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3 years ago

Math help please Let f(x)=x2+5 and g (x)=3x+4; find (g o f)(7); (g o f)(7)=; help me solve!! Please!

Mathematics

1 answer:

lorasvet [3.4K]3 years ago

5 0

f(x) = 2x

g(x) = x + 3

First let us find (fog)(x)

(fog)(x) = f(g(x)

= f(x+3)

= 2(x+3)

= 2x + 6

==> (fog)(x) = 2x + 6

Now let us find (gof)(x):

(gof)(x) = g(f(x)

= g(2x)

= 2x + 3

==> (gof)(x) = 2x + 3

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Subtract the fractions and simplify the answer 7 8/9-5 3/5

weeeeeb [17]

One way in which to do this problem would involve subtracting 5 from 7 (result: 2) and then subtracting 3/5 from 8/9.
To subtract 3/5 from 8/9, you'd need to find the lowest common denominator (LCD) of 3/5 and 8/9, convert both fractions to have this LCD, and then subtract.

The LCD is (5)(9)=45. Then 8/9 and 3/5 become 40/45 and 27/45.

Subtracting 27/45 from 40/45 results in the fraction 13/45.
Then the full solution is 2 13/45.

You could also do this problem by converting 7 8/9 and 5 3/5 into improper fractions:

71/9 - 28/5. Again, the LCD is 45. Can you rewrite both fractions with 45 as the common denominator and then perform the subtraction?

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3 years ago

7x + 5y = -10 solve for y

katen-ka-za [31]

The y intercept is (0,-2)

5 0

3 years ago

Read 2 more answers

Solve the equation for all real values of x. cosxtanx - 2 cos x=-1

IceJOKER [234]

Solution to equation $cosxtanx - 2 cos^2 x=-1$ for all real values of x is $x=2k\pi + \frac{\pi}{6} , x=2k\pi + \frac{5\pi}{6}$ .

Step-by-step explanation:

Here we have , $cosxtanx - 2 cos^2 x=-1$ . Let's solve :

⇒ $cosxtanx - 2 cos^2 x=-1$

⇒ $cosx(\frac{sinx}{cosx}) - 2 cos^2 x=-1$

⇒ $sinx = 2 cos^2 x-1$

⇒ $sinx = 2 (1-sin^2x)-1$

⇒ $sinx = 1-2sin^2x$

⇒ $2sin^2x+sinx-1=0$

By quadratic formula :

⇒ $sinx = \frac{-b \pm \sqrt{b^2-4ac} }{2a}$

⇒ $sinx = \frac{-1 \pm \sqrt{1^2-4(2)(-1)} }{2(2)}$

⇒ $sinx = \frac{-1 \pm3}{4}$

⇒ $sinx = \frac{1}{2} , sinx =-1$

⇒ $sinx = sin\frac{\pi}{6} , sinx = sin\frac{3\pi}{2}$

⇒ $x=\frac{\pi}{6} , x=\frac{3\pi}{2}$

But at $x=\frac{3\pi}{2}$ we have equation undefined as $cos\frac{3\pi}{2}=0$ . Hence only solution is :

⇒ $x=\frac{\pi}{6}$

Since , $sin(\pi -x)=sinx$

⇒ $x=\pi -\frac{\pi}{6} = \frac{5\pi}{6}$

Now , General Solution is given by :

⇒ $x=2k\pi + \frac{\pi}{6} , x=2k\pi + \frac{5\pi}{6}$

Therefore , Solution to equation $cosxtanx - 2 cos^2 x=-1$ for all real values of x is $x=2k\pi + \frac{\pi}{6} , x=2k\pi + \frac{5\pi}{6}$ .

3 0

3 years ago

How can I determine whether fractions are considered decimals

ArbitrLikvidat [17]

Yes they are but just in a different form. Fractions can be converted to a decimal. 3/5 can be shown as .6. Hope I helped!

3 0

3 years ago

If the base of a Pyramid has an area of 144sq ft And if the slant higher of the pyramid is 10ft what would be the higher of the

pogonyaev

Answer:

the height of the pyramid is 8 ft

Step-by-step explanation:

Considering the base of the pyramid to be square whose area is 144 sq ft

This means the side of the base would be √144 = 12 ft.

Now, if you will imagine a pyramid we can easily observe that

Height(H) , slant height( L=10 ft) and half of the side length( 6ft) make a right angle triangle. We can easily calculate height from Pythagoras theorem as

10^2 = H^2 +6^2

⇒ H^2 = 10^2-6^2 = 100-36 = 64

⇒ H = 8 ft

Therefore, the height of the pyramid is 8 ft

3 0

3 years ago