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2 years ago

4. What are the coefficients in the polynomial 7x² - 4x + 6? (1 poin

Mathematics

1 answer:

skad [1K]2 years ago

5 0

Answer:

D.) 7 and -4

Step-by-step explanation:

Coefficients are numbers placed directly before a variable.

(7) is a coefficient because it is placed before x².

(-4) is a coefficient because it is placed before x. The negative is included.

(6) is not a coefficient because it is not altering any variable through multiplication/division.

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Complete the identity. 1) sec^4 x + sec^2 x tan^2 x - 2 tan^4 x = ?

Alecsey [184]

Answer:

See Explanation

Step-by-step explanation:

Question like this are better answered if there are list of options; However, I'll simplify as far as the expression can be simplified

Given

$sec^4 x + sec^2 x tan^2 x - 2 tan^4 x$

Required

Simplify

$(sec^2 x)^2 + sec^2 x tan^2 x - 2 (tan^2 x)^2$

Represent $sec^2x$ with a

Represent $tan^2x$ with b

The expression becomes

$a^2 + ab- 2 b^2$

Factorize

$a^2 + 2ab -ab- 2 b^2$

$a(a + 2b) -b(a+ 2 b)$

$(a -b) (a+ 2 b)$

Recall that

$a = sec^2x$

$b = tan^2x$

The expression $(a -b) (a+ 2 b)$ becomes

$(sec^2x -tan^2x) (sec^2x+ 2 tan^2x)$

..............................................................................................................................

In trigonometry

$sec^2x =1 +tan^2x$

Subtract $tan^2x$ from both sides

$sec^2x - tan^2x =1 +tan^2x - tan^2x$

$sec^2x - tan^2x =1$

..............................................................................................................................

Substitute 1 for $sec^2x - tan^2x$ in $(sec^2x -tan^2x) (sec^2x+ 2 tan^2x)$

$(1) (sec^2x+ 2 tan^2x)$

Open Bracket

$sec^2x+ 2 tan^2x$ ------------------This is an equivalence

$(secx)^2+ 2 (tanx)^2$

Solving further;

................................................................................................................................

In trigonometry

$secx = \frac{1}{cosx}$

$tanx = \frac{sinx}{cosx}$

Substitute the expressions for secx and tanx

................................................................................................................................

$(secx)^2+ 2 (tanx)^2$ becomes

$(\frac{1}{cosx})^2+ 2 (\frac{sinx}{cosx})^2$

Open bracket

$\frac{1}{cos^2x}+ 2 (\frac{sin^2x}{cos^2x})$

$\frac{1}{cos^2x}+ \frac{2sin^2x}{cos^2x}$

Add Fraction

$\frac{1 + 2sin^2x}{cos^2x}$ ------------------------ This is another equivalence

................................................................................................................................

In trigonometry

$sin^2x + cos^2x= 1$

Make $sin^2x$ the subject of formula

$sin^2x= 1 - cos^2x$

................................................................................................................................

Substitute the expressions for $1 - cos^2x$ for $sin^2x$

$\frac{1 + 2(1 - cos^2x)}{cos^2x}$

Open bracket

$\frac{1 + 2 - 2cos^2x}{cos^2x}$

$\frac{3 - 2cos^2x}{cos^2x}$ ---------------------- This is another equivalence

8 0

3 years ago

WILL GIVE BRAINLIEST!! NEED ANSWERS!! Equations. 1. 4x-2-2x-6= -20

Keith_Richards [23]

its 5 buddy

ok its 5 numver 5

6 0

3 years ago

Use the drawing tools to form the correct answers on the graph.

SSSSS [86.1K]

Answer:

(-2,-12), (-1,-6), (0,-3) and (1,-3/2)

Step-by-step explanation:

x g(x)

-2 -3(1/2)^-2 = -12

-1 -3(1/2)^-1 = -6

0 -3(1/2)^0 = -3

1 -3(1/2)^1 = -3/2

Now, making the graph we will plot

(-2,-12), (-1,-6), (0,-3) and (1,-3/2)

Hope this helps!!

8 0

3 years ago

46 3= what is the answer

Andrews [41]

If you mean 46 * 3 = 138
If you mean 46 + 3 = 49
If you mean 46 - 3 = 43
If you mean 46 ÷ 3 = 15.3

Hope it helped

5 0

4 years ago

Ahhh help please find the perimeter

spin [16.1K]

Answer:

12 $x^{2}$ + 6y

Step-by-step explanation:

3 0

3 years ago