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3 years ago

What are the measures of angles a,b, and c? Show your work and explain your answers.

Mathematics

2 answers:

Virty [35]3 years ago

8 0

Answer:

c is 110 degrees

b is 70 degrees

a is 20 degrees

Step-by-step explanation:

for c, 180-70=110

for b, 180- angle c=180-110=70

for a, 180-90-angle b=180-90-70=20

lesantik [10]3 years ago

6 0

Answer:

a = 35°

b = 55°

c = 110°

Step-by-step explanation:

Vertically opposite angles are equal.

a = 35° [Vertically opposite angles]

Sum of all angles of a triangle is 180°.

a + b + 90° = 180° [Angles of a triangle]

=> 35° + b + 90° = 180°

=> 35° + b = 180° - 90°

=> 35° + b = 90°

=> b = 90° - 35°

=> b = 55°

Linear pair of angles are supplementary.

c + 70° = 180° [Linear pair of angles]

=> c = 180° - 70°

=> c = 110°

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Lena paid $18.96 for 3pounds of coffee. What is the cost per pound for this coffee

STatiana [176]

Answer:

6.32

Step-by-step explanation:

divide 18.96 by 3 and the outcome is 6.32

6 0

3 years ago

Cos^2x+cos^2(120°+x)+cos^2(120°-x)<br>i need this asap. pls help me

o-na [289]

Answer:

$\frac{3}{2}$

Step-by-step explanation:

Using the addition formulae for cosine

cos(x ± y) = cosxcosy ∓ sinxsiny

---------------------------------------------------------------

cos(120 + x) = cos120cosx - sin120sinx

= - cos60cosx - sin60sinx

= - $\frac{1}{2}$ cosx - $\frac{\sqrt{3} }{2}$ sinx

squaring to obtain cos² (120 + x)

= $\frac{1}{4}$ cos²x + $\frac{\sqrt{3} }{2}$ sinxcosx + $\frac{3}{4}$ sin²x

--------------------------------------------------------------------

cos(120 - x) = cos120cosx + sin120sinx

= -cos60cosx + sin60sinx

= - $\frac{1}{2}$ cosx + $\frac{\sqrt{3} }{2}$ sinx

squaring to obtain cos²(120 - x)

= $\frac{1}{4}$ cos²x - $\frac{\sqrt{3} }{2}$ sinxcosx + $\frac{3}{4}$ sin²x

--------------------------------------------------------------------------

Putting it all together

cos²x + $\frac{1}{4}$ cos²x + $\frac{\sqrt{3} }{2}$ sinxcosx + $\frac{3}{4}$ sin²x + $\frac{1}{4}$ cos²x - $\frac{\sqrt{3} }{2}$ sinxcosx + $\frac{3}{4}$ sin²x

= cos²x + $\frac{1}{2}$ cos²x + $\frac{3}{2}$ sin²x

= $\frac{3}{2}$ cos²x + $\frac{3}{2}$ sin²x

= $\frac{3}{2}$ (cos²x + sin²x) = $\frac{3}{2}$

5 0

3 years ago

The main goal of a personal budget is to

Evgesh-ka [11]

Make sure you don't spend to much and have no more money left

3 0

3 years ago

Read 2 more answers

At a school fair, students were challenged to hit one of the small congruent circles on the large rectangular board with a ball.

shtirl [24]

Answer:

~4.7%

Step-by-step explanation:

Area of the rectangle: 35*52=1820

Area of 1 small circle: A=πr2=π·32≈28.27433

28.27433*3=84.82299

84.82299/1820=0.04660603846

Therefore, about 4.7%

6 0

2 years ago

∠A and \angle B∠B are complementary angles. If m\angle A=(x+16)^{\circ}∠A=(x+16) ∘ and m\angle B=(x-12)^{\circ}∠B=(x−12) ∘ , the

Elena-2011 [213]

Answer:

Step-by-step explanation:

∠A + ∠B = 90 {∠A & ∠B are complementary}

x + 16 + x - 12 = 90

x + x + 16 - 12 = 90 {Combine like terms}

2x + 4 = 90 { Subtract 4 form both sides}

2x = 90 - 4

2x = 86 {divide both sides by 2

x = 86/2

x = 43

8 0

2 years ago