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2 years ago

10x –3 = 4x + 8 What Is X?

Mathematics

1 answer:

navik [9.2K]2 years ago

7 0

Answer:

x=1.833

Step-by-step explanation:

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Mr.Church had 3 muffins he sold 2 but then baked 6 more and sold 4 more how many muffin did he not sell.

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He failed to sell three muffins

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A Number decreased by the square of 9

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X decreased by the square of nine
x - 9^2 = x - 81

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(x-1)(x-3)(x+5)(x+7)=297

mihalych1998 [28]

First simplify the expression into polynomial form,

$(x-1)(x-3)(x+5)(x+7)=297$

$x^4+8x^3-10x^2-104x+105=297$

$x^4+8x^3-10x^2-104x-192=0$

Now factor into,

$(x-4)(x+8)(x^2+4x+6)=0$

Which means the solutions are,

$x-4=0\implies\boxed{x_1=4}$

$x+8=0\implies\boxed{x_2=-8}$

and then two complex solutions because determinant of the third factor $D\lt0$ ,

$x^2+4x+6=0$

$x^2+4x+4=-2$

$(x+2)^2=-2\implies\boxed{x_3=i\sqrt{2}-2},\boxed{x_4=-i\sqrt{2}-2}$

Hope this helps :)

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3 years ago

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A university is interested in promoting graduates of its honors program by establishing that the mean GPA of these graduates exc

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Step-by-step explanation:

Population Mean (u) = 3.50

Sample (n)= 36

Sample mean (x) = 3.60

Population standard deviation (s)= 0.40

Test statistics:

(Null hypothesis) H0: u= 3.5 (Population mean is equal to 3.5)

(Alternate hypothesis) H1: u> 3.5 (Population mean is greater than 3.5)

Z= $\frac{x-u}{\frac{s}{\sqrt{n} } }$ = $\frac{3.60-3.50}{\frac{0.4}{\sqrt{36} } }$ = $\frac{0.10}{0.067}$ = 1.5

critical value= Z0.05= 1.645 (From Z table)

Since, Z value is less than critical Z value that is Z<1.645

We cannot reject null hypothesis

So, we decide to reject that the mean GPA of graduates exceeds 3.50

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2 years ago