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Identify the factors of x2 − 4x − 21. (x − 7)(x 3) (x 7)(x − 3) (x 21)(x − 1) (x − 21)(x 1)

Tanzania [10]

The factors of the quadratic expression x² - 4x - 21 is (x - 7)(x + 3), making the first option the right choice.

A quadratic expression is of the form ax² + bx + c, which can be factorized using the mid-term factorization method, where b is shown as the sum or difference of two such numbers, whose product is equal to the product of a and c.

In the question, we are asked to factorize the quadratic expression, x² - 4x - 21.

In the given expression, a = 1, b = -4, and c = -21.

Thus, ac = -21.

The numbers having a product 21 are:

1*21 = 21,

3*7 = 21.

Since, 3 - 7 = -4 (That is b), we break b into 3 and -7.

Thus, the expression can now be shown as:

x² - 4x - 21

= x² + (3 - 7)x - 21

= x² + 3x - 7x - 21

= x(x + 3) - 7(x + 3) {By taking common}

= (x - 7)(x + 3) {By taking common}.

Thus, the factors of the quadratic expression x² - 4x - 21 is (x - 7)(x + 3), making the first option the right choice.

Learn more about factorizing a quadratic expression at

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5 0

1 year ago

A recipe for trail mix uses 7 ounces of almonds with 5 ounces of raisins. How many ounces of almonds would be in a one pound bag

Natasha2012 [34]

8 and 3/4 ounces of almonds.

3 0

3 years ago

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A number, y, is equal to twice the sum of a smaller number and 3. The larger number is also equal to 5 more than 3 times the sma

Nata [24]

Answer:

The equations represent the situation is $y=2x+6$ and $y=5+3x$ .

Step-by-step explanation:

Consider the provided information.

First convert the statement into mathematical representation.

Consider the smaller number is x and the larger number is y.

y, is equal to twice the sum of a smaller number and 3.

This information can be written as: $y=2(x+3)$

Which can be further solve as:

$y=2x+6$

The larger number is also equal to 5 more than 3 times the smaller number.

This information can be written as: $y=5+3x$

Thus, the equations represent the situation is $y=2x+6$ and $y=5+3x$ .

Which can be further solve as:

$2x+6=5+3x$

$x=1$

Now, substitute the value of x in $y=5+3x$ .

$y=5+3$

$y=8$

3 0

3 years ago

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Find a factor of 3x^2- 16x - 12

Greeley [361]

Answer:

x= -2/3 and 6

Step-by-step explanation:

3x²-16x-12

3x²-18x+2x-12

(3x²-18x)+(2x-12)

3x(x-6)+2(x-6)

(3x+2)(x-6)

x= -2/3 and 6

8 0

3 years ago

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3 connecting lines are shown. Line D F is horizontal. Line D E is about half the length of line D F. Line F E is about one-third

mars1129 [50]

The inequality that explains why the three segments cannot be used to construct a triangle is ED + EF < DF

<h3>Inequalities </h3>

From the question, we are to determine which of the given inequalities explains why the three segments cannot be used to construct a triangle

From the given information,

Line DE is about half the length of line DF

That is,

ED = 1/2 DF

Also,

Line FE is about one-third of the length of line DF

That is,

EF = 1/3 DF

Then, we can write that

ED + EF = 1/2DF + 1/3DF

ED + EF = 5/6 DF

Since,

5/6 DF < DF

Then,

ED + EF < DF

Hence, the inequality that explains why the three segments cannot be used to construct a triangle is ED + EF < DF

Learn more on Inequalities here: brainly.com/question/1447311

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5 0

2 years ago