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12345 [234]
3 years ago
9

Find the area of the triangle

Mathematics
1 answer:
horsena [70]3 years ago
3 0
Area should be 80
0.5x20x8
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A group of friends went fishing. They each caught 20 fish but not all of them were keepers. Which person was able to keep 3/5 of
Romashka-Z-Leto [24]

Answer:

Those who were able to keep 12 fishes

Step-by-step explanation:

Given

Total = 20 (each)

Required

Which was able to keep 3/5

First, we need to calculate 3/5 of the total number of fishes

Fish = 3/5 * 20

Fish = (3 * 20)/5

Fish = 60/5

Fish = 12

From the calculation above, only those who keep 12 of the 20 fishes were able to keep 3/5 of their fishes

8 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
Which ordered pair is a solution of the equation? 2x+4y=6x-y OPTION A: Only (4,5) OPTION B: Only (5,4) OPTION C Both A and B OPT
sammy [17]

Answer:

option b

Step-by-step explanation:

replace x and y with the x and y of the ordered pair

option a: 2(4)+4(5)=6(4)-5

solve

8+20=24-5

28=19  not true

option b:2(5)+4(4)=6(5)-4

solve

10+16=30-4

26=26  true

6 0
3 years ago
How does sin 30degrees compare to sin -30degrees?
KiRa [710]

The sine function is an odd function, so the sine of -30° is the opposite of the sine of 30°.

sin(30°) = 1/2

sin(-30°) = -1/2

The sine of 30° is greater than the sine of -30°.

7 0
3 years ago
Find the volume of the rectangular prism
user100 [1]
Volume= Length • Width • Height

Given info: 6•8•9= 432cm cubed
8 0
3 years ago
Read 2 more answers
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