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jeyben [28]
3 years ago
15

If 8a + 3b + 2c = 3, what is 64a+24b+16c?

Mathematics
2 answers:
Dmitrij [34]3 years ago
5 0

Answer:

64a+24b+16c = 24

Step-by-step explanation:

Given :  8a + 3b + 2c = 3

We have to find the value of 64a+24b+16c

Consider 64a+24b+16c

Taking 8 common from each term , we have,

64a+24b+16c = 8(8a + 3b + 2c)

Also, given  8a + 3b + 2c = 3

Then , 64a+24b+16c = 8(8a + 3b + 2c)

= 8(3)

Simplify , we have,

= 24

Thus, 64a+24b+16c = 24

algol [13]3 years ago
3 0
The second expression is 8 times the first so the answer is 3 * 8 = 24.
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GREYUIT [131]

Answer:

To find the inverse of:

f (x)=\dfrac{4}{x-2}-1

Set the function to y:

\implies y=\dfrac{4}{x-2}-1

Rearrange to make x the subject:

\implies y+1=\dfrac{4}{x-2}

\implies (y+1)(x-2)=4

\implies xy-2y+x-2=4

\implies xy+x=2y+6

\implies x(y+1)=2y+6

\implies x=\dfrac{2y+6}{y+1}

Swap x and y:

\implies y=\dfrac{2x+6}{x+1}

Change y to the inverse of the function sign:

\implies f\:^{-1}(x)=\dfrac{2x+6}{x+1}

Rewrite g(x) as a fraction:

g(x)=\dfrac{3}{x+2}-2

\implies g(x)=\dfrac{3}{x+2}-\dfrac{2(x+2)}{x+2}

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\implies g(x)=\dfrac{3-2x-4}{x+2}

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1 year ago
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7 0
2 years ago
The cosine of 23° is equivalent to the sine of what angle
Archy [21]

Answer:

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(There are more values since we can go around the circle from 67 degrees numerous times.)

Step-by-step explanation:

You can use a co-function identity.

The co-function of sine is cosine just like the co-function of cosine is sine.

Notice that cosine is co-(sine).

Anyways co-functions have this identity:

\cos(90^\circ-x)=\sin(x)

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\sin(90^\circ-x)=\cos(x)

You can prove those drawing a right triangle.

I drew a triangle in my picture just so I can have something to reference proving both of the identities I just wrote:

The sum of the angles is 180.

So 90+x+(missing angle)=180.

Let's solve for the missing angle.

Subtract 90 on both sides:

x+(missing angle)=90

Subtract x on both sides:

(missing angle)=90-x.

So the missing angle has measurement (90-x).

So cos(90-x)=a/c

and sin(x)=a/c.

Since cos(90-x) and sin(x) have the same value of a/c, then one can conclude that cos(90-x)=sin(x).

We can do this also for cos(x) and sin(90-x).

cos(x)=b/c

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This means sin(90-x)=cos(x).

So back to the problem:

cos(23)=sin(90-23)

cos(23)=sin(67)

So 67 degrees is one value that we can take the sine of such that is equal to cos(23 degrees).

6 0
2 years ago
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Check the picture below.

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For this problem, let (-5, -4) be the "first" point, so  x1 = -5  and  y2 = -4

                      and let (-6, 4) be the "second" point, so  x2 = -6  and  y2 = 4.

 

Then:  d  =  sqrt( (-6 - -5)2 + (4 - -4)2 )  =  sqrt( (-1)2 + (8)2 )  =  sqrt( 1 + 64 )  =  sqrt( 65)

 

The distance formula is just the Pythagorean Theorem applied to an x-y graph.

 

You would get the same final answer if you let (-5, -4) be the second point and (-6, 4) be the first point.

6 0
2 years ago
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