Write the direct variation: The total cost C of gasoline is $3.00 times the number of gallons g

Hi, please help me with this question. what is 45+46+47+ ... +53+54?

Viktor [21]

Answer:

Step-by-step explanation:

1). 91 + 41 + 53 + 54 {Simplify}

2). 138 + 53 + 54 {Simplify}

3). 191 + 54 {Simplify}

4). 245 {Add}

4 0

3 years ago

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50 Points: Name the similar triangles & Prove the similarity with details

Leno4ka [110]

Let's consider the facts at hand:

By Vertical Angle Theorem ⇒ ∠BCE = ∠DCF
∠BEC = ∠DFC
Sides BE = DF

Based on the diagram, triangles BCE and triangles DCF are similar

⇒ based on the Angle-Angle theorem

⇒ since ∠BCE = ∠DCF and ∠BEC = ∠DFC

⇒ the two triangles are similar

Hope that helps!

Definitions of Theorem I used:

Vertical Angle Theorem: opposite angles of two intersecting lines must be equal
Angle-Angle Theorem: if two angles of both triangles are equal, then the given triangles must be similar

8 0

2 years ago

A man walking on a railroad bridge is 2/5 of the way along the bridge when he notices a train at a distance approaching at the c

makkiz [27]

Answer:

The Man needs to run at 9 mph

Step-by-step explanation:

Let M stand for the man's speed in mph. When the man

runs toward point A, the relative speed of the train with respect

to the man is the train's speed plus the man's speed (45 + M).

When he runs toward point B, the relative speed of the train is the

train's speed minus the man's speed (45 - M).

When he runs toward the train the distance he covers is 2 units.

When he runs in the direction of the train the distance he covers

is 3 units. We can now write that the ratio of the relative speed

of the train when he is running toward point A to the relative speed

of the train when he is running toward point B, is equal to the

inverse ratio of the two distance units or

(45 + M) 3

----------- = ---

(45 - M) 2

90+2 M=135-3 M

⇒5 M = 45

⇒ M = 9 mph

The Man needs to run at 9 mph

3 0

3 years ago

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AD←→ is tangent to circle M at point D. The measure of ∠DMQ is 58º.

Marat540 [252]

Answer:

32°

Step-by-step explanation:

Given:

∠DMQ = 58º

In this circle, the radius is DM. Since AD is tangent to the circle M, at point D, and the angle between a tangent and a radius is 90°

Therefore, ∠MDQ = 90°

The total angle in a triangle is 180°. Since we have the values of ∠MDQ and ∠DMQ, ∠DQM will be calculated as:

180 = ∠DMQ + ∠MDQ + ∠DQM

Solving for ∠DQM, we have:

∠DQM = 180 - ∠DMQ - ∠MDQ

∠DQM = 180 - 90 - 58

∠DQM = 32°

The measure of ∠DQM is 32°

6 0

3 years ago

Leah's house has media room with a large flat screen tv. The media room tv has a width of 8 feet and a height of 4.5 feet. The f

neonofarm [45]

The ratio of the media room tv's width to height is 8ft to 4.5ft or 8/4.5

since the ratio of the living room tv's width to height is the same, the ratio would be
x/27 = 8/4.5
with x being the living room tv's width. Solve for x
x = (8/4.5)(27)
= 48
The width of the living room tv is 48 inches

4 0

3 years ago

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