Answer:
x = 4, y = 2
Step-by-step explanation:
Start by multiplying the first equation by 2:
2x + 2y = 12 --> 4x + 4y = 24
Subtract the second from the first:
4x + 4y = 24
- 5x + 4y = 28
4x - 5x = -x
4y = 4y = 0
24 - 28 = -4
so you end with -x + 0 = -4
Solve for x to get x = 4
Plug x = 4 back into 2x + 2y = 12 to find y.
2(4) + 2y = 12
8 + 2y = 12
2y = 4
y = 2
You can solve using the pythagorean theorem which is
a^2+b^2=c^2 where a and b are the legs and c is the hypotenuse in a right triangle.
12^2+x^2=24^2
144+x^2=576
x^2=432
x =20.78 (approximately)
Heya!
Question #15:
To find the perimeter of the object, you can count the amount of squares that are on the outside of the object. After you country all around the object, the perimeters is 22 units (Option D)
Question #16:
Since we know the total perimeter, we can divide by the amount of sides a hexagon has because all of the sides are the same length. A hexagon has 6 sides. 42 / 6 = 7 inches (Option A)
Question #17:
To calculate the perimeter of the rectangle, you can add all the sides together. First, find common denominators.
6 1/2 = 6 2/4 and 3 1/4
Now, add all the sides together.
6 2/4 + 6 2/4 + 3 1/4 + 3 1/4 = 19 1/2 cm (Option B)
Question #18:
We can find the perimeter of the semi circle and square separately. Only take the perimeter of the square using 3 sides since the fourth sides is in the semi circle.
8 + 8 + 8 = 24 inches
Circumference of a semi circle formula: C = πd
C = (3.14)(8)
C = 25.12
Now, add both perimeters together.
24 + 25.12 = 49.12 inches (Option D)
Best of Luck!
X = approximately 633
Steps:
lnx + ln3x = 14
ln3x^2 = 14 : Use the log property of addition which is to multiply same log together so you multiply x and 3x because they have log in common
(ln3x^2) = (14) : take base of e on both sides to get rid of the log
e e
3x^2 = e^14 : e cancels out log on the left side and the right side is e^14
x^2 = e^14 / 3 : divide both sides by 3
√x^2 = <span>√(e^14 / 3) : take square root on both sides to get rid of the square 2 on x
</span>
x = √(e^14) / <span>√3 : square root cancels out square 2 leaving x by itself
x = e^7 / </span>√3 : simplify the √(e^14) so 14 (e^14) divide by 2 (square root) = 7<span>
x = </span>633.141449221 : solve
