Answer:
Step-by-step explanation:
Malcolm's transformation:
First, the blue image is reflected about the line y=-5
Then it is rotated 180 degrees around the point (0,-5)
(you can have other options this is just one example)
Ursa's transformation:
The blue image is reflected about the y axis
(you can have other options this is just one example)
Then, 15 - x is the distance ran in the second part.
The time, t1, for the first part is t1 = xmi / 8mi/h
The time, t2, for the second part is t2 = (15 - x)mi / 20mi/h
The total time is t1 + t2 = 1.125 h
Then x/8 + (15 - x) / 20 = 1.125
To solve for x, multiply both sides by 40 (this is the least common multiple)
5x + 30 - 2x = 45
3x = 15
to find x divide: 15/3=5
And 15 - x = 10 mi.
First part:
Speed: 8mi/h
Distance: 5 mi
Time: 5mi/8mi/h = 5/8 h = 37.5 minutes
Second part
Speed: 20 mi/h
Distance: 10 mi
Average speed: 15mi/1.125h =13.33 mi/h
Distance: 15mi
Time: 1.125 h = 67.5 minutes
Given that
∠ABC and ∠CBD are complementary
Sum of complementary angle = 90°
⇒ m∠ABC + m∠CBD = 90°
⇒ 25° + m∠CBD = 90° [ Given that m∠ABC = 25°]
⇒ m∠CBD = 90° - 25°
⇒ m∠CBD = 65°
Hence proved
<h2>
Height of smaller cone is 14.29</h2>
Step-by-step explanation:

For the first cone
Height, h = 18
Radius, r = 12
Substituting

Volume of new cone formed is half of the older cone.
Volume of new cone = 0.5 x 2714.34 = 1357.17
For the cone as the height reduces to 18 radius reduces to zero.


We have
0.467h₁³ = 1357.17
h₁ = 14.29
Height of smaller cone = 14.29
Answer:
Step-by-step explanation:
Let a and c represent the costs of adult and child tickets, respectively. Then the two purchases can be described by ...
2a +4c = 46 . . . . . . Sue's purchase
4a +7c = 86 . . . . . . Karen's purchase
__
The system can be solved by subtracting the second equation from twice the first:
2(2a +4c) -(4a +7c) = 2(46) -(86)
c = 6 . . . . . . . simplify
We can substitute this value into half the first equation to find "a".
a +2(6) = 23
a = 23 -12 = 11
The cost of 1 adult ticket is $11; the cost of one child ticket is $6.