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2 years ago

Solve 5(r—1)=2(r-4)-6 step by step

Mathematics

1 answer:

frozen [14]2 years ago

6 0

Answer:

r = -3

Step-by-step explanation:

Performing the indicated multiplication on both sides of this equation, we get:

5r - 5 = 2r - 8 - 6

Combining the r terms: 3r - 5 = - 8 - 6.

Combining the constants: 3r = 5 - 14, or 3r = -9.

Dividing both sides by 3, to isolate r, we get: r = -3

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Given that −4i is a zero, factor the following polynomial function completely. Use the Conjugate Roots Theorem, if applicable. f

GalinKa [24]

Answer:

$\large \boxed{\sf \bf \ \ f(x)=(x-4i)(x+4i)(x+3)(x-5) \ \ }$

Step-by-step explanation:

Hello, the Conjugate Roots Theorem states that if a complex number is a zero of real polynomial its conjugate is a zero too. It means that (x-4i)(x+4i) are factors of f(x).

$\text{Meaning that } (x-4i)(x+4i) =x^2-(4i)^2=x^2+16 \text{ is a factor of f(x).}$

The coefficient of the leading term is 1 and the constant term is -240 = 16 * (-15), so we a re looking for a real number such that.

$f(x)=x^4-2x^3+x^2-32x-240\\\\ =(x^2+16)(x^2+ax-15)\\\\ =x^4+ax^3-15x^2+16x^2+16ax-240$

We identify the coefficients for the like terms, it comes

a = -2 and 16a = -32 (which is equivalent). So, we can write in $\mathbb{R}$ .

$\\f(x)=(x^2+16)(x^2-2x-15)$

The sum of the zeroes is 2=5-3 and their product is -15=-3*5, so we can factorise by (x-5)(x+3), which gives.

$f(x)=(x^2+16)(x^2-2x-15)\\\\=(x^2+16)(x^2+3x-5x-15)\\\\=(x^2+16)(x(x+3)-5(x+3))\\\\=\boxed{(x^2+16)(x+3)(x-5)}$

And we can write in $\mathbb{C}$

$f(x)=\boxed{(x-4i)(x+4i)(x+3)(x-5)}$

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

7 0

2 years ago

An 80 meter rope is suspended at its two ends from the tops of two 50 meter flagpoles. If the lowest point to which the midpoint

Agata [3.3K]

Answer:

qwerty

Step-by-step explanation:

7 0

2 years ago

Read 2 more answers

A problem on a multiple-choice quiz is answered correctly with probability 0.9 if a student is prepared. An unprepared student g

lions [1.4K]

Answer:

0.08475

Step-by-step explanation:

The question above is a application of conditional probability.

The formula to use is Baye's Theorem for conditional probability.

From the above question we have the following information:

Probability of answering correctly when prepared = 0.9

Probability of not answering correctly when prepared = 1 - 0.9 = 0.1

Probability of choosing the right answer = 1/4 = 0.25

Probability of choosing the wrong answer = 1 - 0.25 = 0.75

Number of students that prepare for the quiz = 75% = 0.75

Therefore number of students that did not prepare for the quiz = 1 - 0.75

= 0.25

Hence,

The probability of not preparing but choosing the correct answer =

P[ not prepared | correct answer ]

Is calculated as :

P[ not prepared | correct answer ] =

(0.25 × 0.25)/(0.25 × 0.25) + (0.25 × 0.9)

= 0.08475

Therefore, the chance that Mr X did not prepare for the quiz but he gives the right answer = 0.08475

3 0

2 years ago

<img src="https://tex.z-dn.net/?f=%20%5Cunderline%7B%20%5Cunderline%7B%20%5Ctext%7BQuestion%7D%7D%7D%20%3A%20" id="TexFormula1"

Ghella [55]

Answer:

See Below.

Step-by-step explanation:

Statements: Reasons:

$1)\text{ } AD\text{ bisects } \angle BAC$ Given

$2)\text{ } \angle BAD \cong \angle CAD$ Definition of Bisector

$\displaystyle 3) \text{ } A D \parallel E C$ Given

$\displaystyle 4)\text{ } \angle CAD\cong \angle ACE$ Alternate Interior Angles Theorem*

$\displaystyle 5) \text{ } \angle BAD\cong \angle BEC$ Corresponding Angles Theorem*

$6)\text{ } \angle CAD\cong \angle BEC$ Substitution

$7)\text{ } \angle ACE\cong\angle BEC$ Substitution

$\displaystyle 8)\text{ } AC = A E$ Isosceles Theorem Converse

*Please refer to the attachment below.

Let me know if you have any questions!

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2 years ago

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What is the area of a circle with a diameter of 12 m?

mafiozo [28]

area = PIR^2

3.14 x 6^2 = 113.04 m^2

answer is D

4 0

3 years ago