Illustrate the given problem. Refer to the diagram attached to aid our solution.
Area of bigger rectangle:
A = (L+8)(W+16)
Area of smaller rectangle (printed area)
388 = LW
From the second equation, we can express L in terms of W.
L = 388/W
Replace this to the first equation:
A = (388/W+8)(W+16)
A = 388 + 6208/W + 8W + 128
A = 6208/W + 8W + 516
Derive A with respect to W and equate to zero (calculus):
dA/dW = -6208/W² + 8 = 0
-6208/W² = -8
W² = -6208/-8 = 776
W = √776 = 27.86 cm
L = 388/27.86 = 13.93 cm
Thus, the smallest area would be:
A = (13.93 cm)(27.86 cm)
<em>A = 388.09 cm²</em>
I would say it's H because 4 and 3 add to be 7
Answer:
Step-by-step explanation:
1. 96 centimeters squared
2. 300 degrees
3. no, the diagonals of a parallelogram donor intersect at 90 degree ( are not perpendicular) .it is because the adjacent sides of parallelogram are not equal..
4. no
The perimeter is:
P = 2x + 2y = 80
The area is:
A = x * y
The area as a function of a variable is:
A (x) = x * (40-x)
Rewriting we have:
A (x) = 40x-x ^ 2
We derive the function:
A '(x) = 40-2x
We equal zero and clear x:
40-2x = 0
2x = 40
x = 40/2
x = 20 feet
The other dimension is:
y = 40 - x
y = 40 - 20
y = 20 feet
The area will be:
A = x * y
A = 20 * 20
A = 400 feet ^ 2
Answer:
The dimensions are:
x = 20 feet
y = 20 feet
The area is:
A = 400 feet ^ 2
Answer:
The measure of the vertex angle is 94 degrees ⇒ A
Step-by-step explanation:
- In any triangle, the sum of the measures of its interior angle is 180°
- In the isosceles triangle, the two base angles are equal in measures
∵ In an isosceles triangle, the measure of the base angle = (2x + 5)
∵ The base angles of the isosceles triangles are equal in measures
∴ The measures of the base angles are (2x + 5), (2x + 5)
∵ The measure of the vertex angle = (5x - 1)
∵ The sum of the measure of the three angles = 180°
∴ (2x + 5) + (2x + 5) + (5x - 1) = 180
→ Add the like terms in the left side
∵ (2x + 2x + 5x) + (5 + 5 + -1) = 180
∴ 9x + 9 = 180
→ Subtract 9 from both sides
∴ 9x + 9 - 9 = 180 - 9
∴ 9x = 171
→ Divide both sides by 9 to find x
∴ x = 19
→ Substitute the value of x in the measure of the vertex angle to find it
∵ The measure of the vertex angle = 5x - 1
∴ The measure of the vertex angle = 5(19) - 1
∴ The measure of the vertex angle = 95 - 1
∴ The measure of the vertex angle = 94°
∴ The measure of the vertex angle is 94 degrees
