Prove angle ABC is a right angle

Pleasee help I need ASAP

If you have three points in space , we can use direction vector , check if vectors are collinear or proportional to know those 3 points lie on the same line.

If you have three points in space and you find a vector that is projected onto another vector from each of these three points, it is possible to determine if the three points lie on the same line. Here's how you can do it:

Find the direction vector: Calculate the direction vector from one of the points to the other two points.

Check if the projection vectors are collinear: If the projection vectors from all three points are collinear, it means that they are all pointing in the same direction and are proportional to each other.

Check if the projection vectors are proportional: If the projection vectors are proportional, it means that they are all pointing in the same direction, and the three points are on the same line. Note that in order to determine if the projection vectors are proportional, you would need to know the magnitude of the projection vectors.

If the three points do lie on the same line, the direction vector found in step 1 will be proportional to the projection vectors found in step 2 and step 3, and all three points will lie on the same line in space.

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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).

Answer:

E,B are the answers.

Step-by-step explanation:

The total perimeter of all the shaded triangles in Stage 3 is 114 units.

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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If <A = 51° then the measure of angle ABE be 39°.

The term "right triangle" refers to a triangle with an interior angle of 90 degrees. The hypotenuse, the side that faces the right angle and is also the side with the longest side in a right triangle, and the height and base are the two arms of the right angle.

It is 90 degrees at a right angle. Angles smaller than 90 degrees are considered sharp angles. More over 90 degrees is considered an obtuse angle. Additionally, these angles aid in categorizing the various triangular varieties.

ΔABE = 180 degree

Let the equation be

∠A + ∠B  + ∠E = 180 degree

simplifying the above equation, we get

51° + ∠B + 90° = 180°

∠B = 180° - 90° - 51°

∠B = 39°

Therefore, the measure of angle ABE be 39°.

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Answer: dotted/dashed line

On solving the provided question, we can say that from the graph[tex]y = x^2 - 4x[/tex], x = 0, y = 0 and x =2, y = 0

Mathematicians use graphs to logically convey facts or values using visual representations or charts. A graph point will typically reflect a relationship between two or more things. Nodes, or vertices, and edges make form a graph, a non-linear data structure. Glue together the nodes, often referred to as vertices. This graph has vertices V=1, 2, 3, 5, and edges E=1, 2, 1, 3, 2, 4, and (2.5), (3.5). (4.5). Statistical charts (bar charts, pie charts, line charts, etc.) graphical representations of exponential growth. a logarithmic graph in the shape of a triangle.

from the graph,

[tex]y = x^2 - 4x[/tex]

so,

x = 0, y = 0

x = -1,

y = 5

and x =2, y = 0

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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.

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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Answer:

$115

Step-by-step explanation:

If $100 is increased by 15%, it becomes $100 + 0.15 * $100 = $100 + $15 = $115.

Answer: 115

Step-by-step explanation:

100 x 0.15 = 15 so, 100 + 15 = 115

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.

The 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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Answer:

DK = 18

MJ = 3

ML = 8

Step-by-step explanation:

In this problem, we need to use the Median of a Triangle Formula. This formula states that EM/EL = FM/JF = DM/DK = 2/3. To implement this into our question, we can write ML/EL = 1/3, so we get that ML = 24/3 = 8. We also know that MJ/FM = 1/2, so MJ = 6/2 = 3. Finally, DM/DK = 2/3, so DK = (12*3)/2 = 18. Hope this is correct.

function is the answer of this question

For every 12 pop songs played on the streaming music channel, there are 8 hip-hop tracks.

After that, the algebraic relationship is denoted by the equation y = mx + b, where y stands for the distance, x for time, m for the slope, and b for the y-intercept. Distance = (2m/s)time - 1m is the relationship we infer from the graph.

The association between two quantitative variables measured for the same individuals is displayed in a scatterplot. One variable's values are shown on the horizontal axis, and the other variable's values are shown on the vertical axis. Each individual in the data is represented by a point on the graph.

As the values of the independent variables rise, a linear connection shows as a straight line, rising or dropping. A direct relationship is shown by a rising line to the right. If the line curves right, there is an inverse relationship.

For every 12 pop songs played on the streaming music channel, there are 8 hip-hop tracks.

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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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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

The slope of the line will be 5 / 4 for the given graph.

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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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.

the expression are equivalent compound condition for the nested conditionals is (x > 200) and (y < 200).

ii. The equivalent compound condition for the nested conditionals is not (x > 200 and y > 200).

iii. The equivalent compound condition for the nested conditionals is not ((x ≤ 200) or (y ≥ 200)).

The equivalent compound conditions for the given nested conditionals are as follows:

i. The compound condition (x > 200) and (y < 200) is equivalent to the nested conditionals if (x > 200): if (y < 200). This is because the compound condition requires both conditions to be true for the condition to be satisfied.

ii. The compound condition not (x > 200 and y > 200) is equivalent to the nested conditionals if (x > 200): if (y < 200). This is because the compound condition requires both conditions to be false for the condition to be satisfied.

iii. The compound condition not ((x ≤ 200) or (y ≥ 200)) is equivalent to the nested conditionals if (x > 200): if (y < 200). This is because the compound condition requires both conditions to be false for the condition to be satisfied.

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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

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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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

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.

A 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.

The ordered pair lie on the inverse of the function is (62,−3).

Option A is the correct answer.

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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The another term for the average value of a distribution is "mean."

The mean is a commonly used measure of central tendency that represents the average value of a set of data. It is calculated by summing up all the values in a dataset and dividing by the total number of observations. The mean is a useful tool for summarizing the general tendency of a dataset and is used as a basis for other statistical calculations such as variance and standard deviation.

However, the mean is sensitive to outliers, meaning that a few extreme values in a dataset can greatly affect the mean. For this reason, it's sometimes necessary to use other measures of central tendency, such as the median or mode, to get a better understanding of the central tendency of a dataset.

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The surface area to be covered by the label is 904.32 mm²

Assuming the shape of the battery is cylindrical.

The dimensions of the cylindrical battery:

radius r = 4 millimeters

height h = 32 millimeters

We know that the formula for the surface area of cylinder is:

A =  2πrh + 2πr²

where r is the radius of the cylinder and h is the height of the cylinder

Using this formula of surface area of cylider, the surface area to be covered by the label would be,

A =  2πr(h + r)

A = 2π × 4 × (32 + 4)

A = 2 × 3.14 × 4 × 36

A = 904.32 mm²

Thus, the required area = 904.32 sq. mm.

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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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Answer:7 seconds

Step-by-step explanation:

it would take 7 seconds second to fill in a inTIRE empty bike

3 1/2 *2=7

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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