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3 years ago

Complete the equation describing how x and y are related

Mathematics

1 answer:

Natasha2012 [34]3 years ago

6 0

Answer:

? = $\frac{1}{2}$

Step-by-step explanation:

Take two points in this case, (-2,4) and (0,5)

Use rise over run for slope to find ?

5-4/0+2 = 1/2

To find the other blank, enter one of the two points into the existing equation.

y = 1/2x + b

5 = 0 + b

b = 5

The equation is y = 1/2x + 5

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Solve and check the inequality<br> |8m+4|<12

alexgriva [62]

This is the concept of algebra, to solve the inequality we proceed as follows;
|8m+4|<12
given that the absolute value is represented by positive and negative values, we shall have:
-(8m+4)<12
-8m-4<12
-8m<12+4
-8m<16
thus;
m>16/(-8)
m>-2

also:
8m+4<12
8m<12-4
8m<8
m<8/8
m<1
hence the answer is -2<m<1

7 0

3 years ago

Find the y value for the point that divides the line segment CD into a ratio of 4:1.

PIT_PIT [208]

Answer:

Y = 2

Step-by-step explanation:

For point (x1,y1) and (x2,y2) on coordinate plane if is divided in ratio of m:n.

Then point of division is given by

(n*x1+m*x2)/ m+n, (n*y1+m*y2)/ m+n

________________________________

Given point

c = (9,6)

d = (5,1)

ratio = 4:1

using the above formula , point of division is

x= (1*9+4*5)/ 4+1 y= (1*6+4*1)/ 4+1

x= (9+20)/ 5 y= (6+4)/ 5

x= 29/ 5 y= 10/ 5 =2

Thus, answer is y = 2

7 0

3 years ago

For the remaining portion of the living room not covered by the new flooring, Michelle wants to paint the concrete. After carefu

solong [7]

Answer:

$x^2 + 6 = 31$

Step-by-step explanation:

Given

$Painted = 6ft^2$

$Total = 31ft^2$

Dimension of unpainted area:

$Length = Width = x$ --- Square

Required

Determine an expression to solve for x

First, calculate the area of the unpainted space;

$Area = Length *Width$

$Area = x*x$

$Area = x^2$

The unpainted area, added to the painted area, equals the total area.

So, we have:

$Area + Painted = Total$

$x^2 + 6 = 31$

Hence, the expression is: $x^2 + 6 = 31$

5 0

3 years ago

Find the general solution of the following equation. Express the solution explicitly as a function of the independent variable.

Mashcka [7]

Answer:

Therefore the general solution is

$2 \sqrt w = 2 ln(x) - 5 \frac1x +c$

Step-by-step explanation:

Integration Rule:

$\int x^n dx= \frac{x^{n+1}}{n+1}+c$
$\int \frac1x dx= ln(x) +c$

Given differential equation is

$x^2 \frac{dw}{dx}= \sqrt{w}(2x+5)$

$\Rightarrow x^2 dw= \sqrt{w} (2x+5) dx$ [ multiplying dx both sides]

$\Rightarrow \frac{dw}{\sqrt w}= \frac{(2x+5)}{x^2} dx$ [ dividing $x^2\sqrt w$ both sides]

Integrating both sides

$\int \frac{dw}{\sqrt w}=\int \frac{(2x+5)}{x^2} dx$

$\Rightarrow \int w^{-\frac12} dw=\int (\frac{2x}{x^2}+\frac{5}{x^2} )dx$

$\Rightarrow \int w^{-\frac12} dw=\int \frac{2}{x}dx +\int\frac{5}{x^2} dx$

$\Rightarrow \frac{w^{-\frac12+1}}{-\frac12+1} =2ln x+5 \frac{x^{-2+1}}{-2+1}+c$ [ c is arbitrary constant]

$\Rightarrow 2 \sqrt w = 2 ln(x) - 5 \frac1x +c$

Therefore the general solution is

$2 \sqrt w = 2 ln(x) - 5 \frac1x +c$

6 0

3 years ago

Need assistance on some geometry

lukranit [14]

Answer:

So I can't actually put a picture in, put heres the easiest way to understand this. If it says y-1, take the coordinates for y, and subtract 1. do that to all of them, not just 1. For example, R is 4,1. To translate it, you would take the y coordinate (1) and subtract 1. We know to do this because it shows translation x,y)->(x,y-1). Thus, the new point would be 4,0. apply this to all of the points.

8 0

3 years ago