Find an equation of the line satisfying the given conditions
Through (6,4); perpendicular to 3X + 5Y =38

Answers

Answer 1

Answer: To answer this, we will need to know:

• The slope of the equation we are trying to get
• The point it passes through using the

First, we will need to find the slope of this equation. To find this, we must simplify the equation $3x+5y=38$ into $y=mx+b$ form. Lets do it!

$3x+5y=38$
= $5y = -3x+38$ (Subtract 3x from both sides)
= $y= -(3)/(5)x+ (38)/(5)$ (Divide both sides by 5)

The slope of a line perpendicular would have to multiply with the equation we just changed to equal -1. In other words, it would have to equal the negative reciprocal.

The negative reciprocal of the line given is $(5)/(3)$ .

Now that we know the slope, we have to find out the rest of the equation using the slope formula, which is:

$(y-y _(1) )/(x- x_(1) )=m$

Substituting values, we find that:

$(y-4)/(x-6)= (5)/(3)$

By simplifying this equation to slope-intercept form (By cross-multiplying then simplifying), we then get that:

$y= (5)/(3)x-6$ , which is our final answer.

Thank you, and I wish you luck.

Answer 2

Answer: $(6,4); 3x + 5y =38 \ subtract \ 3x \ from \ each \ side \n \n 5y = -3x + 8 \ divide \ each \term \ by \ 5 \n \n y = -\frac{3} {5}x + (38)/(5)\n \n The \ slope \ is :m _(1) = - (3)/(5) \n \n If \ m_(1) \ and \ m _(2) \ are \ the \ gradients \ of \ two \ perpendicular \n \n lines \ we \ have \ m _(1)*m _(2) = -1$

$m _(1) \cdot m _(2) = -1 \n \n -(3)/(5) \cdot m_(2)=-1 \ \ / \cdot (-(5)/(3)) \n \n m_(2)=(5)/(3)$

$Now \ your \ equation \ of \ line \ passing \ through \ (6,4) would \ be: \n \n y=m_(2)x+b \n \n4=(5)/(\not3^1) \cdot \not 6^2 + b$

$4=5 \cdot 2+b\n \n4=10+b \n \nb=4-10\n \nb=-6 \n \n y = (5)/(3)x -6$

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How to write repeating 3.01 as a mixed number

Answers

3.010101.. = 3 + 0.010101... = 3 + 1/(100 - 1) = 3 + 1/99 = 3 1/99

Given f(x)=10x over 2+7, find f^-1(x)I have provided a picture of the equation for it to be easier to read

Answers

Answer:

$f(x)^(-1)$ = 1/(5x+7) [ 1 over (5x + 7)] with x≠ -1.4

Step-by-step explanation:

Given the function f(x), if f(x) ≠ 0, we would have the formula as following:

+) $f(x)^(-1)$ = 1/f(x)

We have the given equation:

f(x) = (10x/2) + 7 = 5x + 7

f(x) ≠ 0 when and only when (5x + 7) ≠ 0

(5x + 7) ≠ 0

⇔ 5x ≠ 0 - 7

⇔ 5x ≠ -7

⇔ x ≠ -7 ÷ 5

⇔ x ≠ -1.4

So with x≠ -1.4, f(x) ≠ 0, we have:

$f(x)^(-1)$ = 1/f(x) = 1/ (5x + 7)

Conclusion: $f(x)^(-1)$ = 1/(5x+7) [ 1 over (5x + 7)] with x≠ -1.4

The seventh term of an arithmetic sequence is 21, the tenth term is 126. The first term is

Answers

Hi,
$a_(10)=a_0+10*r\na_7=a_0+7*r\na_(10)-a_7=3\ \Rightarrow 126-21=3r\ \Rightarrow r=35\na_7=a_0+7*r\ \Rightarrow 21=a_0+7*35\n\Rightarrow a_0=-224\n\Rightarrow a_1=-224+35\n\boxed{a_1=-189}$

Write the equation of a line through the points (2,3) and (-1,-9)

Answers

Answer:

with the points (2,3) and (-1,-9) the answer is y=4x+10

Step-by-step explanation:

you have to do (x1,y1) (x2,y2) thats for each point

the equation to get the slope is y2-y1 divided by x2,x1

to get the y-intercept to plug in one of the points to the slope-intercept equation

y=4x+5

I picked the points (2,3) but you should get the same answer with the other points

3=4(2)=5

3=8+5

3=13

-3+-3

=10 thats your y intercept.

A lamp is on sale and it's price is reduced from $80 to $50. what is the percentage decrease?

Answers

Percentage change =Final value -Initial value / initial value * 100\
= 50 - 80 / 80 * 100
= -30/80 * 100
= -3/8 * 100
= -300/8
= -37.5%

In short, Your Answer would be -37.5%

Hope this helps!

1
4
a +
1
3
a + 8 = 22