7) What is the slope-intercept form of this equation? Show all your work. 6x + 2y = 12

A line contains the points (8, 9) and (–12, –7). Using point-slope form, write the equation of the line that is parallel to the

navik [9.2K]

The lines have equal gradients;
m $\frac{16}{20} = \frac{4}{5}$

Equation of line 2;
y=mx+c
y= $\frac{4}{5}$ x+c
-15= $\frac{4}{5*(-5)}$ +c
c=-11
y=4/5x-11

7 0

3 years ago

Finding area of a sector

katen-ka-za [31]

The smaller sector is 360-255=105 degree
it is 105/360 portion of the whole circle, and the area of the whole circle is πr², r is 14
so the area of the smaller sector is (105/360)*π*14²
run those numbers through your calculator, use 3.14 for π, you get 179.5

if you are looking for area of the larger sector, it would be
(255/360)*π*14²=435.94

3 0

3 years ago

Grace and her brother Sid want to raise money to go to band camp. Their parents have agreed to help them up to $400 by paying th

Leona [35]

Step-by-step explanation:

25m + 10b = 400

not enough info to solve for m or b. but that's the equation you would use.

5 0

3 years ago

You have a wire that is 20 cm long. You wish to cut it into two pieces. One piece will be bent into the shape of a square. The o

Aleksandr [31]

Answer:

Therefore the circumference of the circle is $=\frac{20\pi}{4+\pi}$

Step-by-step explanation:

Let the side of the square be s

and the radius of the circle be r

The perimeter of the square is = 4s

The circumference of the circle is =2πr

Given that the length of the wire is 20 cm.

According to the problem,

4s + 2πr =20

⇒2s+πr =10

$\Rightarrow s=\frac{10-\pi r}{2}$

The area of the circle is = πr²

The area of the square is = s²

A represent the total area of the square and circle.

A=πr²+s²

Putting the value of s

$A=\pi r^2+ (\frac{10-\pi r}{2})^2$

$\Rightarrow A= \pi r^2+(\frac{10}{2})^2-2.\frac{10}{2}.\frac{\pi r}{2}+ (\frac{\pi r}{2})^2$

$\Rightarrow A=\pi r^2 +25-5 \pi r +\frac{\pi^2r^2}{4}$

$\Rightarrow A=\pi r^2\frac{4+\pi}{4} -5\pi r +25$

For maximum or minimum $\frac{dA}{dr}=0$

Differentiating with respect to r

$\frac{dA}{dr}= \frac{2\pi r(4+\pi)}{4} -5\pi$

Again differentiating with respect to r

$\frac{d^2A}{dr^2}=\frac{2\pi (4+\pi)}{4}$ > 0

For maximum or minimum

$\frac{dA}{dr}=0$

$\Rightarrow \frac{2\pi r(4+\pi)}{4} -5\pi=0$

$\Rightarrow r = \frac{10\pi }{\pi(4+\pi)}$

$\Rightarrow r=\frac{10}{4+\pi}$

$\frac{d^2A}{dr^2}|_{ r=\frac{10}{4+\pi}}=\frac{2\pi (4+\pi)}{4}>0$

Therefore at $r=\frac{10}{4+\pi}$ , A is minimum.

Therefore the circumference of the circle is

$=2 \pi \frac{10}{4+\pi}$

$=\frac{20\pi}{4+\pi}$

4 0

2 years ago

3. Write the equation. Slope: riset Run y intercept: equation: y=mx+b;

larisa [96]

Answer: y = 1/4 x – 4

OR y = x/4 –4

m is the slope. b is the y-intercept.

Without numbers on the x and y axis, it may not be correct. But assuming a normal scale, the slope is positive 1/4 and the y-intercept is -4

Step-by-step explanation: To find the slope, m, determine "rise over run"

Look for places where the graphed line crosses the grid at intersections. There seems to be such places at (–4,–5), (0,–4) and (4,–3)

The "rise" is the difference in y-values. Here, they increase by 1.

The "run" is the difference in x-values. Here they increase by 4.

So the slope is 1/4. Put that in place of m.

The graphed line crosses the y-axis at –4

That is the y-intercept. Use -4 in the place of b

Keep the y and x; substitute the values for m and b we found.

y = 1/4 x – 4

OR

y = x/4 – 4 This makes it clear that x is not in the denominator of the fraction, 1/4, and in calculations with given coordinates, the value of x will be divided by 4.

3 0

3 years ago

7) What is the slope-intercept form of this equation? Show all your work. 6x + 2y = 12​

7) What is the slope-intercept form of this equation? Show all your work. 6x + 2y = 12