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2 years ago

5

A map has a scale of 3 in. = 16 mi. If you measured the distance between two cities to be 23 in. on the map, how many miles woul

d it actually be?

1 answer:

Scrat [10]2 years ago

8 0

Answer:

122.667

Step-by-step explanation:

23/3=7.667

7.667*16=122.667

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1462 divided by 58<br><br> To mixed number

GaryK [48]

Ur answer is 25/6/29 plz give brainliest

6 0

2 years ago

In the figure, AB=12, BC=8, DE=6, PD=4, and A is the point of tangency. Find the radius of circle P.

Lelu [443]

Answer:

The radius of the circle P = 2√10 = 6.325

Step-by-step explanation:

∵ AB is a tangent to circle P at A

∴ (AB)² = BC × BE

∵ BC = 8 , AB = 12 , ED = 6

∵ BE = ED + DC + CB

∴ BE = 6 + CD + 8 = 14 + CD

∴ (12)² = 8 × (14 + DC) ⇒ (12)²/8 = 14 + CD ⇒ CD = (12)²/8 - 14

∴ CD = 4

Join PC and PE (radii)

In ΔBDC and ΔPDE ⇒ ∵ ∠PDC = Ф , ∴ ∠PDE = 180 - Ф

Use cos Rule:

∵ r² = (PD)² + (DC)² - 2(PD)(DC)cosФ

∴ r² = 16 + 16 - 32cosФ = 32 - 32cosФ ⇒ (1)

∵ r² = (PD)² + (DE)² - 2(PD)(DE)cos(180 - Ф) ⇒ cos(180 - Ф) = -cosФ

∴ r² = 16 + 36 + 48cosФ = 52 + 48cosФ ⇒ (2)

∵ (1) = (2)

∴ 32 - 32 cosФ = 52 + 48cosФ

∴ 32 - 52 = 48cosФ + 32cosФ

∴ -20 = 80cosФ

∴ cosФ = -20/80 = -1/4

∴ r² = 32 - 32(-1/4) = 32 + 8 = 40

∴ r = √40 = 2√10 = 6.325

7 0

2 years ago

At a store each notebook has a cost of X dollars. which situation can be represented by this inequality

nadezda [96]

Answer:

a

the cot of 5 notebook is greater than the cost of 3notebooks plus a $2 pen

7 0

3 years ago

PLZ HELP ASAP!!

Lilit [14]

The measure of first angle is 34 degrees and measure of second angle is 56 degrees

<em><u>Solution:</u></em>

Given that, the exterior sides of two adjacent angles make a right angle

Therefore, these adjacent angles forms 90 degrees

Let the second angle be "x"

The first angle has a measure that is six more than half the second

Therefore,

first angle = 6 + half of "x"

$\text{ first angle } = 6 + \frac{x}{2}$

Since these two angles forms 90 degrees,

first angle + second angle = 90

$x + 6 + \frac{x}{2} = 90\\\\\frac{2x + 12 + x}{2} = 90\\\\2x + 12+x = 180\\\\3x + 12 = 180\\\\3x = 180 - 12\\\\3x = 168\\\\x = 56$

<em><u>Therefore, first angle is:</u></em>

$\rightarrow 6 + \frac{56}{2} = 6 + 28 = 34$

Thus measure of first angle is 34 degrees and measure of second angle is 56 degrees

6 0

3 years ago

your friend says that the volume of a sphere with a radius r is four times the volume of a cone with radius r. when is this true

Ierofanga [76]

Volume of a sphere is given by the formula: $V_{\circ}=\frac43\pi r^3$

If we pull the 4 out front we have, $V_{\circ}=4\left(\frac13\pi r^3\right)$ .

Volume of a cone is given by the formula: $V_{\triangle}=\frac{1}{3}\pi r^2\cdot h$

Notice that if the height of the cone is equal to the radius, $V_{\triangle}=\frac13\pi r^2\cdot r$

then it's exactly what we see in our volume formula without the 4!

7 0

2 years ago