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2 years ago

13

Find the equation of a line perpendicular to -x=4-y that passes through the point (-3,8)

1 answer:

Wewaii [24]2 years ago

8 0

9514 1404 393

Answer:

y = -x +5

Step-by-step explanation:

Solving the given equation for y, we have ...

y = x +4

The slope of this line is the coefficient of x: 1. The slope of the perpendicular line will be the opposite reciprocal of this: -1/1 = -1. The y-intercept of the perpendicular line can be found from ...

b = y -mx = 8 -(-1)(-3) = 5

The perpendicular line has equation ...

y = -x +5

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saul85 [17]

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

<u>Let us assume that:</u>

$\sf \longmapsto x = \sqrt{6 + \sqrt{6 + \sqrt{6 + ... \infty } } }$

We can also write it as:

$\sf \longmapsto x = \sqrt{6 + x }$

Squaring both sides, we get:

$\sf \longmapsto {x}^{2} =6 + x$

$\sf \longmapsto {x}^{2} - x - 6 =0$

By splitting the middle term:

$\sf \longmapsto {x}^{2} - 3x + 2x - 6 =0$

$\sf \longmapsto x(x - 3) + 2(x - 3 ) =0$

$\sf \longmapsto (x+ 2)(x - 3 ) =0$

<u>Therefore:</u>

$\longmapsto\begin{cases} \sf (x+ 2) =0 \\ \sf (x - 3) = 0 \end{cases}$

$\sf \longmapsto x = - 2,3$

<u>But x cannot be negative. </u>

$\sf \longmapsto x = 3$

Therefore, the value of the expression is 3.

$\large\underline{\sf{Verification-}}$

Given:

$\sf\longmapsto x=3$

We can also write it as:

$\sf\longmapsto x = \sqrt{9}$

$\sf\longmapsto x = \sqrt{6+3}$

$\sf\longmapsto x = \sqrt{6 + \sqrt{9}}$

$\sf\longmapsto x = \sqrt{6 + \sqrt{6+3}}$

$\sf\longmapsto x = \sqrt{6 + \sqrt{6+\sqrt{9}}}$

$\sf\longmapsto x = \sqrt{6 + \sqrt{6+\sqrt{6+3}}}$

This pattern will continue.

$\sf\longmapsto x = \sqrt{6 + \sqrt{6+\sqrt{6+...\infty}}}$

7 0

2 years ago

Mr. Thomas spent $1,600 of his savings on a television set and 2/5 of the remainder on a refrigerator. He had 1/3 of his origina

Katena32 [7]

Answer:

The amount spent on the refrigerator is $ 800 .

Step-by-step explanation:

Given as :

The amount spent on television = $ 1600

Le The total amount in the account = $ A

so, The amount left in account after spent on television = $ A - $ 1600

The amount spent on refrigerator = $\frac{2}{5}$ × ( A - 1600 )

The amount left in his saving account = $\frac{1}{3}$ × A

Now, According to question

A - ( 1600 + $\frac{2}{5}$ × ( A - 1600 ) ) = $\frac{1}{3}$ × A

Or, A - $\frac{1}{3}$ × A = 1600 + $\frac{2}{5}$ × ( A - 1600 )

Or, $\frac{2}{3}$ × A = 1600 + $\frac{2}{5}$ × A - $\frac{2}{5}$ × 1600

or, $\frac{2}{3}$ × A - $\frac{2}{5}$ × A = 1600 - 640

Or, $\frac{10 - 6 }{15}$ × A = 960

or, $\frac{4}{15}$ × A = 960

∴ A = $\frac{960\times 15}{4}$

I.e A = 3600

So, The amount in the saving account is $3600

∵ , The amount spent on refrigerator = $\frac{2}{5}$ × ( 3600 - 1600 )

Or, The amount spent on refrigerator = $\frac{2}{5}$ × 2000

I.e The amount spent on refrigerator = $ 800

Hence The amount spent on the refrigerator is $ 800 . Answer

4 0

3 years ago

Find the period of the graph shown below<br> A. 4π<br> B. π<br> C. 2π<br> D. 2/3π

4vir4ik [10]

A I believe is the answer

8 0

2 years ago

Read 2 more answers

Find y<br>Solve the simultaneous <br>equations<br><br><br>3x + 2y = 27 3x - Y = 9<br>

lutik1710 [3]

Answer:

$y = 6$

Step-by-step explanation:

To find $y$ , we need to eliminate $x$ in this system of equations:

$3\cdot x + 2\cdot y = 27$ (1)

$3\cdot x - y = 9$ (2)

From (1) and (2):

$x = \frac{27-2\cdot y}{3}$

$x = \frac{9+y}{3}$

Then, we equalize both expressions and solve for $y$ :

$\frac{27-2\cdot y}{3} = \frac{9+y}{3}$

$27-2\cdot y = 9 + y$

$3\cdot y = 18$

$y = 6$

6 0

2 years ago

Which one is the right answer ?

Darina [25.2K]

Answer:

c

Step-by-step explanation:

4 0

2 years ago