Answer:
Step-by-step explanation:
Let the initial price be x
<u>Then the reduced price is </u>
<u>If 5 mugs cost $28.20, we have equation:</u>
- (x - 1.75)*5 = 28.20
- x - 1.75 = 28.20/5
- x - 1.75 = 5.64
- x = 1.75 + 5.64
- x = 7.39
Initial price for 1 mug was $7.39
Answer:
404 cm³ Anyway... Look down here for my explanation.
Step-by-step explanation:
Let's Draw a line from the center of the circle to one of the ends of the chord (water surface) and another to the point at greatest depth on your paper. A right-angled triangle is formed too. The Length of side to the water-surface is 5 cm, the hospot is 7 cm.
We Calculate the angle θ in the corner of the right-angled triangle by: cos θ = 5/7 ⇒ θ = cos ˉ¹ (5/7)
44.4°, so the angle subtended at the center of the circle by the water surface is roughly 88.8°
The area shaded will then be the area of the sector minus the area of the triangle above the water in your diagram.
Shaded area 88.8/360*area of circle - ½*7*788.8°
= 88.8/360*π*7² - 24.5*sin 88.8°
13.5 cm²
(using area of ∆ = ½.a.b.sin C for the triangle)
Volume of water = cross-sectional area * length
13.5 * 30 cm³
404 cm³
2.
We have a transversal across parallel lines so we get the usual array of congruent and supplementary angles. We just have to figure out which is which, and the diagram, even though not to scale, makes it pretty obvious.
Angle x isn't the same as the 40° angle so it must be its supplement.
Answer: C 140°
3.
r=1.2, h=2.9, V = (1/3) πr²h
Nothing hard here, we just plug in the numbers,
V = (1/3) π (1.2)² (2.9) ≈ 4.37310
Answer: B. 4.4 cubic inches
4.
Dilation by .5 makes a similar triangle, and reflection is an isomorphism (i.e. it doesn't change the size or shape) so the answer is
Answer: B similar not congruent
5.
The corresponding interior and exterior angles of a triangle form a linear pair, so supplementary angles. x=180-110 = 70°
Answer: A 70°
Answer: after 5 hours, 75 cupcakes
Step-by-step explanation:
