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3 years ago

15

Suppose a line parallel to side BC of triangle ABC intersects AB and AC at point D and E, respectively. Find the length of AE if

DB = 32, AB= 48 and AC = 39

1 answer:

MrRissso [65]3 years ago

4 0

Answer: AE=13

Step-by-step explanation: took test

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Find the equation of the linear function 'g' going through (20,5) and (-5,-8). Use 'u' for your input variable.

frosja888 [35]

Answer:

See below

Step-by-step explanation:

<u>Use the slope-intercept form, which will be in this case:</u>

g(u) = mu + b, where m is the slope, b is the y- intercept

<u>Find the slope:</u>

$m=(y_2-y_1)/(x_2-x_1)$
$m=(-8-5)/(-5-20)=(-13)/(-25)=13/25$

<u>Find the value of the y-intercept:</u>

$5=1/25*20+b$
$b=5-4/5=21/5$

<u>The equation is:</u>

$g(u)=\frac{13}{25} u+\frac{21}{5}$

3 0

2 years ago

Use triangle ABC drawn below & only the sides labeled. Find the side of length AB in terms of side a, side b & angle C o

Brrunno [24]

Answer:

$AB = \sqrt{a^2 + b^2-2abCos\ C}$

Step-by-step explanation:

Given:

The above triangle

Required

Solve for AB in terms of a, b and angle C

Considering right angled triangle BOC where O is the point between b-x and x

From BOC, we have that:

$Sin\ C = \frac{h}{a}$

Make h the subject:

$h = aSin\ C$

Also, in BOC (Using Pythagoras)

$a^2 = h^2 + x^2$

Make $x^2$ the subject

$x^2 = a^2 - h^2$

Substitute $aSin\ C$ for h

$x^2 = a^2 - h^2$ becomes

$x^2 = a^2 - (aSin\ C)^2$

$x^2 = a^2 - a^2Sin^2\ C$

Factorize

$x^2 = a^2 (1 - Sin^2\ C)$

In trigonometry:

$Cos^2C = 1-Sin^2C$

So, we have that:

$x^2 = a^2 Cos^2\ C$

Take square roots of both sides

$x= aCos\ C$

In triangle BOA, applying Pythagoras theorem, we have that:

$AB^2 = h^2 + (b-x)^2$

Open bracket

$AB^2 = h^2 + b^2-2bx+x^2$

Substitute $x= aCos\ C$ and $h = aSin\ C$ in $AB^2 = h^2 + b^2-2bx+x^2$

$AB^2 = h^2 + b^2-2bx+x^2$

$AB^2 = (aSin\ C)^2 + b^2-2b(aCos\ C)+(aCos\ C)^2$

Open Bracket

$AB^2 = a^2Sin^2\ C + b^2-2abCos\ C+a^2Cos^2\ C$

Reorder

$AB^2 = a^2Sin^2\ C +a^2Cos^2\ C + b^2-2abCos\ C$

Factorize:

$AB^2 = a^2(Sin^2\ C +Cos^2\ C) + b^2-2abCos\ C$

In trigonometry:

$Sin^2C + Cos^2 = 1$

So, we have that:

$AB^2 = a^2 * 1 + b^2-2abCos\ C$

$AB^2 = a^2 + b^2-2abCos\ C$

Take square roots of both sides

$AB = \sqrt{a^2 + b^2-2abCos\ C}$

6 0

3 years ago

35,000 divided by 120

Naya [18.7K]

Answer:

291.666666667

Step-by-step explanation:

Rounds to 291.7

8 0

2 years ago

Read 2 more answers

A sheet of plastic has an area of 35 square cm. If the sheet is 5 cm thick, what is the volume?

Andre45 [30]

Answer:

175 cm³

Step-by-step explanation:

Volume = área * thick

Volume = 35cm² * 5cn

Volume = 175 cm³

3 0

2 years ago

Read 2 more answers

A cab ride f I'm your home to the airport cost $23.47. If you want to tip the cab driver close to 10 percent of the fare, how mu

Westkost [7]

10% of 23.47 is 2.347 so about $2.35

5 0

3 years ago