X+7=6x-3 brainliest for best answer

How does quadrupling the side lengths of a rectangle affect its area

EleoNora [17]

Well first you find the area of your basic rectangle with equation:
area (a) = length (L) * width (w)

So we got:
a = L * w

Now we find the area of a new rectangle with quadruple side lengths than our (a) rectangle and im going to call this area A:
A = 4L * 4w or A = 4 (L * w)

we want to see how the ratio of A to a or A/a so we can set both equations equal to 1 by dividing the areas to both sides of their respective equations:
1 = (L * w) / a and
1= 4(L * w) / A

since they both equal 1 then the equations have to equal each other:
(L * w) / a = [4 (L * w) / A

cross multiply
A *(L * w) = a *[4 (L * w)]

divide both sides by (L * w)
A = 4a

as you can see by quadrupling the sides by 4, this small rectangles area would also increase by a factor of four

5 0

4 years ago

How do you find a rate of change

ddd [48]

Consider the line y = 2x + 1, shown at the right. Notice that this slope will be the same if the points (1,3) and (2, 5) are used for the calculations. For straight lines, the rate of change (slope) is constant (always the same). For every one unit that is moved on the x-axis, two units are moved on the y-axis.hope this helped.

5 0

3 years ago

50pts... I really don't get this can someone help pls I'd appreciate it a lot

Pachacha [2.7K]

Answer:

(a) center: (1, -2); radius √10

(b) distance from (4, -1) to center is √10, so is on the circle

(c) work shown below

(d) y = -1/3x +5/3

Step-by-step explanation:

It is well you should have difficulty, as point B is not defined. If we assume it is (0, -5), then we can proceed as follows.

_____

(a) The center of the circle will be the midpoint of AB, so will be the average of their coordinates.

C = (A+B)/2 = ((2, 1) +(0, -5))/2 = (2, -4)/2

C = (1, -2) . . . . the center of the circle

__

The radius of the circle is the distance between the center and either end of the diameter. (It can also be figured as half the diameter.)

Here, we choose ...

r = ║A-C║ = ║(2, 1) -(1, -2)║ = ║(1, 3)║

r = √(1² +3²)

r = √10 . . . . the radius of the circle

__

(b) There are a couple of ways to show (4, -1) is a point on the circle. One of them is to show that its distance from the center is the same as the radius. That distance is ...

║(4, -1) -(1, -2)║ = ║(3, 1)║ = √(3² +1²) = √10 . . . . same as the radius

(4, -1) is on the circle

__

(c) The standard form equation of a circle with center (h, k) and radius r is ...

(x -h)² +(y -k)² = r²

To get to the desired general form, we need to eliminate parentheses and subtract r². Filling in the values (h, k) = (1, -2) and r = √10, we have ...

(x -1)² +(y +2)² = 10

x² -2x +1 + y² +4y +4 = 10 . . . . . eliminate parentheses

x² +y² -2x +4y -5 = 0 . . . . . . . . subtract 10 and put in appropriate order

__

(d) We can write the equation of the tangent at point A starting with a point-slope form of the equation for the line, then rearranging it to slope-intercept form.

You know the tangent to a circle is perpendicular to the radius at the point of tangency. You know from the work in part (a) that the segment from C to A has a rise of 3 and a run of 1, so a slope of 3/1 = 3. The tangent is perpendicular, so its slope is the negative reciprocal of that, or -1/3.

Now we know the slope of the tangent and the point of tangency (A), so we can write the equation as ...

y -1 = (-1/3)(x -2)

Adding 1 and eliminating parentheses, we get ...

y = -1/3x +2/3 +1

y = -1/3x +5/3

_____

Comment on notation above

We have used the notation ║(a, b)║ to refer to the length of a segment with components (a, b). It is fully equivalent to √(a²+b²) in this context.

7 0

4 years ago

Read 2 more answers

What is the difference 7/4-1/8?

DaniilM [7]

For finding difference or sum of unlike fractions ( fractions with different denominators) then we need to make their denominators same ...so for that we take their denominators LCM ...
7/4 - 1/8 (LCM of 4 and 8 is 8)
=> 7/4 X 2 - 1/8
=> 14/8 - 1/8
= 13/8 ..

Hope it helps !!!

7 0

4 years ago

A circle is graphed with its center on the origin.The area of the circle is 49 square units.What are the coordinates of the x-in

neonofarm [45]

Answer:

3.95 and -3.95

Step-by-step explanation:

To graph a circle you can use the formula or (x – h)^2 + (y – k)^2 = r^2. So substituting in the given, we get x^2+y^2=49/pi. The x intercept is when y=0. So x^2=49/pi and so

x = sqrt(49/pi) and rounding to the nearest tenth, we get 3.95 and -3.95 because it isn’t a principal square root.

3 0

4 years ago