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Gre4nikov [31]
3 years ago
7

Give statements and reasons

Mathematics
1 answer:
PolarNik [594]3 years ago
6 0

Answer:

A two column proof is presented as follows;

Statement {}                                     Reason

1. AB ║ DE, BD bisects AE        {}    Given

2. ∠BAE = ∠AED, ∠ABD = ∠BDA {} Alternate ∠s are equal

3.  \overline {AC} =  \overline {EC} ,  \overline {BC} =  \overline {CD} {} {}            By definition of bisection of line AE by BD

4. ΔABC ≅ ΔEDC  {}                         By SAA, rule of congruency

Step-by-step explanation:

Step 1. AB ║ DE, BD bisects AE        {}    Given

Step 2. ∠BAE , ∠AED, and ∠ABD, ∠BDA {} are pairs of alternate angles formed by the parallel lines, AB and DE and are therefore, equal

Step 3.  \overline {AC} =  \overline {EC} ,  \overline {BC} =  \overline {CD}  The bisection of line gives two lines of equal length. The bisection of AE by BD gives,  \overline {AC} and  \overline {EC} where \overline {AC} =  \overline {EC}

Similarly, the bisection of BD by AE gives, \overline {BC} and  \overline {CD}, where  \overline {BC} =  \overline {CD}

Step 4. ΔABC ≅ ΔEDC  {}  By the Side-Angle-Angle (SAA), rule of congruency, which states that two triangles having two angles and the corresponding non included sides of each triangle equal to the other, the two triangles are congruent.

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Which point lies on the graph of the equation 10y = 3x - 11?
GaryK [48]

Answer:

A. (2,-0.5)

Step-by-step explanation:

A pair of coordinates is always (x,y) so

If you insert the numbers into the equation you get

10(-0.5) = 3(2) - 11

-5 = 6 - 11

-5 = -5

Therefore (2,-0.5) is the point that likes on the graph

5 0
3 years ago
Donnel practiced the piano 3 hours longer than Marcus. Together they practiced the piano for 11 hours. How many hours did each b
andriy [413]
Here is the equation: x+(x+3)=11 ⇒x+x+3=11


You need to get "x" by itself so minus 3 from each side

x+x+3-3=11-3 ⇒ x+x=8 ⇒ 2x=8

Divide 8 by 2

8 ÷ 2=4

x=4

So each 4 is equivalent to 4 

Lets check:

4+(4+3)=11 ⇒ 4+4+3=11 ⇒ 11=11

So that means that Marcus practiced the piano for 4 hours and Donnel practiced for 7 
4 0
3 years ago
Ill be giving brainlist:( please help
WITCHER [35]

Answer:

Step-by-step explanation:

The translation vector < 4, - 2 > means each point is being moved 4 units to the right and 2 units down.

X(0, 3) ------> X' ( 0 + 4, 3 - 2 ) = X'(4, 1)

Y( - 1, 1) ------> Y' ( - 1 + 4, 1 - 2 ) = Y'(3, - 1)

Z( - 3, 4) -----> Z' ( - 3 + 4, 4 - 2 ) = Z'(1, 2)

5 0
3 years ago
2. Solve the<br> triangle.<br> a = 12, b = 22, C = 95°
djyliett [7]

this is the answer to this question - Two weather tracking stations are on the equator 146 miles apart. A weather balloon is located on a bearing of N 35°E from the western station and on a bearing of N 23°E from the eastern station. How far is the balloon from the western station?

Answer:

Reasons:

The given parameters are;

Distance between the two stations = 146 miles

Location of the weather balloon from the Western station = N35°E

Location of the weather balloon from the Eastern station = N23°E

The location of the station = On the equator

Required:

The distance of the balloon from the Western station

Solution:

- The angle formed between the horizontal, and the line from the Western station

to the balloon = 90° - 35° = 55°

- The angle formed between the horizontal, and the line from the Eastern station

to the balloon = 90° + 23° = 113°

The angle at the vertex of the triangle formed by the balloon and the two stations is 180° - (55 + 113)° = 12°

By sine rule,

Distance from balloon to western station = 146/sin(12 dg) = Distance from balloon to western station/sin(113 dg)

Therefore;

Distance from balloon to western station = 146/sin(12 dg) x sin(113 dg) ~ 646.4

Step-by-step explanation:

7 0
2 years ago
The ages of max and his father add up to 35 years. Max's father's age is the same as five more than the square of max's age
34kurt
M+f=35
f=5+m^2
sub 5+m^2 for f
m+5+m^2=35
m^2+m+5=35
minus 35 both sides
m^2+m-30=0
factor
what 2 numbers mulitply to get -30 and add to get 1
-5 and 6
(m-5)(m+6)=0
set to zto
m-5=0
m=5

m+6=0
m=-6
age can't be negative

max is 5
father is 30
5 0
3 years ago
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