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2 years ago

I need #2 done ASAP (Must show work) Will give brainliest

Mathematics

2 answers:

Leto [7]2 years ago

8 0

Answer:

Using the Vertical Angle Theorem,

if two angles are vertical, then they are congruent

therefore, ∡4=∡5 and ∡6=∡7

since ∡4≅∡7

then ∡5 must also be ≅ to ∡6

Step-by-step explanation:

Tems11 [23]2 years ago

3 0

Step-by-step explanation:

Statement Reason

∠4 ≅ ∠7 Given

∠4 and ∠5 are vertical angles Vertical angles theorem

∠6 and ∠7 are vertical angles Vertical angles theorem

∠4 ≅ ∠5 and ∠ 6≅ ∠7 Definition of vertical angles

∠5 ≅ ∠6 Substitution property of equality

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( 1/2 ) ^2 HELP! ME!

VLD [36.1K]

Answer:

1/4 is the answer

just multiply 1/2 x 1/2

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have a good day :)

Step-by-step explanation:

5 0

2 years ago

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Solve for the roots in simplest form using the quadratic formula: 4x2 – 12x = -5

Art [367]

Answer:

x=2.5&.5

Step-by-step explanation:

The quadratic formula is (-b+or-sqrt(b^2-4ac)/2a

12+or-sqrt((-12^2)-4(4)(5))

12+or-sqrt(144-80)

12+or-sqrt(64)

(12+8)/8 and (12-8)/8

x=2.5 and x=.5

7 0

3 years ago

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The perimeter of a rectangle is 30.8 km and it’s diagonal length is 11 km. Find it’s length and width

blsea [12.9K]

Answer:

Length of the rectangle is 15.0325 km and width is 0.3765 km.

Explanation:

Given:

Perimeter of a rectangle = 30.8 km

Length of diagonal of rectangle = 11 km

To find:

The length and width of rectangle=?

Solution:

Lets assume length of the rectangle = x km

And assume width of the rectangle = y km

Lets first create equation using given perimeter

perimeter of rectangle = 2 ( length + width )

=> 30.8 km = 2 ( x + y )

=> $x + y = \frac{30.8}{2}$

=> y = 15.4 – x ------(1)

As diagonal and two sides of rectangle forms right angle triangle whose hypoteneus is diagonal ,

=> $length^2 + width^2 = diagonal^2$

=> $x^2 + y^2 = 11^2$

=> $x^2 + y^2 = 121$

On substituting value of y from (1) in above equation we get

=> $x^2 + (15.4-x)^2 = 121$

=> $x^2 + (15.4)^2 + x^2 – 2 x 15.4 \times x = 121$

=> $2x^2-30.8x + 237.16 -121 = 0$

=> $2x^2-30.8x + 116.16 = 0$

Solving above quadratic equation using quadratic formula

General form of quadratic equation is

$ax^2 +bx +c = 0$

And quadratic formula for getting roots of quadratic equation is

$x= \frac{ -b\pm\sqrt{(b^2-4ac)}}{2a}$

As equation is $2x^2-30.8x + 116.16 = 0$ , in our case

a = 2 , b = -30.8 and c = 116.16

Calculating roots of the equation we get

$x=\frac{ -(-30.8)\pm\sqrt{(-30.8)^2-4(2)( 11)} } {(2\times2)}$

$x=\frac{30.8\pm\sqrt{(948.64-88)}}{4}$

$x=\frac{30.8\pm\sqrt{860.64}}{4}$

$x=\frac{(30.8\pm29.33)}4$

$x=\frac{(30.8+29.33)}{4}$

$x=\frac{(30.8-29.33)}{4}$

=> x = 15.0325 or x = 0.3675

As generally length is longer one ,

So x = 1.0325

From equation (1) y = 15.4 – x = 0.3765

Hence length of the rectangle is 15.0325 km and width is 0.3765 km.

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3 years ago

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Oxana [17]

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3 years ago

How are the slopes of parallel lines and perpendicular lines related?

ELEN [110]

Answer:

Let's see what you can do with parallel and perpendicular. In other words, the slopes of parallel lines are equal. Note that two lines are parallel if their slopes are equal and they have different y-intercepts. In other words, perpendicular slopes are negative reciprocals of each other

8 0

2 years ago

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