The linear equation is y = 4 + 0.5x
<h3>How to determine the equation?</h3>
The points are given as: (-2,3) and (4,6)
The equation is then calculated using:

Substitute the known values

Evaluate
y = 0.5 *(x+2) + 3
Expand
y = 0.5x + 1 + 3
Evaluate the sum
y = 0.5x + 4
Rewrite as:
y = 4 + 0.5x
Hence, the equation is y = 4 + 0.5x
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Answer:
142.932
Step-by-step explanation:
given that in triangle ABC, AC =24
Angle A = 30 and Angle B =45
If we draw altitude from C, we get
h = 24sin 30 = 12
Since BC = h (45, 45,90 triangle)
BC=12
By sine formula for triangle

Area of triangle
= 
Answer:

Step-by-step explanation:
Since we know we only have 640 feet of fence available, we know that L + W + L = 640,
2L + W = 640. This allows us to represent the width, W, in terms of L: W = 640 – 2L
Remember, the area of a rectangle is equal to the product of its width and length, therefore,
Notice that, quadratic has been vertically reflected, since the coefficient on the squared term is negative, so the graph will open downwards, and the vertex will be a maximum value for the area.
recall,
Since our function is A(L)=640L-2L², we get
plug in the value of a and b into the first formula:


hence,the dimensions of the pen that will maximize the area are<u> </u><u>L=</u><u>1</u><u>6</u><u>0</u><u>m</u><u> </u>and<u> </u><u>W=</u><u>7</u><u>6</u><u>8</u><u>0</u><u>0</u><u>/</u><u>1</u><u>6</u><u>0</u><u>=</u><u>4</u><u>8</u><u>0</u><u>m</u>
and we're done!
Answer:
17; 22; 27; 32
the terms increase by 5 each time
17 + 5 = 22 (the second term)
17 + 5 * 2 = 27 (third term)
So to get to the 52nd term, we have to add 5* 51 = 255 to 17
17 + 255 = 272
Step-by-step explanation: