A student draws a triangle with a perimeter of 36cm. The student says the longest length is 18cm. How do you know the student is
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Answer:
We conclude that the initial value and y-intercept are the same thing on a graph.
Please check the attached graph of the equation y = 2x+1.
Step-by-step explanation:
We know that the initial value on a graph is basically the out-put value y of the point where the line meets or crosses the y-axis.
In other words, the initial value is the y-value or output of the point at x = 0
For example,
Let the equation
y = 2x+1
substitute x = 0
y = 2(0)+1
y = 0+1
y = 1
Thus, the initial value of the equation y = 2x+1 is: y = 1
Please check the attached graph of the equation y = 2x+1.
It is clear from the graph that at x = 0, the value of y = 1.
Thus, at y = 1, the line meets the y-axis.
Hence, the initial value of the line is: y = 1
Similarly, we know that the value of the y-intercept can be determined by setting x = 0 and determining the corresponding value of y.
For example,
Let the equation
y = 2x+1
substitute x = 0
y = 2(0)+1
y = 0+1
y = 1
Thus, the y-intercept of y = 2x+1 is y = 1.
Please check the attached graph of the equation y = 2x+1.
It is clear from the graph that at x = 0, the value of y = 1.
Therefore, the y-intercept of y = 2x+1 is y = 1.
Conclusion:
Therefore, we conclude that the initial value and y-intercept are the same thing on a graph.
Please check the attached graph of the equation y = 2x+1.
Answer:
Step-by-step explanation:
<h3><u>The Law of Sines</u></h3>The Law of Sines states that for a given triangle (in a plane), the ratio formed by the Sine of any one of the three interior angles and the side across from it is equal to a common number.
If a triangle is drawn in standard form, with the three vertices identified as A, B, and C, and the interior angles at each vertex simply identified as angleA, angleB, angleC, the sides across from those angles are identified as a, b, and c, respectively. Given such a labeling for a triangle, the Law of Sines gives the following equation:
From the picture you presented, with triangle RST, side r is on the right and unlabeled, side s is shown in red, and side T is shown in green. The interior angles for R and S are unlabeled, and angle T is defined as 74 degrees. The Law of Sines would give the following relationship for your triangle:
Substituting known values...
It should be noted that without information about the length of side r, angle R cannot be found directly with the Law of Sines because that portion of the equation holds two unknowns. However, if the other two angles of the triangle are known, angle R can be solved for by using the Triangle Sum Theorem.
<h3><u>Finding Angle S</u></h3>
Focusing in on the ratio with known values on the far right, and the ratio containing angleS first:
... multiplying both sides of the equation by 12.7 ft...
Note that the right side of the equation has units of feet in both the numerator and denominator (with no addition or subtraction), so the units will cancel. Simplifying the right side of the equation by evaluating the expression in a calculator (make sure you're in "degree" mode), will yield a unit-less number:
Undoing the sine function, and solving for the measure of angle S will require taking the "arcsin" of both sides of the equation...
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<h3><u>Finding Angle R</u></h3>Knowing both angleS and angleT, we can apply the Triangle Sum Theorem to solve for angle R.
Triangle Sum Theorem: The sum of all 3 interior angles in a triangle (in a plane) is 180 degrees.
Using the subtraction property of equality to isolate angleR and combining like terms...