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3 years ago

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Rewrite 7x + 4 = x – 2 as a system.

1 answer:

s344n2d4d5 [400]3 years ago

3 0

7x + 4 = x - 2 -- (1)

To rewrite the equation above as a system, we simply let (1) be equal to y, i.e.

7x + 4 = x - 2 = y -- (2)

Recall from the rule of transitivity: If a = b = c, then this implies that a = c & b = c. From this, we have (2) to be expressed as

y = 7x + 4 -- (i)
y = x - 2 -- (ii)

Note: (i) & (ii) are both regarded as a system of linear equation which can be evaluated simultaneously.

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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

4 years ago

D = 8a The variable a represents the number of attendees, and the variable d represents the cost in dollars. At most how many at

suter [353]

Answer: At most 9 attendees can be there.

Step-by-step explanation:

Given equation:<em> d = 8a</em> , where <em>a</em> represents the number of attendees, and the variable <em>d </em>represents the cost in dollars.

To find : the number of attendees, if Will budgets a total of $72 for his graduation picnic.

72=8a

⇒ 9 = a [divide both sides by 8]

∴ a= 9

Hence, at most 9 attendees can be there.

4 0

3 years ago

55" TV: $669 with a 23% markup

Flauer [41]

Answer:

what is the question?

Step-by-step explanation:

6 0

3 years ago

A group of 3 friends spends a total of $17.25 for brunch at a restaurant before tax and tip. Everyone orders the same thing: scr

liubo4ka [24]

Answer:

17.25/3 = 5.75

Step-by-step explanation:

You divide 17.25 by 3.

It equals 5.75. Each friend has 5.75 on spend on brunch.

Toast is $1. Orange Juice is $1.75. Eggs are $2.

Hope this helps.

3 0

3 years ago

How to get the equation

Olenka [21]

ITS EASY AND IF YOU TRY YOU CAN FIND THE ANSWER JUST WORK HARD AND TRY

6 0

3 years ago