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Natasha_Volkova [10]
2 years ago
5

Which of the following is the slope of the line passing through the

Mathematics
1 answer:
julia-pushkina [17]2 years ago
6 0

Answer:

I think the slope is UNDEFINED

y²-y¹/x²-x¹

(-5)-(16)/(-12)-(-12)

-21/0

=Undefined

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Tara is the editor of the school newspaper. She tries to devote about 1/2 of the paper to news, 1/3 to pictures, and the remaind
Klio2033 [76]
5/6 of the paper is devoted to news and pictures

first I made the fraction have equal denominators which was 6 by doing that I multiplyed the numerator and the denominator

1/2
1×3=3
2×3=6
therefore 1/2 being equivalent to 3/6


1/3
1×2=2
3×2=6
therefore 1/3 being equivalent to 2/6

now you would be able to add the numerators, so 2+3=5
therefore being 5/6 of the paper is devoted to news and pictures
4 0
3 years ago
Find the angle between u =the square root of 5i-8j and v =the square root of 5i+j.
fenix001 [56]

Answer:

The angle between vector \vec{u} = 5\, \vec{i} - 8\, \vec{j} and \vec{v} = 5\, \vec{i} + \, \vec{j} is approximately 1.21 radians, which is equivalent to approximately 69.3^\circ.

Step-by-step explanation:

The angle between two vectors can be found from the ratio between:

  • their dot products, and
  • the product of their lengths.

To be precise, if \theta denotes the angle between \vec{u} and \vec{v} (assume that 0^\circ \le \theta < 180^\circ or equivalently 0 \le \theta < \pi,) then:

\displaystyle \cos(\theta) = \frac{\vec{u} \cdot \vec{v}}{\| u \| \cdot \| v \|}.

<h3>Dot product of the two vectors</h3>

The first component of \vec{u} is 5 and the first component of \vec{v} is also

The second component of \vec{u} is (-8) while the second component of \vec{v} is 1. The product of these two second components is (-8) \times 1= (-8).

The dot product of \vec{u} and \vec{v} will thus be:

\begin{aligned} \vec{u} \cdot \vec{v} = 5 \times 5 + (-8) \times1 = 17 \end{aligned}.

<h3>Lengths of the two vectors</h3>

Apply the Pythagorean Theorem to both \vec{u} and \vec{v}:

  • \| u \| = \sqrt{5^2 + (-8)^2} = \sqrt{89}.
  • \| v \| = \sqrt{5^2 + 1^2} = \sqrt{26}.

<h3>Angle between the two vectors</h3>

Let \theta represent the angle between \vec{u} and \vec{v}. Apply the formula\displaystyle \cos(\theta) = \frac{\vec{u} \cdot \vec{v}}{\| u \| \cdot \| v \|} to find the cosine of this angle:

\begin{aligned} \cos(\theta)&= \frac{\vec{u} \cdot \vec{v}}{\| u \| \cdot \| v \|} = \frac{17}{\sqrt{89}\cdot \sqrt{26}}\end{aligned}.

Since \theta is the angle between two vectors, its value should be between 0\; \rm radians and \pi \; \rm radians (0^\circ and 180^\circ.) That is: 0 \le \theta < \pi and 0^\circ \le \theta < 180^\circ. Apply the arccosine function (the inverse of the cosine function) to find the value of \theta:

\displaystyle \cos^{-1}\left(\frac{17}{\sqrt{89}\cdot \sqrt{26}}\right) \approx 1.21 \;\rm radians \approx 69.3^\circ .

3 0
3 years ago
Can you answer 14.15.16
Ne4ueva [31]

Answer:

can you please tell me the question there's nothing there

Step-by-step explanation:

8 0
3 years ago
Read 2 more answers
A yearly subscription to the monthly magazine cost $41.40. The regular news stand price is $4.25 per issue. How much is saved pe
Elanso [62]
41.40 ÷ 12 = 3.45
So if you are buying a yearly subscription it is $3.45 per issue.
4.25 - 3.45 = 0.8 that is how much you save.

5 0
3 years ago
A manufacturing company with 450 employees begins a new product line and must increase their numbers of employees by 18%. How ma
pogonyaev

You are adding 18%, which makes it 118% of original employees

Times 450 by 1.18 = 531

6 0
3 years ago
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