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GrogVix [38]
3 years ago
13

The systems shown have the same solution set.

Mathematics
2 answers:
Sonbull [250]3 years ago
6 0
The answer is true :) hope this helped
yuradex [85]3 years ago
4 0

Answer: true

Step-by-step explanation:

Sry if I’m wrong

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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
3 years ago
What is the volume of this prism?
HACTEHA [7]

Answer:

Step-by-step explanation:The formula for the volume of a prism is V=Bh , where B is the base area and h is the height. The base of the prism is a rectangle. The length of the rectangle is 9 cm and the width is 7 cm. The area A of a rectangle with length l and width w is A=lw .

7 0
2 years ago
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What is the equation of the line that is parallel to the
erastovalidia [21]

Answer:

Step-by-step explanation:

A parallel line will have the same slope as the reference line.  In this case, I don't see the "given line" as promised in the question.  If it does appear, and it looks like y = 5x + 3, for example, the slope is 5 and the new line will have the same slope.

<h3><u>If this slope is correct</u>, we can start the equation for the parallel line that goes through point (-3,2) by starting with:</h3><h3 /><h3>y = 5x + b</h3><h3 /><h3>We need a value of b that forces the line to go through point (-3,2).  We can do that by using the given point in the equation and solving for b:</h3><h3>y = 5x + b</h3><h3>2 = 5(-3) + b</h3><h3>b = 17</h3><h3 /><h3>The parallel line to y=5x+3 is</h3><h3>y = 5x + 17</h3><h3 /><h3>See attachment.</h3><h3 /><h3 /><h3 />

5 0
2 years ago
Someone tell me where everyone is going right please !!
iVinArrow [24]

Answer:

<em>1min = 0.25miles</em>

5.25miles / 0.25miles = 25 = 25minutes

Step-by-step explanation:

<u>Hope this is right I'm not the best at worded time/distance math questions.</u>

8 0
3 years ago
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I need help thank youuu
WITCHER [35]

Answer:

.

Step-by-step explanation:

6 0
3 years ago
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