n, p]]`.
The question asks for the calculation of probabilities in two scenarios: more than seven and less than four people out of a group of ten will cover their mouths when sneezing, using the probability of an individual covering his or her mouth when sneezing.
Explanation:The subject of this question is mathematics, specifically, the field of probability. The question asks for the probability that more than seven individuals and less than four individuals will cover their mouth when sneezing out of a group of 10 randomly selected individuals.
We can solve this using the binomial probability formula, P(X=k) = C(n, k) * (p^k) * ((1-p)^(n-k)), where p is the probability of a single trial, k is the number of success, n is the total number of trials.
Let's analyze the case when more than seven (8, 9, or 10) individuals will cover their mouth:
P(X > 7) = P(X=8) + P(X=9) + P(X =10).
Substitute k with 8, 9 and 10 in the formula and sum them together to get the probability.
For the case where less than four individuals will cover their mouth, we do a similar task:
P(X < 4) = P(X=0) + P(X=1) + P(X=2) + P(X=3).
Substitute k with 0, 1, 2, and 3 in the formula and sum them up to get the probability.
In both cases, remember to round your answer to four decimal places as per the request in the question.
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What point on the number line is three fifths of the way from the point −3 to the point 3?
The point that is three-fifths of the way from -3 to 3 on the number line is 0.6.
To find the point on the number line that is three-fifths of the way from -3 to 3, we can use the concept of the distance between two points and the idea of a fraction of that distance.
The distance between -3 and 3 is 3 - (-3) = 6.
To find three-fifths of this distance, we can multiply the distance by the fraction 3/5.
(6) * (3/5) = 18/5 = 3.6
So, three-fifths of the distance from -3 to 3 is 3.6.
To find the point that is three-fifths of the way from -3 to 3, we start at -3 and move 3.6 units to the right.
-3 + 3.6 = 0.6
Therefore, the point that is three-fifths of the way from -3 to 3 on the number line is 0.6.
In conclusion, the point 0.6 is three-fifths of the way from -3 to 3 on the number line.
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1. If mLABH = 24° and BH bisects LABC, then find the m/ABC.
Answer:
∠ ABC = 48°
Step-by-step explanation:
∠ ABH and ∠ CBH form ∠ ABC , that is
∠ ABC = ∠ ABH + ∠ CBH
given that BH bisects ∠ ABC , then
∠ ABH = ∠ CBH = 24°
∠ ABC = 24° + 24° = 48°
Complete the conditional statement.
If a +2b+ 3, then ____.
If a + 2b + 3 = 0, then the statement could imply that the expression evaluates to zero.
If a + 2b + 3 > 0, then the statement could indicate that the expression is greater than zero.
If a + 2b + 3 = c, then the statement could suggest that the expression is equal to some value c.
If a + 2b + 3, then the statement is incomplete. It does not provide any specific condition or outcome that follows the "then" part of the statement.
A conditional statement typically follows the form "If [condition], then [outcome]." In this case, we have the expression a + 2b + 3, but it is not clear what condition or outcome is being referred to.
To complete the conditional statement, we need additional information to specify the condition and the corresponding outcome. For example:
If a + 2b + 3 = 0, then the statement could imply that the expression evaluates to zero.
If a + 2b + 3 > 0, then the statement could indicate that the expression is greater than zero.
If a + 2b + 3 = c, then the statement could suggest that the expression is equal to some value c.
Without further context or specific instructions, it is not possible to determine the exact completion of the conditional statement.
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Analyze the table below and determine what the transformation occurred
between f(x) and g(x).
In summary, the transformation between f(x) and g(x) is a vertical stretch with a scale factor of 3.
To analyze the table and determine the transformation between f(x) and g(x), we need to examine the changes in the values of x and the corresponding values of f(x) and g(x).
Looking at the table:
x | f(x) | g(x)
1 | 2 | 6
2 | 4 | 8
3 | 6 | 10
4 | 8 | 12
In general, transformations can include translations, reflections, stretches, compressions, and combinations thereof.
These transformations modify the original function in different ways, altering its shape, position, or both.
We can observe that the values of g(x) are obtained by multiplying the values of f(x) by 3. Specifically, g(x) = 3 * f(x).
Therefore, the transformation between f(x) and g(x) can be described as a scaling transformation, where the values of f(x) are multiplied by a factor of 3 to obtain the values of g(x).
This means that the transfFor example, if g(x) is obtained by shifting f(x) vertically or horizontally, there might be a constant added or subtracted to the function, or the x-values might be increased or decreased.
If g(x) is a scaled or stretched version of f(x), the function values may be multiplied or divided by a constant.
ormation from f(x) to g(x) involves a vertical stretch by a factor of 3. The function g(x) is essentially an amplified version of f(x), where each value of f(x) is multiplied by 3 to obtain the corresponding value of g(x).
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Ali’s latest photo got 42 likes. This is 3 times as many likes as Kate’s latest photo. How many likes did Kate’s photo get? Select the correct solution method below, using x to represent Kate’s likes.
The number of likes Ali's photo received is 42 and it is three times the number of likes that Kate's photo received. Let x represent the number of likes Kate's photo received. The equation that represents this relationship is 3x = 42. Solving for x gives x = 14, which means Kate's photo received 14 likes. Kate’s photo got 14 likes.
To solve this problem, we can use a basic algebraic equation where we let x represent Kate’s likes and 3x represents Ali’s likes.
This is because Ali got 3 times as many likes as Kate. Since Ali’s latest photo got 42 likes, we can set 3x equal to 42. This gives us the equation: 3x = 42.
To solve for x, we can divide both sides of the equation by 3, which gives x = 14.
Thus, Kate's photo got 14 likes.
In summary, to find the number of likes that Kate’s photo got, we can use the equation 3x = 42, where 3x represents Ali’s likes and x represents Kate’s likes. Solving for x gives us x = 14, which means that Kate’s photo got 14 likes.
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Point C has a coordinate of (-6, -4) and point D has a coordinate of (1, -6), how far are they apart?
Answer: D=[tex]\sqrt{53}[/tex]
Step-by-step explanation:
The distance between two points in a plane can be calculated using the distance formula, which is derived from the Pythagorean Theorem. The distance between points (x1, y1) and (x2, y2) is given by:
[tex]D=\sqrt{(x2-x1)^{2} } +\sqrt{(y2-y1)^{2} }[/tex]
Use this formula to find the distance between points C and D.
C: x1 = -6, y1 = -4
D: x2 = 1, y2 = -6
[tex]D=\sqrt{[(1-(-6)]^{2} } +\sqrt{[(-6-(-4)]^{2} }[/tex]
[tex]D=\sqrt{49+4}[/tex]
[tex]D=\sqrt{53}[/tex]
Please answer asap!
Find the experimental probability that 4 of 4
children in a family are boys.
The problem has been simulated by tossing 4
coins (one to represent each child). Let "heads"
represent a boy and "tails" represent a girl. A
sample of 20 coin tosses is shown.
The experimental probability that 4 of 4 children in a family are boys is 5%.
How to find the experimental probability that 4 of 4 children in a family are boys?Probability is the likelihood of a desired event happening.
Experimental probability is a probability that relies mainly on a series of experiments.
Since heads represent a boy and we want to find the experimental probability that 4 of 4 children in a family are boys. Thus, we need to look for 4 heads (HHHH) in the table.
From the table:
4 heads (HHHH) appears once (1) out of 20 (See the attached image).
Thus, the experimental probability that 4 of 4 will be:
Experimental probability = 1/20 * 100 = 5%
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please answer ASAP i will brainlist
a) The graph of the function represents an exponential decay.
b) The numeric values are given as follows:
f(0) = 1.f(1) = 0.3.How to define an exponential function?An exponential function has the definition presented according to the equation as follows:
[tex]y = ab^x[/tex]
In which the parameters are given as follows:
a is the value of y when x = 0.b is the rate of change.The function for this problem is given as follows:
[tex]f(x) = 0.3^x[/tex]
The parameters for this problem are given as follows:
a = 1, b = 0.3.
Hence the shape of the graph is of exponential decay, as |b| < 1.
The numeric values are given as follows:
[tex]f(0) = (0.3)^0 = 1[/tex][tex]f(1) = (0.3)^1 = 0.3[/tex]More can be learned about exponential functions at brainly.com/question/2456547
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system of equations. x+y+z=11 y+z=5 z=9
find the solution
Answer:
z=9y add z= 5or, y add 9=5or, y= 5 - 9 = - 4y = - 4x add y add z = 11
x sub 4 add 9= 11
x add 5= 11
x = ll sub 5
x= 6
Mithra finished 16th in the baking competition. Tiffani finished two places in front of Mithra. Betsy finished 3 places behind Mithra. In which position did Tiffany and Betsy finish?
Tiffani finished in the 18th position, and Betsy finished in the 13th position.
Mithra finished 16th.
Tiffani finished 18th.
Betsy finished 13th.
Based on the given information, we know the following:
Mithra finished 16th in the baking competition.
Tiffani finished two places in front of Mithra.
Betsy finished 3 places behind Mithra.
From this, we can determine the positions of Tiffani and Betsy as follows:
Since Tiffani finished two places in front of Mithra, her position is 16th + 2 places = 18th.
Since Betsy finished 3 places behind Mithra, her position is 16th - 3 places = 13th.
Tiffani finished in the 18th position, and Betsy finished in the 13th position.
Mithra finished 16th.
Tiffani finished 18th.
Betsy finished 13th.
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Let F(x)x = X^2 -1 and G(x) 3-x.
Find (F-G)(-5).
The value of (F - G)(-5) when F(x) = x² - 1 and G(x) = 3 - x is -13.
To find (F - G)(-5), we need to substitute -5 for x in both F(x) and G(x) and then subtract G(-5) from F(-5).
So, F(-5) = (-5)² - 1 = 24 and G(-5) = 3 - (-5) = 8.
Therefore, (F - G)(-5) = F(-5) - G(-5) = 24 - 8 = -13.
In order to find (F - G)(-5), we first need to determine what F(x) and G(x) are.
F(x) is given as x² - 1, so we can write F(x) as:
F(x) = x² - 1
Similarly, G(x) is given as 3 - x, so we can write G(x) as:
G(x) = 3 - x
We now need to find (F - G)(-5), which means we need to evaluate F(-5) and G(-5) and then subtract G(-5) from F(-5).
Let's start by finding F(-5). To do this, we simply substitute -5 for x in F(x):F(-5) = (-5)² - 1F(-5) = 25 - 1F(-5) = 24
Now we need to find G(-5). To do this, we substitute -5 for x in G(x):G(-5) = 3 - (-5)G(-5) = 3 + 5G(-5) = 8
We now have F(-5) and G(-5), so we can find (F - G)(-5) by subtracting G(-5) from F(-5):
(F - G)(-5) = F(-5) - G(-5)(F - G)(-5) = 24 - 8(F - G)(-5) = -13
Therefore, (F - G)(-5) = -13.
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Find the local maximum and local minimum
Answer:
Maximum= (-2,15)
Minimum= (2,-15)
Pls help with my homework
The surface area of the smaller ornament to 1 d.p is 1952.0 cm²
What is scale factor?The scale factor is a measure for similar figures, who look the same but have different scales or measures.
Scale factor is expressed as;
scale factor = new dimension/original dimension
We can also say that the ratio of the corresponding sides of similar shapes is equal and it is the scale factor.
Scale factor = (area factor)²
scale factor = 220/55 = 4
area factor = 4² = 16
Therefore;
16= 31232/x
16x = 31232
Divide both sides by 16
x = 31232/16
x = 1952.0 cm²
Therefore the area of smaller ornament is 1952.0
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A 7-foot piece of twine costs $3.36. What is the price per inch?
Answer:
$0.04 per inch.
Step-by-step explanation:
A 7-foot piece of twine costs $3.36. To find the price per inch, we need to convert 7 feet to inches. Since 1 foot is equal to 12 inches, 7 feet is equal to 84 inches. Therefore, the price per inch is $3.36 divided by 84 inches which is equal to $0.04 per inch.
Find the unit rate. Enter your answer as a mixed number.
A fertilizer covers 5/6 square foot in 1/4 hour.
The unit rate is ______ square feet per hour.
A fertilizer covers 5/6 square foot in 1/4 hour. The unit rate is 31/3 square feet per hour.
To find the unit rate in this problem, we need to determine the amount of square feet covered per hour. The given information tells us that the fertilizer covers 5/6 square foot in 1/4 hour.
To calculate the unit rate, we can divide the amount covered by the time it takes. In this case, we divide 5/6 square foot by 1/4 hour.
To divide fractions, we multiply the first fraction by the reciprocal of the second fraction. Therefore, we have:
(5/6 square foot) ÷ (1/4 hour) = (5/6) * (4/1)
Now, we can multiply the numerators (top numbers) together and the denominators (bottom numbers) together:
(5/6) * (4/1) = (5 * 4) / (6 * 1) = 20/6
To simplify this fraction, we can divide both the numerator and denominator by their greatest common divisor, which is 2:
(20/6) ÷ 2/2 = 10/3
The resulting fraction, 10/3, represents the unit rate. However, the question asks us to express it as a mixed number.
To convert an improper fraction (a fraction with a numerator greater than the denominator) to a mixed number, we divide the numerator by the denominator and express the remainder as a fraction.
In this case, 10 divided by 3 is 3 with a remainder of 1.
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The inequality 5m − 7 > 16 holds true for all numbers less or greater
than
in the set {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
The inequality 5m - 7 > 16 holds true for all numbers greater than 4.6 in the set {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}.
To determine the numbers for which the inequality 5m - 7 > 16 holds true in the set {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}, we can solve the inequality by isolating the variable m.
Starting with the given inequality:
5m - 7 > 16
We can add 7 to both sides of the inequality:
5m > 16 + 7
5m > 23
Next, we divide both sides of the inequality by 5:
m > 23/5
To simplify, we divide 23 by 5:
m > 4.6
Now, we can analyze the set {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} to determine thenumbers for which m is greater than 4.6.
Looking at the set, we find that the numbers greater than 4.6 are: 5, 6, 7, 8, 9, 10.
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See the attached math problem, please help
Fill in the blanks with the correct number. (please spell out your solution using lower case lettering.)Mitosis results in genetically identical cells.Meiosis results in sex cells.
Home werk copy and compele сору ca 33 +23
Answer:
56
Step-by-step explanation:
33 + 23 = 56
There is a .99963 probability that a randomly selected 28-year-old female lives through the year. An insurance company wants to offer her a one-year policy with a death benefit of $600,000. How much should the company charge for this policy if it wants an expected return of $600 from all similar policies?
The probability of dying in one year = 1 - 0.99963 = 0.00037 The insurance company should charge a premium such that the expected return on all similar policies equals $600.
Given, Probability of a 28-year-old female lives through the year = 0.99963
Death benefit of policy = $600,000
The expected return of all similar policies = $600
Now, the probability of dying in one year can be calculated by subtracting the probability of living through the year from 1.
Since there are only two possible outcomes of this policy, either the person will live or she will die.
Therefore, the expected value of the policy is given by: Expected value = (Probability of living * Amount paid if the person lives) + (Probability of dying * Amount paid if a person dies)
Let x be the premium the company should charge. Then we can form the following equation: Expected value = (0.99963 * x) + (0.00037 * $600,000)Expected return of all similar policies = $600Therefore,0.99963x + 0.00037($600,000) = $600
Solving for x,0.99963x + $222 = $600
0.99963x = $378
x = $378 / 0.99963
x ≈ $ 378,450
The company should charge the premium of $378,450 for this policy if it wants an expected return of $600 from all similar policies.
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wich line is a skew line to ad?
A . gh
B . ab
C. cd
D. bc
Answer:
BC
Step by step explanation:
opposite
If -15 represents 15m below sea level then +20 represents
If -15 represents 15m below sea level then +20 represents 20m above sea level.
These values represent changes in altitude or height from a fixed reference point, which is usually the sea level.In this context, the term "sea level" refers to the average height of the surface of the ocean in a given location over time.
It is typically used as a baseline for measuring elevation or depth.In this case, -15 represents 15m below the sea level. This means that the location is 15 meters below the average height of the ocean surface.
Similarly, +20 represents 20m above sea level. This means that the location is 20 meters above the average height of the ocean surface.The plus sign indicates that the location is above the sea level, while the minus sign indicates that it is below sea level.
Therefore, when there is a minus sign in front of a number, it represents the distance below sea level, and when there is a plus sign, it represents the distance above sea level.
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Are b and c the is thing?
Answer:
A) [tex]f[/tex] is continuous at [tex]x=1[/tex]
Step-by-step explanation:
Compute the left and right side limits of f(x) as x approaches 1
[tex]\displaystyle \lim_{x \to 1^-} f(x)=2^1=2\\\\\lim_{x \to 1^+}f(x)=\frac{1}{2}(1)^2-1+\frac{5}{2}=2[/tex]
Since [tex]\displaystyle \lim_{x \to 1^-} f(x)= \lim_{x \to 1^+} f(x)[/tex], then [tex]\displaystyle \lim_{x \to 1} f(x)[/tex] exists, which makes A true.
Please help me i will mark brainliest! Worth 100 points!
ANSWER 157.46 units²
For problems 1 - 2, determine the area of each figure.
The area of the circle is approximately 78.5 square meters.
To determine the area of a figure, we need to know what type of figure it is and what its dimensions are. The formulas for finding the areas of different types of figures are as follows:
Rectangles: Area = length x widthSquares: Area = side x sideTriangles: Area = 1/2(base x height)
Circles: Area = πr² (where π is pi and r is the radius)Problem 1:Let's say we have a rectangle with a length of 6 cm and a width of 4 cm.
To find its area, we use the formula Area = length x width. Substituting in our values,
we get:Area = 6 cm x 4 cm = 24 cm²Therefore, the area of the rectangle is 24 square centimeters.Problem 2:Next, let's look at a circle with a radius of 5 meters.
To find its area, we use the formula Area = πr². Substituting in our values, we get:Area = π(5 m)² = π(25 m²) ≈ 78.5 m²
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lve for m.
-3 + m
9 = 10
A.
-30
B.
63
C.
87
D.
93
The value of m that satisfies the equation -3 + m = 9 is m = 12.
To solve the equation -3 + m = 9, we can isolate the variable m by moving the constant term -3 to the other side of the equation.
-3 + m = 9
To move -3 to the other side, we can add 3 to both sides of the equation:
-3 + 3 + m = 9 + 3
Simplifying, we have:
m = 12
Therefore, the value of m that satisfies the equation -3 + m = 9 is m = 12.
None of the provided answer options (A, B, C, D) match the correct solution.
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On a coordinate plane, a dashed straight line has a positive slope and goes through (negative 3, 1) and (0, 3). Everything to the left of the line is shaded.
Which linear inequality is represented by the graph?
y < Two-thirdsx + 3
y > Three-halvesx + 3
y > Two-thirdsx + 3
y < Three-halvesx + 3
Since the region is below the line, the correct inequality is: y < (2/3)x + 3. Option A
To determine the linear inequality represented by the graph described, we can start by finding the slope of the line using the given points (negative 3, 1) and (0, 3).
The slope (m) can be calculated using the formula:
m = (y2 - y1) / (x2 - x1)
Using the coordinates of the two points, we have:
m = (3 - 1) / (0 - (-3))
m = 2 / 3
So, the slope of the line is 2/3.
Next, we can write the equation of the line using the slope-intercept form, which is y = mx + b, where m is the slope and b is the y-intercept.
Substituting the known values, we have:
y = (2/3)x + b
To find the value of b, we can substitute one of the given points into the equation. Let's use the point (0, 3):
3 = (2/3)(0) + b
3 = b
Therefore, the equation of the line is y = (2/3)x + 3.
Now, we need to determine whether the shaded region is above or below the line. Since the shaded region is to the left of the line, we need to find the inequality that represents the region below the line.
Option A
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Roni wants to write an equation to represent a proportional relationship that has a constant of proportionality equal to StartFraction 7 over 25 EndFraction. She writes the equation y = x + StartFraction 7 over 25 EndFraction. What error is Roni making?
She should have written y = negative x + StartFraction 7 over 25 EndFraction so that x and y have a constant sum.
She should have written x y = StartFraction 7 over 25 EndFraction so that x and y have a constant product.
She should have written y = StartFraction 7 over 25 EndFraction x so that x and y have a constant quotient.
She should have written y = StartFraction 7 over 25 EndFraction so that y has a constant value.
Mark this and return
The correct thing that should be written is "She should have written y = StartFraction 7 over 25 EndFraction x so that x and y have a constant quotient."
We express direct proportionality as :
y = kxWhere k = constant ; x and y are variables
Since the value of k given , which is a proportionality constant = 7/25
Then , we have the equation thus ;
y = 7/25xTo isolate x, divide both x and y by 7/25 and thus have a constant quotient.
Hence, the correct thing to do is option C.
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