- Angle 1 is congruent to angle 2, since BD bisects <ABC and the two angles created on each side of the bisector at point B are equal.
- <2 ≅ <3 because of the corresponding angles theorem.
- <1 ≅ <4 because alternate angles are congruent if two parallel lines are cut by a transversal.
- <3 ≅ <4 by the substitution property of equality.
- AD/CD = EB/CB by the triangle proportionality theorem.
- If two angles in a triangle are congruent, the sides opposite the angles are congruent, so AE = EB.
- AD/CD = AB/CB by the substitution property of equality.
<h3>The properties of similar triangles.</h3>
In Geometry, two (2) triangles are said to be similar when the ratio of their corresponding side lengths are equal and their corresponding angles are congruent.
<h3>What is the substitution property of equality?</h3>
The substitution property of equality states that assuming x, y, and z are three (3) quantities, and if x is equal to y (x = y) based on a rule and y is equal to z (y = z) by the same rule, then, x and z (x = y) are equal to each other by the same rule.
In this context, we can reasonably infer and logically deduce that the ratio of AD/CD is equal to AB/CB based on the substitution property of equality.
Read more on substitution property here: brainly.com/question/2459140
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Complete Question:
In ΔABC, side BC is extended to point E. When connected to vertex A, segment EA is parallel to segment BD. In this construction, you are given that BD bisects <ABC.
Prove: AD/CD = AB/CB.
Complete the paragraph proof.
Step-by-step explanation:
First, replace f(x) with y ⇒ f(x)=6x-19 ⇒ y=6x-19
Then y with x and x with y ⇒ y=6x-19 ⇒ x=6y-19
Solve the equation from for y:
x=6y-19
x+19=6y dividing with 6
1/6 x +(19/6) = y
Replace y with f−1(x) ⇒ f−1(x)= 1/6 x +(19/6)
hope this helps!
The inverse function of the function f(x) will be f⁻¹(x) = 4x + 48. Then the correct option is D.
The complete question is attached below.
<h3>What is inverse of a function?</h3>
Suppose that the given function is
f: X → Y
Then, if function 'f' is one-to-one and onto function (a needed condition for inverses to exist), then, the inverse of the considered function is
f⁻¹: Y → X
It simply means, inverse of 'f' is an undo operator, that takes back the effect of 'f'
The function is given below.
f(x) = (1/4)x – 12
Then the inverse function of the function f(x) will be
(1/4)f⁻¹(x) - 12 = x
f⁻¹(x) = 4x + 48
Then the correct option is D.
Learn more about inverse function here:
brainly.com/question/19425567
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The total cost of the meal is $30.02
Step-by-step explanation:
Given,
Cost of meal = $24.62
Tax = 6%
Tax amount = 6% of cost of meal
Cost after sales tax = 24.62+1.48 = $26.10
Tip = 15%
Tip amount = 15% of cost after sales tax
Total cost of meal = Cost after sales tax + Tip amount
Total cost of meal = 26.10+3.92 = $30.02
The total cost of the meal is $30.02
Keywords: percentage, sales tax
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Answer:
the numbers are 18 and 38
Step-by-step explanation:
x =smaller integer and y =larger integer
