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4 years ago

A triangle with sides measuring 8, 15 and 17 units is inscribed in a circle. What is the radius of the circle, in units?

Mathematics

1 answer:

Lubov Fominskaja [6]4 years ago

5 0

Answer: radius of the circle is 8.5 units

Step-by-step explanation:

The diagram of the circle and the inscribed triangle is shown in the attached photo. Looking at the length of each side of the triangle given, the lengths form a Pythagorean triple. We can confirm by applying Pythagoras theorem

Hypotenuse^2 = opposite side^2 + adjacent^2. It becomes

17^2 = 8^2 + ``15^2

289 = 64 + 225

289 = 289

This means that the triangle formed is a right angle triangle.

According to Thales theorem,

The diameter of the circle always subtends a right angle to any point on the circle. Since the diameter is the longest side of the circle and the angles is formed on a point on the circle,

Diameter = 17

Radius = diameter/2 = 17/2 = 8.5

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The perimeter (P) of a rectangular field is 1,672 ft. Suppose the width (w) of the field is 230 feet. What is the length (l) of

muminat

Answer: b) 606 ft

Step-by-step explanation: P=2L +2w

1,672=2(L)+2(230)

1,672=2(L)+460

1,212=2(L)

606=L

7 0

4 years ago

Read 2 more answers

Dominic is stacking legos to make a tower. He takes a break when the tower is 4 1/2 feet tall, which is 3/8 of the height of the

Lynna [10]

Answer:

Tower is 9 ft tall when it is finished.

Step-by-step explanation:

Given that:

Height of the tower when Dominic takes a break = $4\frac{1}{2}$ feet

The height of the tower as built by Dominic = $\frac{3}8$ of the total height

Let the total height of the tower to be built = $x$ feet

Let us have a look at the method to convert mixed fraction to a fractional number.

$a\dfrac{b}{c} = \dfrac{a\times c +b}c\\\Rightarrow 4\dfrac{1}{2} = \dfrac{4\times 2 +1}{2}=\dfrac{9}2$

As per question statement, $\frac{3}8$ of the total height is equal to $4\frac{1}{2}$ feet.

We can write the equation as:

$\dfrac{3}{8}x = \dfrac{9}{2}\\\Rightarrow x = \dfrac{9}{2}\times \dfrac{8}{3}\\\Rightarrow x = \dfrac{72}{6}\\\Rightarrow x = \bold{9\ ft}$

Therefore, tower is <em>9 ft</em> tall when it is finished.

4 0

3 years ago

What is y in the equation 2/3 (2y+1) = 3/7 (2-y)

Alik [6]

Answer:

$y=\frac{4}{37}$

Step-by-step explanation:

$\frac{2}{3}(2y+1)=\frac{3}{7}(2-y)$

$\frac{4}{3}y+\frac{2}{3} =\frac{6}{7}- \frac{3}{7}y$

Add $\frac{3}{7}y$ on both sides and subtract $\frac{2}{3}$ on both sides.

$(\frac{3}{7}y- \frac{2}{3})+\frac{4}{3}y+\frac{2}{3} =\frac{6}{7}- \frac{3}{7}y+(\frac{3}{7}y- \frac{2}{3})$

$\frac{3}{7}y+\frac{4}{3}y=\frac{6}{7}-\frac{2}{3}$

Solve the fractions.

$\frac{(3)(3)+(7)(4)}{(7)(3)}y=\frac{(6)(3)-(7)(2)}{(7)(3)}$

$\frac{9+28}{21} y=\frac{18-14}{21}$

$\frac{37}{21}y =\frac{4}{21}$

Multiply by the reciprocal of the fraction with the variable to isolate the variable. The reciprocal is the inverted fraction.

$\frac{21}{37}*\frac{37}{21}y =\frac{4}{21}*\frac{21}{37}$

$y=\frac{4}{37}$

4 0

4 years ago

Read 2 more answers

What is the equation of the graph below? A graph shows a parabola that opens up and crosses the x axis at negative two and negat

Anastaziya [24]

Answer:

$y=(x+3)^{2} -1$

Step-by-step explanation:

General equation of a parabola that opens up is $y=a(x-h)^{2} +k$ , a>0

So equation becomes $y=(x-h)^{2} +k$ which implies option A and option B can never be true for this parabola.

Also this parabola's vertex lies in 3rd quadrant where coordinates of both x and y will be negative.

So, the equation of parabola will be of the form $y=(x+h)^{2} - k$

Hence, option 4 that is $y=(x+3)^{2} -1$ is correct.

4 0

3 years ago

Read 2 more answers

Can someone please help me?

liubo4ka [24]

a. 0

b. -5

c. 8

d. 12

e. -9

f. 5

g. -6

h. -91

i. -15

j. 6

k. 17

l. 11

7 0

4 years ago