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2 years ago

Factor completely 4x4 − 24x3 + 36x2.

Mathematics

1 answer:

ipn [44]2 years ago

6 0

The previous answer from another person got deleted, so I'm here to put it back in my own words.

(Edit: The answer is A)

First of all, you can take 4 out of each, so simplify everything by 4.

4(x^4 - 6x^3 + 9x^2)

Next, you can see that you're able to take out x^2

4x^2(x^2 - 6x + 9)

You can see that both x^2 and 9 are perfect squares, meaning you can crunch them together like this

(x+3)^2 or (x-3)^2

Of course, only one would work, and as fate has it, (x-3)^ produces x^2 - 6x + 9

This would turn the now factored equation into :

4x^2(x-3)^2 or 4x^2(x-3)(x-3), this means the answer is A

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A 100 foot wire is extended from the

Kisachek [45]

The angle that the wire makes with the ground is
36.869
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6 0

2 years ago

An article gave the following summary information for fracture strengths (MPa) of n = 196 ceramic bars fired in a particular kil

Oliga [24]

Answer:

54.80 MPa to 55.92 MPa

Step-by-step explanation:

Sample mean fracture strength (x) = 55.36 MPa

Sample standard deviation (s) = 3.99 MPa

Sample size (n) = 196.

The upper and lower bounds for a 95% confidence interval are given by:

$U=x+1.960*\frac{s}{\sqrt{n}} \\L=x-1.960*\frac{s}{\sqrt{n}}$

The upper and lower bounds of the confidence interval are;

$U=55.36+1.960*\frac{3.99}{\sqrt{196}}\\U= 55.92\\L=55.36-1.960*\frac{3.99}{\sqrt{196}}\\L= 54.80\\$

The 95% confidence interval for true average fracture strength is 54.80 MPa to 55.92 MPa

4 0

3 years ago

Consider the function f(x)= 2/5x-4

Gre4nikov [31]

Answer: a) $\frac{5}{2}x+10=f^{-1}(x)=g(x)$

Step-by-step explanation:

Since we have given that

$f(x)=\frac{2}{5}x-4$

a.) Find the inverse of f(x) and name it g(x).

Let f(x) = y

So, it becomes

$y=\frac{2}{5}x-4$

Switching x to y , we get

$x=\frac{2}{5}y-4$

$5x=2y-20\\\\5x+20=2y\\\\\frac{5x+20}{2}=y\\\\\frac{5}{2}x+10=y\\\\\frac{5}{2}x+10=f^{-1}(x)=g(x)$

b) . Use composition to show that f(x) and g(x) are inverses of each other.

$\mathrm{For}\:f=\frac{2}{5}x-4\:\\\\\mathrm{substitute}\:x\:\mathrm{with}\:g\left(x\right)=\frac{5}{2}x+10\\\\=\frac{2}{5}\left(\frac{5}{2}x+10\right)-4\\\\=x$

Similarly,

$\mathrm{g\left(x\right)=\frac{5}{2}x+10,\:f\left(x\right)=\frac{2}{5}x-4,\:g\left(x\right)\circ \:f\left(x\right)}\\\\\mathrm{For}\:g=\frac{5}{2}x+10\:\mathrm{substitute}\:x\:\mathrm{with}\:f\left(x\right)=\frac{2}{5}x-4\\\\=\frac{5}{2}\left(\frac{2}{5}x-4\right)+10\\\\=x$

so, both are inverses of each other.

c) Draw the graphs of f(x) and g(x) on the same coordinate plane.

As shown below in the graph , Since for inverse function we need an axis of symmetry i.e. y=x

And both f(x) and g(x) are symmetry to y=x.

∴ f(x) and g(x) are inverses of each other.

5 0

3 years ago

9. Leonard made a deposit of $4,500 into a

taurus [48]

Answer:

id say a

Step-by-step explanation:

5 0

3 years ago

Find angles b,c and d

Mazyrski [523]

Answer:

B = 73°, c = 107°, d= 107°

Step-by-step explanation:

$b + 107 \degree = 180 \degree..(straight \: line \: \angle s) \\ b = 180 \degree - 107 \degree \\ \huge \red{ \boxed{b = 73 \degree}} \\ \\ \huge \purple{ \boxed{c = 107 \degree }}\\..(vertical \: \angle s) \\ \\ \huge \orange{ \boxed{d = 107 \degree }}\\..(corresponding \: \angle s) \\ \\$

8 0

3 years ago