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marysya [2.9K]
3 years ago
9

Which statements are always true about ABCD? Select all that apply.

Mathematics
1 answer:
tangare [24]3 years ago
7 0

Answer:

It doesn't show the statements so I'll create some.

Step-by-step explanation:

ABCD make a shape with 2 pairs of parallel lines.

ABCD when broken apart can create 4 triangles

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X^2 + 4x - 16 - 11/(x + 2)
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Answer:

x=11\\

Step-by-step explanation:

6x^2=726 First, you need to divide everything by 6.

x^2=121Then you put everything in a radical to get this:

x=11

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What is a correct name for the angle shown?
Masteriza [31]

Answer:

the answer is option B. angle S.

when naming an angle we place the vertex of the angle in the middle. here the angle is RST. But that option is unavailable. very often when there are no other angles interfering with the parent angle, we represent it using one letter that is the mid letter, the vertex. here in this case it is S.

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3 years ago
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. For each of these intervals, list all its elements or explain why it is empty. a) [a, a] b) [a, a) c) (a, a] d) (a, a) e) (a,
Eva8 [605]

Answer:

Elements are of the form

 (i) [a,a]=\{[x,y] : a\leq x\leq a, a\leq y\leq a; a\in \mathbb R\}

(ii) [a,b)=\{[x,y) :a\leq x

(iii)(a,a]=\{(x,y] :a

(iv)(a,a)=\{(x,y): a

(v) (a,b) where a>b=\{(x,y) : a>x>b,a>y>b;a>b,a,b \in \mathbb R\}

(vi) [a,b] where a>b=\{[x,y] : a\geq x\geq b,a\geq y\geq b;a>b,a,b \in \mathbb R\}

Step-by-step explanation:

Given intervals are,

(i) [a,a] (ii) [a,a) (iii) (a,a] (iv) (a,a) (v) (a,b) where a>b (vi)  [a,b] where a>b.

To show all its elements,

(i) [a,a]

Imply the set including aa from left as well as right side.

Its elements are of the form.

\{[a,a] : a\in \mathbb R\}=\{[0,0],[1, 1],[-1,-1],[2,2],[-2,-2],[3,3],[-3,-3],........\}

Since there is a singleton element a of real numbers, this set is empty.

Because there is no increment so if a\in \mathbb R then the set  [a,a] represents singleton sets, and singleton sets are empty so is [a,a].

(ii) [a,a)

This means given interval containing a by left and exclude a by right.

Its elements are of the form.

[ 1, 1),[-1,-1),[2,2),[-2,-2),[3,3),[-3,-3),........

Since there is a singleton element a of real numbers withis the set, this set is empty.

Because there is no increment so if a\in \mathbb R then the set  [a,a) represents singleton sets, and singleton sets are empty so is [a.a).

(iii) (a,a]

It means the interval not taking a by left and include a by right.

Its elements are of the form.

( 1, 1],(-1,-1],(2,2],(-2,-2],(3,3],(-3,-3],........

Since there is a singleton element a of real numbers, this set is empty.

Because there is no increment so if a\in \mathbb R then the set  (a,a] represents singleton sets, and singleton sets are empty so is (a,a].

(iv) (a,a)

Means given set excluding a by left as well as right.

Since there is a singleton element a of real numbers, this set is empty.

Its elements are of the form.

( 1, 1),(-1,-1],(2,2],(-2,-2],(3,3],(-3,-3],........

Because there is no increment so if a\in \mathbb R then the set  (a,a) represents singleton sets, and singleton sets are empty, so is (a,a).

(v) (a,b) where a>b.

Which indicate the interval containing a, b such that increment of x is always greater than increment of y which not take x and y by any side of the interval.

That is the graph is bounded by value of a and it contains elements like it we fixed a=5 then,

(a,b)=\{(5,0),(5,1),(5,2).....\} e.t.c

So this set is connected and we know singletons are connected in \mathbb R. Hence given set is empty.

(vi) [a,b] where a\leq b.

Which indicate the interval containing a, b such that increment of x is always greater than increment of y which include both x and y.

That is the graph is bounded by value of a and it contains elements like it we fixed a=5 then,

[a,b]=\{[5,0],[5,1],[5,2].....\} e.t.c

So this set is connected and we know singletons are connected in \mathbb R. Hence given set is empty.

8 0
3 years ago
RSTU is a rectangle with vertices at R(-3,1), S(1 ,1), T(-3,3) and U (1, 3). Describe two lines of reflection that would carry t
miss Akunina [59]

Answer:

The two lines of reflection are x=-1 and y=2

Step-by-step explanation:

I will attach a file with the graph of the rectangle and the lines of reflection.

We know that RSTU is a rectangle with vertices at R=(-3,1) , S=(1,1),

T=(-3,3) and U=(1,3)

The first step is to draw the vertices on the plane and them the rectangle.

The rectangle is a symmetrical figure. Therefore if we want to carry the rectangle onto itself using a line of reflection this line must goes through the centroid of the rectangle.

Given that we have a rectangle whose width is a and its length is b its centroid will be place at (\frac{a}{2},\frac{b}{2}).

Looking at the graph and using this information we find that the two lines of reflection are x=-1 and y=2.

6 0
3 years ago
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