12x+32=12x-7 how many solutions are there to the equation?

The figure shows part of a freeway interchange. The raised freeway is supported by vertical, parallel pillars. Set up a ratio an

Ugo [173]

We will use ratio and proportion between the inclined sides with its corresponding horizontal bases. Then we could determine for the value of segment AQ.

PA/SB = AQ/BR
32/30 = AQ/24
AQ = 25.6 yd

Since what is asked is segment PQ,
PQ = PA + AQ
PQ = 32 + 25.6
PQ = 57.6 yards

7 0

3 years ago

Use the identity tan(theta) = sin(theta) / cos(theta) to show that tan(???? + ????) = tan(????)+tan(????) / 1−tan(????) tan(????

VMariaS [17]

Answer:

See the proof below.

Step-by-step explanation:

For this case we need to proof the following indentity:

$tan(x+y) = \frac{tan (x) + tan(y)}{1- tan(x) tan(y)}$

So we need to begin with the definition of tangent, we know that $tan (x) =\frac{sin(x)}{cos(x)}$ and we can do this:

$tan (x+y) = \frac{sin (x+y)}{cos(x+y)}$ (1)

We also have the following identities:

$sin (a+b) = sin (a) cos(b) + sin (b) cos(a)$

$cos(a+b)= cos(a) cos(b) - sin(a) sin(b)$

Now we can apply those identities into equation (1) like this:

$tan (x+y) =\frac{sin (x) cos(y) + sin (y) cos(x)}{cos(x) cos(y) - sin(x) sin(y)}$ (2)

We can divide numerator and denominator from expression (2) by $\frac{1}{cos(x) cos(y)}$ we got this:

$tan (x+y) = \frac{\frac{sin (x) cos(y)}{cos (x) cos(y)} + \frac{sin(y) cos(x)}{cos(x) cos(y)}}{\frac{cos(x) cos(y)}{cos(x) cos(y)} -\frac{sin(x)sin(y)}{cos(x) cos(y)}}$

And simplifying we got:

$tan (x+y) = \frac{tan(x) + tan(y)}{1-tan(x) tan(y)}$

And that complete the proof.

8 0

3 years ago

What is the volume of a cube with a length of 4/5 m?

a_sh-v [17]

Answer:

64/125 cubic meter

Step-by-step explanation:

volume = l × b × h

volume of a cube = s × s × s

∴ 4/5 × 4/5 × 4/5 = 64/125

8 0

3 years ago

Which expression is equivalent to 1.5 raised to the fifth power divided by 0.7 raised to the fourth power, all raised to the thi

harina [27]

The expression which is equivalent to the given expression as in the task content is; 1.5 raised to the fifteenth power divided by 0.7 raised to the twelfth power.

<h3>What is the expression which is equivalent to the given expression?</h3>

According to the task content, it follows that the expression given is;

(1.5⁵/0.7⁴)³

= 1.5^(3×5) /0.7^(4×3)

= 1.5¹⁵/0.7¹².

Hence, the expression which is equivalent is; 1.5 raised to the fifteenth power divided by 0.7 raised to the twelfth power.