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3 years ago

11

The cost, including sales tax, of a Ford Focus SE is $19,392.70. If the sales tax is 6%, find the cost of the car before the tax

was added.

1 answer:

Ilia_Sergeevich [38]3 years ago

6 0

Answer:

the price before taxes was $18,229.13

Step-by-step explanation:

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Calculate the length of sides triangle pqr and determine weather or not triangle is a right angled. P(-4,6) q(6,1) r(2,9)

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$\bold{\huge{\underline{ Solution }}}$

<h3><u>Given </u><u>:</u><u>-</u></h3>

We have given the coordinates of the triangle PQR that is P(-4,6) , Q(6,1) and R(2,9)

<h3><u>To</u><u> </u><u>Find </u><u>:</u><u>-</u></h3>

<u>We </u><u>have </u><u>to </u><u>calculate </u><u>the </u><u>length </u><u>of </u><u>the </u><u>sides </u><u>of </u><u>given </u><u>triangle </u><u>and </u><u>also </u><u>we </u><u>have </u><u>to </u><u>determine </u><u>whether </u><u>it </u><u>is </u><u>right </u><u>angled </u><u>triangle </u><u>or </u><u>not </u>

<h3><u>Let's </u><u>Begin </u><u>:</u><u>-</u></h3>

<u>Here</u><u>, </u><u> </u><u>we </u><u>have </u>

Coordinates of P =( x1 = -4 , y1 = 6)
Coordinates of Q = ( x2 = 6 , y2 = 1 )
Coordinates of R = ( x3 = 2 , y3 = 9 )

<u>By </u><u>using </u><u>distance </u><u>formula </u>

$\pink{\bigstar}\boxed{\sf{Distance=\sqrt{(x_1-x_2)^2+(y_1-y_2)^2\;}}}$

<u>Subsitute </u><u>the </u><u>required </u><u>values </u><u>in </u><u>the </u><u>above </u><u>formula </u><u>:</u><u>-</u>

Length of side PQ

$\sf{ = }{\sf\sqrt{ (6 - (-4))^{2} + (1 - 6)^{2}}}$

$\sf{ = }{\sf\sqrt{ (6 + 4 )^{2} + (- 5)^{2}}}$

$\sf{ = }{\sf\sqrt{ (10)^{2} + (- 5)^{2}}}$

$\sf{ = }{\sf\sqrt{ 100 + 25 }}$

$\sf{ = }{\sf\sqrt{ 125 }}$

$\sf{ = 5 }{\sf\sqrt{ 5 }}$

Length of QR

$\sf{ = }{\sf\sqrt{(2 - 6)^{2} + (9 - 1)^{2}}}$

$\sf{ = }{\sf\sqrt{(- 4 )^{2} + (8)^{2}}}$

$\sf{ = }{\sf\sqrt{16 + 64 }}$

$\sf{ = }{\sf\sqrt{80 }}$

$\sf{ = 4 }{\sf\sqrt{5 }}$

Length of RP

$\sf{ = }{\sf\sqrt{ (-4 - 2 )^{2} + (6 - 9)^{2}}}$

$\sf{ = }{\sf\sqrt{ (-6 )^{2} + (-3)^{2}}}$

$\sf{ = }{\sf\sqrt{ 36 + 9 }}$

$\sf{ = }{\sf\sqrt{ 45 }}$

$\sf{ = 3}{\sf\sqrt{ 5 }}$

<h3><u>Now</u><u>, </u></h3>

We have to determine whether the triangle PQR is right angled triangle

<h3>Therefore, </h3>

<u>By </u><u>using </u><u>Pythagoras </u><u>theorem </u><u>:</u><u>-</u>

Pythagoras theorem states that the sum of squares of two sides that is sum of squares of 2 smaller sides of triangle is equal to the square of hypotenuse that is square of longest side of triangle

<u>That </u><u>is</u><u>, </u>

$\bold{ PQ^{2} + QR^{2} = PR^{2}}$

<u>Subsitute </u><u>the </u><u>required </u><u>values</u><u>,</u>

$\bold{ 125 + 80 = 45 }$

$\bold{ 205 = 45 }$

<u>From </u><u>above </u><u>we </u><u>can </u><u>conclude </u><u>that</u><u>, </u>

The triangle PQR is not a right angled triangle because 205 ≠ 45 .

6 0

3 years ago