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3 years ago

Combine like terms to create an equivalent expression 2/5m - 4/5 - 3/5m

Mathematics

1 answer:

AnnZ [28]3 years ago

3 0

Answer:

-1/5m-4/5

Step-by-step explanation:

2/5m-4/5-3/5m

2/5m-3/5m-4/5

-1/5m-4/5

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100 points!!! Pre calculus. I need helpppppppppp

Fantom [35]

Answer:

We have function,

$y = 3 - 6 \sin {}^{} (2x + \frac{\pi}{2} )$

Standard Form of Sinusoid is

$y = - 6 \sin(2x + \frac{\pi}{2} ) + 3$

Which corresponds to

$y = a \sin(b(x + c)) + d$

where a is the amplitude

2pi/b is the period

c is phase shift

d is vertical shift or midline.

In the equation equation, we must factor out 2 so we get

$y = - 6(2(x + \frac{\pi}{4} )) + 3$

Also remeber a and b is always positive

So now let answer the questions.

a. The period is

$\frac{2\pi}{ |b| }$

$\frac{2\pi}{ |2| } = \pi$

So the period is pi radians.

b. Amplitude is

$| - 6| = 6$

Amplitude is 6.

c. Domain of a sinusoid is all reals. Here that stays the same. Range of a sinusoid is [-a+c, a-c]. Put the least number first, and the greatest next.

So using that<em> rule, our range is [6+3, -6+3]= [9,-3] So our range</em> is [-3,9].

D. Plug in 0 for x.

$3 - 6 \sin((2(0) + \frac{\pi}{2} )$

$3 - 6 \sin( \frac{\pi}{2} )$

$3 - 6(1)$

$3 - 6$

$= - 3$

So the y intercept is (0,-3)

E. To find phase shift, set x-c=0 to solve for phase shift.

$x + \frac{\pi}{4} = 0$

$x = - \frac{\pi}{4}$

Negative means to the left, so the phase shift is pi/4 units to the left.

f. Period is PI, so use interval [0,2pi].

Look at the graph above,

6 0

3 years ago

A grocer mixed pecans worth $0.84 per pound with cashews worth $1.40 per pound. If he made 88 pounds of a mixture worth $1.26 pe

Vsevolod [243]

Answer:

There are 22 pounds of pecans in the mixture

Step-by-step explanation:

Let the number of pounds of pecans be p and the number of cashews be c

We have 88 pounds in total, mathematically, this means;

c + p = 88

Now, the 88 mixtures cost $1.4 per pounds. This means the total amount of the 88 would be 88 * 1.26= $110.88

The pecans are worth 0.84 per pound while the cashews are worth 1.4 per pound. If the total is at a cost of 110.88, this can be translated mathematically as:

0.84p + 1.4c = 110.88

We now have two different equations that we can solve simultaneously.

c + p = 88

0.84p + 1.4c = 110.88

From the first equation, we can say c = 88 - p

We can then substitute the into the second equation:

0.84p + 1.4(88 - p) = 110.88

0.84p + 123.2 - 1.4p = 110.88

-0.56p = 110.88 - 123.2

0.56p = 12.32

p = 12.32/0.56 = 22

Now, we know c = 88 - p = 88 - 22 = 66