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3 years ago

The lines shown below are parallel. If the green line has a slope of -14, what

Mathematics

1 answer:

Goshia [24]3 years ago

6 0

Answer:

-1/11

Step-by-step explanation:

Parallel lines have the same slope, but different y-intercepts. So, if the slope of the green line is -1/11, then the slope of the red line would also be -1/11.

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Please please help!!

shepuryov [24]

Answer:

$\large\boxed{x=0\ and\ x=\pi}$

Step-by-step explanation:

$\tan^2x\sec^2x+2\sec^2x-\tan^2x=2\\\\\text{Use}\ \tan x=\dfrac{\sin x}{\cos x},\ \sec x=\dfrac{1}{\cos x}:\\\\\left(\dfrac{\sin x}{\cos x}\right)^2\left(\dfrac{1}{\cos x}\right)^2+2\left(\dfrac{1}{\cos x}\right)^2-\left(\dfrac{\sin x}{\cos x}\right)^2=2\\\\\left(\dfrac{\sin^2x}{\cos^2x}\right)\left(\dfrac{1}{\cos^2x}\right)+\dfrac{2}{\cos^2x}-\dfrac{\sin^2x}{\cos^2x}=2$

$\dfrac{\sin^2x}{(\cos^2x)^2}+\dfrac{2-\sin^2x}{\cos^2x}=2\\\\\text{Use}\ \sin^2x+\cos^2x=1\to\sin^2x=1-\cos^2x\\\\\dfrac{1-\cos^2x}{(\cos^2x)^2}+\dfrac{2-(1-\cos^2x)}{\cos^2x}=2\\\\\dfrac{1-\cos^2x}{(\cos^2x)^2}+\dfrac{2-1+\cos^2x}{\cos^2x}=2\\\\\dfrac{1-\cos^2x}{(\cos^2x)^2}+\dfrac{1+\cos^2x}{\cos^2x}=2$

$\dfrac{1-\cos^2x}{(\cos^2x)^2}+\dfrac{(1+\cos^2x)(\cos^2x)}{(\cos^2x)^2}=2\qquad\text{Use the distributive property}\\\\\dfrac{1-\cos^2x+\cos^2x+\cos^4x}{\cos^4x}=2\\\\\dfrac{1+\cos^4x}{\cos^4x}=2\qquad\text{multiply both sides by}\ \cos^4x\neq0\\\\1+\cos^4x=2\cos^4x\qquad\text{subtract}\ \cos^4x\ \text{from both sides}\\\\1=\cos^4x\iff \cos x=\pm\sqrt1\to\cos x=\pm1\\\\ x=k\pi\ for\ k\in\mathbb{Z}\\\\\text{On the interval}\ 0\leq x$

4 0

2 years ago

On March 1, 2022, Carla Vista Co. acquired real estate, on which it planned to construct a small office building, by paying $79,

const2013 [10]

Answer:

Cost of the land = $90,900

Step-by-step explanation:

Cash Paid for the construction = $79,000

Cost of demolition of the old warehouse = $8,000

Salvage (i.e Proceeds from the salvaged materials) = $1,660

Additional Expenditure before construction began

Attorney's fee = $1,160

Real estate broker's fee = $4,400

Architect's fee = $8,660 ( Note that this will be capitalized to building cost)

Driveways and parking lot = $13,800 ( Note that this is capitalized to land improvements)

Sum of additional expenditure = Attorney's fee + Real estate broker's fee

Sum of the additional expenditure = 1160 + 4400

Sum of the additional expenditure = $5,560

Cost of the land = Cash paid + cost of demolition + Additional expenditure - salvage

Cost of the land = 79000 + 8000 + 5560 - 1660

Cost of the land = $90,900

3 0

3 years ago

Read 2 more answers

At a hardware store, each wooden plank costs $3.57. How much do 12 planks cost?

777dan777 [17]

To find this answer, we need to multiply 3.57 by 12.
$3.57 * 12 = 42.84$
Therefore, 12 planks will cost $42.84.

5 0

3 years ago

Read 2 more answers

Factor completely. x2+7x−18 Answer now PLZZZZZ

zimovet [89]

Answer: ( − 2) ( + 9)

4 0

3 years ago

A King in ancient times agreed to reward the inventor of chess with one grain of wheat on the first of the 64 squares of a chess

statuscvo [17]

Let's start by visualising this concept.

Number of grains on square:
1 2 4 8 16 ...

We can see that it starts to form a geometric sequence, with the common ratio being 2.

For the first question, we simply want the fifteenth term, so we just use the nth term geometric form:
$T_n = ar^{n - 1}$
$T_{15} = 2^{14} = 16384$

Thus, there are 16, 384 grains on the fifteenth square.

The second question begs the same process, only this time, it's a summation. Using our sum to n terms of geometric sequence, we get:
$S_n = \frac{a(r^{n} - 1)}{r - 1}$
$S_{15} = \frac{2^{15} - 1}{2 - 1}$
$S_{15} = 2^{15} - 1 = 32767$

Thus, there are 32, 767 total grains on the first 15 squares, and you should be able to work the rest from here.

6 0

2 years ago

Read 2 more answers