When 3 times the number x is subtracted from 20, the result is 14. What number results when 4 times x is added to 5?

Write the slip-intercept form of the equation of the line described

kompoz [17]

Answer:

1) y=⅚x -2⅓

2) y=8/3x -5

Step-by-step explanation:

<u>Point-slope form:</u>

y=mx+c, where m is the gradient and c is the y-intercept.

Parallel lines have the same gradient.

Gradient of given line= $\frac{5}{6}$

Thus, m=⅚

Susbt. m=⅚ into the equation,

y= ⅚x +c

Since the line passes through the point (4, 1), (4, 1) must satisfy the equation. Thus, substitute (4, 1) into the equation to find c.

When x=4, y=1,

1= ⅚(4) +c

$1 = \frac{20}{6} + c \\ c = 1 - \frac{20}{6} \\ c = 1 - 3 \frac{1}{3} \\ c = - 2 \frac{1}{3}$

Thus the equation of the line is $y = \frac{5}{6} x - 2 \frac{1}{3}$ .

The gradients of perpendicular lines= -1.

Gradient of given line= -⅜

-⅜(gradient of line)= -1

gradient of line

= -1 ÷ (-⅜)

= -1 ×(-8/3)

= $\frac{8}{3}$

$y = \frac{8}{3} x + c$

When x=3, y=3,

$3 = \frac{8}{3} (3) + c \\ 3 = 8 + c \\ c = 3 - 8 \\ c = - 5$

Thus the equation of the line is $y = \frac{8}{3} x - 5$ .

4 0

3 years ago

How to find the length of the radius of circle O

Andrei [34K]

You would have to find Circumference

5 0

3 years ago

A pencil consists of a cone stacked on top of a cylinder. The diameter of the cylindrical base of the pencil is 10 mm and the he

11Alexandr11 [23.1K]

Answer:

790π

Step-by-step explanation:

We are given;

Diameter of cylinder;d = 10 mm

So, radius;r = 10/2 = 5 mm

Height of cylinder;h = 70mm

Surface area of cylinder is given by the formula; S.A = 2πr² + 2πrh

Plugging in the relevant values, we have;S.A = 2π(5)² + 2π(5)(70)

S.A = 50π + 700π

S.A = 750π

Now, because one base of the cylinder is hidden as the cone is stacked on that face, we will deduct the area of that base face;

Thus, Surface area = 750π - π(5)² = 750π - 25π = 725π

For the cone,

Height;h = 12mm

Since this is stacked directly on the cylinder, it will have the same radius. Thus; radius;r = 5mm

Now,formula for surface area of cone is;

S.A = πr² + πrL

Where L is slant height.

We can use pythagoras theorem to get L.

So, L² = r² + h²

L = √r² + h²

L = √(5² + 12²)

L = √(25 + 144)

L = √169

L = 13

So, S.A of cone = π(5)² + (π×5×13)

S.A = 25π + 65π = 90π

Similar to what was done to the Cylinder, since the circular base of the cone is stacked on the cylinder, we will deduct the surface area of that base as it is hidden.

So, S.A is now = 90π - π(5)²

= 90π - 25π = 65π

Thus,total surface area of the pencil = 725π + 65π = 790π

7 0

3 years ago

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When 3 times the number x is subtracted from 20, the result is 14. What number results when 4 times x is added to 5?​

When 3 times the number x is subtracted from 20, the result is 14. What number results when 4 times x is added to 5?