Straight Line Graphs Question. I tried to solve the section (a) part of the question correctly I followed the gradient method plugging in the values and got [tex]y = \frac{1}{6} x + 1.6 (recurring). However the answer is y = \frac{1}{2} x + 3.[/tex]. Where am I going wrong? Can someone explain step by step how to solve this please.
Answers
The equation of the straight line joining A to B is y = (1/2)x + 3, the equation of the straight line joining B to C is y = (1/2)x + 3, and A, B, and C are collinear.
What are collinear points?
Collinear points are three or more points that lie on the same straight line. In other words, if three points A, B, and C are collinear, then there exists a straight line that passes through all three points. To determine if three or more points are collinear, we can find the slope of the line that passes through any two of the points. If the slope is the same for all possible pairs of points, then the points are collinear. Otherwise, they are not collinear.
a) To find the equation of the straight line joining A to B, we can use the slope-intercept form of the equation of a line:
y = mx + b
where m is the slope of the line, and b is the y-intercept.
The slope of the line passing through A and B is:
m = (y₂ - y₁) / (x₂ - x₁)
where (x₁, y₁) = (-8, -1) and (x₂, y₂) = (-4, 1).
m = (1 - (-1)) / (-4 - (-8)) = 2/4 = 1/2
To find the y-intercept, we can use the point-slope form of the equation of a line:
y - y₁ = m(x - x₁)
where (x₁, y₁) = (-8, -1) and m = 1/2.
y - (-1) = (1/2)(x - (-8))
y + 1 = (1/2)(x + 8)
y = (1/2)x + 3
Therefore, the equation of the straight line joining A to B is y = (1/2)x + 3.
b) To find the equation of the straight line joining B to C, we can use the same method:
m = (y₂ - y₁) / (x₂ - x₁)
where (x₁, y₁) = (-4, 1) and (x₂, y₂) = (12, 9).
m = (9 - 1) / (12 - (-4)) = 8/16 = 1/2
Using point-slope form with the point (x₁, y₁) = (-4, 1) and slope m = 1/2:
y - 1 = (1/2)(x - (-4))
y - 1 = (1/2)x + 2
y = (1/2)x + 3
Therefore, the equation of the straight line joining B to C is y = (1/2)x + 3.
c) From the equations of the lines joining A to B and B to C, we can see that both lines have the same slope of 1/2. This implies that the three points A, B, and C are collinear, i.e., they lie on the same straight line.
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Related Questions
Select the expression that results in a rational number.
Answers
Answer:
The answer is A
Step-by-step explanation:
thats all
math proportion calculation
Answers
In respοnse tο the given questiοn, we can state that This signifies that 3 equatiοn οut οf every 10 apples sοld were red, οr that the red apple percentage was 3/10.
What is equatiοn?A algebraic equatiοn is a technique that links twο statements and utilises the equals sign (=) tο express equivalence. In algebra, an equatiοn refers tο the mathematical statement that prοves the equality οf twο fοrmulas. Fοr example, in the cοmputatiοn 3x + 5 = 14, a nοrmalise inserts a gap between the numbers 3x + 5 and 14. A mathematical fοrmula may be used tο explain the link between the twο phrases written οn either side οf a letter. The emblem and the prοgramme are usually the same. Fοr example, 2x - 4 equals 2.
Tο cοmpute prοpοrtiοns in arithmetic, yοu must first create a ratiο οf twο related numbers. Fοr example, if yοu want tο knοw what percentage οf all apples sοld were red, yοu wοuld put up a ratiο οf the number οf red apples sοld tο the οverall number οf apples sοld.
Assume that 200 apples were sοld in tοtal, with 60 οf them being red. Tο get the prοpοrtiοn οf red apples, use the fοllοwing fοrmula:
60 / 200 = red apples / tοtal apples
3/10 = red apples / tοtal apples
This signifies that 3 οut οf every 10 apples sοld were red, οr that the red apple percentage was 3/10.
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Complete question:
Assume that 200 apples were sοld in tοtal, with 60 οf them being red.
What is proportion of red apples?
(PLEASE HURRY!) A table giving various values of linear functions f(x) and g(x) is shown below. What is the solution to the system?
Answers
Answer:
A. (2, 1)
Step-by-step explanation:
You want the solution to the system of equations represented by the given table and graph.
SolutionWhen we are given two functions and asked for "the solution to the system", we generally mean the value of x that satisfies f(x) = g(x). That will be represented on a graph as the point (x, f(x)), or (x, g(x)), where the function graphs intersect.
TableWhen you're looking for the solution in a table, you look for the row of the table where the value of f(x) is the same as the value of g(x). For the given table, we see that f(x) = g(x) = 1 on the last row of the table, where x=2. This means the solution is ...
(x, f(x)) = (2, 1)
A(-4,-6) and B (3,2) find midpoint of AB
Answers
[tex]~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ A(\stackrel{x_1}{-4}~,~\stackrel{y_1}{-6})\qquad B(\stackrel{x_2}{3}~,~\stackrel{y_2}{2}) \qquad \left(\cfrac{ x_2 + x_1}{2}~~~ ,~~~ \cfrac{ y_2 + y_1}{2} \right) \\\\\\ \left(\cfrac{ 3 -4}{2}~~~ ,~~~ \cfrac{ 2 -6}{2} \right) \implies \left(\cfrac{ -1 }{2}~~~ ,~~~ \cfrac{ -4 }{2} \right)\implies \left(-\frac{1}{2}~~,~~-2 \right)[/tex]
Select which points are solutions to this inequality.
y ≥ 5x - 7
(-5, -3)
(-4, 2)
(1, -2)
(-1, 0)
(3, 0)
(4, 1)
Answers
(-5,-3)
(-4,2)
(-1,0)
whats the slope of y=-4
Answers
Answer: The slope of y = -4 is 0.
Step-by-step explanation:
write an equation of vertical line through the point (9,-10)
Answers
Answer:
x = 9
Step-by-step explanation:
An equation for a vertical line is in the form:
x = anumber
The given information is the point (9,-10) this is in the form (x,y). So this gives us the information that x is 9. That is the equation!
x = 9
The equation of the vertical line through (9,-10) is
x = 9
CAN U HELP ME ASAP ????????
Answers
The solution to the system of equations is given as follows:
(1,9).
How to obtain the solution to the system of equations?We want to obtain the graphic solution for the system of equations, hence we obtain the point of intersection of the two equations.
The point of intersection on the graph means that the two functions have the same numeric value, hence on a table we must identify the point which the functions have the same numeric value.
From the table, function f(x) and g(x) both contain the point (1,9), hence this is the point of intersection of the two lines, and the solution is given as follows:
(1,9).
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Please answer the question in the picture, I will mark brainliest. Show all work pls!!!
Circle A has been transformed to circle B. What is the translation rule for these circles?
Answer choices are:
(x+4),(y+3)
(x-1),(y+4)
(x-2),(y+3)
(x+2),(y+3)
Answers
The translation rule for these circles is (x+2),(y+3).
What does translation mean?This translation involves shifting the points of the original figure without rotating or reflecting it.
In the given transformation, circle A has been transformed to circle B.
Thus, the transformation rule is the x and y-coordinates of the points of the original figure added with certain values to obtain the coordinates of the points in the transformed figure.
In the given case, the x-coordinates of all the points of the circle A have been increased by 2 units, while the y-coordinates of all the points of the circle A have been increased by 3 units.
Thus, the translation rule for these circles is (x+2),(y+3).
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What is the value of the next term in the geometric sequence graphed below?
O A. 6
B. 3
OC. 0.1875
OD. 0.375
Answers
Based on the readings from the graph, the sequence has a next term of the 16
How to determine the next term of the sequenceThe missing information is attached
The readings on the graph can be represented as
1, 2, 4, 8, .....
We can see that multiplying 2 to the previous term to gives the next term
Using the above parameters, we have the following equation
Next term = 2 * Current term
The current term in the graph is 8
So, we have
Next term = 2 * 8
Evaluate
Next term = 16
Hence, the next term is 16
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A triangle has a base of 8 cm and a height of 12 cm.
What is the area of the triangle?
________________________________
(reporting wrong/spam answers)
(giving brainliest to the correct answer)
(No picture of the question was given)
________________________________
Answers
Answer:
A = 48 cm²
Step-by-step explanation:
A = (1/2)bh
A = (1/2)(8 cm)(12 cm)
A = 48 cm²
Answer:
48cm^2
Step-by-step explanation:
8×12=96
96÷2=48cm^2
The scheme that you thought of is to start saving 10% of your allowance in the first week of every month, then add 10% more every week for the 3 weeks. And the cycle goes on for 12 months of a year. If you're weekly allowance is 500, how much will you be able to earn after a year? Show your computation here
Answers
Using percentage concept, we would have saved 2784.6 dollars after a year
How much is saved at the end of the yearTo calculate how much you will have saved after a year, we can break down the savings for each week of each month, and then add up the total. Here's how it works:
We can use percentage to calculate how much is saved each week
In the first week of each month, you save 10% of your weekly allowance, which is 10 percent of 500 = 50 dollars.
In the second week of each month, you save 10% more than the previous week, which is 10% of (500 + 50) = 55 dollars.
In the third week of each month, you save 10% more than the previous week, which is 10% of (500 + 50 + 55) = 60.5 dollars.
In the fourth week of each month, you save 10% more than the previous week, which is 10% of (500 + 50 + 55 + 60.5) = 66.55 dollars.
So in total, you save 50 + 55 + 60.5 + 66.55 = 232.05 dollars per month.
Over the course of a year, you will have saved 232.05 dollars per month * 12 months = 2784.6 dollars.
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Show that multiplication this following:
Answers
Since AB and BA are not equal for n > 1, we have shown that multiplication in M_n(R) is not commutative for n > 1.
How to solveTo show that multiplication in M_n(R) is not commutative when n > 1, we need to find two matrices A and B in M_n(R) such that AB is not equal to BA.
Let's consider two matrices A and B in M_n(R) such that:
A = [a_ij], where a_ij = 1 if i=j, and a_ij = 0 otherwise.B = [b_ij], where b_ij = 1 if i+j = n+1, and b_ij = 0 otherwise.That is, A is the n x n identity matrix, and B is the matrix with 1's on the anti-diagonal and 0's elsewhere.
Now let's compute AB and BA:
AB = [c_ij], where c_ij = Σ_k=1^n a_ik * b_kj
If i+j = n+1, then b_kj = 1 only if k = i, and a_ik = 1 only if k = j.
Therefore,
c_ij = a_i1 * b_1j + a_i2 * b_2j + ... + a_in * b_nj = a_ii * b_jj = 1 * 1 = 1
If i+j ≠ n+1, then b_kj = 0 for all k, and hence c_ij = 0.
Therefore, AB is the matrix with 1's on the anti-diagonal and 0's elsewhere, just like B.
Now let's compute BA:
BA = [d_ij], where d_ij = Σ_k=1^n b_ik * a_kj
If i=j, then a_kj = 1 only if k = i, and b_ik = 1 only if k = i. Therefore,
d_ij = b_i1 * a_1j + b_i2 * a_2j + ... + b_in * a_nj = b_ii * a_jj = 1 * 1 = 1
If i ≠ j, then a_kj = 0 for all k, and hence d_ij = 0.
Therefore, BA is the matrix with 1's on the diagonal and 0's elsewhere, just like A.
Since AB and BA are not equal for n > 1, we have shown that multiplication in M_n(R) is not commutative for n > 1.
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Likert scale A survey attempted to evaluate student interest about a range of classroom topics. Students were asked to rank their interest in various potential topics according to this scale: 10 if they felt a topic was very interesting if they felt a tapic was above average interest If they felt a topic was below average interest if they felt a topic was not worth studying in class 6 4 1 Please note that only four responses were permitted: 10, 6, 4, and 1. Is this an acceptable survey design? Explain your answer. Answer
Answers
The survey design that we have here is not an acceptable standard survey design for research.
Why is this not an acceptable survey design?This survey design has limitations and may not be the most optimal way to measure student interest in classroom topics. Here are some of the reasons why:
Limited response options: By only allowing four responses, the survey restricts the range of possible responses that students can give. For instance, some students may feel that a topic is somewhat interesting, but not interesting enough to warrant a score of 6. Similarly, some students may feel that a topic is not worth studying, but not to the extreme level of giving it a score of 1. This design does not account for such nuances in student opinions.
Lack of neutral option: The survey does not include a neutral option such as "no opinion" or "undecided". This means that students who do not have a strong opinion about a topic may be forced to pick a score that does not accurately reflect their level of interest.
Lack of context: The survey does not provide any context or information about the topics being evaluated. Without such information, students may base their scores on assumptions or incomplete knowledge about the topics, which may not accurately reflect their actual level of interest.
Lack of reliability and validity: The survey's reliability and validity may be questionable. The limited response options and lack of context may lead to responses that are not reliable or valid measures of student interest.
In conclusion, while this survey design may be simple and easy to administer, it has limitations that make it less than ideal for measuring student interest in classroom topics. A more comprehensive survey design that includes a wider range of response options and provides contextual information about the topics may provide more reliable and valid results.
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Please help with this
Answers
a. The probability that a real number between 3 and 5 is picked is
b. The probability that a real number between 3 and 7 is picked is
What is probability?A probability is a number that reflects the chance or likelihood that a particular event will occur. Probabilities can be expressed as proportions that range from 0 to 1, and they can also be expressed as percentages ranging from 0% to 100%.
Probability = sample space / total outcome
The sample space is the area between the real numbers and the total outcome is the total area
Total area = 0.12 + 0.56+ 0.32
= 1
a. The probability a real number between 3 and 5 is picked = 0.56/1
= 0.56
b. The probability a real number between 3 and 7 is picked is( 0.56+0.32)/1
= 0.88
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Plot the point where θ =
Answers
It’s the first from the bottom in the lower right quadrant or 4th quadrant
16 lakh students in India use Khan Academy today. The number of users is expected to grow by 50% every year. How many students in India will be using Khan Academy two years from now?
Answers
Answer: Let's first calculate the number of users after one year:
Number of users after one year = 16 lakh + 50% of 16 lakh
= 16 lakh + 8 lakh
= 24 lakh
Now, we can calculate the number of users after two years by applying the same growth rate:
Number of users after two years = 24 lakh + 50% of 24 lakh
= 24 lakh + 12 lakh
= 36 lakh
Therefore, two years from now, it is expected that 36 lakh (3.6 million) students in India will be using Khan Academy.
Step-by-step explanation:
Answer:
36 Iakh Students
Step-by-step explanation:
Which is the bette buy 3 pints of
at $3.60 or 6 pints are all at $8.10
Answers
Answer:
It is better to buy 6 pints at $8.10
Step-by-step explanation:
To compare the cost per pint in each option, we can divide the total cost by the total number of pints.
For the first option, buying 3 pints at $3.60, the cost per pint is shown by the following:
3 pints ÷ $3.60 = $0.83 / pint
For the second option, buying 6 pints at $8.10, the cost per pint is shown by the following:
6 pints ÷ $8.10 = $0.74 / pint
Therefore, buying 6 pints at $8.10 is less expensive per pint than buying 3 pints at $3.60. Each pint when buying 3 at a time costs $0.83 whereas each pint when buying 6 at a time costs $0.74.
Find the weight in pounds of a 140-kilagram person round to nearest hundredth
Answers
Answer: 308.65
:) Good luck
[tex]1 \ \text{lb} = 0.45359 \ \text{kg}[/tex]
[tex]140 \ \text{kg} \times (1 \ \text{lb})\div(0.45359 \ \text{kg}) = 308.65 \ \text{lb}[/tex]
[tex]\bold{140 \ kg=308.65 \ lb}[/tex]
A neighborhood group goes to the movies every Saturday night. Last week, they purchased 29 adult tickets and 17 youth tickets for $254. This week they purchased 21 adult tickets and 22 youth tickets for $213. Find the cost of one adult ticket.
Answers
The cost of one adult ticket is $7.
What is the cost of one adult ticket?The first step is to set up a pair of linear equations that represent the information in the question.
29a + 17y = 254 equation 1
21a + 22y = 213 equation 2
Where:
a = cost of one adult tickety = cost of one youth ticketThe elimination method would be used to solve the equations
Multiply equation 1 by 22:
638a + 374y = 5588 equation 3
Multiply equation 2 by 17:
357a + 374y = 3621 equation 4
Subtract equation 4 from equation 3
1967 = 281a
Divide both sides of the equation by 281
1967 / 281 = a
a = 7
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Find the measure of
Answers
The similar triangles have adjacent angles A and R to be supplementary and value of the variable x is equal to 11. The angles m∠A = 106°, m∠R = 74°, and m∠S = 58°
How to evaluate for variable x of the adjacent anglesThe triangles RDS and ADB area similar thus the lines AB and RS are parallel to each other and the adjacent angles of m∠SRA and m∠BAR are supplementary, so their sum is equal to 180°.
m∠SRA and m∠BAR are supplementary so;
(6x + 8)° + (9x + 7)° = 180°
15x + 15 = 180°
15x = 180° - 15 {subtract 15 from both sides}
15x = 165
x = 165/15 {divide through by 15}
x = 11
m∠A = 9(11) + 7 = 106°
m∠R = 6(11) + 8 = 74°
m∠S = 4(11) + 14 = 58°
Therefore, the similar triangles have adjacent angles A and R to be supplementary and value of the variable x is equal to 11. The angles m∠A = 106°, m∠R = 74°, and m∠S = 58°
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Possible question:
Find the measure of the angles with the variable x for the similar triangles ∆RDS and ∆ADB.
An isosceles triangle (two sides are the same length) has a base of 40 inches. The sides are 25 inches. Draw the height of the triangle from the top vertex perpendicular to the base. Find the height of the triangle.
Answers
The height οf the triangle is 15 inches. The diagram is attached belοw.
What is an isοsceles triangle?An isοsceles triangle therefοre has bοth twο equal sides and twο equal angles. The Greek wοrds isο (same) and skelοs are the sοurce οf the name. An equilateral triangle is οne with all three sides equal, and a scalene triangle is οne with nο equal sides.
Given that the length οf the base is 40 inches. The length οf equal sides is 25 inches.
The altitude οf an isοsceles triangle bisects the base.
The length οf BD = DC = 20 inches.
△ABD fοrms a right-angle triangle since AD is perpendicular tο BC.
Tο find the height apply Pythagοrean theοrem.
The widely accepted geοmetric principle knοwn as the Pythagοrean Theοrem states that the square οn the hypοtenuse οf a right triangle equals the sum οf the squares οn its legs.
Cοnsider △ABD:
AB² = BD² + AD²
25² = 20² +AD²
625 = 400 +AD²
AD² = 625 - 400
AD² = 225
Take square rοοt οn bοth sides:
AD = 15
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Please help me Geometric Sequences
Answers
Step-by-step explanation:
The given sequence is a geometric sequence with the first term being 1 and the common ratio being -3.
To find the 7th term, we can use the formula for the nth term of a geometric sequence:
a_n = a_1 * r^(n-1)
where a_1 is the first term, r is the common ratio, and n is the term number we want to find.
Plugging in the values we have, we get:
a_7 = 1 * (-3)^(7-1)
= 1 * (-3)^6
= 1 * 729
= 729
Use the diagram to name two points that are collinear with P, two planes that contain J, and all the points that are in more than one plane.
Answers
Step-by-step explanation:
colinear with P means they are in the same line as P.
that is K and N.
2 planes with J :
JKL (the ceiling) and JOKPN (the wall with J).
all the points that are in more than one plane : all of them, as they are all on an edge.
The coefficient of variation for a poisson distribution with A=5 is
Answers
The coefficient of variation for a Poisson distribution with A=5 is equal to 1/A, which is equal to 0.2.
What is Poisson distribution?Poisson Distribution is a type of probability distribution used for independent events which occur at a known average rate within a given interval of time or space. It is used to model the number of times an event is likely to occur within a specified period of time or space. It is used in fields such as healthcare, quality control, finance, and engineering.
Coefficient of variation (CV) is a measure of relative variability or dispersion. It is a measure of the relative dispersion of a set of data points around its mean. It is calculated by dividing the standard deviation of the data points by the mean.
The coefficient of variation for a Poisson distribution with A=5 is equal to 1/A, which is equal to 0.2. This means that the relative variability of a Poisson distribution with A=5 is 0.2. This is because the standard deviation of a Poisson distribution is equal to the square root of the mean, and in this case, the mean is 5. Therefore, the standard deviation is the square root of 5, or 2.236. When divided by the mean, the coefficient of variation is 0.2.
In general, the coefficient of variation is used to compare the variability of two different datasets. A low coefficient of variation indicates that the data points are relatively close to the mean and that there is not much variability in the data. A high coefficient of variation indicates that the data points are further away from the mean and that there is a greater amount of variability in the data.
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Part 1
The population of a small town can be modeled by Pt, where t is the number of years since 1975. Interpret the slope of the graph of this function as a rate of change.
Answers
The slοpe οf the graph οf Pt represents the rate οf change οf the pοpulatiοn οver time, and its value tells us hοw fast the pοpulatiοn is grοwing οr declining.
What is the slοpe?The slοpe οf a line is a measure οf its steepness. Mathematically, the slοpe is calculated as "rise οver run" (change in y divided by change in x).
The slοpe οf the graph οf Pt is the rate οf change οf the pοpulatiοn with respect tο time.
Specifically, it tells us hοw much the pοpulatiοn is changing fοr every unit change in time.
Since t represents the number οf years since 1975, the slοpe οf Pt can be interpreted as the annual rate οf change in pοpulatiοn. Fοr example, if the slοpe οf Pt is 100, then the pοpulatiοn is increasing by 100 peοple per year.
Therefοre, the slοpe οf the graph οf Pt represents the rate οf change οf the pοpulatiοn οver time, and its value tells us hοw fast the pοpulatiοn is grοwing οr declining.
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Julie and Hammad each make a glass of orange drink. Julie uses 42ml of juice and 210ml of lemonade. Hammad uses 30ml of juice and 170ml of lemonade. Who has made their drink stronger in taste?
Answers
Answer:
Hammad has made his drink stronger in taste than Julie.
Step-by-step explanation:
We need to compare the ratio of juice to lemonade in each drink.
Julie's drink has a ratio of 42ml juice to 210ml lemonade, which simplifies to 1:5.
Hammad's drink has a ratio of 30ml juice to 170ml lemonade, which simplifies to 3:17.
To compare the strength of their drinks, we need to compare the ratios of juice to lemonade. Since a higher ratio of juice to lemonade indicates a stronger taste, we can see that Hammad's drink has a stronger taste, since his ratio of juice to lemonade is higher than Julie's.
Therefore, Hammad has made his drink stronger in taste than Julie.
Solve for x, using a
tangent and a secant line.
?]°
x = [?
X
15°
40°
Remember : a = b
Answers
I think that the answer is 40 degreee
The required measure of section x on the circle is 95°.
What is simplification?Simplification involves applying rules of arithmetic and algebra to remove unnecessary terms, factors, or operations from an expression. The goal is to obtain an expression that is easier to work with, manipulate, or solve. For example, simplifying an algebraic expression might involve combining like terms, factoring, or using the distributive property.
Here,
From the given we have,
a = 40,
c = x
b = 15
Now, put this value in the given formula,
a = c-b / 2
So,
40 = x - 15/2
x -15 = 80
x = 95°
Thus, the required measure of section x on the circle is 95°.
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In a pack of 36 trading cards, 1/4 of them are fire animals, 1/6 of them are water, animals, and the rest of them are grass animals, how many more cards are grass animals than fire animals?
Answers
Answer:
Fire animals = 36 * 1/4 = 9
Water animals = 36 * 1/6 = 6
Grass animals = 36 - (9 + 6) = 21
There are 21 - 9 = 12 more grass animals than fire animals
Would a triangle with a vertical length of 6 and a horizontal length of 10 have the same slope as the blue and red triangles shown in the graph
A: yes, the slopes would be the same
B: No, the slope of the new triangle would be 2 : 4
C: no, the slope of the new triangle would be 2 : 5
D: no, the slope of the new triangle would be 3 : 5
Answers
Therefore , the solution of the given problem of slope comes out to be option D 3:5 is the correct slope.
Describe slope.The slope of a line determines how steep it is. Gradient overflow is a condition that can occur in equations based on gradients. By dividing the total of the run (width difference) and emergence (climbing distinction) among both two points, one can calculate the slope. The fixed path problem is modelled using the equation y = mx + b with the hill variant. where slope is millimeters, a = bc, and the location of the line's y-intercept.
Here,
Given :
Vertical length = 6
and
horizontal length = 10
=> Slope: Y/X=6/10=0.6
=> 6/10 = 3/5(D)
Thus , option D 3:5 is the correct slope.
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Answer:
A
Step-by-step explanation: