Please help, easy geometry
1 answer:
Answer:
Step-by-step explanation:
There are a few ways to go about doing this problem. One method would to divide the shape into two triangles and a rectangle and then find the area of those shapes and then add them all up. I am not going to do that because that is the long way to solve this problem.
<u>With that said, you can use the trapezoid formula</u>
b1 = 3
b2 = 11
h = 9
<u>Plugin the data into our model and do the math.</u>
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Answer = 55,25 inches
Solution -
let's take x as length and y as width of the metal piece. As per the question x is 30 more than y,
⇒ x = y + 30
Then four square pieces of side 6 are cut from each corner,
so the new length and width are
x-12 , y-12
Then the volume of the new box created will be
(x-12)(y-12)6
in the question the volume of the given figure is given to be 3354
so (x-12)(y-12)6 = 3354
putting the value of x in the the above equation
⇒ (y+30 - 12)(x-12) = 3354/6 = 559
⇒ (y+18)(y-12) = 559
⇒ y² + 6y - 775 = 0
⇒ y² + 31y - 25y -775 = 0
⇒ (y+31)(y-25) = 0
⇒ y = -31, 25
as length can not be -ve , so y = 25
then x = 25+30 = 55
Hence the dimensions of the metal piece are 55, 25 inches
Answer:
a = 2
Step-by-step explanation:
Let's find the equation of the line using the 2 points given.
Let's call -1 as x_1 and -5 as y_1
also, 4 as x_2 and 5 as y_2
The equation of line is :
<em>Let's plug the points and get the equation of the line:</em>
Now, to find a, we substitute a in x and 1 in y of the equation of the line we just got: