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nasty-shy [4]
3 years ago
9

A triangle has an angle that measures 10°. The other two angles are in a ratio of 3:14. What

Mathematics
1 answer:
ivann1987 [24]3 years ago
5 0

Step-by-step explanation:

<h3>Need to FinD :</h3>

  • We have to find the measures of other two angles of triangle.

\red{\frak{Given}} \begin{cases} & \sf{The\ measure\ of\ one\ angle\ of\ traingle\ is\ {\pmb{\sf{10^{\circ}}}}.} \\ & \sf{The\ other\ two\ angles\ are\ in\ the\ ratio\ of\ {\pmb{\sf{3\ :\ 14}}}.} \end{cases}

We know that,

  • The other two angles of triangle are in the ratio of 3 : 14. So, let us consider the other two angles of the triangle be 3x and 14x.

Angle sum property,

  • The angle sum property of triangle states that the sum of interior angles of triangle is 180°. By using this property, we'll find the other two angles of the triangle.

\rule{200}{3}

\sf \dashrightarrow {10^{\circ}\ +\ 3x\ +\ 14x\ =\ 180^{\circ}} \\ \\ \\ \sf \dashrightarrow {10^{\circ}\ +\ 17x\ =\ 180^{\circ}} \\ \\ \\ \sf \dashrightarrow {17x\ =\ 180^{\circ}\ -\ 10^{\circ}} \\ \\ \\ \sf \dashrightarrow {17x\ =\ 170^{\circ}} \\ \\ \\ \sf \dashrightarrow {x\ =\ \dfrac{\cancel{170^{\circ}}}{\cancel{17}}} \\ \\ \\ \dashrightarrow {\underbrace{\boxed{\pink{\frak{x\ =\ 10^{\circ}.}}}}_{\sf \blue {\tiny{Value\ of\ x}}}}

∴ Hence, the value of x is 10°. Now, let us find out the other two angles of the triangle.

\rule{200}{3}

Second AnglE :

  • 3x
  • 3 × 10
  • 30°

∴ Hence, the measure of the second angle of triangle is 30°. Now, let us find out the third angle of triangle.

\rule{200}{3}

Third AnglE :

  • 14x
  • 14 × 10
  • 140°

∴ Hence, the measure of the third angle of the triangle is 140°.

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Step-by-step explanation:

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U<br>10<br>15list all factors of list all factors of 22 ​
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The ABC Company has a net income of $56,000, assets at the beginning of the year are $263,000 and assets at the end of the year
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Answer:

19.4 %

Step-by-step explanation:

The formula for<em> return on assets</em> (ROA) is

ROA = Net income /Total assets × 100 %

Since assets vary, we use the <em>average</em> of the total assets over the period.

<em>Calculate the average total assets</em>

At beginning of year, total assets = $263 000

At end of year, total assets            = $313 000

Average = (313 000 + 263 000)/2

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Average = $288 000

===============

<em>Calculate the ROA</em>

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4 0
3 years ago
Read 2 more answers
Tanya took a cab from her home to the airport. Her total fare including a tip of $5.00, was $28.50. EZ Cab Company has a pick-up
ValentinkaMS [17]
16.2 miles.

Since she paid a $5 tip, the cost for her fare was $23.50.  Let x be the number of 0.2-mile increments in the trip:
23.50 = 2.50 + 1 + 0.25(x-1)

This equation comes from the 2.50 home pick-up fee; $1 for the first 0.2-mile increment; and 0.25 for each other 0.2-mile increment.

Using the distributive property, we have:
23.50 = 2.50 + 1 + 0.25*x - 0.25*1
23.50 = 2.50 + 1 + 0.25x - 0.25

Combining like terms,
23.50 = 0.25x + 2.75

Subtracting 2.75 from both sides, we have:
23.50 - 2.75 = 0.25x + 2.75 - 2.75
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Dividing both sides by 0.25, we have:
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This means there are 81 0.2-mile increments in her trip.  81(0.2) = 16.2 miles
6 0
4 years ago
Given z1 = 1+i and z2 = 2+3i.
Margaret [11]

Answer:

(a) w=2+5i-6=-4+5i

Multiplicative inverse of w will be \frac{1}{-4+5i}

(B) As w is same as the product of z_1\ and\ z_2

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Step-by-step explanation:

We have given two complex numbers

z_1=1+i and z_2=3+2i

(a) First we have to find w=z_1z_2

So w=(1+i)(2+3i)=2+3i+2i+6i^2=2+5i+6i^2

As we know that i^2=-1

So w=2+5i-6=-4+5i

Multiplicative inverse :

It is that number when multiply with the number which we have have to find the multiplicative inverse gives result as 1

So multiplicative inverse of w will be \frac{1}{-4+5i}

Because when we multiply -4+5i with \frac{1}{-4+5i} it gives result as 1

(b) As w is same as the product of z_1\ and\ z_2

So there multiplicative inverse will also be same

4 0
3 years ago
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