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marta [7]
2 years ago
8

The trinomial x2 bx – c has factors of (x m)(x – n), where m, n, and b are positive. what is the relationship between the values

of m and n? explain.
Mathematics
1 answer:
Mashcka [7]2 years ago
8 0

The relationship between the values of m and n for the trinomial x²+bx -c is (m+n) is the sum of the roots and (mn) is the product of the roots.

<h3>What is trinomial?</h3>

A trinomial is the type of algebraic expression in which there are three terms present and more than one variable are present.

The trinomial given in the problem is,

x^2 +bx - c

This trinomial has factors of,

(x +m)(x - n),

Where <em>m, n</em>, and <em>b</em> are positive.

If this factors multiply by each other, we get,

(x +m)(x - n)\\x^2+nx+mx+nm\\x^2+(n+m)x+nm

Compare it with the trinomial, we get,

b=(m+n)

Which is the sum of the terms,

c=nm

Which is the product of the terms.

Hence, the relationship between the values of m and n for the trinomial x²+bx -c is (m+n) is the sum of the roots and (mn) is the product of the roots.

Learn more about the trinomial here;

brainly.com/question/1538726

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Which property explains how we get the equation shown in step 2? Given: -5(x -4) - 20 = -15 Step 1: -5x + 20 -20 = -15 (Distribu
Talja [164]
Step 2: <span>Inverse Property of Addition
</span><span>any number added to its opposite will equal zero
</span>in this case + 20 - 20 = 0

answer
Inverse Property of Addition
8 0
3 years ago
Read 2 more answers
A map of the park can be divided into a grid of 9^2 equal sections of land. It is estimated that there are 9^6 ants per section
kenny6666 [7]

Answer:

9^8

Step-by-step explanation:

The total number of ants is

(total number of sections)(ants in each section).

let x be the total number of ants.

Substitute the given values.

x = (9^2)(9^6)

x = 9^(2+6)  <= exponent rule: when multiplying exponents with the same base, add the exponents.

x = 9^8

4 0
3 years ago
Can someone help me with these and show the work also?
Snezhnost [94]

QUESTION:

Simplify each expression

ANSWER:

1.) \green{{- 8n}}

2.) \green{{- 2b - 60}}

3.) \green{{- 10x - 14}}

4.) for number 4 study my step-by-step explanation so you can answer that

STEP-BY-STEP EXPLANATION:

1.) First, If the term doesn't have a coefficients, it is considered that the coefficients is 1

WHY?

Learn why:

Why is it considered that the coefficient is 1?

Remember that any term multiplied by \blue{{1}} remains the same :

\blue{{1}} {× x = x}

Step 1:

The equality can be read in the other way as a well, so any term can be written as a product of \blue{{1}} and itself:

{x = } \blue{{1}} {× x}

Step 2:

Usually, we don't need to write multiplacation sign between the coefficient and variable, so the simple form is:

{x = 1x}

This is why we can write the term without the coefficient as a term with coefficient {1}

Now let's go back to solving as what i said if a term doesn't have a coefficient, it is considered that the coefficient is 1

{n - 9n}

\red{{1}} {n -9n}

Second, Collect like terms by subtracting their coefficients

\red{{1n - 9n}}

\red{{( 1 - 9)n}}

Third, Calculate the difference

how?

Keep the sign of the number with the larger absolute value and subtract the smaller absolute value from larger

\red{{1 - 9}}

\red{{- (9 - 1)}}

Subtract the numbers

- (\red{{9 - 1}})n

- \red{{8}}n

\green{\boxed{- 8n}}

2.) First, Distribute - 6 through the parentheses

how?

Multiply each term in the parentheses by - 6

\red{{- 6(b + 10)}}

\red{{- 6b - 6 × 10}}

Multiply the numbers

- {6b} - \red{{6 × 10}}

- {6b} - \red{{60}}

Second, Collect like term

how?

Collect like terms by calculating the sum or difference of their coefficient

\red{{- 6b + 4b}}

\red{{(- 6 + 4)b}}

Calculate the sum

\red{{(- 6 + 4)}}b

\red{{-2}}b

\green{\boxed{- 2b - 60}}

3.) First, Distribute 2 through parentheses

how?

Multiply each term in the parentheses by 2

\red{{2(x - 5)}}

\red{{2x - 2 × 5}}

Multiply the numbers

{2x -} \red{{2 × 5}}

{2x -} \red{{10}}

Second, Distribute - 4 through the parentheses

how?

Multiply each term in the parentheses by - 4

\red{{- 4(3x + 1)}}

\red{{- 4 × 3x - 4}}

Calculate the product

- \red{{4 × 3}}x - 4

- \red{{12}}x - 4

Third, Collect like terms

how?

Collect like terms by subtracting their coefficient

\red{{2x - 12x}}

\red{{(2 - 12)x}}

Calculate the difference

\red{{(2 - 12)}}x

\red{{- 10}}x

Fourth, Calculate the difference

how?

Factor out the negative sign from the expression

\red{{- 10 - 4}}

\red{{- (10 + 4)}}

Add the numbers

- (\red{{10 + 4}})

- \red{{14}}

\green{\boxed{- 10x - 14}}

That's all I know sorry but I hope it helps :)

6 0
2 years ago
Identify the area of the figure.
Leto [7]
To answer this, you need to break it up into sections. I found the area of each rectangle and added them; finding the area of the triangle is useless because we already know that the area is more than 172cm^2, so the only answer it could be is 184cm^2.

Hope this helped.

8 0
2 years ago
What is the perimeter of a yard with length = 4 x + 6 2 x + 1 feet and width = x − 3 2 x + 1 feet? 4 x − 3 4 x + 12 feet 4 x − 3
vodomira [7]

The perimeter of the given yard is P = 10x + 6

<h3>Perimeter of a rectangle</h3>

The formula for calculating the perimeter of a rectangle is expressed as:

P = 2(l + w)

where

l is the length

w is the width

Given the following parameters

length = 4x+6

width = x-3

Substitute

P = 2(4x+6+x-3)

P = 2(5x + 3)

P = 10x + 6

Hence the perimeter of the given yard is P = 10x + 6

Learn more on perimeter of a rectangle here: brainly.com/question/19819849

#SPJ1

4 0
1 year ago
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