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3 years ago

Find the length of AB.

Mathematics

1 answer:

alexdok [17]3 years ago

4 0

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

ivann1987 [24]

Step-by-step explanation:

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°.

5 0

3 years ago

Scott wants to cover his patio with concrete pavers. If the patio is shaped like a trapezoid whose bases are 11 feet and 13 feet

GenaCL600 [577]

Answer:

Scott will need 168 ft² of pavers to cover his patio

Explanation:

Scott wants to cover a trapezoid-shaped patio

This means that:

To get the number of square feet of pavers he'll need, we need to get the area of his patio

Area of trapezium id calculated as follows:

$Area = \frac{base_{1}+base_{2}}{2} * height$

We are given that:

base₁ = 11 ft

base₂ = 13 ft

height = 14 ft

We now substitute with the givens to get the area as follows:

$Area = \frac{11+13}{2} * 14 = 168ft^2$

This means that:

Scott will need 168 ft² of pavers to cover his patio

Hope this helps :)

5 0

3 years ago

Consider a series circuit consisting of a resistor of R ohms, an inductor of L henries, and variable voltage source of V(t) volt

ser-zykov [4K]

Answer:

$I(t)=\frac{1}{3}(1-e^{-30t})$

Step-by-step explanation:

We are given that

$\frac{dI}{dt}+\frac{R}{L}I=\frac{V(t)}{L}$

R=150 ohm

L=5 H

V(t)=10 V

$P=\frac{R}{L}=\frac{150}{5}=30$

$I.F=e^{\int Pdt}=e^{\int 30 dt}=e^{30 t}$

$I(t)\times I.F=\int e^{30 t}\times 10 dt+C$

$I(t)\times e^{30 t}=\frac{10}{30}e^{30 t}+C$

$I(t)=\frac{1}{3}+Ce^{-30 t}$

I(0)=0

Substitute t=0

$0=\frac{1}{3}+C$

$C=-\frac{1}{3}$

Substitute the values

$I(t)=\frac{1}{3}-\frac{1}{3}e^{-30 t}$

$I(t)=\frac{1}{3}(1-e^{-30t})$

5 0

3 years ago

Please Help!

natita [175]

$\bf (7x-6)\times (3x^2-4x+5)\implies \begin{array}{cllll} 3x^2-4x+5\\ \times 7x\\\cline{1-1} 21x^3-28x^2+35x \end{array}~~ +~~ \begin{array}{cllll} 3x^2-4x+5\\ \times -6\\\cline{1-1} -18x^2+24x-30 \end{array} \\\\\\ 21x^3-28x^2+35x~~+~~(-18x^2+24x-30)\implies \boxed{21x^3-46x^2+59x-30}$

3 0

3 years ago

Sahir took 1 h 22 min to do his english homework 45 min to do his maths homework, and 10 min to do his urdu. How long did he tak

andre [41]

Answer:

2 hr and 17 minutes

Step-by-step explanation:

add 45 to 10+= 55

55+ 1 hr 22 = 1 hour and 77 minutes which converts to:

2 hour and 17 minutes

good luck!

6 0

3 years ago

Find the length of AB.​

Find the length of AB.