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3 years ago

For f(x)=4x+1 and g(x)=x^2-5,find(f•g)(4)

Mathematics

2 answers:

RoseWind [281]3 years ago

8 0

Answer:

(f•g)(4) = 45

Step-by-step explanation:

f(x)=4x+1

g(x)=x^2-5

(f•g)(x) = 4(x^2 -5)+1

(f•g)(4) = 4(4^2 -5)+1

(f•g)(4) = 4(16-5)+1

(f•g)(4) = 4(11)+1

(f•g)(4) = 44 + 1

(f•g)(4) = 45

lianna [129]3 years ago

4 0

Answer:

Step-by-step explanation:

Assuming f∘g, it is the function composition of two given function. So, f(g(x))=(f∘g)(x).

Function Composition is when we nest two functions creating another one, so if we nest f(x) and g(x) we'll have another one f(g(x)).

If f(x)=4x+1 and g(x)=x^2-5, (fg)(x)

If we replace x in the second function, namely, g(x) then we have:

f(g(x))

$4(x^2-5)+1=0\\\\4x^2-20+1=0\\\\4x^2-19=0$

Now, let's plug it in the value of 4 for x

$f(g(4))=4(4)^2-19\\$

$(f(g(4))=45$

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A string passing over a smooth pulley carries a stone at one end. While its other end is attached to a vibrating tuning fork and

nasty-shy [4]

Answer:

correct option is C) 2.8

Step-by-step explanation:

given data

string vibrates form = 8 loops

in water loop formed = 10 loops

solution

we consider mass of stone = m

string length = l

frequency of tuning = f

volume = v

density of stone = $\rho$

case (1)

when 8 loop form with 2 adjacent node is $\frac{\lambda }{2}$

so here

$l = \frac{8 \lambda _1}{2}$ ..............1

$l = 4 \lambda_1\\\\\lambda_1 = \frac{l}{4}$

and we know velocity is express as

velocity = frequency × wavelength .....................2

$\sqrt{\frac{Tension}{mass\ per\ unit \length }}$ = f × $\lambda_1$

here tension = mg

$\sqrt{\frac{mg}{\mu}}$ = f × $\lambda_1$ ..........................3

and

case (2)

when 8 loop form with 2 adjacent node is $\frac{\lambda }{2}$

$l = \frac{10 \lambda _1}{2}$ ..............4

$l = 5 \lambda_1\\\\\lambda_1 = \frac{l}{5}$

when block is immersed

equilibrium eq will be

Tenion + force of buoyancy = mg

T + v × $\rho$ × g = mg

and

T = v × $\rho$ - v × $\rho$ × g

from equation 2

f × $\lambda_2$ = f × $\frac{1}{5}$

$\sqrt{\frac{v\rho _{stone} g - v\rho _{water} g}{\mu}} = f \times \frac{1}{5}$ .......................5

now we divide eq 5 by the eq 3

$\sqrt{\frac{vg (\rho _{stone} - \rho _{water})}{\mu vg \times \rho _{stone}}} = \frac{fl}{5} \times \frac{4}{fl}$

solve irt we get

$1 - \frac{\rho _{stone}}{\rho _{water}} = \frac{16}{25}$

relative density $\frac{\rho _{stone}}{\rho _{water}} = \frac{25}{9}$

relative density = 2.78 ≈ 2.8

so correct option is C) 2.8

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3 years ago

Which equation has a graph that is a parabola with a vertex at (–2, 0)?

MaRussiya [10]

Answer:

The vertex of a quadratic equation corresponds to the point where the maximum or minimum value is located.

If the function has a positive leading coefficient, the vertex corresponds to the minimum value.

If it has a negative leading coefficient, the vertex corresponds to the maximum valuevalue

If the vertex is located at

(–2, 0)

The possibilities are

y = (x-2)^2

or,

y = - (x-2)^2

Since the problem tells us the answer, we adopt the positive values

Answer:

y = (x-2)^2

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2 years ago

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2 years ago

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Help me with this math problem please

mrs_skeptik [129]

Answer:

$y=8$

$RS=77, ST=31$

Step-by-step explanation:

Note that the entire segment RT is the combined lengths of RS and ST. So:

$RT=RS+ST$

We know that RT is 108, RS is (9y+5), and ST is (3y+7). Substitute:

$108=(9y+5)+(3y+7)$

On the right, combine like terms:

$108=(9y+3y)+(5+7)$

Add:

$108=12y+12$

Subtract 12 from both sides. The right cancels:

$96=12y$

Divide both sides by 12:

$y=8$

So, the value of y is 8.

To find RS and ST, substitute 8 for y. So:

$RS=9y+5$

Substitute 8 for y:

$RS=9(8)+5$

Multiply:

$RS=72+5$

Add:

$RS=77$

Do the same for ST:

$ST=3y+7$

Substitute 8 for y:

$ST=3(8)+7$

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$ST=24+7$

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What is the value of -16 +9?

ki77a [65]

Answer

the answer is -7

Step-by-step explanation: −(16−9) =-7

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3 years ago