Lets write equation of a function:
y = kx + n
Direct variation in simple is equation of a line which has n=0 or in other words which y to x ratio is k.
First option gets 7=7 but it isnt direct variation because n is not equal to 0
third option is indeed correct. once we implement coordinates (2,7) we get 7=7
Answer is
y = 7/2x
0.4(420) = 4(420)/10
(0.4 is essentially 4/10)
1680/10 = 168
There are 168 sixth graders
The equation below does not have one solution, or no solutions, but instead it has an infinite number of solutions
<h3>How to determine whether the equation below has a one solutions, no solutions, or an infinite number of solutions?</h3>
The equation is given as:
x + 2 = 2 + x
Collect the like terms
x - x =2 - 2
Evaluate the like terms
0 = 0
An equation that has a solution of 0 = 0 has an infinite number of solutions
Possible values of x are x = 8 and x = -8
Hence, the equation below does not have one solution, or no solutions, but instead it has an infinite number of solutions
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The relationship that sin x° and cos y° share is that; cos x = sin y and sin x = cos y = 12/13
<h3>How to work with Pythagoras Theorem?</h3>
From the definitions of trigonometric ratios, we know that;
sin x = opposite leg/hypotenuse
cos y = adjacent leg/hypotenuse
From the Pythagorean theorem, we can find the hypotenuse as;
6² + 8² = hypotenuse²
The cosine is the sine of the complementary angle. Since x and y are complementary angles as they sum up to 90°, we have cos x = sin y and sin x = cos y = 12/13
Read more about Pythagoras Theorem at; brainly.com/question/27572671
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<u>Given</u>:
Given that the diameter of the hemisphere is 48 inches.
We need to determine the volume of the hemisphere.
<u>Radius:</u>
The radius of the hemisphere can be determined using the formula,

Substituting d = 48, we get;


Thus, the radius of the hemisphere is 24 inches.
<u>Volume of the hemisphere:</u>
The volume of the hemisphere can be determined using the formula,

Substituting r = 24, we get;



Thus, the volume of the hemisphere is 9216π cubic inches.