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Masteriza [31]
1 year ago
8

Each month, Morse budgets $2,704 for fixed expenses, $ 687 for living expenses,and $454 for annual expenses. His annual net inco

me is $ 46,752. Describe hismonthly budget by using a positive number to show how much of a surplus there is, anegative number to show how much of a deficient there is, or zero if it is a balancebudget. Round answer to the nearest whole number.
Mathematics
1 answer:
Elena-2011 [213]1 year ago
4 0

Morse's monthly expenses are:

* $2,704 for fixed expenses.

* $687 for living expenses.

* $454 for annual expenses.

His total monthly expenses are:

$2,704 + $687 + $454 = $3,845

His annual total expenses are:

12 × $3,845 = $46,140

His annual net income is $46,752. Thus his annual balance is:

$46,752 - $46,140 = $612

His monthly balance is $612/12 = $51.

There is a surplus of $51

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If : f(x)=x^2, g(x)=x-1. Find (f×g)(x).<br>​
kramer

Answer:

  • \boxed{ f\cdot{g}(x) = x {}^{3}  - x {}^{2}}

Step by step explanation:

Given that,

f(x) =  {x}^{2}

g(x) = x - 1

Solution:

Solving for (f•g)(x):

= f(x) \cdot g(x)

Now substitute the given values.

= x {}^{2}  \cdot(x - 1)

= x {}^{2} (x - 1)

Apply distributive property:

= (x ^{2}  \cdot x) - x {}^{2}  \cdot 1

  • \boxed{ f\cdot{g}(x) =  x {}^{3}  - x {}^{2}}

Hence,f•g(x) will be x {}^{3}  - x {}^{2}.

8 0
2 years ago
Form quadratic functions given the following information:
nignag [31]

Answer:

f(x)=-\frac{4}{7}(x-\sqrt{2}-3)(x+\sqrt{2}-3)

or

f(x)=-\frac{4}{7}(x^2-6x+7)

Step-by-step explanation:

we have

f(3+√2 )=f(3− √2 )=0

so

x1=3+√2 and x2=3−√2 are the roots or x-intercepts of the quadratic equation

The quadratic equation in factored form is equal to

f(x)=a(x-x1)(x-x2)

substitute

f(x)=a(x-(3+\sqrt{2}))(x-(3-\sqrt{2}))

Find the value of the coefficient a

Remember that

f(1)=−8

so

For x=-1 -----> f(x)=-8

substitute

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solve for a

-8=a(-4-\sqrt{2}))(-4+\sqrt{2}))

apply difference of squares

-8=a(14)

a=-\frac{4}{7}

therefore

f(x)=-\frac{4}{7}(x-(3+\sqrt{2}))(x-(3-\sqrt{2}))

f(x)=-\frac{4}{7}(x-\sqrt{2}-3)(x+\sqrt{2}-3)

simplify

Applying distributive property

f(x)=-\frac{4}{7}(x^2+\sqrt{2}x-3x-\sqrt{2}x-2+3\sqrt{2}-3x-3\sqrt{2}+9)

f(x)=-\frac{4}{7}(x^2-6x+7)

5 0
4 years ago
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