hectictar

I don't know how to make an "inequality" out of this, but I can tell you Elliot's height exactly.

Sam is 5 feet tall. Sam is 2 feet taller than Elliot.

5 + 2 = Elliot's height.

7 feet = Elliot's height.

\((\frac{7 + (2 + 6) 2 ÷ 4 ⋅ 1}{2})^{4}\)

Just follow the orders of operation: Parenthesees, Exponents, Multiplication/Division, Addtion/Subtraction

\(= (\frac{7 + (8) 2 ÷ 4 ⋅ 1}{2})^{4}\)

\(=(\frac{7 + 16 ÷ 4 ⋅ 1}{2})^{4}\)

\(=(\frac{7 + 4 ⋅ 1}{2})^{4}\)

\(=(\frac{7 + 4}{2})^{4}\)

\(=(\frac{11}{2})^{4}\)

\(=(5.5)^{4}\)

\(=\frac{14641}{16} = 915.0625\)

First we need to find the length of the extra piece of triangle that isn't drawn on the picture, the part that is behind the man. Let's call that part "x." Two similar triangles are formed. The first one is formed by the man, the line of sight, and the ground, x. The second one is formed by the surveying pole, the line of sight, and the ground, x+10. Since these triangles are similar, the height of the man over the length of his ground equals the height of the pole over the length of its ground.

\(\frac{6}{x}=\frac{7}{x+10}\)

6(x+10)=7x

6x+60=7x

60=x

Now that we know x, we can make two different similar triangles. The first one is formed by the mountain, the line of sight, and the ground, c+60. The second is formed by the man, the line of sight, and the ground, 60.

So

\(\frac{m}{c+60}=\frac{6}{60}\)

Where "m" is the height of the mountain. Before we put "c" in, we have to convert it to feet. 5 miles = 5(5280) ft = 26400 ft.

\(\frac{m}{26400+60}=\frac{6}{60}\)

\(\frac{m}{26460}=\frac{6}{60}\)

m = 0.1(26460) = 2,646 ft

2.25+2.25-2(1.5x1.5) x (cos 1.5)

Rewrite it to take out the "x" multiplication signs. Also I'm assuming it's 1.5 degrees.

2.25+2.25-(2)(1.5)(1.5)(cos 1.5°)

= 4.5 - 4.5(cos 1.5°)

≈ 4.5 - 4.5(0.9996573)

≈ 0.001542

7(g-4) = 42

To solve for g, first divide both sides by 7.

(g-4) = 6

g-4 = 6

Then add four to both sides.

g = 10

x²+4x-5x²-1

= -4x² + 4x - 1

= \(-4(x^{2}-x+\frac{1}{4})\)

= \(-4(x - \frac{1}{2})(x - \frac{1}{2})\)

= \(-4(x - \frac{1}{2})^{2}\)

The wall, ladder and ground form a right triangle. The hypotenuse is the ladder, which is 20 ft.

sin85°= x/20

20sin85°=x

x ≈ 19.924 ft.

arctan x = 90°

tangent both sides

tan(arctan x) = tan 90°

x = undefined, its 1/0

I got 1.375301942 just from plugging the whole thing ito my calculator.

(110-90)/[(110+90)/2]/(12-8)/[(12+8)/2]

= (20)/[(200)/2]/(4)/[(20)/2]

= 20/[100]/4/[10]

= 0.2/4/10

= 0.05/10

= 0.005