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3 years ago

What is the solution to the system of equations? y = 2x + 4 y = -x + 1

Mathematics

1 answer:

den301095 [7]3 years ago

5 0

Step-by-step explanation:

start by setting each equation to each other

$2x + 4 = - x + 1$

first we are going to subtract 2x from both side of the equation

$4 = - 3x + 1$

now subtract 1 from both sides

$3 = - 3x$

now divide by -3 on both sides

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inysia [295]

$\large \bigstar \frak{ } \large\underline{\sf{Solution-}}$

Consider, LHS

$\begin{gathered}\rm \: \dfrac { \tan \theta + \sec \theta - 1 } { \tan \theta - \sec \theta + 1 } \\ \end{gathered}$

We know,

$\begin{gathered}\boxed{\sf{ \:\rm \: {sec}^{2}x - {tan}^{2}x = 1 \: \: }} \\ \end{gathered} \\ \\ \text{So, using this identity, we get} \\ \\ \begin{gathered}\rm \: = \:\dfrac { \tan \theta + \sec \theta - ( {sec}^{2}\theta - {tan}^{2}\theta )} { \tan \theta - \sec \theta + 1 } \\ \end{gathered}$

We know,

$\begin{gathered}\boxed{\sf{ \:\rm \: {x}^{2} - {y}^{2} = (x + y)(x - y) \: \: }} \\ \end{gathered} \\$

So, using this identity, we get

$\begin{gathered}\rm \: = \:\dfrac { \tan \theta + \sec \theta - (sec\theta + tan\theta )(sec\theta - tan\theta )} { \tan \theta - \sec \theta + 1 } \\ \end{gathered}$

can be rewritten as

$\begin{gathered}\rm\:=\:\dfrac {(\sec \theta + tan\theta ) - (sec\theta + tan\theta )(sec\theta -tan\theta )} { \tan \theta - \sec \theta + 1 } \\ \end{gathered} \\ \\ \\\begin{gathered}\rm \: = \:\dfrac {(\sec \theta + tan\theta ) \: \cancel{(1 - sec\theta + tan\theta )}} { \cancel{ \tan \theta - \sec \theta + 1} } \\ \end{gathered} \\ \\ \\\begin{gathered}\rm \: = \:sec\theta + tan\theta \\\end{gathered} \\ \\ \\\begin{gathered}\rm \: = \:\dfrac{1}{cos\theta } + \dfrac{sin\theta }{cos\theta } \\ \end{gathered} \\ \\ \\\begin{gathered}\rm \: = \:\dfrac{1 + sin\theta }{cos\theta } \\ \end{gathered}$

<h2>Hence,</h2>

$\begin{gathered} \\ \rm\implies \:\boxed{\sf{ \:\rm \: \dfrac { \tan \theta + \sec \theta - 1 } { \tan \theta - \sec \theta + 1 } = \:\dfrac{1 + sin\theta }{cos\theta } \: \: }} \\ \\ \end{gathered}$

$\rule{190pt}{2pt}$

5 0

2 years ago

Need help ASAP please! 60 points! -Does anyone have an idea as to how the function should be drawn? I think that there should be

Nesterboy [21]

P(x) to P(x+2), you need to graph the same but shift 2 units to the left.

New function :

Max = 4 ,coordinate points (-5, 0) and (5,0)

6 0

3 years ago

A pack of four bags of coffee cost $39.96. How much would 16 bags of coffee cost.<br> SHOW YOUR WORK

Bumek [7]

Answer:

$159.84

Step-by-step explanation:

We can solve this by simply knowing how many times 4 goes into 16. We can do this by writing the equation 16 ÷ 4 = 4. We now know that 4 goes into 16 4 times. By doing this we can now multiply $39.96 by 4 to get the cost of 16 bags which is $159.84.

Hope this Helps!!! :) Please comment below with some feedback!

6 0

2 years ago

There are 134 Girl Scouts going camping each cabin can hold 8 girls. How many cabins will they need for all the Girl Scouts? Sho

anyanavicka [17]

134 divided by 8 = 16.75, round it to nearest number
they would need 17 cabins

6 0

3 years ago

Which relation is a functions?

Anni [7]

Answer:

Step-by-step explanation:

What makes it a function?

If an x is unique but y can be duplicated

A is correct because the x are unique

B is incorrect because 3 is used twice

C is incorrect because -5 and -10 is used twice

D is incorrect because 20 is used twice

7 0

2 years ago