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3 years ago

Find the slope of every line that is perpendicular

Mathematics

1 answer:

Liula [17]3 years ago

6 0

Answer:

- 1/3

Step-by-step explanation:

First you find the slope of the line.

2-(-4) 6

——— = — = 3

2-0 2

To find the slope of the line that is perpendicular to that line, you take the opposite reciprocal of the slope.

-1/3

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50 points and brainlist!

Lady bird [3.3K]

Answer:

Step-by-step explanation:

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3 years ago

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Which of the following is true about a parallelogram? A. Opposite angles of a parallelogram are not congruent. B. Parallelograms

mafiozo [28]

Answer: The option is D.

Step-by-step explanation:

A line that intersects another line segment and separates it into two equal parts is called a bisector.

In a quadrangle, the line connecting two opposite corners is called a diagonal. We will show that in a parallelogram, each diagonal bisects the other diagonal.

Problem

ABCD is a parallelogram, and AC and BD are its two diagonals. Show that AO = OC and that BO = OD

Strategy

Once again, since we are trying to show line segments are equal, we will use congruent triangles. And here, the triangles practically present themselves. Let’s start with showing that AO is equal in length to OC, by using the two triangles in which AO and OC are sides: ΔAOD and ΔCOB.

There are all sorts of equal angles here that we can use. Several pairs of (equal) vertical angles, and several pairs of alternating angles created by a transversal line intersecting two parallel lines. So finding equal angles is not a problem. But we need at least one side, in addition to the angles, to show congruency.

As we have already proven, the opposite sides of a parallelogram are equal in size, giving us our needed side.

Once we show that ΔAOD and ΔCOB are congruent, we will have the proof needed, not just for AO=OC, but for both diagonals, since BO and OD are alsocorresponding sides of these same congruent triangles.

ABCD is a parallelogram

Given

AD || BC

From the definition of a parallelogram

AD = BC Opposite sides of a parallelogram are equal in size

∠OBC ≅ ∠ODA Alternate Interior Angles Theorem, ∠OCB ≅ ∠OAD Alternate Interior Angles Theorem,

ΔOBC ≅ ΔODA

Angle-Side-Angle

BO=OD Corresponding sides in congruent triangles AO=OC Corresponding sides in congruent triangles.

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3 years ago

125 A football stadium holds 55,296 people. The seating is divided into

stiks02 [169]

Answer:

1536

Step-by-step explanation:

simply divide 55296 by 36

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3 years ago

Destiny poured 24 ounces of juice into 4 1/2 ounce servings. She has 1 1/2 ounces of juice left over. How many 4 1/2 ounce servi

Nataly_w [17]

She poured 5 servings because 5 x 4 1/2 = 22 1/2. so when you add the left over 1 1/2 to that you get 24

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3 years ago

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Given the function f(x) = 2|x + 6| – 4, for what values of x is f(x) = 6?

lara [203]

Answer:

x = -1 , - 11,

Step-by-step explanation:

| x | = x

|- x | = x

f(x) = 2 | x + 6 | - 4

x = - 1 , f( - 1) = 2 | - 1 + 6 | - 4 = 2 | 5 | - 4 = 10 - 4 = 6 , True

x = 1 , f( 1 ) = 2 | 1 + 6 | - 4 = 2 | 7 | - 4 = 14 - 4 = 10 , False

x = 11, f( 11 ) = 2 | 11 + 6 | - 4 = 2 | 17 | - 4 = 34 - 4 = 30 , False

x = - 11, f( - 11) = 2 | -11 + 6 | - 4 = 2 | - 5 | - 4 = 10 - 4 = 6 , True

x = 14 , f( 14 ) = 2 | 14 + 6 | - 4 = 2 | 20 | - 4 = 40 - 4 = 36 , False

x = -14 , f( - 14 ) = 2 | - 14 + 6 | - 4 = 2 | - 8 | - 4 = 16 - 4 = 12 , False

x = - 26 , f( - 26) = 2 | -26 + 6 | - 4 = 2 | -20 | - 4 = 40 - 4 = 36 , False

x = 26, f( 26 ) = 2 | 26 + 6 | - 4 = 2 | 32 | - 4 = 64 - 4 = 60 , False

Given f ( x ) = 6

f( x ) = 2 | x + 6 | - 4

6 = 2 | x + 6 | - 4

6 + 4 = 2 | x + 6| - 4 + 4 [ adding 4 to both sides ]

10 = 2 | x + 6 | + 0

5 = | x + 6 | [ dividing both sides by 2 ]

$- 5 =\ ( x+ 6) \ = 5\\\\$ $[ \ | x | = a\ => \ -a \ = x \ = a \ ]$

$- 5 - 6 = \ x + 6 - 6 \ = \ 5 - 6\\$ $[ \ subtracting \ by \ 6 \ ]$

$-11 = \ x \ = - 1$

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2 years ago