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Schach [20]
3 years ago
15

If f(1) = 10 and f(n) = f(n = 1) – 4 then find the value of f(5).

Mathematics
1 answer:
svetoff [14.1K]3 years ago
5 0

Given:

f(1)=10 and f(n)=f(n-1)-4.

To find:

The value of f(5).

Solution:

We have,

f(n)=f(n-1)-4

For n=2,

f(2)=f(2-1)-4

f(2)=f(1)-4

f(2)=10-4

f(2)=6

For n=3,

f(3)=f(3-1)-4

f(3)=f(2)-4

f(3)=6-4

f(3)=2

For n=4,

f(4)=f(4-1)-4

f(4)=f(3)-4

f(4)=2-4

f(4)=-2

For n=5,

f(5)=f(5-1)-4

f(5)=f(4)-4

f(5)=-2-4

f(5)=-6

Therefore, the value of f(5) is -6.

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If the original square had a side length of
irina [24]

Answer:

Part a) The new rectangle labeled in the attached figure N 2

Part b) The diagram of the new rectangle with their areas  in the attached figure N 3, and the trinomial is x^{2} +11x+28

Part c) The area of the second rectangle is 54 in^2

Part d) see the explanation

Step-by-step explanation:

The complete question in the attached figure N 1

Part a) If the original square is shown below with side lengths marked with x, label the second diagram to represent the new rectangle constructed by increasing the sides as described above

we know that

The dimensions of the new rectangle will be

Length=(x+4)\ in

width=(x+7)\ in

The diagram of the new rectangle in the attached figure N 2

Part b) Label each portion of the second diagram with their areas in terms of x (when applicable) State the product of (x+4) and (x+7) as a trinomial

The diagram of the new rectangle with their areas  in the attached figure N 3

we have that

To find out the area of each portion, multiply its length by its width

A1=(x)(x)=x^{2}\ in^2

A2=(4)(x)=4x\ in^2

A3=(x)(7)=7x\ in^2

A4=(4)(7)=28\ in^2

The total area of the second rectangle is the sum of the four areas

A=A1+A2+A3+A4

State the product of (x+4) and (x+7) as a trinomial

(x+4)(x+7)=x^{2}+7x+4x+28=x^{2} +11x+28

Part c) If the original square had a side length of  x = 2 inches, then what is the area of the  second rectangle?

we know that

The area of the second rectangle is equal to

A=A1+A2+A3+A4

For x=2 in

substitute the value of x in the area of each portion

A1=(2)(2)=4\ in^2

A2=(4)(2)=8\ in^2

A3=(2)(7)=14\ in^2

A4=(4)(7)=28\ in^2

A=4+8+14+28

A=54\ in^2

Part d) Verify that the trinomial you found in Part b) has the same value as Part c) for x=2 in

We have that

The trinomial is

A(x)=x^{2} +11x+28

For x=2 in

substitute and solve for A(x)

A(2)=2^{2} +11(2)+28

A(2)=4 +22+28

A(2)=54\ in^2 ----> verified

therefore

The trinomial represent the total area of the second rectangle

7 0
3 years ago
In ΔOPQ, o = 58 cm, q = 13 cm and ∠Q=52°. Find all possible values of ∠O, to the nearest degree.
PSYCHO15rus [73]

Answer:

There is no possible triangles

Step-by-step explanation:

\frac{\sin A}{a}=\frac{\sin B}{b}

a

sinA

​  

=  

b

sinB

​  

 

From the reference sheet (reciprocal version).

\frac{\sin O}{58}=\frac{\sin 52}{13}

58

sinO

​  

=  

13

sin52

​  

 

Plug in values.

\sin O=\frac{58\sin 52}{13}\approx 3.5157403

sinO=  

13

58sin52

​  

≈3.5157403O=\sin^{-1}(3.5157403)= \text{ERROR}

O=sin  

−1

(3.5157403)=ERROR

Sine cannot be greater than 1.

{No Possible Triangles}

No Possible Triangles

{}

{}

7 0
3 years ago
Which pair of numbers has the same greatest common factor as that of 48 and 78
tangare [24]
<span>48: 1,2,3,4,6,8,12,16,24,48 
</span><span>
78: 1,2,3,6,13, 26, 39, 78 
</span>
The answer is 6 :)
8 0
3 years ago
Brandon earns $6 for every shirt he sells. Which equation could Brandon use to determine the amount of money he earns (E) for an
BigorU [14]
I think it would D) E = 6 + s
7 0
3 years ago
Read 2 more answers
(-5, 3), (-1, 0), (3, -4), (-1, 2) pls find domain range and function
Nonamiya [84]

Answer:

Domain: {-5,-1,3} and Range: {3,0,-4,2}

Step-by-step explanation:

Just take my word for it please.

4 0
3 years ago
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