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2 years ago

1. Lisa and Tomas Lopez are buying a new minivan that has a base

Mathematics

1 answer:

Dimas [21]2 years ago

4 0

The question is incomplete:

Lisa and Tomas Lopez are buying a new minivan that has a base price of $22,510.the options total $8,062 and destination charge is $770. The dealer's cost is estimated to be 91% of the base price and 88% of the options.

-What is the sticker price of the vehicle?

-Find the dealer's percent of the base price.

-Find the dealer's percent of the options price.

-What is the estimated dealer's cost?

Answer:

-What is the sticker price of the vehicle? $31,342

-Find the dealer's percent of the base price: $20,484

-Find the dealer's percent of the options price: $7,094

-What is the estimated dealer's cost? $28,348

Step-by-step explanation:

-The sticker price is the result of adding the base price plus the options plus the destination charge.

Sticker price= base price + options + destination charge

Sticker price= $22,510+$8,062+$770

Sticker price= $31,342

-Dealer's percent of the base price: It is 91% of the base price:

$22,510*91%= $20,484

-Dealer's percent of the options price: It is 88% of the options:

$8,062*88%= $7,094

-Estimated dealer's cost= Percent of base price+percent of options price+destination charge

Estimated dealer's cost= $20,484+$7,094+$770

Estimated dealer's cost=$28,348

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Find the measures of the three angles, in radians, of the triangle with the given vertices: d(1,1,1), e(1,−5,2), and f(−2,2,7).

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Consider triangle DEF with vertices D(1,1,1), E(1,-5,2) and F(-2,2,7).

1. Find

$\overrightarrow{DE}=(1-1,-5-1,2-1)=(0,-6,1),\\ \\\overrightarrow{DF}=(-2-1,2-1,7-1)=(-3,1,6).$

Then

$\cos \angle D=\dfrac{0\cdot (-3)+(-6)\cdot 1+1\cdot 6}{\sqrt{0^2+(-6)^2+1^2}\cdot \sqrt{(-3)^2+1^2+6^2}}=\dfrac{0}{\sqrt{37} \cdot \sqrt{46} }=0.$

2. Find

$\overrightarrow{ED}=(1-1,1-(-5),1-2)=(0,6,-1),\\ \\\overrightarrow{EF}=(-2-1,2-(-5),7-2)=(-3,7,5).$

Then

$\cos \angle E=\dfrac{0\cdot (-2)+6\cdot 7+(-1)\cdot 5}{\sqrt{0^2+6^2+(-1)^2}\cdot \sqrt{(-3)^2+7^2+5^2}}=\dfrac{37}{\sqrt{37} \cdot \sqrt{83} }=\sqrt{\dfrac{37}{83}}.$

3. Find

$\overrightarrow{FE}=(1-(-2),-5-2,2-7)=(3,-7,-5),\\ \\\overrightarrow{FD}=(1-(-2),1-2,1-7)=(3,-1,-6).$

Then

$\cos \angle F=\dfrac{3\cdot 3+(-7)\cdot (-1)+(-5)\cdot (-6)}{\sqrt{3^2+(-7)^2+(-5)^2}\cdot \sqrt{3^2+(-1)^2+(-6)^2}}=\dfrac{46}{\sqrt{83} \cdot \sqrt{46} }=\sqrt{\dfrac{46}{83}}.$

$\angle E=\arccos0=\dfrac{\pi}{2},\\ \\
\angle D=\arccos\letf(\sqrt{\dfrac{37}{83}}\right)\approx 0.27\pi,\\ \\
\angle F=\arccos\letf(\sqrt{\dfrac{46}{83}}\right)\approx 0.23\pi.$