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3 years ago

For an angle θ with the point (−5, −12) on its terminating side, what is the value of cosine?

Mathematics

1 answer:

viva [34]3 years ago

8 0

Answer:

option C. $-\frac{5}{13}$

Step-by-step explanation:

we have that

The point (-5,-12) belong to the III quadrant

The value of the cosine is negative

Applying the Pythagoras Theorem

Find the value of the hypotenuse

$h^{2}=5^{2}+12^{2}\\ h^{2} =25+144\\ h^{2}=169\\h=13\ units$

The value of cosine of angle θ is the ratio between the side adjacent to angle θ and the hypotenuse

$cos(\theta)=-\frac{5}{13}$

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Rajan needs 1 liter of 15% hydrochloric acid solution for an experiment. He checks his storage cabinet, but he only has a 5-lite

yarga [219]

Answer:

Rajan must use 0.75 liters of 5% hydrochloric acid solution and 0.25 liters of 45% hydrochloric acid solution.

Step-by-step explanation:

Let us assume that, x liters of the 5% hydrochloric acid and y liters of the 45% hydrochloric acid solutions are combined.

As Rajan need total of 1 liter of solution, so

$x+y=1$

i.e $x=1-y$ --------------------1

As Rajan needs 5% hydrochloric acid and 45% hydrochloric acid to make a 1 liter batch of 15% hydrochloric acid, hence acid content of the mixture of two acids will be same as of the final one, so

$0.05x+0.45y=1\times 0.15$

i.e $5x+45y=15$ -------------2

Putting value of x from equation 1 in equation 2,

$\Rightarrow 5(1-y)+45y=15$

$\Rightarrow 5-5y+45y=15$

$\Rightarrow 5+40y=15$

$\Rightarrow 40y=15-5=10$

$\Rightarrow y=0.25$

Putting the value of y in equation 1,

$x=1-0.25=0.75$

Therefore, Rajan must use 0.75 liters of 5% hydrochloric acid solution and 0.25 liters of 45% hydrochloric acid solution.

5 0

3 years ago

If the perimeter of Triangle XYZ is 56 cm, what is the perimeter of Triangle ABC?

Troyanec [42]

Answer:

28 cm

Step-by-step explanation:

Triangle ABC is obtained by joining the mid points of the sides of triangle XYZ.

So, perimeter of triangle ABC will be equal to half of the perimeter of triangle XYZ.

$P(\triangle ABC) = \frac{1}{2} \times P(\triangle XYZ)$

$P(\triangle ABC) = \frac{1}{2} \times 56$

$P(\triangle ABC) = 28\: cm$

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2 years ago

All these Barbz coming for me for saying "Superbass is trash" like if you dont agree dont say nothing or come for me its literal

Xelga [282]

Answer:

Step-by-step explanation:

ummm ok

7 0

2 years ago

Read 2 more answers

Please help with this paper!! asap please

neonofarm [45]

1 is L
2 is N
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Look back at your notes if you have any.

7 0

2 years ago

Combine these unlike fractions, then simplify. 4 2/3 - 2 2/5 need answer asap and plz explain

Zielflug [23.3K]

Answer: 2 4/5

Step-by-step explanation:

14/3 - 2 2/5

14/3 - 12/5

= 34/15

= 2 4/15

3 0

3 years ago