All categories

3 years ago

What is the arc measure of minor arc AB in degrees?

Mathematics

1 answer:

Ratling [72]3 years ago

3 0

Answer:

$m\widehat{AB} =55 \degree$

Step-by-step explanation:

$\because m\angle APC=m\angle DPE$

(Vertical angles)

$\therefore m\widehat {ABC} =m\widehat {DE}$

(Measure of minor arc is equal to the measure of it's corresponding central angle)

$\therefore m\widehat {AB}+m\widehat {BC} = m\widehat {DE}$

$\therefore m\widehat{AB} = m\widehat {DE} - m\widehat {BC} \\ \\ m\widehat{AB} =93 \degree - 38 \degree \\ \\ m\widehat{AB} =55 \degree$

You might be interested in

16)

elixir [45]

$78

The difference between choice A and B is 5 meals and $80 so 1 meal is $16. So we can subtract $16 from $250 and we get $234 for 3 nights. 1 night is $78

8 0

3 years ago

A train travels 4.4 miles in

Ugo [173]

Answer:

63.8 miles

Step-by-step explanation:

If the train travels 4.4 miles in 4 minutes, then you have to divide 4.4/4 to find the miles the train travels per minute.

4.4/4 = 1.1

So, since the train travels 1.1 miles per minute, and we want to know how fast it travels in 58 minutes, we have to multiply 1.1 by 58. Since 1.1 is a decimal number, we have to multiply both sides by 10 to get 11x580.

11x580 = 5800+ 580 = 6380

Since we multiplied both numbers by 10, we have to divide 6380 by 100.

6380/100 = 63.8

So, the train travels 63.8 miles in 58 minutes.

3 0

3 years ago

Consider the line y=1 x -1 and the point P=(2,0).

Montano1993 [528]

Answer:

Step-by-step explanation:

d(x)=√((x-2)2+(y-0)²)

=√((x-2)²+y²)

=√((x-2)²+(x-1)²)

=√(x²-4x+4+x²-2x+1)

=√(2x²-6x+5)

D=d²(x)=2x²-6x+5

$b.\\\frac{dD}{dx}=4x-6\\\frac{dD}{dx}=0,gives \\4x-6=0\\x=\frac{3}{2}\\\frac{d^2D}{dx^2}=4 >0 at x=\frac{3}{2}\\so~D~or~d^2~or~d~is~minimum~at~x=\frac{3}{2}\\so~y=1(\frac{3}{2} )-1=1/2=0.5\\so~nearest~point~is~(1.5,0.5)$

8 0

3 years ago

(+×9)(×-2) can some one solve it

marshall27 [118]

X2 - 2x + 9x - 18
X2 + 7x - 18

4 0

3 years ago

Given: KL ║ NM , LM = 45, m∠M = 50° KN ⊥ NM , NL ⊥ LM Find: KN and KL

Mice21 [21]

Answer:

$KL=45\tan 50^{\circ}\sin 50^{\circ}\approx 41.08\\ \\KN=45\sin 50^{\circ}\approx 34.47$

Step-by-step explanation:

Given:

KL ║ NM ,

LM = 45

m∠M = 50°

KN ⊥ NM

NL ⊥ LM

Find: KN and KL

1. Consider triangle NLM. This is a right triangle, because NL ⊥ LM. In this triangle,

LM = 45

m∠M = 50°

So,

$\tan \angle M=\dfrac{\text{opposite leg}}{\text{adjacent leg}}=\dfrac{NL}{LM}=\dfrac{NL}{45}\\ \\NL=45\tan 50^{\circ}$

Also

$m\angle LNM=90^{\circ}-50^{\circ}=40^{\circ}$ (angles LNM and M are complementary).

2. Consider triangle NKL. This is a right triangle, because KN ⊥ NM . In this triangle,

$NL=45\tan 50^{\circ}$

$m\angle KLN=m\angle LNM=40^{\circ}$ (alternate interior angles)

$m\angle KNL=90^{\circ}-40^{\circ}=50^{\circ}$ (angles KNL and KLN are complementary).

So,

$\sin \angle KNL=\dfrac{\text{opposite leg}}{\text{hypotenuse}}=\dfrac{KL}{LN}=\dfrac{KL}{45\tan 50^{\circ}}\\ \\KL=45\tan 50^{\circ}\sin 50^{\circ}\approx 41.08$

and

$\cos \angle KNL=\dfrac{\text{adjacent leg}}{\text{hypotenuse}}=\dfrac{KN}{LN}=\dfrac{KN}{45\tan 50^{\circ}}\\ \\KN=45\tan 50^{\circ}\cos 50^{\circ}=45\sin 50^{\circ}\approx 34.47$

3 0

3 years ago

Read 2 more answers