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olga55 [171]
3 years ago
13

In the figure below, segment AC is congruent to segment AB.

Mathematics
2 answers:
sattari [20]3 years ago
4 0

Answer:

Option B is correct.

Angle DAC is congruent to angle DAB

Step-by-step explanation:

Given: Segment AC is congruent to segment AB.

In  ΔABD and ΔACD

AB \cong AC    [Given]

[Congruent sides have the same length]

AB = AC         [Side]

AD = AD        [Common side]

\angle DAC =\angle DAB      [Angle]

Side Angle Side(SAS) Postulate states that if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the two triangles are congruent.

Then by SAS,

\triangle ABD \cong \triangle ACD

By CPCT [Corresponding Parts of congruent Triangles are congruent]

then;

\angle ABD \cong \angle ACD

therefore, only statement which is used to prove that angle ABD is congruent to angle ACD is: Angle DAC is congruent to DAB

brilliants [131]3 years ago
4 0
The right answer for the question that is being asked and shown above is that: "Angle DAC is congruent to angle DAB." The statement that is used to prove that angle ABD is congruent to angle ACD is that <span>Angle DAC is congruent to angle DAB.</span>
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Erik's disabled sailboat is floating stationary 3 miles east and 2 miles north of Kingston. A ferry leaves Kingston heading towa
sergij07 [2.7K]

Answer:

Step-by-step explanation:

Let's suppose that Ballard is an origin with coordinates (0;0)

Ballard is 8 miles south and 1 mile west of Edmonds ⇒ Edmonds is 1 mile east and 8 miles north of Ballard.

Thus, coordinates of Edmonds (0+1; 0+8) (1;8)

Edmonds is 6 miles due east of Kingston. So, is 6 miles due of Edmonds

Thus, Kingston coordinates (1-6;8) (-5:8)

Sailboat is 3 miles east and 2 miles north of kingston

So, coordinates of sailboat are (-5+3; 8+2) (-2;10)

a)

Ferry leaves Kingston towards Edmonds at mph and Edmonds is 6 miles due east of Kingston.

Initial ferry coordinates as calculated above are equal to Kingston coordinates (-5;8)

After 20 minutes the ferry turns to south.

This distance travelled (20min) is d=9mph*20/60h=3 miles

So, ferry travelled 3 miles toward east in 20 min

Then, coordinates became (-5+3;8+0) (-2;8)

Thus, we have a line connecting two points (-5;8) and (-2;8)

Line connecting them has an equation:

y-8 = (8-8)/(-2+5) * (x+5)

y-8=0

y=8 - This is the equation for the first 20 minutes of travel

Then, ferry turns due south (-2;8) and has a vertiacl line

The equation of verical line is x=a, so the equation will be x=2

b) The sailboat has a radar scope that will detect any object within 3 miles of the sailboat.

region looks like a circular disc with a center (-2;10)

(x+2)^2+(y-10)^2=3^2

(x+2)^2+(y-10)^2 <9 (interior of the circular disc)

(x+2)^2+(y-10)^2 >9 (exterior)

The equation of the line joining the Kingston and Edmonds is y=8

the point of intersection:

(x+2)^2+(8-10)^2=9

(x+2)^2=5

x is approximately 0.24; -4.24

(0.24;8) (-4.24;8) - intersection points

c) The ferry exits the radar during the trid due south long x=-2

The points of intersection of the circle and the line x=-2:

(-2+2)^2+(y-10)^2=9

0+(y-10)^2=0

y is 7.13

(-2;7)

d) Takes south turn at (-2;8), then ferry travels 0.8 miles up to point (-2;7) where it exists the radar zone

Speed is 9mph

The time taken to cover 1 mile = t=1/9hr=1/9 *60=6.667min

So, it exists after 6.67 minutes

e) Ferry enters at (-4.24;8) and takes turn due to south at (-2;8)

The distance travelled is = [-4.24+2]=2.24 miles

The time taken to cover these miles is = t=2.24/9 *60=14.93 min

After turning to south ferry remains in radar for 6.7 min

So, it remains in radar zone for 14.93+6.7=21.63min

8 0
3 years ago
How would i write 4.67 as a mixed number?
gavmur [86]
4.67= 4 67/100
67 is a prime number, so the only fraction 67 hundredths can be represented by is 67/100.
8 0
3 years ago
Which expression is equivalent to -3x + 9?
Olenka [21]

Answer:

B

Step-by-step explanation:

You use the distributive Property

-3(x-3)

-3x+9

4 0
3 years ago
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William is planning a party. He spent $110.74 to buy 9.8 pounds of candy for favors. What was the cost per pound of the candy? (
AfilCa [17]

Answer: $11.30 per pound

Step-by-step explanation:

William spent $110.74 to buy 9.8 pounds of candy.

To find the cost per candy, divide the amount spent by the quantity of candy:

=Amount spent on candy / Quantity of candy

= 110.74 / 9.8

= $11.30 per pound

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2 years ago
Someone help please
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