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Rainbow [258]
1 year ago
14

I need to know the new equation, I’ve provided a picture

Mathematics
1 answer:
Juli2301 [7.4K]1 year ago
3 0

Hello there. To solve this question, we'll simply have to make x => x + 5 in the function.

Given the function:

f(x)=4x^2-3^{}

We have to determine f(x + 5)

By making x => x + 5 in this function, we get:

f(x+5)=4\cdot(x+5)^2-3

Now remember the binomial expansion of order 2:

(a+b)^2=a^2+2ab+b^2

Therefore we have:

f(x+5)=4\cdot(x^2+2\cdot x\cdot5+5^2)-3

Multiply the terms inside parentheses and calculate the square.

f(x+5)=4\cdot(x^2_{}+10x+25)-3

Apply the distributive property

f(x+5)=4x^2+4\cdot10x+4\cdot25-3

Multiply and add the numbers

\begin{gathered} f(x+5)=4x^2+40x+100-3 \\ \boxed{f(x+5)=4x^2+40x+97} \end{gathered}

This is the answer we're looking for.

A way of showing this is the correct answer is to make x = 1 and x = 6 in the former function:

\begin{gathered} f(1)=4\cdot1^2-3=4\cdot1-3=4-3=1 \\ f(6)=4\cdot6^2-3=4\cdot36-3=144-3=141 \end{gathered}

Then making x = 1 in the expression we found after:

f(1+5)=f(6)=4\cdot1^2+40\cdot1+97=4+40+97=141

As expected.

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Two boards, one four inches wide and the other six inches wide, are nailed together to form an X. The angle at which they cross
Sunny_sXe [5.5K]

Answer:

The area of the unpainted region on the four inch board = 160·√3 in.²

Step-by-step explanation:

Here we have that the boards are crossing each other on their flat sides Therefore, when the boards are separated, the area of the unpainted region is the area of a parallelogram

The dimensions of the formed parallelogram are;

Interior angles = 60° and 120° (adjacent angles of a parallelogram)

Height, h of parallelogram formed = 4 inches

From the angle of crossing of the parallelogram, we have;

Angle between the width or perpendicular cross section of the 6 inches board and the angle of crossing of the two boards = 90° - 60° = 30°

Therefore, length of base, b of the parallelogram formed by the unpainted region is given as follows;

b = \frac{60}{cos(30)}  = 40\cdot \sqrt{3} \ inches

Therefore, the area of the parallelogram = b × h = 4 × 40·√3 = 160·√3 in.²

Hence, the area of the unpainted region on the four inch board = 160·√3 in.².

3 0
3 years ago
Please follow me <br>Type: "Follow KelvinSu From:(your name)"<br>Thank you in advance​
KiRa [710]

Follow KelvinSu From: Thadd

5 0
2 years ago
Read 2 more answers
Evaluate the expression [(12x2.4) -(8.4*0.6)] +27-5.1
MariettaO [177]

Answer:45.66

Step-by-step explanation: Simplify the expression.

Hope this helps you out! ☺

6 0
3 years ago
Type the missing number in this sequence: 90, 78, 72, 66, 60, 54​
ZanzabumX [31]

Answer:

48

Step-by-step explanation:

minus 6 every number

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3 years ago
Does (0, 0) make the equation y = 9x − 5 true?
Vera_Pavlovna [14]

Answer:

no

Step-by-step explanation:

y = 9x − 5

The point (0,0) means x=0 and y=0

Substitute this into the equation and see it is true

0 = 9*0 -5

0 = 0-5

0 = -5

This is not true so the point is not a solution.

7 0
3 years ago
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