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3 years ago

15

Simplify the expression 12c-c

1 answer:

Klio2033 [76]3 years ago

5 0

Answer:

11c

Step-by-step explanation:

Think of it like 12c-1c.

When it is c by itself, then it is just 1c.

Subtract 12-1, get 11.

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Find the angle between the given vectors. Round your answer, in degrees, to two decimal places. u=⟨2,−6⟩u=⟨2,−6⟩, v=⟨4,−7⟩

NISA [10]

Answer:

$\theta = 108.29$

Step-by-step explanation:

Given

$u =$

$v =$

Required:

Calculate the angle between u and v

The angle $\theta$ is calculated as thus:

$cos\theta = \frac{u.v}{|u|.|v|}$

For a vector

$A =$

$A = a * b$

$cos\theta = \frac{u.v}{|u|.|v|}$ becomes

$cos\theta = \frac{.}{|u|.|v|}$

$cos\theta = \frac{2*6+4*-7}{|u|.|v|}$

$cos\theta = \frac{12-28}{|u|.|v|}$

$cos\theta = \frac{-16}{|u|.|v|}$

For a vector

$A =$

$|A| = \sqrt{a^2 + b^2}$

So;

$|u| = \sqrt{2^2 + 6^2}$

$|u| = \sqrt{4 + 36}$

$|u| = \sqrt{40}$

$|v| = \sqrt{4^2+(-7)^2}$

$|v| = \sqrt{16+49}$

$|v| = \sqrt{65}$

So:

$cos\theta = \frac{-16}{|u|.|v|}$

$cos\theta = \frac{-16}{\sqrt{40}*\sqrt{65}}$

$cos\theta = \frac{-16}{\sqrt{2600}}$

$cos\theta = \frac{-16}{\sqrt{100*26}}$

$cos\theta = \frac{-16}{10\sqrt{26}}$

$cos\theta = \frac{-8}{5\sqrt{26}}$

Take arccos of both sides

$\theta = cos^{-1}(\frac{-8}{5\sqrt{26}})$

$\theta = cos^{-1}(\frac{-8}{5 * 5.0990})$

$\theta = cos^{-1}(\frac{-8}{25.495})$

$\theta = cos^{-1}(-0.31378701706)$

$\theta = 108.288386087$

<em></em> $\theta = 108.29$ <em> (approximated)</em>

4 0

3 years ago

Does anyone know this answer??

DochEvi [55]

Answer:

Option (4)

Step-by-step explanation:

Equation of a line passing through a point $(x_1,y_1)$ and with slope 'm' is,

y - y₁ = m(x - x₁)

Given → Slope 'm' = -2

Point through which the line is passing is (-1, -2)

x₁ = -1 and y₁ = -2

Therefore, equation will be,

y + 2 = -2(x + 1)

y = -2x - 2 - 2

y = -2x - 4

Option (4) is the correct option.

4 0

3 years ago

A proper fraction is converted to a decimal equivalent by dividing the denominator into the numerator. True

kondaur [170]

False, it's the other way around: you divide the numerator by the denominator.

For example, to evaluate $\frac{8}{15}$ you divide 8 by 15:

$\dfrac{8}{15} = 8\div 15 = 0.5\overline{3}$

7 0

3 years ago

Tammy has 4 times as many books as Willy . Willy has 180 fewer books than Tammy . How many books does Willy have ?

enyata [817]

Answer:

60 books

Step-by-step explanation:

let the number of books Willy has be x , then

Tammy has 4x books

Willy has 180 fewer books , that is Tammy has 180 more than Willy , so

4x = x + 180 ( subtract x from both sides )

3x = 180 ( divide both sides by 3 )

x = 60

Thus

Willy has 60 books andTammy has 4 × 60 = 240 books

which is 180 more than Willy

7 0

2 years ago

Which of these is an equivalent expression for X ^-3 that uses positive exponents

qaws [65]

X^-3 = 1/(x³)

............,.......

5 0

4 years ago