p
Line m has a y-intercept of cand a slope of 9, where p>0, q> 0, and p + q.
What is the slope of a line that is perpendicular to line m?
-q/p
P/q
q/p
-p/q
Answers
So slope of the line m is 9
We know perpendicular lines have slopes negative reciprocal to each other and their product of slopes is -1
9m2=-1m2=-1/9If slope of m is p/q then slope of perpendicular line is -q/p and vice versa
Answer:
\(-\dfrac{q}{p}\)
Step-by-step explanation:
Slope-intercept form of a Linear Equation:
\(y = mx + b\)
where:
m is the slopeb is the y-interceptIf line m has a y-intercept of c and a slope of p/q, then:
\(\textsf{Equation of line m}: \quad y = \dfrac{p}{q}x + c\)
If two lines are perpendicular to each other, the product of their slopes will be -1.
Let a = slope of the line perpendicular to line m.
\(\implies a \times \dfrac{p}{q}=-1\)
\(\implies a=-\dfrac{q}{p}\)
Therefore, the slope of the a line that is perpendicular to line m is:
\(-\dfrac{q}{p}\)
Related Questions
Write 1 1/6 as an improper fraction
Answers
Step-by-step explanation:
Improper fractions have a numerator that is larger than the denominator
1 = 6/6
so 1 1/6 = 7/6
rational numbers
-2 + -(\(\frac{1}{2}\)+\(\frac{1}{3}\)+\(\frac{1}{5}\))
a)-\(\frac{1}{30}\)
b)\(\frac{-29}{30}\)
c)\(\frac{29}{30}\)
d)1\(\frac{1}{30}\)
Answer in fraction
Answers
The fraction is simplified to - 29/30 . Option B
What is a fraction?
A fraction is simply known as the part of a whole.
Types of fractions;
Mixed fractionsSimple fractionsProper fractionsImproper fractionsGiven the fraction;
-2 + ( 1/ 2 + 1/ 3 + 1/ 5 )
Find the lowest common multiple
- 2 + ( 15 + 10 + 6 /30 )
-2 + ( 31/30)
expand the bracket by finding the lowest common multiple, we have;
-60 + 31 / 30
Add the numerators
- 29/30
Thus, the fraction is simplified to - 29/30 . Option B
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If x = 4 cm, what is the surface area of the geometric shape formed by this net?
A.
70 cm2
B.
30 cm2
C.
25 cm2
D.
96 cm2
Answers
Find that the radius of curvature of ^2y=x^3-a^3
at the point where the
curves cut the X-axis.
Answers
The radius of curvature of the curve \(a^{2y\)=x³-a³ at the point where the curve intersects the x-axis is 27\(a^{\frac{3}{2}\).
To find the radius of curvature of the curve \(a^{2y\)=x³-a³ at the point where the curve intersects the x-axis, we need to first find the equation of the curve and then determine the value of y and its derivative at that point.
When the curve intersects the x-axis, y=0. Therefore, we have:
a⁰ = x³ - a³
x³ = a³
x = a
Next, we need to find the derivative of y with respect to x:
dy/dx = -2x/(3a²√(x³-a³))
At the point where x=a and y=0, we have:
dy/dx = -2a/(3a²√(a³-a³)) = 0
Therefore, the radius of curvature is given by:
R = (1/|d²y/dx²|) = (1/|d/dx(dy/dx)|)
To find d/dx(dy/dx), we need to differentiate the expression for dy/dx with respect to x:
d/dx(dy/dx) = -2/(3a²(x³-a³\()^{\frac{3}{2}\)) + 4x²/(9a⁴(x³-a³\()^{\frac{1}{2}\))
At x=a, we have:
d/dx(dy/dx) = -2/(3a²(a³-a³\()^{\frac{3}{2}\)) + 4a²/(9a⁴(a³-a³\()^{\frac{1}{2}\)) = -2/27a³
Therefore, the radius of curvature is:
R = (1/|-2/27a³|) = 27\(a^{\frac{3}{2}\)
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A two-digit number is 3 more than 4 times the sum of its digits. If 18 is added to the number, the digits are reversed. Find the number.
Answers
Answer:
Let the required number be ab.
Sum of digits = a + b ........ ( 1 )
10 a + b = 4 ( a + b )
10 a + b + 18 = 10 b + a
=> 9 a + 18 = 9 b
=> a + 2 = b
10 a + a + 2 = 4 ( a + a + 2 )
=> 11 a + 2 = 8 a + 8
=> 3 a = 6
=> a = 3
=> a + 2 = 5
=>ab = 35......... [ A ]
So the number becomes 35.
ANSWER :
The original number is 35.
hope it helps you
• (two-digit number) = 3 + 4(sum of its digits)
• (two-digit number) + 18 = Digit gets reverse
To Find :• The number.
Concept :-We will first assume the number on one's place be \(x\) and ten's place be \(y\) [why? because the given conditions are about the digits of number]
-Two-digit number then formed will be 10y + x and its reverse will be 10x + y[why? well let's take an example like a number 42. This number can be written in expanded form as 10×4+2×1 here 4 is number at ten's place (y) and 2 at one's place(x) It's reverse will be 24 it can be written in expanded form as 10×2+4×1 here 2 is number at ten's place (y) and 4 at one's place(x)]
-Then we will use given conditions to form the equation and will solve the equations to get the answer.
So now let's get started with our solution! :D
Solution :Let the one's and ten's digit of the number be \(x\) and \(y\) respectively.
According to first condition,
=> (10y + x) = 3 + 4(x + y)
=> 10y + x = 3 + 4x + 4y
=> 10y - 4y = 3 + 4x - x
=> 6y = 3 + 3x
\( \implies \sf \frac{6y}{3} = \frac{3}{3} + \frac{3x}{3} \)
=> 2y - 1 = x ___(equation 1)
According to second condition,
=> (10y + x) + 18 = 10x + y
=> 10y - y + 18 = 10x - x
=> 9y + 18 = 9x
\( \implies \sf \frac{9y}{9} + \frac{18}{9} = \frac{9x}{9} \)
=> y + 2 = x ___(equation 2)
Solving equation 1 and 2
y + 2 = x (equation 2)
y + 2 = 2y - 1 [From equation 1]
3 = 2y - y
3 = y (ten's place)
Now put value of y = 3 in equation 2
y + 2 = x (equation 2)
3 + 2 = x
5 = x (one's place)
So, the number formed is 35.
find f
f '(t) =20/1+t^2 f(1) = 0
Answers
If f '(t) =20/1 + t2 f(1) = 0, f is f(x) = 20tan⁻¹(t) - 5π.
Integrals are the values of the function seen by the process of integration.
The procedure of getting f(x) from F (x) is called integration.
Given f '(t) = 20/ 1 + t2 and f(1) = 0
We know that by definition of the integral of tan⁻¹(x) = 1/1 + t2
f '(t) = 20 / 1 + t2 = 20(1/ 1 + t2)
Integrate on both sides, we get
f(t) = 20tan⁻¹(t) + c
f(1) = 0; f(1) = 20tan⁻¹(1) + c = 0
c = -20(π/4) = -5π.
Therefore, f(x) = 20tan⁻¹(t) -5π.
If f '(t) =20/1 + t2 f(1) = 0, f is f(x) = 20tan⁻¹(t) - 5π.
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Find the value of f(3) for the function. f(3)=-5(x+5)
Answers
Answer:
Step-by-step explanation:
f(3)=-5(x+5)
=5(3) +5
=15+5
f(3) =20
what is the value of h ? give answer in 1 decimal.
trigonometry.
Answers
The value of h is 13.3 cm
Let the triangle be ABC where
AB = 18 cm
AC = h cm
∠ABC = 48°
Since, ∠ACB = 90°, therefore the given triangle is a right angle triangle.
We know that
Sinθ = Perpendicular / Hypotenuse
Put θ = 48, we get
Sin 48 = \(\frac{h}{18}\)
The value of Sin 48 is 0.74
0.74 × 18 = h
h = 13.3 cm
Therefore the value of h is 13.3 cm
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A store is having a sale on chocolate chips and walnuts. For 5 pounds of chocolate chips and 3 pounds of walnuts, the total cost is $25 . For 7 pounds of chocolate chips and 9 pounds of walnuts, the total cost is $53 . Find the cost for each pound of chocolate chips and each pound of walnuts.
Answers
Answer:
one pound of chocolate chips = $2.75
one pound of walnuts = $3.75
Step-by-step explanation:
we can solve this by first making an equation
let's write the number of chocolate chips in c
and the number of walnuts in w
5c + 3w = 25
7c + 9w = 53
let's first solve for c by multiplying the top equation by 3 and subtracting the bottom equation from it
(15c + 9w = 75) - (7c + 9w = 53)
8c = 22
c = $2.75
Let's now start to solve for w by inputting c into one of the equations.
(2.75)7 + 9w = 53
19.25 + 9w = 53
9w = 53 - 19.25
9w = 33.75
w = $3.75
a pound of chocolate chips = 2.75
a pound of walnuts = 3.75
give me brainliest, please!
Hope this helps :)
Answer:
each pound of chocolate chips costs $2.75
each pound of walnuts costs $3.75
Step-by-step explanation:
let c be the cost of a pound of chocolate chips
and w be the cost of a pound of chocolate chips
For 5 pounds of chocolate chips and 3 pounds of walnuts,
the total cost is $25 means 5c + 3w = 25
For 7 pounds of chocolate chips and 9 pounds of walnuts,
the total cost is $53 means 7c + 9w = 53
Now we have to solve the system:
\(\begin{cases}5c+3w=25&\\ 7c+9w=53&\end{cases}\)
\(\Longleftrightarrow \begin{cases}15c+9w=75&\\ 7c+9w=53&\end{cases}\)
\(\Longleftrightarrow \begin{cases}15c+9w=75&\\ 8c=22&\end{cases}\)
\(\Longleftrightarrow \begin{cases}15c+9w=75&\\ c=\frac{11}{4} &\end{cases}\)
\(\Longleftrightarrow \begin{cases}9w=75-15 \times \frac{11}{4} &\\ c=\frac{11}{4} &\end{cases}\)
\(\Longleftrightarrow \begin{cases}9w=\frac{135}{4} &\\ c=\frac{11}{4} &\end{cases}\)
\(\Longleftrightarrow \begin{cases}w= \frac{15}{4} &\\ c=\frac{11}{4} &\end{cases}\)
A survey of 500 randomly selected adults found that 57% say that they would take a ride in a fully self-driving car. The 95% confidence interval for the true proportion of all adults who would take a ride in a full self-driving car is found to be (0.5266, 0.6134). Can we conclude that the majority of all adults would take a ride in a fully self-driving car?
Yes; Since the confidence interval limits are both greater than 50%, we can reasonably conclude that more than half of all adults would take a ride in a fully self-driving car.
No; The data does not include all adults, so we cannot make a conclusion about the population.
No; The confidence interval limits are not large enough to determine that a majority rely only on cellular phones. The proportion would need to be much greater than 50%, and the one above is only slightly larger.
Yes; Since the proportion of adults who said yes is 57%, and this is higher than 50%, we can conclude that a majority would take a ride in a fully self-driving car.
Answers
Answer:
Yes; Since the confidence interval limits are both greater than 50%, we can reasonably conclude that more than half of all adults would take a ride in a fully self-driving car.
Step-by-step explanation:
From the question we are told that
The sample size is n = 500
The sample proportion is \(\r p = 0.57\)
The 95% confidence interval is (0.5266, 0.6134)
Looking at the 95% confidence level interval we see that the sample proportion is within the interval and given that the confidence interval limits are both greater than 50%, we can reasonably conclude that more than half of all adults would take a ride in a fully self-driving car.
50 POINTS!!! PLS HELP FAST AND CORRECTLY WITH EXPLANATION!!
Answers
Answer:
a) 1/9
b) 1/18
c) 0
Step-by-step explanation:
a) if we make a chart, like the one I attached, (the numbers aren't correct, just look at the template), we find the answers by subtracting each number.
What is the range of the function y=e4x7
A- Y <0
B- Y > O
C- y <4
D- Y> 4
Answers
We have been given the function We know that the range is set of y values for which the function is defined. Therefore, we will find the value for x and then observe the restriction is y's values.
Now, we know that logarithm function is not defined for negative values. Hence, the value for y is always greater than zero.
Therefore, the range of the function is given by y>0B is the correct option.
Find the length of side of square ABCD when diagonal is √ cm long. Also find the perimeter and area of the square
Answers
The length of each side of the square is 16 cm, the perimeter is 64 cm, and the area is 256 cm^2.
Let's solve the problem step by step. We have a square ABCD, and we need to find the length of its sides when the diagonal is 16√2 cm long.
In a square, the diagonal forms a right triangle with the sides. The sides of a square are equal in length, so let's assume the length of one side of the square is 'x' cm.
Using the Pythagorean theorem, we can find the relationship between the side length and the diagonal:
x^2 + x^2 = (16√2)^2
2x^2 = 512
Dividing both sides by 2, we have:
x^2 = 256
Taking the square root of both sides:
x = √256
x = 16 cm
So, the length of each side of the square is 16 cm.
To find the perimeter of the square, we simply multiply the length of one side by 4 since all sides are equal:
Perimeter = 4 * 16 cm = 64 cm
To find the area of the square, we square the length of one side:
Area = (16 cm)^2 = 256 cm^2
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Note the complete question is:
Find the length of side of square ABCD when diagonal is 16√2 cm long. Also find the perimeter and area of the square?
which expression is equivalent to the given expression -2x^2+8x-9+4x+7x^2+2
Answers
Answer:
-2x^2+8x-9+4x+7x^2+2 = 5x²+12x-7
Step-by-step explanation:
solve this sum plsss urgent
Answers
1. 1 and -1 are two such rational numbers whose multiplicative inverse is same as they are.
2. absolute value is resembled using the formula : |x|
Here,
\(\hookrightarrow \sf |\dfrac{-3}{11} |\)
\(\hookrightarrow \sf \dfrac{3}{11}\)
final answer: 3/11
3.
\(\hookrightarrow \sf \dfrac{1}{2} \div \dfrac{3}{5}\)
\(\hookrightarrow \sf \dfrac{1}{2} * \dfrac{5}{3}\)
\(\hookrightarrow \sf \dfrac{5}{6}\)
4.
Associative property can only be used with addition and multiplication
What's the LCM of 16,24,40
Answers
Step-by-step explanation:
explanation is in the attachment
hope it is helpful to you
what are the similarities and differences in linear and exponential in intercepts?
what are the similarities and differences in linear and exponential in domain and range?
what are the similarities and differences in linear and exponential in asymptotes?
what are the similarities and differences in linear and exponential in misc.?
Answers
Answer:
What is a linear function? A linear function is a function whose graph is a straight line. The rate of change of a linear function is constant. The function shown in the graph below, y = x + 2, is an example of a linear function.
Graph of linear function
Graph of linear function
A linear function has a constant rate of change. The rate of change is the slope of the linear function. In the linear function shown above, the rate of change is 1. For every increase of one in the independent variable, x, there is a corresponding increase of one in the dependent variable, y. This gives a slope of 1/1 = 1.
A linear function is typically given in the form y = mx + b, where m is equal to the slope, or constant rate of change.
Examples of linear functions include:
If a person drives at a constant speed, the relationship between the time spent driving (independent variable) and the distance traveled (dependent variable) will remain constant.
Assuming no change in price, the relationship between the number of pounds of bananas a person buys (independent variable) and the total cost of the bananas (dependent variable) will remain constant.
If a person earns an hourly wage at their job, the relationship between the time spent working (independent variable) and the amount earned (dependent variable) will remain constant.
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Exponential Functions
What is an exponential function? An exponential function is a function that involves exponents and whose graph is a smooth curve. The rate of change in an exponential function is not constant. The functions shown in the graph below, y = 0.5x and y = 2x, are examples of exponential functions.
Graphs of exponential functions
Graphs of exponential functions
An exponential function does not have a constant rate of change. The rate of change in an exponential function is the value of the independent variable, x. As the value of x increases or decreases, the rate of change increases or decreases as well. Rather than a constant change, as in the linear function, there is a percent change.
An exponential function is typically given in the form y = (1 + r)x, where r represents the percent change.
Examples of exponential functions include:
Step-by-step explanation:
46.231 divided by 1000
Answers
Answer:
0.046231
just use a calculator my dude
Answer:
0.046231
Step-by-step explanation:
Not really much of an explanation but
46.231/1000=0.046231
PLS PLS PLS HELP!!! I'LL MARK BRAINLIEST!!!
Answers
Answer:
Its B
Step-by-step explanation:
Part 1) A school is selling tickets to a play. Tickets cost $12 at the door and $8.50 if purchased in advance. The school has a goal of selling at least $1050 worth of tickets to Saturday's show. Write an inequality modeling the amount of tickets sold at the door (d) and purchased in advance (a) that they must sell.
Part 2) If the school sold 36 tickets in advance, what is the minimum number of tickets that it must sell in order to make $1050?
Answers
Answer:
See belowStep-by-step explanation:
Given:
Tickets cost $12 at the door, number of tickets dTickets cost $8.50 if purchased in advance, number of tickets aMinimum target from tickets sold $1050Part 1Required inequality to meet the goal:
12d + 8.5a ≥ 1050Part 2If a = 36 then minimum value of d:
12d + 36*8.5 ≥ 105012d + 306 ≥ 105012d ≥ 1050 - 30612d ≥ 744d ≥ 744/12d ≥ 62Minimum 62 tickets must sell
A researcher wanted to test the claim that, "Seat belts are effective in reducing fatalities." A simple random sample of front-seat occupants involved in car crashes is obtained. Among 2823 occupants not wearing seat belts, 31 were killed. Among 7765 occupants wearing seat belts, 16 were killed. If a significance level of 5% is used, which of the following statements gives the correct conclusion?
a. Since p >α we conclude that this data shows that seat belts are effective in reducing fatalities.
b. Since p <α, we conclude that this data shows that seat belts are effective in reducing fatalities U
c. Since p >α we conclude that this data shows that seat belts aren't effective in reducing fatalities.
d. Since p<α, we conclude that this data shes that seat belts aren't effective in reducing fatalities.
Answers
Answer:
Step-by-step explanation:
This is a test of 2 population proportions. Let 1 and 2 be the subscript for the occupants not wearing seat belts and occupants wearing seat belts. The population proportion of occupants not wearing seat belts and occupants wearing seat belts would be p1 and p2 respectively.
P1 - P2 = difference in the proportion of occupants not wearing seat belts and occupants wearing seat belts.
The null hypothesis is
H0 : p1 = p2
p1 - p2 = 0
The alternative hypothesis is
Ha : p1 > p2
p1 - p2 > 0
it is a right tailed test
Sample proportion = x/n
Where
x represents number of success
n represents number of samples.
For occupants not wearing seat belts,
x1 = 31
n1 = 2823
P1 = 31/2823 = 0.011
For occupants wearing seat belts,
x2 = 16
n2 = 7765
P2 = 16/7765 = 0.0021
The pooled proportion, pc is
pc = (x1 + x2)/(n1 + n2)
pc = (31 + 16)/(2823 + 7765) = 0.0044
1 - pc = 1 - 0.0044 = 0.9956
z = (P1 - P2)/√pc(1 - pc)(1/n1 + 1/n2)
z = (0.011 - 0.0021)/√(0.0044)(0.9956)(1/2823 + 1/7765) = - 0.0089/0.00145462023
z = 6.81
From the normal distribution table,
p < 0.00001
0.00001 < 0.05, we would reject the null hypothesis.
Therefore,
b. Since p <α, we conclude that this data shows that seat belts are effective in reducing fatalities
At the market, Joey buys 3 avocados for $0.40 each and 5 lemons for $0.40 each. The cashier in training rings up 3 × 0.40 and then 5 × 0.40 to get the total. The experienced cashier says to add the 3 plus 5 in his head and then ring up 8 × 0.40.
What property says that these two totals would be the same?
multiplicative identity
associative property of multiplication
distributive property
commutative property of multiplication
Answers
Answer:
Distributive property
Step-by-step explanation:
3*$0.40 + 5*$0.40 = (3+5)*$0.40
Distributive law, in mathematics, the law relating the operations of multiplication and addition, stated symbolically, a(b + c) = ab + acAccording to distributive property multiplying the sum of two or more addends by a number will give the same result as multiplying each addend individually by the number and then adding the products together.answer is distributive property
Step-by-step explanation:
hope this answer helps :)
fill in the blank. Toward the end of a game of Scrabble, you hold the letters D, O, G, and Q. You can choose 3 of these 4 letters and arrange them in order in ______ different ways. (Give your answer as a whole number.)
Answers
Toward the end of a game of Scrabble, you hold the letters D, O, G, and Q. You can choose 3 of these 4 letters and arrange them in order in 24 different ways.
To solve this problem, we need to use the concept of permutations. A permutation is an arrangement of objects in a specific order. In this case, we need to find the number of permutations that can be made from the letters D, O, G, and Q when we choose 3 of these 4 letters.
The formula for finding the number of permutations is:
n! / (n-r)!
where n is the total number of objects and r is the number of objects we choose.
Using this formula, we can calculate the number of permutations as follows:
4! / (4-3)!
= 4! / 1!
= 4 x 3 x 2 x 1 / 1
= 24
Therefore, we can arrange the chosen 3 letters in 24 different ways.
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Write the following in interval notation: {x/ x< 20}
Answers
Do you mean \(\frac{x}{x} < 20\) ? If so, after converting the inequality into interval notation, your solution would be (-∞, ∞).
Hope this helps! If not, feel free to comment below on any further questions you may have regarding this topic/question, and I'll see how I can help. Thanks and good luck!
The table shows the weight of apples at a grocery store complete the table so that there is a proportional relationship between the number of apples and their weight
Answers
Answer:
Step-by-step explanation: At any spot on time (x axis) if you go up to lines , line B is less water – therefore it is getting less water in same amount of time.
At any position aligned with y axis (Water) if you go across to lines, line A will be in less time, therefore it is getting more water in less time or line A is faster and B is filling slower.
Answer:
$0.50 per apple
Step-by-step explanation:
(QUICK DUE IN 50 MINUTES)
What is the slope?
Simplify your answer and write it as a proper fraction, improper fraction, or integer.
Answers
70,80) (10,40)
(80-40)/(70-10) = 40/60
4/6
2/3
Solve for N
2/9n= −6
Answers
Answer:
n=-27
Step-by-step explanation:
Step-By-Step on how to solve it is in the image shown below.
Hope this helps! :)
Differential Equations--Population
Suppose that a population develops according to the logistic equation
dP/dt=0.1P-0.0001P2
where t is measured in weeks.
(a) What is the carrying capacity?
(b) Is the solution increasing or decreasing when P is between 0 and the carrying capacity?
(c) Is the solution increasing or decreasing when P is greater than the carrying capacity?
Thank you for your help. It is much appreciated.
Answers
a) The carrying capacity is 10000.
b)The solution is increasing when P is between 0 and the carrying capacity.
c)The solution is decreasing when P is greater than the carrying capacity.
(a) The carrying capacity is the maximum population that can be sustained in a given environment, and it is defined by the equation
K = P_max = 1/0.0001 = 10000
where K is the carrying capacity and 0.0001 is the coefficient of the quadratic term.
(b) The solution is increasing when P is between 0 and the carrying capacity. This can be seen from the logistic equation:
dP/dt = 0.1P - 0.0001P^2
When P is small, the first term 0.1P dominates, causing P to increase. As P approaches the carrying capacity, the second term -0.0001P^2 becomes more significant and slows down the rate of increase.
(c) The solution is decreasing when P is greater than the carrying capacity. The second term -0.0001P^2 dominates and causes P to decrease, since it is negative for P > K.
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Determine the slope of the line between (2,3) and (4,0)
Answers
SOLUTION
Given the question in the image, the following are the solution steps to answer the question.
STEP 1: Write the given points
\((2,3)\text{ }and\text{ }(4,0)\)STEP 2: Find the slope of the points
\(\begin{gathered} \mathrm{Slope\:between\:two\:points}:\quad \mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1} \\ \left(x_1,\:y_1\right)=\left(2,\:3\right),\:\left(x_2,\:y_2\right)=\left(4,\:0\right) \\ m=\frac{0-3}{4-2} \\ m=-\frac{3}{2} \end{gathered}\)Hence, the slope of the line is -3/2
the length and breadth of a room are in the ratio of 3 :2 find the length of breadth if 8.6 meters
Answers
Answer:
7.33
Step-by-step explanation:
l/b=3/2
8.6/b=3/2
3b=8.6*2
b=17.2/3
b=7.33