MATHEMATICS HIGH SCHOOL

What is the completely factored form of f(x) = 6x3 – 13x2 – 4x + 15?(x + 1)(6x2 – 19x + 15)
(x + 1)2(2x – 3)
(x + 1)(3x – 2)(5x – 3)
(x + 1)(2x – 3)(3x – 5)

Answers

Answer 1

Answer:

We have to determine the complete factored form of the given polynomial

$f(x)=6x^3-13x^2-4x+15$ .

Let x= -1 in the given polynomial.

So, $f(-1)= 6(-1)^3-13(-1)^2-4(-1)+15 = -6-13+4+15 = 0$

So, by factor theorem

(x+1) is a factor of the given polynomial.

So, dividing the given polynomial by (x+1), we get quotient as $6x^2-19x+15$ .

So, $6x^3-13x^2-4x+15$ = (x+1) $6x^2-19x+15$ .

= $(x+1)(6x^2-10x-9x+15)$

= $(x+1)[ 2x(3x-5)-3(3x-5)]$

= $(x+1)(2x-3)(3x-5)$ is the completely factored form of the given polynomial.

Option D is the correct answer.

Answer 2

Answer:

Answer:

D) (x + 1)(2x – 3)(3x – 5)

Step-by-step explanation:

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During the "free banking" era, A. only the U.S. Treasury could issue currency. B. value and denominations were standard across the nation. C. the number of state chartered banks stayed the same. D. all banks were able to issue currency.

Answers

the answer is A. only the U.S. treasury could issue currency

If (x2 +3x +5)(x2 +3x - 5) = m2-n2, then find m ?

Answers

$(x^2+3x+5)(x^2+3x-5)=m^2-n^2\n\n\ [(x^2+3x)+5][(x^2+3x)-5]=(m+n)(m-n)\n\nm=x^2+3x;\ n=5$

In the parallelogram shown, AE = t + 2, CE = 3t − 14, and DE = 2t + 8.What is the length of line segment DB?

20 units
24 units
48 units
68 units

Answers

Answer: 48 units

Given,
ABCD is a parallelogram
The diagonals bisect at E
Line segment AE = t + 2
Line segment CE = 3t – 14
Line segment DE = 2t + 8

Line segment DB is unknown

Since ABCD is a Parallelogram, Midpoint AC = Midpoint DB
The midpoint is E
Therefore
AE = CE … (Equation I)
DE = BE … (Equation II)

DB = DE + BE
Since DE = BE (Equation II),
DB = 2DE = 2BE

Given, DE = 2t + 8
DB = 2(2t + 8)
DB = 4t + 16 … (Equation III)

To solve for the value of ‘t’
AE = CE … (Equation I)
Line segment AE = t + 2
Line segment CE = 3t – 14
Therefore, t + 2 = 3t – 14

Subtract t from both sides of the equation
3t – 14 – t = t + 2 – t
2t – 14 = 2

Add 14 to both sides of the equation
2t – 14 + 14 = 2 + 14
2t = 16
t = 8

Substitute 8 for t in Equation III to solve for the length of line segment DB
DB = 4t + 16 … (Equation III)
DB = (4*8) + 16
DB = 32 + 16
DB = 48

Therefore, the length of line segment DB is 48 units

the answer is 48 units

Determine whether or not a regular polygon can have an interior angle of 100

Answers

Answer: No.

Explanation:

A polygon must be made up of at least 3 sides. It has to be at least 180° (A triangle)

Ann has to make payments twice a year on her health insurance. if each payment is $2,316, how much money should she budget for health insurance each month?A. $579
B. $386
C. $1,158
D. $193

Answers

Answer:

Option B. She should budget $386 each month.

Step-by-step explanation:

Ann has to make payments twice a year on her health insurance = $2,316

Therefore Ann makes payment annually = $2,316 × 2 = $4,632

To find out how much money should she budget for health insurance each month.

we divide annual premium by 12

= 4,632 ÷ 12 = $386

She should budget $386 each month.

B. Because if she has to make a payment of $2,316 twice a year it would be $4,632. Then you divide that by how many months there are in a year so 12. Then you get B. $386

Medical researchers have determined that for exercise to be beneficial, a person’s desirable heart rate, R, in beats per minute, can be approximated by the formulasR=143-0.65a for women
R=165-0.75a for men,

where a represents the person’s age. What would the desirable heart rate be for a 46 year old woman?
a. 113 beats per minute
b. 172.9 beats per minute
c. 143.7 beats per minute
d. 63 beats per minute