2. Rewrite the sum 15y + 4x using the Commutative Property of Addition.

4.

zubka84 [21]

Answer:

See Explanation Below

Step-by-step explanation:

Given

$(sin x - cos x)^2 = sec^2x - tan^2x - 2sinx.cos x.$

Required

Prove

To start with; we open the bracket on the left hand side

$(sin x - cos x)^2 = (sin x - cos x)(sin x - cos x)$

$(sin x - cos x)^2 = (sin x )(sin x - cos x)- (cos x)(sin x - cos x)$

$(sin x - cos x)^2 = sin^2 x -sinx cos x - sin xcos x + cos^2 x$

$(sin x - cos x)^2 = sin^2 x -2sinx cos x + cos^2 x$

Reorder

$(sin x - cos x)^2 = sin^2 x + cos^2 x - 2sinx cos x$

From trigonometry;

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

So;

$(sin x - cos x)^2 = sin^2 x + cos^2 x - 2sinx cos x$

becomes

$(sin x - cos x)^2 = 1 - 2sinx cos x$

Also from trigonometry;

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

So,

$(sin x - cos x)^2 = 1 - 2sinx cos x$

becomes

$(sin x - cos x)^2 = sec^2x - tan^2x - 2sinx cos x$

Proved

3 0

3 years ago

A baseball field is being constructed. The builders noticed that the batters would have the sun in their eyes when batting from

Leona [35]

Answer:

$A' =(-y,x)$

Step-by-step explanation:

Given

Represent point A as thus;

$A = (x,y)$

Required

Determine the new position of A, when rotated counterclockwise

The new position will be denoted as A'

When a point is rotated counterclockwise, we start by switching the positions of x and y as follows:

$Pos = (y,x)$

Then, y is negated to give A'

$A' =(-y,x)$

5 0

3 years ago

Write 900.000+80.000+500+7 in standard from.

Bas_tet [7]

980,507 i believe... maybe

3 0

3 years ago

Read 2 more answers

Identify the name and label the parts of the following polynomial: − 2x^4+24^2-10

lianna [129]

-2x^4 + 24x^2 - 10

u have 3 terms.....and since u are only dealing with 1 variable with the highest exponent being 4, then what u have here is a 4th degree trinomial.
U have a lead coefficient of -2.
Ur constant term is -10
And ur middle term (24x^2) has a degree of 2

a cubic binomial.....a binomial has 2 terms and it being cubic means the highest term has a degree of 3
example would be : x^3 - 4

how many constants can a polynomial have ? I am not sure about this one...I wanna say 1 because u can simplify it if it has more then 1...but I am not 100% sure on this one

3x^2 + 6xy -10x^5 + y^6 - 10x^3y^5

when u have a polynomial with more then 1 variable, such as this one, the degree is not the highest exponent, it is the highest term.....-10x^3y^5...u add the exponents....so this term has a degree of 8, and it is the highest one in this problem....so this is an 8th degree polynomial with 5 terms

7 0

3 years ago

A rectangle is 20 meters long and 20 meters wide. If the length is increased by 10% and the width is decreased by 10%, what is t

Solnce55 [7]

Consider that the initial length and width of the rectangle are given as,

$\begin{gathered} l=20 \\ b=20 \end{gathered}$

After the length is increased by 10%, the new length (L) of the rectangle is calculated as,

$\begin{gathered} L=(1+\frac{10}{100})\cdot l \\ L=(\frac{110}{100})\cdot20 \\ L=22 \end{gathered}$

After the width is decreased by 10%, the new width (B) of the rectangle is calculated as,

$\begin{gathered} B=(1-\frac{10}{100})\cdot b \\ B=(\frac{90}{100})\cdot20 \\ B=18 \end{gathered}$

Then the area (A) of the new rectangle is calculated as,

$\begin{gathered} A=L\times B \\ A=22\times18 \\ A=396 \end{gathered}$

Thus, the new area of the rectangle is 396 square meters.

7 0

1 year ago