The change in x values and y values are proportional to each other for the given case. The correct option is (D).
The slope of a straight line is the tangent of the angle formed by it with the positive x axis as the reference.
The negative slope indicates the rate of decrease while the positive shows the rate of increase.
In order to form a linear equation from a table,
The slope has to be found first.
For this, the ratio of the difference in the values of x and y are taken.
Which implies that the change in x values are directly proportional to the change in the values of y.
And the proportionality constant is known as the slope.
=> (y₂ - y₁) ∝ (x₂ - x₁)
=> (y₂ - y₁)/(x₂ - x₁) = m
Hence, the change in y values are constant for change in x values.
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ANSWER:
the answer is D.
Answer:
Which mode of transmission of heat is shown in the given figure?Explain the mechanism of convection of heat.
The circular exercise run provides more area for Rico's dog to run than the rectangular lawn. This is determined by calculating the maximum possible area for a rectangle with a perimeter of 36 meters and a circle with a circumference of 36 meters.
To answer which shape will give Rico's dog more area to run, we need to calculate the areas of the given shapes - a rectangle and a circle - using their respective perimeters/circumferences.
For a rectangle with a perimeter of 36 meters, one plausible dimension could be a rectangle with a length of 10 meters and a width of 8 meters, giving an area of 80 square meters assuming the shape is a square. (This gives the maximum area for a given perimeter).
The circumference of a circle is given by the formula 2πr, where r is the radius of the circle. If the circumference is 36 meters, then the radius would be 36/(2π) ≈ 5.73 meters. The area of this circle would then be πr², approximately 103.07 square meters.
In conclusion, the circle will offer more area for Rico's dog to run, despite the rectangular lawn and circular exercise run having the same perimeter and circumference lengths respectively.
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The greatest possible value of x is the largest value that satisfies all of these inequalities. The largest value of x that satisfies all three inequalities is 6.4 .
In an obtuse triangle, the longest side is opposite the obtuse angle. To determine the greatest possible value of x, we need to consider the triangle inequality theorem, which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
In this case, the longest side measures 20 cm, and the two shorter sides are x cm and 3x cm. So, we have the following inequalities:
x + 3x > 20 (sum of the two shorter sides must be greater than the longest side)
20 + x > 3x (sum of the longest side and the shorter side must be greater than the other shorter side)
20 + 3x > x (sum of the longest side and the other shorter side must be greater than the remaining shorter side)
Let's solve these inequalities:
4x > 20
x > 5
20 + x > 3x
20 > 2x
10 > x
20 + 3x > x
20 > -2x
-10 < x
So, the greatest possible value of x is the largest value that satisfies all of these inequalities. The largest value of x that satisfies all three inequalities is 6.4 (rounded to the nearest tenth). Therefore, the greatest possible value of x is 6.4 cm.
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Answer:
7.1
Step-by-step explanation:
because pythagorean theorem
c² > a² + b²
20² > x² + 3x²
400 > 4x²
÷4 ÷4
100 > x²
10 > x 400 > 4(7.1)²
400 > 4(50.41)
400 > 201.64
IMAGE below!
Answer:
x =22.5
Step-by-step explanation:
x+3x = 90
x and 3x are complementary so they add to 90 degrees
Combine like terms
4x =90
Divide each side by 4
4x/4 = 90/4
x =22.5
answer: x = 22.5
explanation:
as the 3x and x are on a straight line with the angle of 90° we know that
3x +x = 90
4x = 90
x = 22.5
Answer:
angle 4 is 31
angle 5 is 59.
Step-by-step explanation:
M<4 and M<5 add up to a right angle which is 90 degrees . so you put it in a equation form.
2x-5+4x-13=90
rearrange it
2x+4x-5-13=90
6x-18=90
add 18 on both sides
6x=108
divide 6 from both sides
and you get x= 18
Plug in x for angle 4 =2(18)-5 = 31
plug in x for angle 5 = 4(18)-13 = 59