Answer:
![15 in { }^{2}](https://tex.z-dn.net/?f=15%20in%20%7B%20%7D%5E%7B2%7D%20)
Step-by-step explanation:
![area \: of \: \: a \: triangle \: = 1 \2 \: \ b \: \times h \\ = 1 \2 \:(6in \: \times 5in) \\ = 1(3in \: \times 5in) \\ = 15in {}^{2}](https://tex.z-dn.net/?f=area%20%5C%3A%20of%20%5C%3A%20%20%5C%3A%20a%20%5C%3A%20triangle%20%5C%3A%20%20%3D%201%20%20%5C2%20%5C%3A%20%5C%20b%20%5C%3A%20%20%5Ctimes%20h%20%5C%5C%20%20%20%20%3D%201%20%5C2%20%5C%3A%286in%20%5C%3A%20%20%5Ctimes%205in%29%20%5C%5C%20%20%3D%201%283in%20%5C%3A%20%20%5Ctimes%205in%29%20%5C%5C%20%20%3D%2015in%20%7B%7D%5E%7B2%7D%20%20%20)
Answer:
Based on the calculations, the store with the better buy is The Eyewear Shoppe
Step-by-step explanation:
Jake wants to buy two pairs of a particular style of sunglasses. The sunglasses are sold at two different stores.
For The Eyewear Shoppe:
The Eyewear Shoppe sells the sunglasses for $60 but is having a “Buy 1 Pair, Get 1 Pair Free” promotion.
Based on this promotion, you can get 2 sunglasses for $60
For Sunglass House
Sunglass House sells the sunglasses go 20% off the $40 retail price.
A Sunglass = $40 - ( 20%× $40)
= $40 - $8
= $32
Two sunglasses will cost = $32 × 2
= $64
Therefore, based on the above calculations, the store with the better buy is The Eyewear Shoppe
The angle between the vectors t and u is 45°. And the vector t and vector w are orthogonal to each other.
<h3>What is a vector?</h3>
The quantity which has magnitude, direction and follows the law of vector addition is called a vector.
The vectors are given below.
t = −5i + 2j, u = −3i + 7j, and v = 8i + 20j
Part A: Then the angle between vectors t and u will be
![\cos \theta = \dfrac{\overrightarrow{a} \cdot \overrightarrow{b}}{|\overrightarrow{a}| + |\overrightarrow{b}|}](https://tex.z-dn.net/?f=%5Ccos%20%5Ctheta%20%3D%20%5Cdfrac%7B%5Coverrightarrow%7Ba%7D%20%5Ccdot%20%5Coverrightarrow%7Bb%7D%7D%7B%7C%5Coverrightarrow%7Ba%7D%7C%20%2B%20%7C%5Coverrightarrow%7Bb%7D%7C%7D)
Then we have
cos θ = [(−5i + 2j)(−3i + 7j)] / [√{(-5²) + 2²} + √{(-3)² + 7²}]
cos θ = 1 / √2
θ = 45°
Part B: c is a scalar
If
, then ![\rm c\overrightarrow{\rm v} = c(ca, cb)](https://tex.z-dn.net/?f=%5Crm%20c%5Coverrightarrow%7B%5Crm%20v%7D%20%3D%20c%28ca%2C%20cb%29)
Let c = 2, then we have
![\overrightarrow{\rm w} = c\overrightarrow{v}\\\\\overrightarrow{\rm w} = (2*8, 2*20)\\\\\overrightarrow{\rm w} = (16, 40)](https://tex.z-dn.net/?f=%5Coverrightarrow%7B%5Crm%20w%7D%20%3D%20c%5Coverrightarrow%7Bv%7D%5C%5C%5C%5C%5Coverrightarrow%7B%5Crm%20w%7D%20%3D%20%282%2A8%2C%202%2A20%29%5C%5C%5C%5C%5Coverrightarrow%7B%5Crm%20w%7D%20%3D%20%2816%2C%2040%29)
Part C: Use the dot product to determine if t and w are parallel or orthogonal.
![\overrightarrow{\rm t} \cdot \overrightarrow{\rm w} = (-5, 2)(16, 40)\\\\ \overrightarrow{\rm t} \cdot \overrightarrow{\rm w} = -5*16+ 2*40\\\\ \overrightarrow{\rm t} \cdot \overrightarrow{\rm w} = -80+ 80\\\\ \overrightarrow{\rm t} \cdot \overrightarrow{\rm w} = 0](https://tex.z-dn.net/?f=%5Coverrightarrow%7B%5Crm%20t%7D%20%5Ccdot%20%20%5Coverrightarrow%7B%5Crm%20w%7D%20%3D%20%28-5%2C%202%29%2816%2C%2040%29%5C%5C%5C%5C%20%5Coverrightarrow%7B%5Crm%20t%7D%20%5Ccdot%20%20%5Coverrightarrow%7B%5Crm%20w%7D%20%3D%20-5%2A16%2B%202%2A40%5C%5C%5C%5C%20%5Coverrightarrow%7B%5Crm%20t%7D%20%5Ccdot%20%20%5Coverrightarrow%7B%5Crm%20w%7D%20%3D%20-80%2B%2080%5C%5C%5C%5C%20%5Coverrightarrow%7B%5Crm%20t%7D%20%5Ccdot%20%20%5Coverrightarrow%7B%5Crm%20w%7D%20%3D%200)
More about the vector link is given below.
brainly.com/question/13188123
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