Which are the possible side lengths of a triangle?

Diego made a scale drawing of a theater. The scale of the drawing was 1 inch : 3 feet. The

Artyom0805 [142]

Answer:

The actual stage is 42 feet long

Step-by-step explanation:

Step 1

Determine the conversion factor as shown;

1 inch in the drawing represents 3 feet in the actual drawing

To convert a measurement in inches in the drawing to an actual measurement, we use a conversion factor of 3. In the same way, to convert a measurement in feet in the actual stage to the drawing measurement in inches, we use a conversion factor of (1/3).

Step 2

Convert 14 inches in the drawing to the actual measurement of the stage as follows;

Actual stage length=drawing length×conversion factor

where;

drawing length=14 inches

conversion factor=3

replacing;

Actual stage length=(14×3)=42 feet

The actual stage is 42 feet long

3 0

3 years ago

Find z1z2 if z1 = 2/5(cos63° + isin63°) and z2 = 10/3(cos117° + isin117°).

Airida [17]

Answer:

-10/3 is the answer

Step-by-step explanation:

Given are two complex numbers as

$z1=\frac{2}{5} (cos63 + isin63)\\z2=\frac{10}{3} (cos 117 + isin117})$

Recall Demoivre theorem as

(cosA+isinA)(cos A+isin B) = cos(A+B)+isin(A+B)

Hence here we have sum of angles as

A+B = 63+117 =180

$z1z2=\frac{2}{5} \frac{10}{3} (cos180+isin180)$

= $\frac{-10}{3}$

Since sin180=0 and cos 180=-1

7 0

4 years ago

Please help, I’ll mark your answer as brainliest!

statuscvo [17]

Answer:

$(x-230)^2+(y-220)^2=6100$

Step-by-step explanation:

The equation for a circle is $(x-h)^2+(y-k)^2=r^2$ , where $(h,k)$ is the vertex of the circle and $r$ is the radius. Immediately, since the center of the circle is given, we know what $h$ and $k$ are. $h$ is 230 and $k$ is 220.

The only thing we need to find is the radius, which will just be the distance from the center (230,220) to a point on the circumference (170,170). The distance between them can be calculated using the distance formula, which is really just the Pythagorean Theorem rearranged. The formula states that $d=\sqrt{x^2+y^2}$ , where $x$ is the change in the x-coordinates of the two points and $y$ is the change in the y-coordinates of the two points. Plug-in $x$ for 60 and $y$ for 50 to get $d=\sqrt{50^2+60^2}$ . Solve for $d$ , arriving at $\sqrt{6100}$ . Therefore, the radius of the circle is $\sqrt{6100}$ .

Finally, we have all of the components to create the equation of the circle. Plug-in 230 for $h$ , 220 for $k$ , and $\sqrt{6100}$ for $r$ .

The equation of the circle will be $(x-230)^2+(y-220)^2=6100$ .

Hope this helps :)

4 0

2 years ago

Which equation would intersect the line on the graph at the point (1, 2)

Inga [223]

Show the graphs so we can see

7 0

3 years ago

Find a irrational number between 5.2 and 5.3 .. Explain why its irrational. Include the decimal approximation of thr nearest hun

mihalych1998 [28]

$\sqrt{28}$
It is in between
$\sqrt{25}$
And
$\sqrt{36}$
There for it is in between 5 and 6
Additionally, it is closer to root 25, meaning that it is closer to 5

Rounded to the nearest hundredth is

5.29

4 0

4 years ago