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3 years ago

Line t passes through points (10, 1) and (2, 6). Line u is perpendicular to t. What is the slope of line u?

Mathematics

1 answer:

diamong [38]3 years ago

8 0

Let's find the slope for line t first.

We can use the given points 2,6 and 10,1 to find the slope using the slope formula.

$\frac{y.2 - y.1}{x.2 - x.1} = m$

1 - 6 / 10 - 2

-5/8

The slope is -5/8.

Because we know the slope of this line, we can find the slope of the next line instantly, as they are perpendicular.

When a slope is perpendicular to another, it is equal to the negative reciprocal.

Negative reciprocal of -5/8 = 8/5

<h3>The slope of line u is 8/5</h3>

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X:(x+4)=3:5<br> find the value of x

Allushta [10]

$x:(x+4) = 3:5\\\\\implies \dfrac x{x+4} = \dfrac 35 \\\\\implies 5x = 3x +12\\\\\implies 5x -3x = 12\\\\\implies 2x = 12\\\\\implies x = \dfrac{12}2 = 6$

8 0

2 years ago

Read 2 more answers

The length of a rectangle field is represented by the expression 14 X minus 3X squared +2 Y. The width of the field is represent

Assoli18 [71]

Answer:

$9x+4x^2-5y$

Step-by-step explanation:

Hi there!

Length of the field: $14x-3x^2+2y$ units

Width of the field: $5x-7x^2+7y$ units

To find how much greater the length of the field is than the width, subtract the width from the length:

$14x-3x^2+2y-(5x-7x^2+7y)$

Open up the parentheses

$= 14x-3x^2+2y-5x+7x^2-7y$

Combine like terms

$= 14x-5x-3x^2+7x^2+2y-7y\\= 9x+4x^2-5y$

Therefore, the length is $9x+4x^2-5y$ units greater than the width.

I hope this helps!

7 0

2 years ago

What is the area of this figure?

s2008m [1.1K]

Step-by-step explanation:

it clearly consists of 2 rectangles and 1 triangle (as you tried correctly to point out by drawing the separating lines).

we only need to calculate all 3 areas and add them up for the total.

the area of a rectangle is

length × width

so, in our 2 cases we have

6 × 2 = 12 km²

5 × (3 + 2 + 3) = 5×8 = 40 km²

the area of a triangle is

baseline × height / 2

in case of a right-angled triangle the 2 sides enclosing the 90° angle can be used as baseline and height.

so, in our case

6 × (5 + 2 + (3 + 2 + 3 - 2)) / 2 = 6×(7 + 6)/2 = 3×13 = 39 km²

in total, the whole area is

12 + 40 + 39 = 91 km²

4 0

2 years ago

The Length of a rectangle exceeds its breadth by 9 cm. if length and breadth are each increased by 3 cm, the area of new rectang

gizmo_the_mogwai [7]

Answer:

Breadth = 8 cm

Length = 17 cm

Step-by-step explanation:

Given rectangle:

Breadth = x cm

Length = x + 9 cm

Area = length * breadth

= x * (x + 9)

= x² + 9x

Rectangle with length and breadth increased:

Breadth = x + 3 cm

Length = x + 9 + 3 = x + 12 cm

Area = 84 + (x² + 9x) cm²

(x +3) * (x +12) = 84 + x² + 9x

Use FOIL method

x*x + x*12 + 3*x + 3*12 = 84 + x² + 9x

x² + 12x + 3x + 36 = 84 + x² + 9x {add the like terms}

x² + 15x + 36 = 84 + x² + 9x

x² + 15x + 36 - 84 - x² - 9x = 0

6x - 48 = 0

6x = 48

x = 48/6

x = 8

Breadth = x = 8 cm

Length = x + 9 = 8 +9 = 17 cm

7 0

3 years ago

In a list of 100 numbers , the fraction of numbers greater than 15 is (19/25) and the fraction of numbers less than 15 is (7/50)

Bingel [31]

19/25 * 100 = 1900/25 = 76 ....numbers greater then 15
7/50 * 100 = 700/50 = 14....numbers less then 15

100 - (76 + 14) = 100 - 90 = 10 <== numbers equal to 15

6 0

3 years ago