Answer:
5x +4y
Step-by-step explanation:
The perimeter of a triangle is the sum of side lengths. That fact can be used to find z, the length of the third side.
(2x +3y) +(5x -2y) +z = 12x +5y . . . . sum of sides is perimeter
z = (12x +5y) -(7x +y) . . . . . . . . . . . . subtract (7x+y) from both sides
z = 5x +4y . . . . . . . . . collect terms; the length of the third side
The third side of the triangle is (5x +4y).
Answer:
1,280
Step-by-step explanation:
Answer:
The other side was decreased to approximately .89 times its original size, meaning it was reduced by approximately 11%
Step-by-step explanation:
We can start with the basic equation for the area of a rectangle:
l × w = a
And now express the changes described above as an equation, using "p" as the amount that the width is changed:
(l × 1.1) × (w × p) = a × .98
Now let's rearrange both of those equations to solve for a / l. Starting with the first and easiest:
w = a/l
now the second one:
1.1l × wp = 0.98a
wp = 0.98a / 1.1l
1.1 wp / 0.98 = a/l
Now with both of those equalling a/l, we can equate them:
1.1 wp / 0.98 = w
We can then divide both sides by w, eliminating it
1.1wp / 0.98w = w/w
1.1p / 0.98 = 1
And solve for p
1.1p = 0.98
p = 0.98 / 1.1
p ≈ 0.89
So the width is scaled by approximately 89%
We can double check that too. Let's multiply that by the scaled length and see if we get the two percent decrease:
.89 × 1.1 = 0.979
That should be 0.98, and we're close enough. That difference of 1/1000 is due to rounding the 0.98 / 1.1 to .89. The actual result of that fraction is 0.89090909... if we multiply that by 1.1, we get exactly .98.
Answer:
(x, y) = (-1, 1)
Step-by-step explanation:
8x + y = −7
for y = 1
8x + 1 = -7
subtract 1 from boh sides
8x = -8
divide bot sides by 8
x = -1
(x, y) = (-1, 1)
Answer:
$3089.4
Step-by-step explanation:
A circle is a locus of a point such that its distance from a point known as the center is always constant.
The area of a circle is given by the formula:
Area = πr²; where r is the radius of the circle.
From the image attached, we can see that the garden is circular with a radius of 5.5 yard. Hence:
Amount of mulch needed to cover garden = area of garden = πr² = π(5.5)² = 95 yd²
Since mulch cost $32.52 per square yard, hence:
Cost of mulch needed = $32.52 per yd² * 95 yd² = $3089.4
