All categories

3 years ago

Show that 6 – 4x - x^2 can never be greater than 10. ( This is an Additional Math Question )

Mathematics

1 answer:

notsponge [240]3 years ago

7 0

Answer:

see explanation

Step-by-step explanation:

Given

6 - 4x - x²

Since the coefficient of the x² term < 0 then parabola has a maximum vertex.

To find the x- coordinate of the vertex

$x_{vertex}$ = - $\frac{b}{2a}$

with a = - 1 and b = - 4 , then

$x_{vertex}$ = - $\frac{-4}{-2}$ = - 2

The corresponding y- coordinate is found by substituting x = - 2 , that is

6 - 4(- 2) - (- 2)² = 6 + 8 - 4 = 10

vertex = (- 2, 10 )

The maximum value of the function is the y- coordinate of the vertex

Then maximum value is 10

Thus 6 - 4x - x² is never greater than 10

You might be interested in

Complete the tables of values.

Vladimir [108]

Answer:

$a=1\\b=\frac{1}{16}\\\\c=\frac{1}{256}\\\\d=1\\e=\frac{4}{9}\\\\f=\frac{16}{81}$

Step-by-step explanation:

For the orange table:

Substitute the corresponding values of x into the function $f(x)=4^{-x}$ , then:

For a:

x=0

$f(0)=4^0=1$

For b:

x=2

$f(x)=4^{-2}=\frac{1}{16}$

For c:

x=4

$f(x)=4^{-4}=\frac{1}{256}$

For the blue table:

Substitute the corresponding values of x into the function $g(x)=(\frac{2}{3})^x$ , then:

For d:

x=0

$g(x)=(\frac{2}{3})^0=1$

For e:

x=2

$g(x)=(\frac{2}{3})^2=\frac{4}{9}$

For f:

x=4

$g(x)=(\frac{2}{3})^4=\frac{16}{81}$

3 0

2 years ago

What is the volume of a cubic crystal with one face that has an area of 9 cm²?

Ulleksa [173]

Answer:

The volume is 27 cubic cm.

Step-by-step explanation:

4 0

3 years ago

B/c =a what is c ????????????

timama [110]

If you only want to know what it means ¨c¨ then it is the Denominator, cause you are referring a fraction.

6 0

2 years ago

at the dog show there are 4 times as many boxers as spaniel if there is a total of 30 dogs. how many dogs are spaniel

alexgriva [62]

4x+x = 30

5x = 30

x = 30/5 =6

6*4 = 24 boxers

and 6 spaniels

5 0

3 years ago

M(4,2) is the midpoint of RS. The coordinates of S are (6, 1). what are the coordinates of R?

nirvana33 [79]

Remark
You are using the midpoint formula. Instead of finding the midpoint, you are looking for one of the points, so you have to rearrange the formula a little bit.

Givens
Midpoint (4,2)
One endpoint (6,1)

Object
Find the other endpoint.

Formula
m(x,y) = (x1 + x2)/2, (y1 + y2)/2)

Solution
Find the x value
4 = (6 + x2)/2 Multiply both sides by 2
4*2 = 6 + x2 Subtract 6 from both sides.
8 - 6 = x2
x2 = 2

Find the y value
2 = (1 + y2)/2 Multiply by 2
4 = 1 + y2 Subtract 1 from both sides.
4 - 1 = y2
y2 = 3

Conclusion
R(x,y) = (2,3)

8 0

2 years ago