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2 years ago

Pleaseee help me asap

Mathematics

1 answer:

pychu [463]2 years ago

8 0

Answer:

k = 13.5

Step-by-step explanation:

Setup proportion and solve for k:

$\frac{k}{9} =\frac{4.5}{3} \\3k = 40.5\\k=13.5$

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For f(x) = 4x +1 and g(x) = x2 - 5, find (g/f) (x).

Softa [21]

Answer:

$\left(g/f\right)\left(x\right)=\frac{x}{4}-\frac{1}{16}-\frac{79}{16\left(4x+1\right)}$

Step-by-step explanation:

$f(x)=4x+1$

$g\left(x\right)=x^2\:-\:5$

(g/f)(x) = g(x) / f(x)

$=\:\frac{x^2\:-\:5}{4x+1}\:\:\:\:\:\:$

$=\frac{x}{4}+\frac{-\frac{x}{4}-5}{4x+1}$

$=\frac{x}{4}-\frac{1}{16}+\frac{-\frac{79}{16}}{4x+1}$

$=\frac{x}{4}-\frac{1}{16}-\frac{79}{16\left(4x+1\right)}$

Therefore,

$\left(g/f\right)\left(x\right)=\frac{x}{4}-\frac{1}{16}-\frac{79}{16\left(4x+1\right)}$

8 0

2 years ago

If you answer it correctly then I will give you brainliest 5 stars and a thank you

shepuryov [24]

Step-by-step explanation:

L H J because they are all on the same line.

8 0

2 years ago

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A calculator is required to obtain the final answer on this question. A solid metal sphere at room temperature 20oC is dropped i

yKpoI14uk [10]

Answer:

T = 47.1875°C

Step-by-step explanation:

Given:

Surrounding temp, Ts = 100°C

Initial Temperature ,T0= 20°C

Increase in temperature = 15°C

Final temperature, T = 20 + 15 = 35°C

Time, t = 9 seconds

Let's take Newton's law of cooling:

$T - Ts = (T_0 - Ts)e^k^t$

We'll solve for k

$35 - 100 = (20 - 100)e^9^k$

$-65 = (-80)e^9^k$

Divide both sides by -5

$13 = (16)e^9^k$

$9k = ln (\frac{13}{16})$

$k = \frac{1}{9} ln (\frac{13}{16})$

$k = -0.02307104053$

Let's now find the temperature of the ball after 18 seconds in boiling water.

Use the Newton's equation again:

$T - Ts = (T_0 - Ts)e^k^t$

$T - 100 = (20 - 100)e^-0.0^2^3^0^7^1^0^4^0^5^3^*^1^8$

$T - 100 = (-80)e^-0.0^2^3^0^7^1^0^4^0^5^3^*^1^8$

$T - 100= -52.8125$

$T = 100 - 52.8125$

T = 47.1875°C

Temperature of the ball after 18 seconds in boiling water is 47.1875°C

5 0

3 years ago

What is the equation of this line? y=−3/2x y=2/3x y=3/2x y=−2/3x Graph of a line passing through the origin and the point begin

iogann1982 [59]

Correct answer: y=(2/3)x

The line passes through the origin (0,0) and the pair (3,2)

the equation y=(2/3)x satisfies both points:

for (0,0): 0=(2/3)*0 = 0

for (3,2): 2 = (2/3)*3 = 2

and therefore is the correct linear function of the line described.

4 0

3 years ago

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A linear function includes the points (2, 3) and (6, 8). What is the rate of change of the linear function?

Sindrei [870]

Answer:

The rate of change of a linear function = 5/4

Step-by-step explanation:

Given that a linear function includes the points (2, 3) and (6, 8).

So we have the points

(2, 3)

(6, 8)

We know that the rate of change of a function is also termed as the slope of the function.

In other words, the slope of the linear function gives us the rate of change of the linear function.

Thus,

Determining the rate of change or slope between (2, 3) and (6, 8)

(x₁, y₁) = (2, 3)

(x₂, y₂) = (6, 8)

Using the formula

Rate of change = Slope = [y₂ - y₁] / [x₂ - x₁]

= [8 - 3 / [6 - 2]

= 5 / 4

Thus, the rate of change of a linear function = 5/4

7 0

2 years ago

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