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3 years ago

An apple cost Php x per piece. How many will 3 dozen cost?

Mathematics

1 answer:

Gwar [14]3 years ago

6 0

D.Php 36x because 1 dozen is = 12 pieces so if there’s 3 dozen of apple it would be 12 x 3 the answer which is 36

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Elapsed time is 4 hours and 51 minutes, what is the start time?

Vlada [557]

Answer:

may 22

Step-by-step explanation:

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4 years ago

A. Use composition to prove whether or not the functions are inverses of each other. B. Express the domain of the compositions u

Kryger [21]

Given: $f(x) = \frac{1}{x-2}$

$g(x) = \frac{2x+1}{x}$

A.)Consider

$f(g(x))= f(\frac{2x+1}{x} )$

$f(\frac{2x+1}{x} )=\frac{1}{(\frac{2x+1}{x})-2}$

$f(\frac{2x+1}{x} )=\frac{1}{\frac{2x+1-2x}{x}}$

$f(\frac{2x+1}{x} )=\frac{x}{1}$

$f(\frac{2x+1}{x} )=1$

Also,

$g(f(x))= g(\frac{1}{x-2} )$

$g(\frac{1}{x-2} )= \frac{2(\frac{1}{x-2}) +1 }{\frac{1}{x-2}}$

$g(\frac{1}{x-2} )= \frac{\frac{2+x-2}{x-2} }{\frac{1}{x-2}}$

$g(\frac{1}{x-2} )= \frac{x }{1}$

$g(\frac{1}{x-2} )= x$

Since, $f(g(x))=g(f(x))=x$

Therefore, both functions are inverses of each other.

For the Composition function $f(g(x)) = f(\frac{2x+1}{x} )=x$

Since, the function $f(g(x))$ is not defined for $x=0$ .

Therefore, the domain is $(-\infty,0)\cup(0,\infty)$

For the Composition function $g(f(x)) =g(\frac{1}{x-2} )=x$

Since, the function $g(f(x))$ is not defined for $x=2$ .

Therefore, the domain is $(-\infty,2)\cup(2,\infty)$

8 0

4 years ago

Solve for x.<br> 4^0.2x + 6 = 43, enter your answe with four decimal places.

Juliette [100K]

Answer:

13.0236

Step-by-step explanation:

4^0.2x +6=43

(2^2)^0.2x +6=43

2^2*0.2x +6=43

4 0

2 years ago

Which is true regarding the triangular frame? It is an acute triangle. About 0.8 foot needs to be removed from the 20-foot board

Ivanshal [37]

Question:

Arielle is building the wooden framework for the roof of a house. she needs the angle created by the vertical and horizontal boards of the frame to be a right angle. the height of the vertical board is 12 feet. the length of the horizontal board is 15 feet. the support beam that will connect the ends of the two boards measures 20 feet. which is true regarding the triangular frame? it is an acute triangle. about 0.8 foot needs to be removed from the 20-foot board to create a right triangle. it is an obtuse triangle. about 0.8 foot needs to be removed from the 20-foot board to create a right triangle. it is an acute triangle. about 7 feet need to be removed from the 20-foot board to create a right triangle. it is an obtuse triangle. about 7 feet need to be removed from the 20-foot board to create a right triangle.

Answer:

It is an obtuse triangle.About 0.8 foot needs to be removed from the 20 foot board to create a right triangle.

Explanation:

Let us use pythagorean theorem to check whether it is a right triangle.

The vertical board is 12 feet and the horizontal board is 15 feet.

By pythagoean theorem,

$\begin{aligned}c^{2} &=12^{2}+15^{2} \\&=144+225 \\c &=\sqrt{369} \\c &=19.2\end{aligned}$

Thus, we need to remove 0.8 foot from the 20 foot board to create a right triangle.

Now, we shall find the angle of the triangle.

Since, the vertical board is 12 and the horizontal board is 15 feet, the tangent ratio is given by opposite/adjacent.

$\begin{aligned}\tan x &=\frac{o p p}{a d j} \\&=\frac{15}{12}\end{aligned}$

To find the angle x, we shall take $tan^{-1}$ on both sides,

$\begin{aligned}\tan ^{-1}(\tan x) &=\tan ^{-1} \frac{15}{12} \\x &=51.34^{\circ}\end{aligned}$

The total angle of the triangle is $51.34+51.34=102.68$ which is an obtuse triangle.

5 0

3 years ago

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Logs5(3x-2) = 1 + Logs5 (x-4)

AnnZ [28]

Answer:

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3 years ago