Answer:$104.5
Step-by-step explanation:
cats=c
Dogs=d
2c+3d=455
d=82
Substitute d=82 in 2c+3d=455
2c+3(82)=455
2c+246=455
Collect like terms
2c=455-246
2c=209
Divide both sides by 2
2c/2=209/2
c=104.5
1 cat cost $104.5
(1) ∠ABC = 65°, ∠DBE = 65°, ∠CBE = 115°, ∠ABD = 115°
(2) ∠ABC = 62°, ∠DBE = 62°, ∠CBE = 118°, ∠ABD = 118°
Solution:
(1) In the given image ABC and DBE are vertical angles.
<u>Vertical angle theorem:</u>
If two angles are vertical then they are congruent.
⇒ ∠ABC = ∠DBE
⇒ 3x° + 38° = 5x° + 20°
Arrange like terms one side.
⇒ 38° – 20° = 5x° – 3x°
⇒ 18° = 2x°
⇒ x° = 9°
∠ABC = 3(9°) + 38° = 65°
∠DBE = 5(9°) + 20° = 65°
Adjacent angles in a straight line = 180°
⇒ ∠ABC + ∠CBE = 180°
⇒ 65° + ∠CBE = 180°
⇒ ∠CBE = 115°
∠ABD and ∠CBE are vertical angles.
∠ABD = 115°
(2) In the given image ABC and DBE are vertical angles.
⇒ ∠ABC = ∠DBE
⇒ 4x° + 2° = 5x° – 13°
Arrange like terms one side.
⇒ 13° + 2° = 5x° – 4x°
⇒ 15° = x°
∠ABC = (4(15°) + 2°) = 62°
∠DBE = 5(15°) – 13° = 62°
Adjacent angles in a straight line = 180°
⇒ ∠ABC + ∠CBE = 180°
⇒ 62° + ∠CBE = 180°
⇒ ∠CBE = 118°
∠ABD and ∠CBE are vertical angles.
∠ABD = 118°
Answer:
a
Step-by-step explanation:
;)
The concept that is useful in order to answer this item is the concept of ratio and proportion. Let x be the height of the rock from the ground. We use the equation below to answer.
5.5 ft / 18 ft = x ft / 209.5 ft
The value of x from the equation is 64 ft. Thus, they will be needing approximately 64 ft of rope.
Answer: LAST OPTION.
Step-by-step explanation:
The Pythagorean Theorem states the following relationship between the three sides of a triangle that has an angle of 90 degrees, known as "Right triangle":
Where "a"is the hypotenuse and "b" and "c" are the legs of the right triangle.
If the triangle ABC is a right triangle then AB must be equal to 
, then, you need to substitute the values into to check this:
Then the triangle ABC is not a right triangle.
Therefore, the statement that justifies why this triangle is not a right triangle is:
