For me, it’s easiest when i distribute the negative sign if i need to and then reorder to put the like terms together. and then solve.
(also sorry if it’s a little confusing with all the parentheses, i use them because it helps me organize everything)
21. (4x-9y) + (6x+10) + (8y-4)
= 4x + 6x - 9y + 8y + 10 - 4
= 10x - y + 6
—> D
22. (6x+9y-15) + (2x-9y+8)
= 6x + 2x + 9y - 9y - 15 + 8 (the 9y - 9y = 0, so you can leave it out of the final equation)
= 8x - 7
—> D
23. (9x^2-8x+3) - (5x^2-6x+4)
= 9x^2 - 8x + 3 - 5x^2 -(-6x) - 4
= 9x^2 - 5x^2 - 8x + 6x + 3 - 4 (remember that two - signs next to each other make a + sign)
= 4x^2 - 2x - 1
—> A
24. (9x^3-7x+8) - (5x^2+7x-10)
= 9x^3 - 7x + 8 - 5x^2 - 7x -(-10)
= 9x^3 - 5x^2 - 7x - 7x + 8 + 10
= 9x^3 - 5x^2 - 14x + 18
—> D
25. (6x+14y) - ((7x+5y) + (x-8y))
= (6x+14y) - (7x + x + 5y - 8y)
= (6x+14y) - (8x-3y)
= 6x + 14y - 8x -(-3y)
= 6x - 8x + 14y + 3y
= -2x + 17y
—> B
Answer: old McDonald has 54 chickens and 2 cows.
Step-by-step explanation:
Let x represent the number of chickens that old McDonald have.
Let y represent the number of cows that old McDonald have.
He counted 56 heads. A chicken and a cow has one head each. It means that
x + y = 56
He counted 116 legs. A chicken has 2 legs and a cow has 4 legs. It means that
2x + 4y = 116 - - - - - - - - -1
Substituting x = 56 - y into equation 1, it becomes
2(56 - y) + 4y = 116
112 - 2y + 4y = 116
- 2y + 4y = 116 - 112
2y = 4
y = 4/2 = 2
x = 56 - y = 56 - 2
x = 54
Hello there!
To find the zeroes or the roots of a function, you just need to set the function equal to 0 then solve for x
f(x) = 2x² - 8x - 10
Set function equal to 0
2x² - 8x - 10 = 0
Now we can factorize the left side
2(x + 1)(x - 5) = 0
Then set factors equal to 0
x + 1 = 0 or x - 5 = 0
x = 0 - 1 or x = 0 + 5
x = -1 or x = 5
Thus,
The roots are -1 and 5
Let me know if you have any questions. As always, it is my pleasure to help students like you~!
The answer is $911.68.
After a little research on the internet, I found the design of the window.
First, you need to find the area of the window which is a composite figure made up of a rectangle and a circle. So, the total area (A) is the sum of the area of the rectangle (A1) and the area of the circle (A2).
Area of the rectangle with length l and width w is:
A = l * w
According to the image, l = 5 ft and w = 4 ft.
A1 = 5 * 4 = 20 ft²
Area of the circle with radius r is:
A = r²π
According to the image, r = 2 ft.
A2 = 2² * 3.14 = 12.56 ft²
The area of the window is:
A = A1 + A = 20 ft² + 12.56 ft² = 32.56 ft²
<span>The glass costs $28 per square foot, so to replace the glass will cost:
</span>32.56 ft² * $28/ft² = $911.68
