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3 years ago

5

Liz wants to buy her favorite musical group’s new CD. The CD costs $15.24, including tax. Liz gives the store clerk a twenty-dol

lar bill. How much change should Liz get back

2 answers:

Ket [755]3 years ago

8 0

Liz would get $4.76 change

uranmaximum [27]3 years ago

3 0

$4.76 iz the change liz gets bahk

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in exercises 15-20 find the vector component of u along a and the vecomponent of u orthogonal to a u=(2,1,1,2) a=(4,-4,2,-2)

Nimfa-mama [501]

Answer:

The component of $\vec u$ orthogonal to $\vec a$ is $\vec u_{\perp\,\vec a} = \left(\frac{9}{5},\frac{6}{5},\frac{9}{10},\frac{21}{10}\right)$ .

Step-by-step explanation:

Let $\vec u$ and $\vec a$ , from Linear Algebra we get that component of $\vec u$ parallel to $\vec a$ by using this formula:

$\vec u_{\parallel \,\vec a} = \frac{\vec u \bullet\vec a}{\|\vec a\|^{2}} \cdot \vec a$ (Eq. 1)

Where $\|\vec a\|$ is the norm of $\vec a$ , which is equal to $\|\vec a\| = \sqrt{\vec a\bullet \vec a}$ . (Eq. 2)

If we know that $\vec u =(2,1,1,2)$ and $\vec a=(4,-4,2,-2)$ , then we get that vector component of $\vec u$ parallel to $\vec a$ is:

$\vec u_{\parallel\,\vec a} = \left[\frac{(2)\cdot (4)+(1)\cdot (-4)+(1)\cdot (2)+(2)\cdot (-2)}{4^{2}+(-4)^{2}+2^{2}+(-2)^{2}} \right]\cdot (4,-4,2,-2)$

$\vec u_{\parallel\,\vec a} =\frac{1}{20}\cdot (4,-4,2,-2)$

$\vec u_{\parallel\,\vec a} =\left(\frac{1}{5},-\frac{1}{5},\frac{1}{10},-\frac{1}{10} \right)$

Lastly, we find the vector component of $\vec u$ orthogonal to $\vec a$ by applying this vector sum identity:

$\vec u_{\perp\,\vec a} = \vec u - \vec u_{\parallel\,\vec a}$ (Eq. 3)

If we get that $\vec u =(2,1,1,2)$ and $\vec u_{\parallel\,\vec a} =\left(\frac{1}{5},-\frac{1}{5},\frac{1}{10},-\frac{1}{10} \right)$ , the vector component of $\vec u$ is:

$\vec u_{\perp\,\vec a} = (2,1,1,2)-\left(\frac{1}{5},-\frac{1}{5},\frac{1}{10},-\frac{1}{10} \right)$

$\vec u_{\perp\,\vec a} = \left(\frac{9}{5},\frac{6}{5},\frac{9}{10},\frac{21}{10}\right)$

The component of $\vec u$ orthogonal to $\vec a$ is $\vec u_{\perp\,\vec a} = \left(\frac{9}{5},\frac{6}{5},\frac{9}{10},\frac{21}{10}\right)$ .

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3 years ago

The area of a square garden is shown. How long is each side of the garden? A=121ft^2

polet [3.4K]

The answer is 30.25ft

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3 years ago

It takes 3/4 tsp. of vanilla to make a batch of cookies. How many tsp. would I needed for 4 batches of cookies?

IRISSAK [1]

Answer:

3/1 tsp. or 3 tsp.

Step-by-step explanation:

3/4 times 4

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3 years ago

Absolute value of 15

mixer [17]

Answer:

15

Step-by-step explanation:

The absolute value takes any value and makes it positive.

|15| = 15

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4 years ago

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there are 12 teams in the jayhook hockey league each team plays every other team twice per season, once at home and once away. L

Gre4nikov [31]

Answer:

58

Step-by-step explanation:

As there are 12 teams in the league and each teams plays every other team twice per season. so, the total number of matches in the league will be 132.

let the matches won by home team = 'x'

given,

number of matches drawn = 34

matches won by the away team = x - 18

Now, according to the question,

⇒ total matches = matches drawn + matches won by home team + matches won by away team

⇒ 132 = 34 + x + x -18

⇒ x = 58

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3 years ago