The factors of the quadratic expression x² - 4x - 21 is <u>(x - 7)(x + 3)</u>, making the <u>first option</u> 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 <u>(x - 7)(x + 3)</u>, making the <u>first option</u> the right choice.
Learn more about factorizing a quadratic expression at
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Answer:
2003.85
Step-by-step explanation:
I realize I'm a year late, but the math of the previous answer was so terrible I'm honestly too horrified to let this be.
You have save by an increasing amount of 3 pennies per day. You start with 3 and build from that, each day, for 365 days. First, you must figure out what amount of pennies you shoved into your account on the final 365th day.
An= a1+(n-1)d
An=term you want
a1= term you begin with
n= term you want
d= constant amount
A_365= 3 + (365-1)*3
A_365= 1095
Arithmetic Sum: Sn = N/2 (a1 + an)
365/2 * (3 + 1095) = 200385.
This means you've invested a total of 200385 PENNIES after 365 days.
The question asks for dollars, not your rusting lincoln's.
As (I hope) you know, 1 Dollar = 100 pennies
200385 pennies/100 = 2003.85.
This means you have $2003.85 in your account by the conclusion of the 365th day.
The concept of radicals and radical exponents is tricky at first, but makes sense when we look into the logic behind it.
When we write a radical in exponential form, like writing √x as x^(1/2), we are simply putting the power of the radical in the denominator (bottom number) of the exponent, and the numerator is the power we raise the exponent to, or the power that would be inside the radical.
In our example, √x is really ²√(x¹), or the square root of x to the first power. For this reason, we write it as x^(1/2).
Let's say we wanted to write the cubed root of x squared, in exponential form.
In radical form, it would look like this:
³√(x²) . This means we square x, and then take the cubed root.
In exponential form, remember that we take the power of the radical (3), and make that the denominator of the exponent, and keep the numerator as the power that x is raised to (2).
Therefore, it would be x^(2/3), or x to the 2 thirds power.
Just like when multiplying by a fraction, you multiply by the numerator and divide by the denominator, in exponential form, you raise your base number to the power of the numerator, and take the root of the denominator.
In order to get g(x) you would multiply the equation of f(x) by -1/2.
4x(-1/2)=-2x and -2(-1/2)=1.
