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3 years ago

100 points please helpp

Mathematics

1 answer:

Fudgin [204]3 years ago

4 0

Answer:

The answer is J because the line inside the box is at 78

Step-by-step explanation:

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Which expression is equivalent to 45a-10b

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SCORPION-xisa [38]

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Which algebraic expression represents “the difference of fifty-four and seven times a number”? 54 minus 7 n StartFraction 54 Ove

VMariaS [17]

Answer: 54-7n

Step-by-step explanation:

When we talk about mathematical language, the difference between two numbers, quantities or terms is the substraction operation.

For example, the difference between a and b is:

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On the other hand, if we read a numer c times a number n, this means both numbers are multiplied.

For example:

c times n is:

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So, according to the explained above, “the difference of fifty-four and seven times a number n” is:

54-7n

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Luden [163]

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Step-by-step explanation:

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3 years ago

Suppose that θ is an acute angle of a right triangle and that sec(θ)=52. Find cos(θ) and csc(θ).

insens350 [35]

Answer:

$\cos{\theta} = \dfrac{1}{52}$

$\csc{\theta} = \dfrac{52}{\sqrt{2703}}$

Step-by-step explanation:

To solve this question we're going to use trigonometric identities and good ol' Pythagoras theorem.

a) Firstly, sec(θ)=52. we're gonna convert this to cos(θ) using:

$\sec{\theta} = \dfrac{1}{\cos{\theta}}$

we can substitute the value of sec(θ) in this equation:

$52 = \dfrac{1}{\cos{\theta}}$

and solve for for cos(θ)

$\cos{\theta} = \dfrac{1}{52}$

side note: just to confirm we can find the value of θ and verify that is indeed an acute angle by $\theta = \arccos{\left(\dfrac{1}{52}\right)} = 88.8^\circ$

b) since right triangle is mentioned in the question. We can use:

$\cos{\theta} = \dfrac{\text{adj}}{\text{hyp}}$

we know the value of cos(θ)=1\52. and by comparing the two. we can say that:

length of the adjacent side = 1
length of the hypotenuse = 52

we can find the third side using the Pythagoras theorem.

$(\text{hyp})^2=(\text{adj})^2+(\text{opp})^2$

$(52)^2=(1)^2+(\text{opp})^2$

$\text{opp}=\sqrt{(52)^2-1}$

$\text{opp}=\sqrt{2703}$

length of the opposite side = √(2703) ≈ 51.9904

we can find the sin(θ) using this side:

$\sin{\theta} = \dfrac{\text{opp}}{\text{hyp}}$

$\sin{\theta} = \dfrac{\sqrt{2703}}{52}}$

and since $\csc{\theta} = \dfrac{1}{\sin{\theta}}$

$\csc{\theta} = \dfrac{52}{\sqrt{2703}}$

4 0

3 years ago