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3 years ago

Which of these tables represents a linear function?

Mathematics

1 answer:

yulyashka [42]3 years ago

7 0

Answer:

Second.

Step-by-step explanation:

A linear function has one independent variable and one dependent variable. The independent variable is x and the dependent variable is y.

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Zack bought a coat for $69.78. He paid with $100 bill and received $26.73 in change. How much was the sales tax?

Klio2033 [76]

$3.49

Hopefully I helped!

6 0

3 years ago

Read 2 more answers

Sin(A+B) sin(A-B) /sin^A Cos^B=1-cot^A Tan^B

telo118 [61]

In order to prove

$\dfrac{\sin(x+y)\sin(x-y)}{\sin^2(x)\cos^2(x)}=1-\cot^2(x)\tan^2(y)$

Let's write both sides in terms of $\sin(x),\ \sin^2(x),\ \cos(x),\ \cos^2(x)$ only.

Let's start with the left hand side: we can use the formula for sum and subtraction of the sine to write

$\sin(x+y)=\cos(y)\sin(x)+\cos(x)\sin(y)$

and

$\sin(x-y)=\cos(y)\sin(x)-\cos(x)\sin(y)$

So, their multiplication is

$\sin(x+y)\sin(x-y)=(\cos(y)\sin(x))^2-(\cos(x)\sin(y))^2\\=\cos^2(y)\sin^2(x)-\cos^2(x)\sin^2(y)$

So, the left hand side simplifies to

$\dfrac{\cos^2(y)\sin^2(x)-\cos^2(x)\sin^2(y)}{\sin^2(x)\cos^2(y)}$

Now, on with the right hand side. We have

$1-\cot^2(x)\tan^2(y)=1-\dfrac{\cos^2(x)}{\sin^2(x)}\cdot\dfrac{\sin^2(y)}{\cos^2(y)} = 1-\dfrac{\cos^2(x)\sin^2(y)}{\sin^2(x)\cos^2(y)}$

Now simply make this expression one fraction:

$1-\dfrac{\cos^2(x)\sin^2(y)}{\sin^2(x)\cos^2(y)}=\dfrac{\sin^2(x)\cos^2(y)-\cos^2(x)\sin^2(y)}{\sin^2(x)\cos^2(y)}$

And as you can see, the two sides are equal.

6 0

4 years ago

Find the value of x in the triangle shown below

gregori [183]

Answer:

A or 53 squared

Step-by-step explanation:

3 0

3 years ago

Read 2 more answers

Theresa wants new carpeting for her family

svetlana [45]

Answer:

Area

Step-by-step explanation:

Area of a rectangle = L x W

The measurement of the room is 6m by 10m

So,

Area = 6 x 10

= 60 square meters

7 0

3 years ago

Multiply the expressions below. Then simplify if possible. a. 2x(3x – 4) b. (x+3)(2x-5) C. (2x + 5)(2x – 5) d. X(2x + 1)(x-3)

Keith_Richards [23]

Answer:

a) 6x² - 8x

b) 2x² + x - 15

c) 4x² - 25

d) 2x³ + 7x² - 3x

Step-by-step explanation:

a) 2x (3x - 4)

brackets means multiplication or into

base on the question

2x * 3x = 6x^2

and

2x * (-4) = -8x

therefore

6x² - 8x

is the answer

b) (x + 3) (2x - 5)

clear brackets with (x + 3)

i. x * (2x - 5) = 2x^2 - 5x

ii. +3 * (2x - 5) = 6x - 15

add i add ii

2x² - 5x + 6x - 15

if u noticed, there are similar figures 6x and 5x, so we take like term

2x² + x - 15 answer

c) (2x + 5) (2x - 5)

clear bracket

i. 2x * (2x - 5) = 4x² - 10x

ii. 5 * (2x - 5) = 10x - 25

add i and ii

4x² - 10x + 10x - 25

collect terms

4x² - 25 answer

d) x (2x + 1) (x - 3)

I) first we deal with x(2x+1)

x * (2x + 1) = (2x² + x)

II) then we find the multiplication of

(2x² + x) (x - 3)

i. 2x² * (x - 3) = 2x³ - 6x²

ii. x * (x - 3) = x² - 3x

add i and ii

2x³ - 6x² + x² - 3x

collect terms

2x³ - 5x² - 3x

5 0

2 years ago

Which of these tables represents a linear function?​

Which of these tables represents a linear function?