Solve the system using elimination.

omeli [17]

We solve the as follows:

1. Solve proportion 12/15 = 18/b
( 12/15 = 18/b ) b
( 12b/15 = 18 ) 15/12
b = 18(15/12)
b = 45/2

2. Solve equations

A. -x + 4 = x +6
-x + 4 - x = x +6 - x
-2x + 4 - 4 = 6 - 4
-2x = 2
x = -1

B. 5n + 7 =7(n+1) -2n
5n + 7 = 7n + 7 - 2n
5n -7n + 2n = 7 - 7
0 = 0

C. -4(p+2) + 8 = 2(p-1) - 7p + 15
-4p - 8 + 8 = 2p - 2 - 7p + 15
-4p + 7p - 2p = -2 + 15 + 8 - 8
p =13

3. Solve a/b x - c = 0 for x
a/b x - c = 0
( a/b x = c ) b/a
x = bc / a

3 0

3 years ago

Futhe Mathematics <img src="https://tex.z-dn.net/?f=%28Cos%20%7B%7D%5E%7B4%7Dt%20-Sin%20%7B%7D%5E%7B4%7Dt%20%29%20%20%5Cdiv%2

Nastasia [14]

Answer:

cos2t/cos²t

Step-by-step explanation:

Here the given trigonometric expression to us is ,

$\longrightarrow \dfrac{cos^4t - sin^4t }{cos^2t }$

We can write the numerator as ,

$\longrightarrow \dfrac{ (cos^2t)^2-(sin^2t)^2}{cos^2t }$

Recall the identity ,

$\longrightarrow (a-b)(a+b)=a^2-b^2$

Using this we have ,

$\longrightarrow \dfrac{(cos^2t + sin^2t)(cos^2t-sin^2t)}{cos^2t}$

Again , as we know that ,

$\longrightarrow sin^2\phi + cos^2\phi = 1$

Therefore we can rewrite it as ,

$\longrightarrow \dfrac{1(cos^2t - sin^2t)}{cos^2t}$

Again using the first identity mentioned above ,

$\longrightarrow \underline{\underline{\dfrac{(cost + sint )(cost - sint)}{cos^2t}}}$

Or else we can also write it using ,

$\longrightarrow cos2\phi = cos^2\phi - sin^2\phi$

Therefore ,

$\longrightarrow \underline{\underline{\dfrac{cos2t}{cos^2t}}}$

And we are done !

$\rule{200}{4}$

Additional info :-

Derivation of cos²x - sin²x = cos2x :-

We can rewrite cos 2x as ,

$\longrightarrow cos(x + x )$

As we know that ,

$\longrightarrow cos(y + z )= cosy.cosz - siny.sinz$

So that ,

$\longrightarrow cos(x+x) = cos(x).cos(x) - sin(x)sin(x)$

On simplifying,

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

Hence,

$\longrightarrow\underline{\underline{cos (2x) = cos^2x - sin^2x }}$

$\rule{200}{4}$

7 0

2 years ago

Write down a pair of integers whose

liubo4ka [24]

The pair of integers that I chose are:

(a) sum is –3
5 + (-8) = -3

(b) difference is –5
2 - 7 = -5

(c) difference is 2
14 -12 = 2

(d) sum is 0
2 - 2 = 0

3 0

3 years ago

B(n)=−4−2(n−1) What's the 12th term in the sequence?

marysya [2.9K]

The 12th term in the sequence is -26.

Given,

B (n) = -4 – 2(n – 1)

We have to find the 12th term in the sequence:

To find the nth term in an arithmetic sequence:

An arithmetic sequence's nth term is determined by the formula a = a + (n - 1)d. The common difference, or d, is the difference between any two consecutive terms in an arithmetic series; it can be calculated by deducting any pair of terms starting with a and an+1.

Here,

First term, a = -4

Common difference, d = -2

nth term = 12

Now, let’s find 12th term

B(n) = -4 -2(n – 1)

B(12) = -4 – 2(12 – 1)

B(12) = -4 -2(11)

B(12) = -4 -22

B(12) = -26

That is, the 12th term in the sequence is -26.

Learn more about arithmetic sequence here:

brainly.com/question/11570734

#SPJ1

8 0

1 year ago

Anthony goes to the gym for __30____ minutes on Monday. Every day he ___increases____his gym time by _____5 minutes_______. If h

Stolb23 [73]

Geometric sequence is a sequence of numbers that have a common ratio between them.

6 0

3 years ago