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3 years ago

|−12| = 12 True or False please help!!!!!

Mathematics

2 answers:

balu736 [363]3 years ago

8 0

Answer:

true

Step-by-step explanation:

when you put the 2 lines on the left and right side of a (negative) number, it instantly becomes a positive

Alexandra [31]3 years ago

4 0

Answer:

yes

Step-by-step explanation:

|-12| = |12| they always equal to 12

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

4 0

3 years ago

The difference of 3 times a number and 20 is greater then 10

Novosadov [1.4K]

If the number is x, then 3 times x -20 >10 and 3x-20>10. Adding 20 to both sides, we get 3x >30 and by dividing by 3 we get x >10

3 0

3 years ago

PLEASE SHOW FULL SOLUTIONS!!! WILL MARK BRAINLIEST FOR BEST ANSWER!!

Lubov Fominskaja [6]

Answer:

The first option: $265.05

Step-by-step explanation:

<h3>Option 1</h3>

<u>Payment as sequence:</u>

11.75, 12.10, 12.45, ...

The first term a = 11.75
Common difference d = 0.35
Number of terms n = 18

<u>Find the sum of the first 18 terms:</u>

S₁₈ = (a + a₁₈)*18/2 = (a + a + 17d)*9 = (11.75*2 + 17*0.35)*9 = $265.05

<h3>Option 2</h3>

Flat rate $14.50 per hour

$14.50*18 = $261.00

<u>Compared, we see the first option pays more:</u>

$265.05 > $261.00

5 0

2 years ago

A club has members from three grades.

mars1129 [50]

the ratio is 24:30

or the simplified version is 4:5

7 0

3 years ago

John had 80 filers to post around town. Last week, he posted 1/4 of them. This week, he posted 3/5 of the remaining filers. How

Reil [10]

Answer: 24 fliers

Step-by-step explanation:

he had 80 to begin with so last week if he posted 1/4 of them he would have 3/4 left and

3/4 * 80 = 60

and then if he posts 3/5 of the 60 remaining fliers he would have 2/5 left over and

2/5 * 60 = 24

so your answer is 24 fliers

4 0

3 years ago

Read 2 more answers