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Alex_Xolod [135]
3 years ago
12

If ƒ(x) = x − 4 and g(x) = 3x + 5, find (ƒ + g)(x).

Mathematics
2 answers:
siniylev [52]3 years ago
7 0

Answer:

(f+g)(x)=4x+1

Step-by-step explanation:

We are given the two functions:

f(x)=x-4\text{ and } g(x)=3x+5

And we want to find:

(f+g)(x)

This is equivalent to:

=f(x)+g(x)

By substitution:

=(x-4)+(3x+5)

Rearranging yields:

=(x+3x)+(-4+5)

Combine like terms:

=4x+1

Hence:

(f+g)(x)=4x+1

kvv77 [185]3 years ago
3 0

Answer:

please refer to the above attachment

\boxed{(4x + 1) \: is \: the \: right \: answer.}

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A pendulum is 45 cm long. When it swings, it travels along the arc of a circle and covers a distance of 27.5 cm. Calculate the a
11Alexandr11 [23.1K]

Answer: The angle through which the pendulum travels = 35^{\circ}.

Step-by-step explanation:

Formula: Length of arc: l= r\theta , where r= radius ( in radians) , \theta = central angle.

Given: Length of pendulum (radius) = 45 cm

Length of arc= 27.5 cm

Put these values in the formula, we get

27.5=45\theta\\\\\Rightarrow\theta=\dfrac{27.5}{45}=\dfrac{275}{450}\\\\\Rightarrow\ \theta=\dfrac{11}{18}\text{ radians}

In degrees ,

\theta=\dfrac{11}{18}\times\dfrac{180}{\pi}=\dfrac{110\times7}{22} \ \ \ \    [\pi=\dfrac{22}{7}]

\theta=35^{\circ}

Hence, the angle through which the pendulum travels = 35^{\circ}.

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3 years ago
15 pounds of beans are distributed equally into 10 bags to give out at the food bank. How many pounds of beans are in each bag?
Tems11 [23]

Answer:

1.5, or 1 1/2

Step-by-step explanation:

8 0
3 years ago
Which polynomial can be simplified to a difference of squares
Mrrafil [7]
<h2>Hello!</h2>

The answer is:

The polynomial that can be simplified to a difference of squares is the second polynomial:

16a^{2}-4a+4a-1=16a^{2}=(4a)^{2}-(1)^{2}=(4-1)(4+1)

<h2>Why?</h2>

To solve this problem, we need to look for which of the given quadratic terms given for the different polynomials can be a result of squaring (elevating by two).

So,

Discarding, we have:

The quadratic terms of the given polynomials are:

First=10a^{2}

Second=16a^{2}

Third=25a^{2}

Fourth=24a^{2}

We have that the coefficients of the quadratic terms that can be obtained by squaring are:

16a^{2} =(4a)^{2} \\\\25a^{2} =(5a)^{2}

The other two coefficients are not perfect squares since they can not be obtained by square rooting whole numbers.

So, the first and the fourth polynomial are discarded and cannot be simplified to a difference of squares at least using whole numbers.

Therefore, we need to work with the second and the third polynomial.

For the second polynomial, we have:

16a^{2} -4a+4a-1=16a^{2}=(4a)^{2}-(1)^{2} =(4-1)(4+1)

So, the second polynomial can be simplified to a difference of squares.

For the third polynomial, we have:

25a^{2} +6a-6a+36=16a^{2}+36=(5a)^{2}+(6)^{2}

So, the third polynomial cannot be simplified to a difference of squares since it's a sum of squares.

Hence, the polynomial that can be simplified to a difference of squares is the second polynomial:

16a^{2}-4a+4a-1=16a^{2}=(4a)^{2}-(1)^{2}

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Answer:

A

Step-by-step explanation:

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