MATHEMATICS HIGH SCHOOL

If f(–5) = 0, what are all the factors of the function f(x) = x^3 - 19x + 30. Use the Remainder TheoremA (x – 2)(x + 5)(x – 3)
B (x + 2)(x – 5)(x + 3)
C (x – 2)(x + 5)
D (x + 2)(x – 5

Answers

Answer 1

Answer:

If f(-5)=0, then x+5 is first factor of given polynomial.

1. Divide polynomial $x^3 - 19x + 30$ by x+5:

$x^3 - 19x + 30=(x+5)(x^2-5x+6)$ .

2. Factor the trinomial $x^2-5x+6$ :

3. Then

$x^3 - 19x + 30=(x+5)(x-2)(x-3)$ .

Answer: correct choice is A.

Answer 2

Answer:

The factors of the function f(x) = x³ - 19x + 30 are (x + 5)(x - 2)(x - 3).

Option A is the correct answer.

We have,

To determine the factors of the function f(x) = x³ - 19x + 30 using the RemainderTheorem, we need to find the values of x that make the function equal to zero.

Given that f(-5) = 0, we know that (x + 5) is a factor of the function.

Using syntheticdivision, we can divide f(x) by (x + 5):

-5 | 1 0 -19 30

| -5 25 -30

-----------------------

1 -5 6 0

The result is a remainder of zero, indicating that (x + 5) is a factor.

Now we need to factorize the remaining quadratic expression:

1x² - 5x + 6.

This quadraticexpression factors as (x - 2)(x - 3).

Therefore,

The factors of the function f(x) = x³ - 19x + 30 are (x + 5)(x - 2)(x - 3).

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Change the fraction 13/20 to a decimal. A. 0.65
B. 0.015
C. 0.065
D. 0.15

Answers

The fraction 13/20 is equivalent to the decimal 0.65.

To convert the fraction 13/20 to a decimal, simply divide the numerator (13) by the denominator (20):

13 ÷ 20 = 0.65

Therefore, the decimal representation of the fraction 13/20 is 0.65.

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the answer is A

set 13/20=x/100 13x100 is 1300 divided by 20 is 65.
65/100 is 0.65 as a decimal

A triangle has side lengths of (1.3k+3.5m)(1.3k+3.5m) centimeters, (4.1k-1.6n)(4.1k−1.6n) centimeters, and (9.7n+4.4m)(9.7n+4.4m) centimeters. Which expression represents the perimeter, in centimeters, of the triangle?

Answers

Answer:

(5.4k+7.9m+8.1n) centimeters

Step-by-step explanation:

Given the side length of a triangle;

S1 = (1.3k+3.5m) cm

S2 = (4.1k-1.6n) cm

S3 = (9.7n+4.4m) cm

Perimeter of the triangle = S1+S2 + S3

Perimeter of the triangle = (1.3k+3.5m) + (4.1k-1.6n) + (9.7n+4.4m)

Collect the like terms;

Perimeter of the triangle = 1.3k+4.1k+3.5m+4.4m-1.6n+9.7n

Perimeter of the triangle = 5.4k+7.9m+8.1n

Hence the expression that represents the perimeter of the triangle is (5.4k+7.9m+8.1n) centimeters

What is the slope of (1,9) and (6,34)

Answers

Answer:

$m=5$

General Formulas and Concepts:

Pre-Alg

Order of Operations: BPEMDAS

Alg I

Slope Formula: $m=(y_2-y_1)/(x_2-x_1)$

Step-by-step explanation:

Step 1: Define

Point (1, 9)

Point (6, 34)

Step 2: Find slope m

Substitute: $m=(34-9)/(6-1)$
Subtract: $m=(25)/(5)$
Divide: $m=5$

Answer:

The slope is 5

Step-by-step explanation:

so you use formula m= y2-y1/x2-x1 and use 34 as y2, 9 as y1, 6 as x2 and 1 as x1 then plug in numbers when using the formula and do the math and get your slope

I have a 96 in class and i get a 75 on a assignment that’s worth 10% whats my grade?

Answers

Answer:

Step-by-step explanation:

That would either be a B or a C!

Answer:

To calculate your overall grade, we can use the weighting of each component. Since the assignment is worth 10% of your grade, we can calculate its contribution using the following formula:

(96 * 90%) + (75 * 10%)

First, we multiply your current grade of 96 by 90% (which represents the remaining 90% of your grade) to calculate its contribution. Then, we multiply your assignment grade of 75 by 10% to calculate its contribution. Finally, we add these two contributions together:

(96 * 90%) + (75 * 10%) = 86.4 + 7.5 = 93.9

Therefore, your grade after receiving a 75 on an assignment worth 10% would be approximately 93.9%.

Given PQRS ≌ BCDE, what is m∠D?A.
63°

B.
90°

C.
98°

D.
109°

Answers

If they are congrunt, and it seems like the shape was rotated, so the answer is D

Find four consecutive integers such that twice the sum of the two greater integers exceeds three times the first by 91

Answers

Answer:

81, 82, 83, 84.

Step-by-step explanation:

Let x represent 1st integer. Then the next three consecutive integers would be $x+1,x+2\text{ and }x+3$ .

We have been given that twice the sum of the two greater integers exceeds three times the first by 91. We can represent our given information in an equation as:

$2(x+2+x+3)=3x+91$

Let us solve for x.

$2(2x+5)=3x+91$

$4x+10=3x+91$

$4x-3x+10=3x-3x+91$

$x+10=91$

$x+10-10=91-10$

$x=81$

Therefore, the 1st integer would be 81.

The next three consecutive integers would be:

$81+1=82\n81+2=83\n81+3=84$

Therefore, our required four consecutive integers are 81, 82, 83, 84.

Final answer:

To find four consecutive integers, set up an equation using the given information and solve for x. The four consecutive integers are -86, -85, -84, and -83.

Explanation:

To find four consecutive integers, we can let the first integer be x. The next three consecutive integers would then be x+1, x+2, and x+3. According to the given condition, twice the sum of the two greater integers (x+2 + x+3 = 2x+5) exceeds three times the first integer (3x) by 91. So, we can set up the equation 2x+5 = 3x + 91 and solve for x.

Subtracting 2x from both sides yields 5 = x + 91. Subtracting 91 from both sides gives -86 = x. Therefore, the four consecutive integers are -86, -85, -84, and -83.