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dangina [55]
2 years ago
12

What is the midpoint of the x-intercepts of f(x) = (x – 4)(x + 4)?

Mathematics
2 answers:
stellarik [79]2 years ago
9 0
<span>f(x) = (x – 4)(x + 4) = x^2 - 4.  This is the equation of a parabola with vertex at (0,-4) and x-intercepts of (-2,0) and (2,0).  The midpoint of the line segment connecting these 2 points is (0,0).  Draw this situation and see for yourself!

</span>
djverab [1.8K]2 years ago
6 0

Answer:  The correct option is (A) (0, 0).

Step-by-step explanation:  We are given to find the midpoint of the x-intercepts of the following quadratic function:

f(x)=(x-4)(x+4)~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)

We know that the x-intercepts of a function f(x) is found by solving the equation f(x) = 0.

So, from equation (i), we have

f(x)=0\\\\\Rightarrow (x-4)(x+4)=0\\\\\Rightarrow x-4=0,~~~~~x+4=0\\\\\Rightarrow x=4,~-4.

That is, the x-intercepts of the given function are the points (4, 0) and (-4, 0).

Therefore, the co-ordinates of the mid-point of the x-intercepts (4, 0) and (-4, 0) will be

\left(\dfrac{4+(-4)}{2},\dfrac{0+0}{2}\right)\\\\\\=(0,0).

Thus, the required mid-point of the x-intercepts is (0, 0).

Option (A) is correct.

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Find the area of the shape below.
lawyer [7]

9514 1404 393

Answer:

  164π cm²

Step-by-step explanation:

The area of a circle is given by the formula ...

  A = πr²

The radius (r) is half the diameter (d), so the area of a semicircle in terms of its diameter is ...

  1/2A = (1/2)(π)(d/2)² = (π/8)d²

The given shape is the combination of three (3) semicircles. The smallest has a diameter of 6 cm; the middle-sized one has a diameter of (32 cm -6 cm -8 cm) = 18 cm. The largest has a diameter of 32 cm.

The total area will be ...

  area of largest + area of middle-size - area of smallest

  = (π/8)(32² +18² -6²) = (π/8)(1312) . . . . cm²

The area of the shape is 164π cm².

4 0
1 year ago
Will works 7 hours a day, 6 days a week.
exis [7]
A day
= £9.20x7
= £64.40

6 days
£64.40x6= £386.40

The wages he has after he shared it with his mom
£386.40/7x5
= 55.20x5
= £276

£1932/£276= 7

It will take him 7 weeks to afford a car worth £1932.
6 0
2 years ago
Solve 11 - 1/2y= 3 + 6x for y.​
Ilia_Sergeevich [38]

Answer:

y = 12x+16

Step-by-step explanation:

Simplify both sides of the equation then isolate the variable.

Step 1, add 11 to both sides.

−1 /2 y+11+−11=6x+3+−11

−1 /2 y=6x−8

Step 2, divide both sides by (-1)/2.

You will be left with

y = 12x+16

3 0
2 years ago
Which is true about the completely simplified difference of the polynomials a3b + 9a2b2 − 4ab5 and a3b − 3a2b2 + ab5? The differ
tamaranim1 [39]
<span>Let be A =a3b +9a2b2-4ab5, and B=a3b-3a2b2+ab5,so the difference can be defined as A - B =a3b +9a2b2-4ab5 -(a3b-3a2b2+ab5), when there is negative sign in front of the parathesis, all the inside signs must change: that is as follow: A- B= a3b +9a2b2-4ab5 - a3b + 3a2b2 - ab5= a3b-a3b +9a2b2+3a2b2-4ab5- ab5= 12a2b2 -5ab5, the fist term has 2+2=4, as a degree,the second term has 1 +5 =6, so the true answer : The difference is a binomial with a degree of 6</span>
6 0
2 years ago
Read 2 more answers
Which of the following is equivalent to the expression (3ab)(-5ab)?
Scilla [17]
-15a^{2}b^{2}
6 0
2 years ago
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