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dolphi86 [110]
3 years ago
14

Triangle DEF is circumscribed about circle R. Points S, T and U are points of tangency where SD = 4 m and UF = 7 m. What is the

measure of DF
Mathematics
2 answers:
vovikov84 [41]3 years ago
8 0
First of all, we need to establish some known things. Let us call the radius r and the center of the circle R. Consider RD and then consider the 2 triangles DUR and DSR. We have that they have both a 90 degree angle (due to the tangency condition), they have DR common and also SR is equal to UR since both are equal to r. Hence, we have that the triangles are equal, thus, we have that DS=DU. Since DF=DU+UF, we have that DF=11
Svetllana [295]3 years ago
5 0
The measure off DF is 11.

In a circle inscribed within a triangle, the distance from each vertex of the triangle to the two nearest touchpoints (points of tangency on the circle) are equal.  Since SD=4, DT=4 as well.  Since UF=7, then FT=7.  

DF=DT+TF=4+7=11.
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turn the improper fraction into a mixed number c)45/7 d)20/3 turn these numbers in to a mixed number please help
MariettaO [177]
A mixed number looks like this: a(b/c)
The improper fraction currently looks like this: (ab/c)
Round the numerator to something you can divide by the denominator. For example, 45 would be rounded to 42. 42/7=6. 6 would be the whole number.
45-42=3. 3/7 is the new fraction.
So the answer for c is 6(3/7)
Do you know how to do d?
7 0
3 years ago
In ΔVWX, \text{m}\angle V = (4x+3)^{\circ}m∠V=(4x+3) ∘ , \text{m}\angle W = (x+7)^{\circ}m∠W=(x+7) ∘ , and \text{m}\angle X = (5
NemiM [27]

Answer:

The value of x is 17

Step-by-step explanation:

The sum of the angles in a triangles is 180°

From the question:

In ΔVWX,

m∠V=(4x+3) ∘

m∠W=(x+7) ∘

m∠X=(5x+0) ∘ .

Hence:

m∠V + m∠W + m∠V = 180°

4x + 3 + x + 7 + 5x + 0 = 180°

Collect like terms

4x + x + 5x + 3 + 7 + 0 = 180°

10x + 10 = 180°

Subtract 10 from both sides

10x + 10 - 10 = 180° - 10

10x = 170

Divide both sides by 10

10x/10 = 170/10

x = 17

The value of x is 17

4 0
3 years ago
Helpppppp mathhhhhhhhh
zysi [14]
C would be 16 and b would be 8 square root of 3 so the answer would be a
8 0
3 years ago
Tell whether the angles are adjacent or vertical. Then find the value of x. x =?
baherus [9]

Answer:

The triangle of the 360 squared by the square

8 0
2 years ago
(50 Points Please help)
Elina [12.6K]

Answer:

A. Length of a Tour Bus                       ↔     #2.      1.1 × 10¹ meters

B. Width of an apple                             ↔      #3.     4 × 10⁰ centimeters

C. Distance from Earth to a Satellite    ↔    #6.     8 × 10² kilometers

D. Thickness of a human hair               ↔     #5.      9 × 10¹ micrometers

Step-by-step explanation:

The length of a tour bus should be measured in meters. It sure is way less than 1 kilometer and way more than a few centimeters. It could be about some meters, more than 5 meters, may be between 10 meters and 15 meters.

The measurement in the box # 2. is 1.1 × 10¹ meters, which is equivalent to 1.1 × 10 meters = 11 meters. Thus, this is a reasonable length.

B. Width of an apple.  

The most appropriate unit to measure the width of an apple should be centimeter. It certainly is shorter than 1 meter and bigger than 1 mm.

The width of an apple could be, more or less, around 8 centimeters. The only measurement in the boxes that is in that order is that in the box #3., 4 × 10⁰ centimeters, because 10⁰ = 1, so 4 × 10⁰ = 4 × 1 = 4 centimeters.

C. Distance from Earth to a Satellite

The distance from Earth to a satellite should be measured in kilometers.

You can find in the internet that the distances of the satellites are between 700 kilometers and 36,000 kilometers.

The number in the box #1 is too big, in the order of ten trillions of kilometers, because one trillion is 10¹²; thus that is nonseasonal (too big).

The number in the box #6 is  8 × 10² kilometers, which is equal to 8 × 100 = 800 kilometers.

Thus,  8 × 10² kilometers (box #6) is the most reasonable measurement for the distance from Earth to a Satellite

D. Thickness of a human hair

Of course, kilometers, meters, centimeters and even millimeters are units too big to measure the thickness of a human hair.

One micrometer is 10⁻⁶ meters or 10⁻³ millimeters.

In the internet you can find that diameter of the human hair is in the range from 17 micrometers to 181 micrometers.

The measurement in the box #5. is 9 × 10¹ micrometers, which is equivalent to 9 × 10 = 90 micrometers.

Thus, 9 × 10¹ micrometers is the most reasonable measurement for the thickness of a human hair.

5 0
3 years ago
Read 2 more answers
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