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3 years ago

Write the standard form of the equation of a line if the point on the line nearest to the origin is at (6, 8).

Mathematics

1 answer:

Alchen [17]3 years ago

4 0

Answer:

$\large\boxed{y=\dfrac{4}{3}x}$

Step-by-step explanation:

The line passes through the origin has an equation y = mx

m - slope

The formula of a slope of a line passes through the origin

and a point (x, y):

$m=\dfrac{y}{x}$

We have the point (6, 8). Substitute:

$m=\dfrac{8}{6}=\dfrac{8:2}{6:2}=\dfrac{4}{3}$

Finally:

$y=\dfrac{4}{3}x$

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3 years ago

When the sum of a number and 3 is subtracted from 10 the result is 5. What is the integer

Rashid [163]

In algebraic terms this is:

$10-(x+3)=5\\10-x-3=5\\10-x=5+3\\10-x=8\\-x=8-10\\-x=-2\\x=2$

The integer is 2.

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3 years ago

SOMEONE PLEASE HELP MEEE!!!! HOW DO YOU DO THIS

UkoKoshka [18]

Answer:

A. 162 m²

Step-by-step explanation:

==>Given:

Isosceles trapezoid with:

base a = 19m

base b = 35m

Perimeter = 74meters

==>Required:

Area of trapezoid

==>Solution:

Recall: the length of the legs of an isosceles trapezoid are equal.

Perimeter of isosceles trapezoid = sum of the parallel sides + 2(length of a leg of the trapezoid)

Let l = leg of trapezoid.

Perimeter = 74m

Sum of parallel sides = a+b = 19+35 = 54m

Thus,

74 = 54 + 2(l)

74 - 54 = 2(l)

20 = 2(l)

l = 20/2 = 10m

Let's find area:

Area = ½(a+b)*h

a = 19

b = 35

h = ?

Using Pythagorean theorem, let's find h as follows:

h² = l² - [(35-19)/2)²

h² = 10² - [16/2]²

h² = 100 - 64

h² = 36

h = √36 = 6m

Area = ½ x (a+b) × h

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= ½ × 54 × 6

= 27 × 6

Area = 162m²

6 0

3 years ago

6/7 Find the slope of the line.

Feliz [49]

The slope, if you have a graph, is the angle the line is going down so look at this graph:

6 0

3 years ago

Read 2 more answers

The length of a rectangle is 4 cm less than it’s width. If the area of the rectangle is 165 cm^2. What are the dimensions of the

Monica [59]

Answer:

The dimensions are 11 cm by 15 cm

Step-by-step explanation:

Area of a rectangle = (length)(width).

Let L represent the length and W the width.

Since L = W - 4, we have

Area of rectangle = (W - 4)W = 165 cm^2.

Thus, w^2 - 4W - 165 = 0. We can solve for W using the quadratic formula:

a = 1, b = -4 and c = -165. Thus,

-(-4) ± √ [ (-4)² - 4(1)(-165) ]

W = ---------------------------------------

4 ± √ [16 + 660 ]

W = ------------------------------

4 ± √ [ 676 ] 4 ± 26

W = ----------------------- = W = ------------- = W = 2 ± 13

2 2

Thus, W is 2 + 13 = 15. It cannot be negative, so we discard 2 - 13 = -11.

If the width, W, is 15, then the length is 4 less, or L = 11.

The dimensions are 11 cm by 15 cm

6 0

3 years ago