Answer:
7 terms
Step-by-step explanation:
A term is a single mathematical expression. It may be a single number (positive or negative), a single variable ( a letter ), several variables multiplied but never added or subtracted. Some terms contain variables with a number in front of them. ... Examples of single terms: 3x is a single term.
1. 3p: Add 6 to negative 3, and carry over the "p"
3. 6x: Subtract 1 from 7 and carry over the "x"
5. -4v: Add 6 to negative 10 and carry over the "v"
7. -4r + 9: Add 5 to -9 and carry over the "r". Then put "+9" after the variable, since the other 9 was by itself.
9. 14n: Add 5 to 9 and carry over the "n".
I hope this helps!
72+k is equal to 180. So if you set up a equation if looks like:
72+k=180
Subtract 72 from both sides
K=108°
Your answer is 108°
Answer:
<h2><em>
2ft by 2ft by 1 ft</em></h2>
Step-by-step explanation:
Total surface of the cardboard box is expressed as S = 2LW + 2WH + 2LH where L is the length of the box, W is the width and H is the height of the box. Since the cardboard box is without a lid, then the total surface area will be expressed as;
S = lw+2wh+2lh ... 1
Given the volume V = lwh = 4ft³ ... 2
From equation 2;
h = 4/lw
Substituting into r[equation 1;
S = lw + 2w(4/lw)+ 2l(4/lw)
S = lw+8/l+8/w
Differentiating the resulting equation with respect to w and l will give;
dS/dw = l + (-8w⁻²)
dS/dw = l - 8/w²
Similarly,
dS/dl = w + (-8l⁻²)
dS/dw = w - 8/l²
At turning point, ds/dw = 0 and ds/dl = 0
l - 8/w² = 0 and w - 8/l² = 0
l = 8/w² and w =8/l²
l = 8/(8/l² )²
l = 8/(64/I⁴)
l = 8*l⁴/64
l = l⁴/8
8l = l⁴
l³ = 8
l = ∛8
l = 2
Hence the length of the box is 2 feet
Substituting l = 2 into the function l = 8/w² to get the eidth w
2 = 8/w²
1 = 4/w²
w² = 4
w = 2 ft
width of the cardboard is 2 ft
Since Volume = lwh
4 = 2(2)h
4 = 4h
h = 1 ft
Height of the cardboard is 1 ft
<em>The dimensions of the box that requires the least amount of cardboard is 2ft by 2ft by 1 ft</em>
Area of a triangle: 1/2 of area*height
(4*4)/2
16/2 = 8
8 * 4, since there are 4 triangles. = 32
18 * 8 (for the square) = 144
144 - 32 = 112 inches squared.
The triangles aren't shaded, so you can subtract them from the area of the rectangle to get the shaded area. The answer is 112 inches squared.
