Select the approximate values of x that are solutions to f(x) = 0, where f(x) = -8x^2 + 8x + 5.

Answers

Answer 1

Answer: $f(x)=-8x^2+8x+5\n\nf(x)=0\iff-8x^2+8x+5=0\n\na=-8;\ b=8;\ c=5\n\n\Delta=b^2-4ac\n\n\Delta=8^2-4\cdot(-8)\cdot5=64+160=224\n\nx_1=(-b-\sqrt\Delta)/(2a);\ x_2=(-b+\sqrt\Delta)/(2a)\n\n\sqrt\Delta=√(224)\approx√(225)=15\n\nx_1\approx(-8-15)/(2\cdot(-8))=(-23)/(-16)=1(7)/(16)\approx1.5\n\nx_2\approx(-8+15)/(2\cdot(-8))=(7)/(-16)=-(7)/(16)\approx-0.5$

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Blair's garden is four feet shorter than double its width. The perimeter of the garden is 64 feet. The width of the garden is ___ feet.

The length of the garden is ____ feet.

Answers

Answer:

The width of the garden is 12 feet.

The length of the garden is 20 feet.

Step-by-step explanation:

Let l be the length and w be the width

Then according to given statements

$l = 2w-4\ \ \ Eqn\ 1$

Second equation is:

$2l+2w = 64\ \ \ \ Eqn\ 2$

Putting l = 2w -4 in equation 2

$2(2w-4)+2w = 64\n4w-8+2w = 64\n6w -8 = 64\n6w = 64+8\n6w = 72\n(6w)/(6) = (72)/(6)\nw = 12$

Putting w = 12 in equation 1

$l = 2(12)-4 = 24-4 = 20$

Hence,

The width of the garden is 12 feet.

The length of the garden is 20 feet.

How many solutions does the equation 4n + 6 = 4 + 2 + 4n have?Two
Many
None
One

Answers

Answer:

many solutions

Step-by-step explanation:

4n + 6 = 4 + 2 + 4n

We try to solve for n

we try to get the variable alone

4n + 6 = 4 + 2 + 4n

combine like terms

4n + 6 = 6 + 4n

subtract 4n from both sides

6=6

If we arrive at a true statement like 5=5 then the equation has infinitely many soltions

We arrived at a true statement 6=6 so infinitely many solutions

4n+6=4+2+4n, well first combine like terms, 4n+6=6+4n and those are exactly the same, there's no magical n that can make 4n+6 not equal 4n+6, so many

Unknown g (x) = ax + b and g (g (x)) = 16x - 15. Calculate the value of a and b.

Answers

g(g(x))=16x-15
means that when you subsituted g(x) for x in g(x), you got 16x-15

a(ax+b)+b=16x-15
distribute
xa^2+ab+b=16x-15d
we look at the x terms
therefor
xa^2=16x
a^2=16
a=-4 or 4
we will find out

look a constant terms
ab+b=-15
undistribute b
b(a+1)=-15

if a is -4 then
b(-4+1)=-15
b(-3)=-15
b=5

if a=4 then
b(4+1)=-15
b(5)=-15
b=-3

so
g(x)=-4x+5 or
g(x)=4x-3

if a=-4, b=5
if a=4, b=-3

How does the answer for this 09:009 is 10??