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3 years ago

5

In ∆ABC the angle bisectors drawn from vertices A and B intersect at the point D. Find m∠ADB if

1 answer:

Svetllana [295]3 years ago

8 0

Answer: ∠ABD = $\bold{\frac{1}{2}}$ ∠C

<u>Step-by-step explanation:</u>

$\angle A + \angle B + \angle C = 180^o\\\\\dfrac{1}{2}\angle A+\dfrac{1}{2}\angle B+\angle D=180^o\\\\\\\text{Solve the system by multiplying the second equation by -2}\\\angle A + \angle B + \angle C = 180^o\\\underline{-\angle A - \angle B - 2\angle D = -180^o}\\.\qquad \qquad \quad \angle C-2\angle D=0\\.\qquad \qquad \qquad \qquad \angle C=2\angle D\\.\qquad \qquad \qquad \quad \dfrac{1}{2}\angle C=\quad \angle D\\$

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Simplify the expression (5÷5) ÷ 5 * (5^2 - 5)

Katyanochek1 [597]

[ Answer ]

$\boxed{\bold{4}}$

[ Explanation ]

Simplify / Solve: (5 ÷ 5) ÷ 5 · ( $5^{2}$ - 5)

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

Rewrite

$\frac{\frac{5}{5} }{5}$ ( $5^{2}$ - 5)

Apply Rule ( $\frac{a}{a}$ = 1): $\frac{5}{5}$ = 1

$\frac{1}{5}$ ( $5^{2}$ - 5)

Multiply Fractions

$\frac{1 \ * \ 5^{2 \ - \ 5} }{5}$

Simplify

1 · ( $5^{2}$ - 5) = 20

Simplify

= $\frac{20}{5}$

Divide

20 ÷ 5

Answer

= 4

$\boxed{\bold{[] \ Eclipsed \ []}}$

3 0

4 years ago

In the given figure ABCD is a tripepizeum with AB||CD. If AO = x-1, CO = BO = x+1 and CD = x+4. Find the value of x.

Hitman42 [59]

$\longmapsto$ The value of "x" is 5.

$\large\underline{\sf{Solution-}}$

Given that,

A trapezium ABCD in which AB || CD such that

AO = x - 1

CO = BO = x + 1

OD = x + 4

Now,

$\rm In \: \triangle \: AOB \: and \: \triangle \: COD$

$\rm \: \angle \: AOB \: and \: \angle \: COD \: \: \{vertically \: opposite \: angles \}$

$\rm \: \angle \:ABO \: and \: \angle \: CDO \: \: \{alternate \: interior \: angles \}$

$\bf \: \triangle \: AOB \: \sim \: \triangle \: COD \: \: \: \{AA \: similarity \}$

$\bf\longmapsto\:\dfrac{AO}{CO} = \dfrac{BO}{DO}$

$\rm \longmapsto\:\dfrac{x - 1}{x + 1} = \dfrac{x + 1}{x + 4}$

$\rm \longmapsto\:(x - 1)(x + 4) = {(x + 1)}^{2}$

$\rm \longmapsto\: {x}^{2} - x + 4x - 4 = {x}^{2} + 1 + 2x$

$\rm \longmapsto\: 3x - 4 = 1 + 2x$

$\rm \longmapsto\: 3x - 2x= 1 +4$

$\bf\longmapsto \:x = 5$

7 0

3 years ago

Divide 10 into two parts in such a way that when a certain one of these parts is divided by the other and the fraction is multip

finlep [7]

Answer:

The fraction is $\frac{x}{10-x}\times x$ where the numeric value of x = 6 and 10-x =4.

Step-by-step explanation:

Given:

A number 10 we have to divide it into two parts and then when one part is divided by other with multiplication of its numerator the number obtained is 9.

Lets the number in numerator be $x$

Then

The number in denominator is $10-x$

According to the question:

⇒ $\frac{x}{10-x}\times x =9$

⇒ $\frac{x^2}{10-x} =9$

⇒ $x^2=9(10-x)$

⇒ $x^2+9x-90=0$

⇒ $x^2+15x-6x-90=0$ solving by middle term splitting.

⇒ $x(x+15)-6(x+15)=0$

⇒ $(x-6)(x+15)=0$

⇒ $x=6,-15$

Discarding the negative values.

⇒ $x=6$

Check:

So the fraction is $\frac{x}{10-x} \times x =9$

then,

⇒ $\frac{6}{10-6} \times 6 =9$

⇒ $\frac{6\times 6}{4} =9$

⇒ $\frac{36}{4}=9$

⇒ $9=9$

Left terms= Right terms

The fraction is $\frac{x}{10-x}\times x$ where the number 'x' = 6 and 10-x = 4.

6 0

3 years ago

True or false: the standard deviation of a set of data values is never a negative number

Anestetic [448]

True I think !! Not to sure

8 0

3 years ago

My car gets 27 miles per gallon, and gasoline costs $2.50 per gallon. If we consider only the cost of gasoline, how much does it

Andrew [12]

Answer:

$71.50

Step-by-step explanation:
27 times 2.50 equals 71.50

5 0

4 years ago