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Stella [2.4K]
3 years ago
7

AB is tangent to the circle k(O) at B, and AD is a secant, which goes through center O. Point O is between A and D∈k(O). Find m∠

BAD and m∠ADB, if the measure of arc BD is 110°20'.

Mathematics
2 answers:
drek231 [11]3 years ago
5 0

Answer:

∠BAD=20°20'

∠ADB=34°90'

Step-by-step explanation:

AB is tangent to the circle k(O), then AB⊥BO. If the measure of arc BD is 110°20', then central angle ∠BOD=110°20'.

Consider isosceles triangle BOD (BO=OD=radius of the circle). Angles adjacent to the base BD are equal, so ∠DBO=∠BDO. The sum of all triangle's angles is 180°, thus

∠BOD+∠BDO+∠DBO=180°

∠BDO+∠DBO=180°-110°20'=69°80'

∠BDO=∠DBO=34°90'

So ∠ADB=34°90'

Angles BOD and BOA are supplementary (add up to 180°), so

∠BOA=180°-110°20'=69°80'

In right triangle ABO,

∠ABO+∠BOA+∠OAB=180°

90°+69°80'+∠OAB=180°

∠OAB=180°-90°-69°80'

∠OAB=20°20'

So, ∠BAD=20°20'

Sergeu [11.5K]3 years ago
4 0

Answer:

The measure of ∠BAD and ∠ADB is 20°20' and 34°90' respectively.

Step-by-step explanation:

Given that AB is tangent to the circle k(O) at B, and AD is a secant, which goes through center O. Point O is between A and D∈k(O).

measure of arc BD is 110°20'.

we have to find the measure of ∠BAD and ∠ADB

∠4=110°22'

In ΔOBD, by angle sum property of triangle

∠1+∠2+∠4=180°

∠1+∠2+110°20'=180°

∠1+∠2=69°80'

Since OB=OD(both radii of same circle) therefore ∠1=∠2

2\angle 2=69^{\circ}80'

\angle 2=\frac{69^{\circ}80'}{2}=34^{\circ}90'

m∠ADB=34°90'

As OB is radius of circle and AB is tangent therefore by theorem which states that radius is perpendicular on the tangent line gives

\angle 6=90^{\circ}

By exterior angle property

∠5=∠1+∠2=69°80'

By angle sum property in ΔABO

∠3+∠6+∠5=180°

∠3+90°+69°80'=180°

∠3=20°20'

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chubhunter [2.5K]

Answer:

The input is -6, hope this helps :D

Step-by-step explanation:

Represent the machines as expressions:

outputA= 7x-6

outputB= 3x+2

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outputA=3outputB

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7x-6=9x+6

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3 0
3 years ago
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A linear regression is done on data the line of best fit is y= 1.25x-6.25. What is the residual for the point (1,1)?
Damm [24]

Answer:

6

Step-by-step explanation:

Find the predicted y value when x=1:

\hat{y}=1.25x-6.25\\\hat{y}=1.25(1)-6.25\\\hat{y}=1.25-6.25\\\hat{y}=-5

Find the residual:

\text{Residual}=\text{Actual Value}-\text{Predicted Value}\\\text{Residual}=y-\hat{y}\\\text{Residual}=1-(-5)\\\text{Residual}=1+5\\\text{Residual}=6

Because our residual is positive, this is an indicator that our predicted y value is too low.

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2 years ago
Which of these fractions below are equivalent to 3/4? <br><br>Please? Help​
Sphinxa [80]

Answer:

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Step-by-step explanation:

Because to find the equivalents, you have to multiply/ divide the numerator and the denominator with the same number.

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ivann1987 [24]

Answer:

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6 0
3 years ago
How to solve 76×327 step by step
hram777 [196]

Here's a method that takes advantage of the values of these particular numbers.

... 76 = 80 - 4

so

... 76 × 327 = (80 -4)×327

... = 80×327 - 4×327

Repeated doubling will give us values that are 2, 4, and 8 times 327.

... 2×327 = 327+327 = 654

... 2×654 = 4×327 = 654+654 = 1308 . . . . we'll use this later

... 2×1308 = 8×327 = 2616

We want 80×327, so we can add a zero to the end of this last:

... 80×327 = 26160

Now, we can subtract 4×327 to get 76×327

... 80×327 - 4×327 = 26160 -1308 = 24852 = 76×327

_____

More conventionally, you would multiply every digit of one number by every digit of the other and add the products according to their respective place values.

327 × 076 = (3×0)×10000 + (3×7 +2×0)×1000 +(3×6 +7×0 +2×7)×100 +(2×6 +7×7)×10 +(7×6)×1

... = 0 +21,000 +3,200 + 610 +42

... = 24,852

Note the pattern of partial products here. This is a method taught to/by practitioners of Vedic mathematics, and can be done in your head. At most, you would write down the partial product sums 21, 32, 61, and 42 to keep from having to carry more than one number in your head at a time.

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