Given the grid on your work template, plot the points A(4,5) and B(-7,7). Calculate the distance between the 2 points, and find the midpoint.
distance=
u (rounded to hundredths place)
Answer:
distance = 11.1803 units
midpoint : (-1.5, 6).
Step-by-step explanation:
To plot the points A(4, 5) and B(-7, 7) on the grid, we locate the points at the coordinates (4, 5) and (-7, 7) respectively.
The distance between two points (x1, y1) and (x2, y2) can be calculated using the distance formula:
d = √((x2 - x1)^2 + (y2 - y1)^2)
Plugging in the values for A and B, we get:
d = √((-7 - 4)^2 + (7 - 5)^2)
d = √(11^2 + 2^2)
d = √(121 + 4)
d = √125
d = 11.1803 (rounded to hundredths place)
The midpoint of two points (x1, y1) and (x2, y2) can be calculated as follows:
x = (x1 + x2) / 2
y = (y1 + y2) / 2
The midpoint of A and B is:
x = (4 - 7) / 2 = -1.5
y = (5 + 7) / 2 = 6
So the midpoint of A and B is approximately (-1.5, 6).
in investigation 2, if you were to double the length of the paper strip you dropped through the tape timer, would the number of dots on the paper also double?
Yes, when the length of the paper strip doubles, so will the number of dots on it.
Yes, when the length of the paper strip doubles, so will the number of dots on it. This is the case because the dots are uniformly spaced apart, and the total number of spaces between the dots doubles as the length of the strip does. As a result, to occupy the same number of spaces as the strip's length, the number of dots must also double. The same rule holds true for every paper strip of any length; increasing the strip's length will result in doubling the number of dots on it. The quantity of dots on the paper strip is therefore directly proportional to the length.
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To create the design shown, shade the triangle formed by the three midsegments of the triangle. Then repeat the process for each unshaded triangle.
a. What is the perimeter of the shaded triangle in Stage 1?
b. What is the total perimeter of all the shaded triangles in Stage 2?
c. What is the total perimeter of all the shaded triangles in Stage 3?
The total perimeter of all the shaded triangles in Stage 3 is 114 units.
What is midpoint theorem?The midpoint theorem states that the line segment joining the midpoints of any two sides of a triangle is parallel to the third side and equal to half of the length of the third side.
a) The shaded triangle in stage 1 is formed by the three midsegments of the triangle in stage 0 whose side is 16.
As the mid-segment theorem says the mid-segment is parallel and half in length to the third side of the triangle.
Apply the midsegment theorem, the side of the shaded triangle in stage 1 will be half of the side of the triangle in stage 0 i.e.,
16/2 =8
So, the perimeter is 3×8= 24 units
b) Perimeter = Perimeter of small triangle + Perimeter of 3 smaller triangles
= 24+3×3×4
= 60 units
c) Perimeter = Perimeter of small triangle + Perimeter of 3 smaller triangles + Perimeter of 9 smallest triangles
= 24+3×3×4+9×3×2
= 114 units
Therefore, the total perimeter of all the shaded triangles in Stage 3 is 114 units.
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Find the coordinates of point P that lies along the directed line segment from M to N and partitions the deferment in the ratio 3 to 2
The coordinates of point P that lies along the directed line segment from M to N and partitions the deferment in the ratio 3 to 2 is (6/ 5 , 0).
What is section formula?The line segment is divided into two pieces by a point, which may or may not be equal. If we know the coordinates of the point, we may calculate the ratio by which the supplied line segment is divided. Additionally, if we are aware of the ratio that the line segment connecting two places has produced, we can locate the point of division. The two can be accomplished using a section formula from coordinate geometry.
The coordinates of the points on the line are:
M = (-3, -3)
N = (4, 2)
m= 3
n = 2
Using the section formula we have:
M(x, y) = (mx2 + nx1 / m+n , my2 + ny1 /m + n)
M(x, y) = ((3)(4) + (2)(-3)) / (3 + 2) , (3)(2) + (2)(-3) / (3 + 2))
M (x, y) = (12 - 6 / 5 , 6. -6 / 5)
M (x, y) = (6/ 5 , 0)
Hence, the coordinates of point P that lies along the directed line segment from M to N and partitions the deferment in the ratio 3 to 2 is (6/ 5 , 0).
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Please help now asappp
The segments that provided result in true statement are:
NO/KL=PN/KM
Because PN and KM are in the same position of each triangle.
About middle segmentThe middle segment of a triangle connects the midpoints of the two sides of the triangle
The middle part of a triangle theorem states that the middle part of a triangle is parallel to one side of the triangle and its length is half that side.
There are several propositions that apply to triangles:
(1) Theorem of the midpoint of the triangle
The line segment connecting the midpoints of the two sides of a triangle is parallel to the third side and half the length of the third side.
(2) Intercept Theorem
If two or more parallel lines are cut by two intersecting lines, then the ratio of the first intersecting line segments is equal to the ratio of the like segments of the second intersection.
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WILL GIVE brainliest
Answer: 12.2
Step-by-step explanation: I did 8 times 6.3= 50.4
Then 8 times 4.4=35.2.
50.4-35.2=15.2 then minus the 3 is 12.2
1
32^1/25 × 2^x = 8^1/4
Work out the exact value of x
Answer:
Step-by-step explanation:
0.267
What is the order from coolest to warmest? 34 degrees Fahrenheit,100 degrees Fahrenheit,185 degrees Fahrenheit,0 degrees Celsius,37 degrees Celsius, and 100 degrees Celsius
The order from coolest to warmest is 0 degrees Celsius, 37 degrees Celsius, 34 degrees Fahrenheit, 100 degrees Celsius, 100 degrees Fahrenheit, and 185 degrees Fahrenheit.
0 degrees Celsius is the coolest temperature of the given options, followed by 37 degrees Celsius.
34 degrees Fahrenheit is the next coolest temperature.
100 degrees Celsius and 100 degrees Fahrenheit are the next warmest temperatures.
185 degrees Fahrenheit is the next warmest temperature.
100 degrees Celsius is the next warmest temperature.
The warmest temperature of the given options is 185 degrees Fahrenheit.
Therefore, the order from coolest to warmest is 0 degrees Celsius, 37 degrees Celsius, 34 degrees Fahrenheit, 100 degrees Celsius, 100 degrees Fahrenheit, and 185 degrees Fahrenheit.
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these two triangles are similar. find x
first triangle 8 , 6 second triangle 12 , x
The value of x is obtained as follows:
x = 9.
What are similar triangles?Similar triangles are triangles that share these two features presented as follows:
Congruent angle measures.Proportional side lengths.Considering the equivalent side lengths, the proportional relationship for this problem is given as follows:
8/6 = 12/x.
Applying cross multiplication, the value of x is obtained as follows:
8x = 72
x = 72/8
x = 9.
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The ________ means that none of the points in the line will satisfy the inequality.
Answer: dotted/dashed line
A father wishes to distribute his 2 hectare field equally among his 4 sons. How many ares will each son's plot measure?
Answer:
50 ares
Step-by-step explanation:
You want the area each of 4 sons will receive if a 2 hectare plot is divided equally among them.
HectareA hectare is 100 ares, so 2 hectares is 200 ares. One quarter of that area is ...
(200 ares)/4 = 50 ares
Each son's plot will be 50 ares.
21.A man borrowed Rs. 50,000 for 3 years at the rate of 12% simple interest but he could pay only Rs. 25,000 at the end of 3 years and
agreed to clear his debt at the end of next two years at the rate of 10 %
annual compound interest. Find how much should he pay to clear his
debt? Also find the amount of interest he paid altogether.
A bricklayer needs to order 6300 kg of building sand.
a) Write 6300 kg in grams, giving your answer in standard form.
One grain of this sand approximately weighs 7 x 10*g.
b) How many grains of sand are there in 6300 kg of sand?
Give your answer in standard from.
The standard form of 6300 kg in grams is 0.63 x [tex]10^7[/tex] g.
There are 90000 grains in 6300 kg of sand.
What is unit conversion?It is the conversion of one unit to another unit with its standard conversion.
Example:
1 minute = 60 seconds
1 km = 1000 m
We have,
6300 kg
Now,
1 kg = 1000 g
So,
6300 kg = 6300 x 1000 g
6300 kg = 63 x [tex]10^5[/tex] g
6300 kg = 0.63 x [tex]10^7[/tex] g
Now,
One grain = 7 x 10 g
So,
Number of grains in 0.63 x [tex]10^7[/tex] g.
= 0.63 x [tex]10^7[/tex] ÷ 7 x 10
= 90000
Thus,
0.63 x [tex]10^7[/tex] g is the standard form.
90000 grains.
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solve the following systems of linear equations by graphing
x=4 and y=-3/2x - 2
Answer: -8
Step-by-step explanation: I did long division for 3/2 = -1.5 now I have to mutiply -1.5 x 4 = -6 - 2 = -6 + (-2) which now eqauls negative 8
what happens to the power of a study if a statistician decides to decrease the overall alpha level from 0.10 to 0.05
The power of a study refers to the ability of a statistical test to correctly detect a difference or association in the population when it actually exists. Decreasing the overall alpha level from 0.10 to 0.05 would increase the power of the study.
The alpha level, also known as the significance level, is the probability of making a Type I error in a statistical test, which is rejecting the null hypothesis when it is actually true. By decreasing the alpha level, the statistical test becomes more stringent, and the likelihood of making a Type I error decreases.
For example, if the alpha level is 0.10, a statistically significant result would be achieved if the p-value (the probability of observing the test statistic under the null hypothesis) is less than or equal to 0.10. If the alpha level is decreased to 0.05, the p-value must now be less than or equal to 0.05 for the result to be considered statistically significant.
In general, decreasing the alpha level makes the test more conservative and increases the power of the study. However, this comes at the cost of increased likelihood of Type II error, which is failing to reject the null hypothesis when it is actually false.
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Use a graphing tool to solve the system.
1.5x−y3=182x−3y=43
Enter the coordinates of the solution in the boxes. Round each coordinate to the nearest hundredth.
The solution is, x= 50 & y= 19.
What is equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign. In its simplest form in algebra, the definition of an equation is a mathematical statement that shows that two mathematical expressions are equal. For instance, 3x + 5 = 14 is an equation, in which 3x + 5 and 14 are two expressions separated by an 'equal' sign.
here, we have,
given that,
1.5x−y3=18
2x−3y=43
solving the equations in graph , we get,
x= 50
y= 19
Hence, The solution is, x= 50 & y= 19.
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Bonjour j'ai besoin d'aide.
Merci de votre aide.
Answer: en fait je ne sais pas désolé
Step-by-step explanation: désole.
A)How much material does he need to cover the one rectangular side of the tent with the rip? Justify your answer using equations/formulas, models, and/or words to explain your mathematical reasoning.
Answer:
B)If David’s dad wanted to recover the whole tent including the bottom, how much material would he need? Justify your answer using equations/formulas, models, and/or words to explain your mathematical reasoning.
Answer:
C)What is the volume of the tent? Justify your answer using equations/formulas, models, and/or words to explain your mathematical reasoning. (You need to find the area of one of the triangular bases, and then you can take that measurement and multiply it with the height of the entire prism. ) V=Bh, where B = area of one of the triangular bases
Answer
He would need 54 ft² material to cover the one rectangular side of the tent with the rip and 213 ft² to recover the whole tent including the bottom. The volume of the tent is 189 ft³.
Part A
He would need 54 ft² material to cover the one rectangular side of the tent with the rip. As we have to find the area of a rectangular side of a rectangle we will use the formula Area= Length × Width
∴ Area of a Rectangle = length of the rectangle × width of the rectangle
A = 9 × 6
A = 54 ft²
Part B
David's dad would need 213 ft² material to recover the whole tent including the bottom. We know that the 2 sides of the tent are 54 ft² each. So, the total is 54 × 2 = 108 ft².
We will now find the area at the bottom of the tent
A = 7 × 9
A= 63 ft²
We will now find the area of the triangular sides
Triangle Area = 1÷2 × b×h
A = 1÷2 × 7 × 6
A = 1÷2 × 42
A = 21 ft²
As there are 2 triangular sides so we have to multiply it by 2
∴ 21 × 2 = 42 ft²
Add all the sides together 108 63 + 42 = 213 ft²
Part C
The volume of the tent is 189 ft³. It can be found by applying the formula V= b×h
Triangle area = 1÷2 × bh
A = 1÷2 ×7 × 6
A= 1÷2 × 42
A= 21
With a=21 as B and h= 9ft and applying the formula v=Bh
We have,
v = 21 × 9
v = 189 ft³
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find the total cost a) The radius of a circular field is 63 m. Find the perimeter of the field. Also, find the length of wire required to fence it with 5 rounds. =
The perimeter of the circle is 395.64 m, and the length of wire needed to fence it with 5 rounds is 1,978m
How to find the perimeter?We kow that for a circle, the perimeter is equal to its circumference, and the circumference of a circle of radius R is:
C = 2*pi*R
Where pi = 3.14
Then the perimeter of a circle of radius of 63m is:
Perimeter = 2*3.14*63m = 395.64 m
And the length of wire needed to fence it with 5 rounds is 5 times that, so we will get:
total length = 5*395.64 m = 1,978m
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Consider the function g(x)=−(x−1)^3−2. Which ordered pair lies on the inverse of the function?
(62,−3)
(−4, 123)
(3, 1)
(3,−6)
The ordered pair lie on the inverse of the function is (62,−3).
Option A is the correct answer.
What is a function?A function is a relationship between inputs where each input is related to exactly one output.
Example:
f(x) = 2x + 1
f(1) = 2 + 1 = 3
f(2) = 2 x 2 + 1 = 4 + 1 = 5
The outputs of the functions are 3 and 5
The inputs of the function are 1 and 2.
We have,
f(x) = -(x - 1)³ - 2
The inverse of f(x).
y = -(x - 1)³ - 2
interchange x and y and solve for y.
x = -(y - 1)3 - 2
(y - 1)³ = -2 - x
(y - 1)³ = -(2 + x)
Cuberoot on both sides.
y - 1 = ∛-(2 + x)
y = ∛-(2 + x) + 1
Now,
Substitute in the inverse of g(x).
(62, -3) = (x, y)
(−4, 123) = (x, y)
(3, 1) = (x, y)
(3,−6) = (x, y)
So,
y = ∛-(2 + x) + 1
y = ∛-(2 + 62) + 1
∛-1 = -1
y = -1∛64 + 1
y = -1 x 4 + 1
y = -4 + 1
y = -3
So,
(62, -3) ______(1)
And,
y = ∛-(2 + x) + 1
y = ∛-(2 - 4) + 1
∛-1 = -1
y = ∛(-2 + 4) + 1
y = ∛2 + 1
y = 1.26 + 1
y = 2.26
So,
(-4, 2.26) _______(2)
And,
y = ∛-(2 + x) + 1
y = ∛-(2 + 3) + 1
∛-1 = -1
y = -1∛5 + 1
y = -1 x 1.71 + 1
y = -1.71 + 1
y = -0.71
So,
(3, -0.71) _______(3)
And,
y = ∛-(2 + x) + 1
y = ∛-(2 + 3) + 1
∛-1 = -1
y = -1∛5 + 1
y = -1 x 1.71 + 1
y = -1.71 + 1
y = -0.71
So,
(3, -0.71) ______(4)
Thus,
From (1), (2), (3), (4) we see that,
(62, -3) is the solution to the inverse of g(x).
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Ava draws a circle with a radius of 4cm. Elliana draws a circle with a diameter of 6 cm. without calculating, whose circle has the greater area? explain.
Answer:
Elliana's circle with a radius 4 has a greater area
Step-by-step explanation:
The area of a circle is given by πr²
Area is directly proportional to the square of the radius
A ∝ r²
So the greater the radius, the greater the area
Hence, Elliana's circle has a greater area
What rule would you allow to test whether (x,y) is on line l
The slope of the line will be 5 / 4 for the given graph.
What is a slope?Slope or the gradient is the number or the ratio which determines the direction or the steepness of the line. The slope of the line is defined as the ratio of the rise o the line to the run of the line.
Given that the line is passing through points ( 4,5) and ( 8, 10). The slope of the line will be calculated as:-
Slope = ( y₂ - y₁ ) / ( x₂ - x₁ )
Slope = ( 10 - 5 ) / ( 8 - 4 )
Slope = 5 / 4
Hence, the slope of the line is equal to 5 / 4.
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in a positively skewed distribution, the peak of the distribution corresponds to which measurement(s)? a. the median only b. the mean only c. the mode, mean, and median d. the mode only
The correct answer is option d. the mode only.
Positively skewed distribution:
A positively skewed distribution, also known as a right-skewed distribution, is a type of distribution in statistics in which most values are centered around the left tail and the right tail is longer. The distribution that is positively skewed is the exact opposite of one that is negatively skewed.
Positively skewed data differ from normally distributed data. The following inequality can be used to represent the general relationship between the central tendency measurements in a positively skewed distribution:
Mean > Median > Mode
Here
The peak of the distribution corresponds to the mode only
Therefore,
The correct answer is option d. the mode only.
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Tommy had equal sized pieces of wood that measured 3.5 inches on each side. He glued the pieces of wood on top of each other until they reached a height of 7 feet. How many pieces of wood did Tommy glue together to reach a height of 7 feet?
He will need 2 wood in order to reach a height of 7 feet
What is the arithmetic operation?
The four fundamental operations of arithmetic are addition, subtraction, multiplication, and division of two or more quantities. Included in them is the study of numbers, especially the order of operations, which is important for all other areas of mathematics, including algebra, data management, and geometry. The rules of arithmetic operations are required in order to answer the problem.
Tommy had equal-sized pieces of wood that measured 3.5 inches on each side.
He glued the pieces of wood on top of each other until they reached a height of 7 feet.
One is glued above another so the wood add up in the stack.
To make 7 ft in total he need2*3.5 = 7ft
Hence He will need 2 wood in order to reach a height of 7 feet
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what are the coordinates to graph y=-2x-2
Answer: the y intercept is (0,-2)
Step-by-step explanation:
Step-by-step explanation:
it is a line.
so, you need 2 points of the line that you can then connect via a ruler and a pen.
you get a point by picking a value for x and calculate the corresponding y.
like x = 0, y = -2×0 - 2 = -2
or x = -2, y = -2×-2 - 2 = 2
At a specific spot along the coast of North Carolina, the continental shelf extends out from the shoreline into the ocean. At that point, the depth of the water is . From there, the ocean floor slopes down to the oceanic crust which begins from the shoreline at a depth of . Find the slope of the ocean floor connecting the edge of the continental shelf and the beginning of the oceanic crust. That section of the ocean floor is called the continental slope.
The slope formula to calculate the slope of the ocean floor would be
[tex]slope = \frac{y}{x}[/tex].
What is slope?
The slope of a line characterizes its direction.
To find the slope of the ocean floor, we need to calculate the rise (change in depth) and the run (distance along the ocean floor) between the edge of the continental shelf and the beginning of the oceanic crust.
Let's call the depth of the water at the edge of the continental shelf "d1" and the depth of the water at the beginning of the oceanic crust "d2". Then, the rise is:
rise = d2 - d1
We don't have the actual values for d1 and d2, so let's call the rise "y" and the run "x". Then, the slope of the ocean floor is given by:
[tex]slope =\frac{rise}{run} \\\\slope = \frac{y}{x}[/tex]
So, we can use the slope formula to calculate the slope of the ocean floor.
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Simplify the expression. Explain each step. (12+x)+2
Answer:
Step-by-step explanation:
The answer is x + 14. If just adding 2 to (x + 12), the parenthesis can be disregarded.
charlie drove to the mountains last weekend. there was heavy traffic on the way there, and the trip took hours. when charlie drove home, there was no traffic and the trip only took hours. if his average rate was miles per hour faster on the trip home, how far away does charlie live from the mountains?
If his average rate was miles per hour faster on the trip home, Charlie lives 480 miles from the mountain.
Let s = his speed to the mountains,
(s+20) = his return speed
The distance each way is the same,
Using the formula,
Distance = speed * time
12s = 8(s+20)
12s = 8s + 160
12s - 8s = 160
4s = 160
s = 160/4
s = 40 mph
So his speed to the mountain is 40mph
then,
Putting the values of speed and times we get,
40 * 12 = 480 miles to the mountains
Therefore, distance between charlie and the mountains is 480 miles.
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Martha can rake the leaves in her yard in 2 hours. Her brother can do the job in 6 hours. How long will it take them to do the job
working together?
Answer: 4 hours
Step-by-step explanation: the difference (6-2) = 4
The combined rate at which they complete the job is the sum of their individual rates, so their combined rate is 2 + 6 = 8 hours per job.
Therefore, they will do the job in 1/8 of the time it would take either of them working alone, so it will take them 1/8 of 2 hours = 15 minutes to do the job together.
A scuba diver is hired to take underwater photos. He begins swimming straight downward from an elevation of -5 meters relative to sea level. His elevation changes at a constant rate of 2.5 meters per minute. When he stops, his camera is still in a safe depth for use. For how many minutes could he have been swimming? Graph the solution set. Show your work.
Step-by-step explanation:
The scuba diver's elevation after t minutes can be represented by the equation y = -5 + 2.5t. The camera is in a safe depth for use when y is greater than or equal to 0, so we want to find the value of t when y is equal to 0.
Solving for t:
0 = -5 + 2.5t
5 = 2.5t
t = 5/2.5
t = 2
So the scuba diver could have been swimming for 2 minutes.
The graph of the solution set would be a line with slope 2.5 and y-intercept of -5, and the x-axis (y = 0) would be the line where the diver's depth is equal to sea level. The solution to the problem would be the point on the graph where y = 0 and x = 2.