Find the gradient of the line Joining the points p(-2,6) and Q(3,-2)
Answers
Answer:
\( - \frac{8}{5} \)
Step-by-step explanation:
\(\boxed{gradient = \frac{y1 - y2}{x1 - x2} }\)
(x₁, y₁) is the 1st coordinate while (x₂, y₂) is the 2nd coordinate.
Gradient of the line
\( = \frac{6 - ( - 2)}{ - 2 - 3} \)
\( = \frac{6 + 2}{ - 5} \)
\( = - \frac{8}{5} \)
Related Questions
Can anyone help me solve this question?
x = e^y
Answers
Step-by-step explanation:
Pick any point on the graph below for a solution:
solve 9x-10÷2=x+9
explain how
Answers
Answer:
x = 4
Step-by-step explanation:
What is the area of rectangle ABCD? (1 point)
Answers
Answer:
c 20 square units
Step-by-step explanation:
count the total shaded boxes, or count how many boxes are shaded on the left and multiply it by the number of shaded boxes on the bottom.
The area of rectangle ABCD whose coordinates are (0,4)(4,4)(4,-1)(0,-1) is 20 square units.
What is area?Area is the extent of surface covered by the specific shape. Area of rectangle is equal to length * breadth.
How to find area?We have been given rectangle ABCD and we have to find the area of rectangle. Firstly we have to find the coordinates of the rectangle which are A(0,-1), B(0,4),C(4,4),D(4,-1). AD and BC are lengths and AB and DC are breadths. Now we have to find the measurement of length and breadth which can be calculated as under:
AD=\(\sqrt{(4-0)^{2} +(-1+1)^{2} }\)
=\(\sqrt{16+0}\)
=\(\sqrt{16}\)
=4 units.
DC=\(\sqrt{(4-4)^{2} +(-1-4)^{2} }\)
=\(\sqrt{-5^{2} +0^{2} }\)
=\(\sqrt{25}\)
=5 units
Because it is a rectangle so opposite sides are equal to each other. In this way AD=BC=4 units, DC=AB=5 units.
Area =length*breadth
=4*5
=20 square units
Hence the area of rectangle having coordinates (0,-1),(4,-1),(4,4)(0,4) is 20 square units.
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The pounds of bananas sold each week at all Metro Seattle Alberstons stores as a function of price, p, in dollars/pound(lb.) is given by.
q(p) = 100e^(1.5(5-p))
1. What is the price elasticity of demand for bananas at $.20/lb. ?
(nearest 0.01)
2. What is the price elasticity of demand for bananas at $1/lb. ?
3. At what price is the maximum revenue per week achieved?
+/- $0.01
4. What is that maximum revenue per week?
5. How many pounds will be sold each week at that optimal price
Answers
140.55 pounds will be sold approximately each week at the optimal price of $0.67/lb.
How will you solve all the parts of this question?To find the price elasticity of demand for bananas at $0.20/lb, we need to use the formula:
According to the given data:
E(p) = -p(q'/q(p))
where q' is the derivative of q(p) with respect to p.
First, we need to find q'(p):
\(q'(p) = -225e^(1.5(5-p))\)
Then, we can plug in the values:
E(0.20) = -0.20(q'(0.20)/q(0.20))
= \(-0.20(-225e^(1.5(5-0.20)) / 100e^(1.5(5-0.20)))\)
= 2.70
Therefore, the price elasticity of demand for bananas at $0.20/lb is 2.70.
To find the price elasticity of demand for bananas at $1/lb, we can use the same formula:
E(p) = -p(q'/q(p))
First, we need to find q'(p):
\(q'(p) = -225e^(1.5(5-p))\)
Then, we can plug in the values:
E(1) = -1(q'(1)/q(1))
= \(-1(-225e^(1.5(5-1)) / 100e^(1.5(5-1)))\)
= 0.68
Therefore, the price elasticity of demand for bananas at $1/lb is 0.68.
To find the price that maximizes revenue, we need to find the value of p that makes revenue, R(p), maximum.
Revenue is given by:
R(p) = pq(p)
= \(p100e^(1.5(5-p))\)
To maximize revenue, we need to find the critical point of R(p) by taking its derivative and setting it equal to zero:
\(R'(p) = 100e^(1.5(5-p)) - 150pe^(1.5(5-p)) = 0\)
Simplifying this expression, we get:
\(2e^(1.5(5-p)) - 3pe^(1.5(5-p)) = 0\)
2 = 3p
p = 2/3
Therefore, the price that maximizes revenue is $0.67/lb.
To find the maximum revenue per week, we can plug this price back into the revenue equation:
\(R(2/3) = (2/3)*100e^(1.5(5-2/3))\)
= $167.56
Therefore, the maximum revenue per week is $167.56.
To find how many pounds will be sold each week at the optimal price of $0.67/lb, we can plug this price back into the demand equation:
\(q(2/3) = 100e^(1.5(5-2/3))\)
= 140.55
Therefore, approximately 140.55 pounds will be sold each week at the optimal price of $0.67/lb.
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The area of Canada is 17 times the area
of France.
The area of Canada is 3,851,809 square
miles.
What is the area of France?
plsss help
Answers
Answer:
A(Canada) / factor = A(France)
3,851,809/17 = A(France)
226,577 sqmi = A(France)
Hope that helps
NOTE: This answer is a bit off from the actual calculation but it is fine because the original value of Canada's area was given about 5,000 sqmi off.
5. Two unbiased dice are rolled. Calculate the probability that the sum of the two dice is:
ws
(a) 4
(b) 7
(c) Less than 7
Answers
(a). Three pairs add to 4 1,3 2,2 and 3,1 so P(4) = 3/36 = 1/12
(b). 6 pairs add to 7 so P(7) = 6/36 = 1/6
(c) 15 pairs add to less than 7 so P(<7) = 15/36 = 5/12
Evaluate the expression 9 + (7 - 4)2 + 3.
06
O3
0 18
O 12
Answers
Answer:
18
Step-by-step explanation:
PEMDAS
Parenthesis
Exponents
Multiply/Divide (from left to right)
Add/Subtract (from left to right)
A 10 kg ball moves at a speed of 15m/s. The ball collides with a wall causing it to rebound in the opposite direction at a speed of 23 m/s.
Calculate the impulse on the ball?
Answers
Answer:
The impulse on an object is equal to the change in momentum of the object. In this case, the ball's initial momentum is 10 kg * 15 m/s = 150 kg m/s. After the collision, the ball's final momentum is -10 kg * 23 m/s = -230 kg m/s.
The change in momentum of the ball is: -230 kg m/s - 150 kg m/s = -80 kg m/s.
So, the impulse on the ball is -80 kg m/s.
Getsteludydykoydkzkysdykykykd.
a rectangle with area 12 square units is dilated by a scale factor of k find the area of the image for each given value of k
Answers
When the rectangle is dilated, the new and the old rectangles will have a different area
The area of the image of the rectangle is 12k^2
How to determine the area of the imageThe area of the rectangle is given as:
A = 12
The scale of dilation is given as k.
So, the area of the image of the dilation is:
\(A_2 = A * k^2\)
This gives
\(A_2 = 12 * k^2\)
Evaluate the product
\(A_2 = 12k^2\)
Hence, the area of the image of the rectangle is 12k^2
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A town has a population of 70,230 in the year 2020, over the next five years 6556 people move into the town for work, about 4096 moved to other parts of the country, a baby boom sees the birth of 5225 babies but there are also 4978 deaths. what is the population of the town in 2025?
Answers
Step-by-step explanation:
To calculate the population of the town in 2025, we need to add the changes in population over the next five years to the population in 2020.
Starting population in 2020 = 70,230
Change in population over 5 years:
Net migration = 6556 - 4096 = 2460
Natural increase (births - deaths) = 5225 - 4978 = 247
Total change in population = 2460 + 247 = 2707
Population in 2025 = 70,230 + 2,707 = 72,937
Therefore, the population of the town in 2025 is 72,937.
16 families went on a trip which cost them Rs 2,16,352. How much did each
family pay?
Answers
Given that 16 families went on a trip and the cost of the trip was Rs. 2,16,352.The amount paid by each family is to be determined by unitary method Hence each family paid Rs.13522
Now, let's solve this by using the method of unitary method. To find the cost of 1 family trip, we will divide the total cost of the trip by the number of families.2,16,352 / 16 = 13,522 So, the cost of the trip per family is Rs. 13,522.Hence, each family paid Rs. 13,522 for the trip.
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Answer:
Step-by-step explanation
1. The total cost of the trip for all 16 families is Rs 2,16,352.
2. To find out how much each family paid, we need to divide the total cost by the number of families: Rs 2,16,352 ÷ 16.
3. When we do the division, we get the result: Rs 13,522.
Now let's check if this result is correct:
1. If each family paid Rs 13,522 for the trip, then the total cost for all 16 families would be: 16 × Rs 13,522 = Rs 2,16,352.
2. This is exactly the same as the total cost given in the problem statement.
So we have shown that each family paid **Rs 13,522** for the trip
Type an equation of a standard parabola that is shifted right 3 units. Helppp asap
Answers
Answer:
y=(x+5)2 hope this helped!!! :D
Step-by-step explanation:
3. Determine whether the following scenarios are Area or Circumference:
a. How many framed pictures of art can fit on a wall
b. The distance around a circular swimming
c. How many turns of a bike wheel to go one block
d. How much paint is needed to paint a wall
Answers
Answer:
a) area
b) circumference
c) circumference
d) area
Step-by-step explanation:
when thinking about covering a surface, think area
when thinking about revolutions of a wheel, or distance around, think circumference
A and D are area, and C and D are circumference.
A is talking about how much can fit “in” a wall. This is area.
The distance around something is circumference.
C is how many times the wheel can turn, but measuring the area of the wheel can’t figure that out. This is circumference.
You wouldn’t paint only the perimeter of the wall. This has to be area.
Comment any questions down below.
Use the diagonals to determine whether a parallelogram with vertices C(1,2)
, A(5,−1)
, T(2,−5)
, and S(−2,−2)
is a rectangle, a rhombus, or a square. Give all the names that apply.
Answers
need more info. add the question in but try the whole question.
The probability of an event is 0.26. Describe the likelihood of the event.
Answers
Answer:
Not likely
Step-by-step explanation:
0.0 -- 0.32 = Not likely
0.33 -- 0.66 = Neither likely or unlikely
0.67 -- 1.0 = Likely
Hope this helps. Have a nice day.
Answer:26% {not likely}
Step-by-step explanation:
0.26 move the decimal over 2 times = 26%
40 and less let it rest 50 and more raise the score.
Can someone help please
ASAP
Answers
Answer:
see explanation
Step-by-step explanation:
using the tangent ratio in the right triangle
tan A = \(\frac{opposite}{adjacent}\) = \(\frac{BC}{AB}\) = \(\frac{5}{11}\) , then
∠ A = \(tan^{-1}\) ( \(\frac{5}{11}\) ) ≈ 24.4° ( to 1 decimal place )
tan C = \(\frac{opposite}{adjacent}\) = \(\frac{AB}{BC}\) = \(\frac{11}{5}\) , then
∠ C = \(tan^{-1}\) ( \(\frac{11}{5}\) ) ≈ 65.6° ( to 1 decimal place )
using Pythagoras' identity in the right triangle
the square on the hypotenuse is equal to the sum of the squares on the other two sides, that is
AC² = AB² + BC² = 11² + 5² = 121 + 25 = 146 ( take square root of both sides )
AC = \(\sqrt{146}\) ≈ 12.08 ( to 2 decimal places )
Match each letter to its correct term. Efficiency Unobtainable Impossible Inefficiency Underutilization 1. A 2. B 3. C
Answers
Each letter should be matched to its correct term as follows;
1. A ⇔ Efficiency.
2. B ⇔ Impossible.
3. C ⇔ Inefficiency.
What is a production possibilities curve?In Economics and Mathematics, a production possibilities curve (PPC) can be defined as a type of graph that is typically used for illustrating the maximum and best combinations of two (2) products that can be produced by a producer (manufacturer) in an economy, if they both depend on the following two (2) factors;
Technology is fixed.Resources are fixed.Based on the production possibilities curve shown in the image attached above, we can reasonably infer and logically deduce that each of the letters represent the following terminologies;
A ⇔ Efficiency: it represent points on the production possibilities curve.B ⇔ Impossible: it represent points outside the production possibilities curve.C ⇔ Inefficiency: it represent points on the interior of a production possibilities curve.Read more on production possibilities here: brainly.com/question/26460726
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how many balls are there in ten dozen
Answers
Answer:
120 balls
Step-by-step explanation:
Ten dozen is 120.
what is the distance in the image below?
Answers
The distance is:
5 + 3 = 8 units
Since the segment is completely horizontal we need not to use formula for computing the length of a segment in 2D euclidean space.
Instead we can simplify the problem to a single dimension, only considering the x-coordinates of the endpoints of the segment.
The x-coordinates are -5 and 3.
Subtracting and applying absolute value yields the answer,
\(\mathrm{abs}(-5-3)=\boxed{8}\).
Hope this helps.
Which of the following is the equation of the function f(x) graphed above? A. ƒ(x) = x(x − 2)²(x − 1)(x + 1) B. f(x) = (x - 2) (x − 1)(x + 1) c. f(x)= x(x - 2)²(x − 1)(x + 1) + 1)² D. f(x) = (x - 2)²(x - 1)(x - 1)^ E
Answers
Peter set off from Town A at 10 am, driving at an average speed of 84 km/h. He reached
Town B at 2 pm. If William set off 1 hour 25 minutes earlier than Peter and took the
same route at an average speed of 70 km/h, at what time would William reach Town B?
Answers
Peter left Town A around 10 a.m., traveling at an average speed of 84 km/h. William would reach Town B at 1:23 PM.
Firstly, we need to find the distance between Town A and Town B which can be calculated by calculating the distance travelled by Peter
Time taken by Peter = 2PM - 10AM
= 4 hrs
Speed of Peter = 84 km/h
Distance travelled by Peter = speed × time
= 84 × 4
= 336 km
So, the distance between Town A and Town B = distance travelled by Peter = 336 km.
Now, we will calculate time taken by William.
Speed of William = 70 km / hr
Distance travelled by William = distance between Town A and town B = 336 km
Time taken by William = distance / speed
= 336 / 70 hr
= 4.8 hr
This can b converted into hrs and minutes
4.8 hr = 4 hr + 0.8 × 60
= 4 hr 48 mins
Time William took off = 10 AM - 1hr 25 mins
= 8:35 AM
Now, we will calculate the time William would reach town B.
Time = 8:35 + 4hr 48 mins
= 1:23 PM
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What is the value of y
Answers
Answer:
y= 1/15.735. y is o.o64 character so one half is your answer
Answer: 27
Step-by-step explanation:
180-153= 27
y=27
Use the graph below to find the following:
A) what is the slope of the line?
B) what is the y intercept of the line?
C) what is the equation of the line in slope intercept form?
Answers
B.) The y-intercept is b=-5
C.) The equation is: y=-2x-5
These lines are parallel. Is this statement true or false? y = - 2 3 x + 8 y = 2 3 x − 5 A. true B. false
Answers
Answer:
This statement would be false.
Step-by-step explanation:
The given equations have slopes that are positive and negative. Therefore, we know that they will intersect at some point because the slopes are not the same. In fact, they intersect at the point (9 3/4, 1 1/2).
I have attached an image of the graph of these two equations for your reference.
PLEASE HELP !!! ILL GIVE BRAINLIEST!! *DONT SKIP* ILL GIVE 40 POINTS.
Answers
Answer:
12
Step-by-step explanation:
This kinda looks like slop-intercept form. Thats why I'm kinda guessing thats its 12
Step-by-step explanation:
2y-12x=36
2y=12x+36
y=6x+18
The rate of change of the equation is 6.
Evaluate -3- (-4) - (-2) + 1.
Answers
Answer:
4
Step-by-step explanation:
-3+4+2+1=4
Rose's rectangular backyard has an area of 672 square meters. Find the length of the backyard if the backyard is 7 meters wide.
Answers
\(\\ \rm\longmapsto Length(Breadth)=Area\)
\(\\ \rm\longmapsto Length(7)=672\)
\(\\ \rm\longmapsto Length=\dfrac{672}{7}\)
\(\\ \rm\longmapsto Length=96m\)
A clothing company makes a profit of $2.3 million. This is $4.1 million more than last year. What was the profit last year?
Answers
Answer:
-1.8 million. This means that the business likely spent a lot on production and generated very little sales during the first year.
Step-by-step explanation:
2.3 - 4.1= -1.8
Out of 2500 light bulbs that were tested, 135 were defective. Based on this information calculate the following
probabilities. Enter your answers as a reduced fraction using / for the fraction bar.
P(defective) =
P(not defective) =
Answers
Answer:
P(defective)= 135
P(not defective)= 2365
Step-by-step explanation:
2500-135=2365
The probability of picking a defective light bulb is 27 / 500.
The probability of picking a not defective light bulb is 473 /500.
What are the probabilities?Probability is used to determine the odds that a random event would happen. The odds that an event would happen usually lies between 0 and 1.
The probability of picking a defective light bulb = number of defective bulbs / total number of bulbs
135 / 2500 = 27 / 500
The probability of picking a not defective light bulb = number of non defective bulbs / total number of bulbs
(2500 - 135) / 2500 = 2365 / 2500 = 473 /500
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How many triangles can be drawn with the side lengths of 3 units, 4 units, and 5 units? Explain.
Answers
The number of triangles that can be drawn from the given side lengths is; 1 perfect right angle triangle
Right angle triangle proof
We are given the sides of the triangle to be;
3 units, 4 units and 5 units
Now, let us test if it is a right angled triangle by using the Pythagoras theorem as follows where;
a² + b² = c²
let a and b be 3 and 4 respectively. Thus;
3² + 4² = 16 + 9 = 25
c is 5. Thus; 5² = 25
Thus, we see that the 3 given sides fulfill the conditions of a right angle triangle.
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