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Verizon [17]
3 years ago
12

A town planner wants to build two new streets, Elm Street and Garden Road, to connect parallel streets Maple Drive and Pine Aven

ue. Trapezoid E F G H is shown. F G is Maple Drive, G H is Garden road, E H is Pine avenue, and E F is Elm Street. Sides F G and E H are parallel. Angle G is 108 degrees. In trapezoid EFGH, EF ≅ HG. What is the measure of the angle between Elm Street and Pine Avenue? 54° 72° 108° 144°
Mathematics
1 answer:
Advocard [28]3 years ago
3 0

Answer:

72°

Step-by-step explanation:

From the information given:

A town planner wants to build two new streets, Elm Street and Garden Road, to connect parallel streets Maple Drive and Pine Avenue.

We are also told that there is a  Trapezoid EFGH with EH as the Pine avenue and EF as the Elm street.

However, side FG and EH are parallel.

∠G = 108°

From the property of parallel lines :

since FG || EH

Then  ∠G = ∠H  = 108°  (i.e corresponding angle will also be equal)

The required angle between Elm Street and Pine Avenue would be interior angles +  180°  given that  alternate angles are also equal.

The required angle between Elm Street and Pine Avenue = 180° - 108°

The required angle between Elm Street and Pine Avenue = 72°

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MrRissso [65]

Answer:

\therefore x=50\°

Step-by-step explanation:

Let the angle between 2x and 150° be = b°

150\°+b\°=180\° [ Forming a linear pair of angles]

Solving for b by subtracting both sides by 150.

150+b-150=180-150

∴ b=30\°

50\°+2x+b\°=180\°\\ [Angle lying on a straight line add up to 180]

Plugging in b=30\°

50+2x+30=180\\2x+80=180

Solving for x by

subtracting both sides by 80.

2x+80-80=180-80\\2x=100

then dividing both sides by 2.

\frac{2x}{2}=\frac{100}{2}\\\\\therefore x=50\°

4 0
2 years ago
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The dollar value v(t) of a certain car model that is t years old is given by the following exponential function.
dimaraw [331]

Answer:

v(0) = 32,000 . . . dollars

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Step-by-step explanation:

The initial value is the value of the function for t=0. Put that into the formula and evaluate.

v(0) = 32,000(0.95^0) = 32,000 . . . . dollars

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The value after 13 years is the function value for t=13. Put that into the formula and evaluate.

v(13) = 32,000(0.95^13) ≈ 32,000·0.513342 ≈ 16,427 . . . . dollars

5 0
2 years ago
On the first day, a company has 64 orders for shipping crates on backorder. Every day customers order 18 more shipping crates. I
SOVA2 [1]

The <em><u>correct answer </u></em>is:

B. 14

Explanation:

Let x be the number of days.  On day 1, we begin with 64 orders.  We gain 18 orders per day; this is 18x, and gives us

64+18x.

We also make 28 crates per day, which decreases the number of crates we need by 28 per day; this is -28x, and gives us

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Combining like terms, we get

64-10x

For day 5, we replace x with 5:

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3 years ago
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Answer:

y = -2x - 6

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