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Alchen [17]
3 years ago
8

I am looking to decrease my bill by 25%. Can you look at my current plan and tell me what I can remove to achieve this reduction

in cost? My current bill is $140.00 per month
Mathematics
1 answer:
Gennadij [26K]3 years ago
6 0

Answer: $35

Step-by-step explanation:

From the question, we are informed that the current bill of the person is $140.00 per month and that the person wants to decrease the bill by 25%.

To know the amount that the person needs to deduct, we have to calculate 25% of $140.00. This will be:

= 25% of $140

= 25/100 × $140

= 1/4 × $140

= 0.25 × $140

= $35

The person will need to remove $35. The person will now pay ($140 - $35) = $105 monthly.

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Find a factorization of x² + 2x³ + 7x² - 6x + 44, given that<br> −2+i√√7 and 1 - i√/3 are roots.
Levart [38]

A factorization of x^4+2x^3+7x^2-6x+44 is (x^2+4x+11)(x^2-2x+4).

<h3>What are the properties of roots of a polynomial?</h3>
  • The maximum number of roots of a polynomial of degree n is n.
  • For a polynomial with real coefficients, the roots can be real or complex.
  • The complex roots of a polynomial with real coefficients always exist in a pair of conjugate numbers i.e., if a+ib is a root, then a-ib is also a root.

If the roots of the polynomial p(x)=ax^4+bx^3+cx^2+dx+e are r_1,r_2,r_3,r_4, then it can be factorized as p(x)=(x-r_1)(x-r_2)(x-r_3)(x-r_4).

Here, we are to find a factorization of p(x)=x^4+2x^3+7x^2-6x+44. Also, given that -2+i\sqrt{7} and 1-i\sqrt{3} are roots of the polynomial.

Since p(x)=x^4+2x^3+7x^2-6x+44 is a polynomial with real coefficients, so each complex root exists in a pair of conjugates.

Hence, -2-i\sqrt{7} and 1+i\sqrt{3} are also roots of the given polynomial.

Thus, all the four roots of the polynomial p(x)=x^4+2x^3+7x^2-6x+44, are: r_1=-2+i\sqrt{7}, r_2=-2-i\sqrt{7}, r_3=1-i\sqrt{3}, r_4=1+i\sqrt{3}.

So, the polynomial p(x)=x^4+2x^3+7x^2-6x+44 can be factorized as follows:

\{x-(-2+i\sqrt{7})\}\{x-(-2-i\sqrt{7})\}\{x-(1-i\sqrt{3})\}\{x-(1+i\sqrt{3})\}\\=(x+2-i\sqrt{7})(x+2+i\sqrt{7})(x-1+i\sqrt{3})(x-1-i\sqrt{3})\\=\{(x+2)^2+7\}\{(x-1)^2+3\}\hspace{1cm} [\because (a+b)(a-b)=a^2-b^2]\\=(x^2+4x+4+7)(x^2-2x+1+3)\\=(x^2+4x+11)(x^2-2x+4)

Therefore, a factorization of x^4+2x^3+7x^2-6x+44 is (x^2+4x+11)(x^2-2x+4).

To know more about factorization, refer: brainly.com/question/25829061

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3 0
1 year ago
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how do the graphs of f(x) = sin x and g(x) = sin2x+3 compare. Must make two selections of the following that apply.
Elena L [17]

Answer:

The correct options are:

  • g(x) is shifted three units higher than f(x).
  • g(x) has a period that is half the period of  f(x).

Step-by-step explanation:

We have to compare the graphs of the function:

f(x)=\sin x

and g(x)=\sin 2x+3

We have to select the correct options among the following:

As we know that the period of sine function is 2π.

i.e. Period of function f(x) is: 2π.

The period of sin(2 x) is π.

Hence, the period of the function g(x) function is π.

  • Hence, the period of g(x) is half the period of f(x).
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Solve: −4b+4b≥6(−5b+7)−3(b+3)
Mariana [72]

Answer:

Inequality Form:

b ≥ 1

Interval Notation:

[1,∞)

Step-by-step explanation:

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2 years ago
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Answer:

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The distance between City A and City B is 250 miles. A length of 2.3 feet represents this distance on a certain wall map. City C
masya89 [10]

The distance between city C and city D is 450 miles.

<u>Solution:</u>

Given, The distance between City A and City B is 250 miles.  

A length of 2.3 feet represents this distance on a certain wall map.  

City C and City D are 4.14 feet apart on this map.  

We have to find what is the actual distance between City C and City D?

Now, distance between a and b is 250 miles ⇒ 2.3 feet on map

Then, distance between c and d be n miles  ⇒ 4.14 feet on map.

Now, by chris cross method.

250 x 4.14 = 2.3 x n miles.

2.3n = 1035

n = 450

Hence, the distance between city C and city D is 450 miles.

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