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Lady bird [3.3K]
2 years ago
11

8x+9y=-28 -4x=y solve the system by subsitution

Mathematics
2 answers:
bixtya [17]2 years ago
8 0

Answer:

x= 1

y = -4

Step-by-step explanation:

8x + 9y = -28

-4x = y

8x + 9(-4x) = -28

8x - 36x = -28

-28x = - 28

x = 1

y = -4(1) = -4

Zielflug [23.3K]2 years ago
6 0

Answer:

2

Step-by-step explanation:

8 + 9 = 17

17y = 28

28 / 17 = 1.64

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If sin theta = 4/5 and theta is in quadrant 2, the value of cot theta is
trasher [3.6K]

Answer:

Cot(theta) = - 0.75 or -3/4

Step-by-step explanation:

The hypotenuse is 5

The y value is 4

We need to find the corresponding x value.

x^2 + y^2 = z^2

X = ?

y = 4

z = 5

x^2 + 4^2 = 5^2

x^2 + 16 = 25

x^2 = 9

Now in this case, you are in quadrant 2, so the x value is - 3

sqrt(x^2) = sqrt(9)

x = - 3

The cot value is the adjacent (x value) / the opposite ( y ) value

Cot(theta) = -3/4

cot(theta) = -0.75

8 0
3 years ago
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You buy a new laptop for $300$300. The sales tax is 6%6%. What is the total cost for the laptop including the sales tax?
cricket20 [7]

Answer:

Cost Including tax would be $318

Step-by-step explanation:

Given:

Price of laptop = $300

Sales tax = 6% of price

To Find:

Cost with tax = ?

Solution:

Cost with tax = Price of laptop + Value of tax

We have to find the value of tax

Value of tax = 6% of Price

putting the value

Value of tax = 6 % * $300

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Cost with tax = 300 + 18

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3 years ago
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For what values of θ on the polar curve r=θ, with 0≤θ≤2π , are the tangent lines horizontal? Vertical?
Bond [772]
Given that r=\theta, then r'=1

The slope of a tangent line in the polar coordinate is given by:

m= \frac{r'\sin\theta+r\cos\theta}{r'\cos\theta-r\sin\theta}

Thus, we have:

m= \frac{\sin\theta+\theta\cos\theta}{\cos\theta-\theta\sin\theta}



Part A:

For horizontal tangent lines, m = 0.

Thus, we have:

\sin\theta+\theta\cos\theta=0 \\  \\ \theta\cos\theta=-\sin\theta \\  \\ \theta=- \frac{\sin\theta}{\cos\theta} =-\tan\theta

Therefore, the <span>values of θ on the polar curve r = θ, with 0 ≤ θ ≤ 2π, such that the tangent lines are horizontal are:

</span><span>θ = 0

</span>θ = <span>2.02875783811043
</span>
θ = <span>4.91318043943488



Part B:

For vertical tangent lines, \frac{1}{m} =0

Thus, we have:

\cos\theta-\theta\sin\theta=0 \\  \\ \Rightarrow\theta\sin\theta=\cos\theta \\  \\ \Rightarrow\theta= \frac{\cos\theta}{\sin\theta} =\sec\theta

</span>Therefore, the <span>values of θ on the polar curve r = θ, with 0 ≤ θ ≤ 2π, such that the tangent lines are vertical are:

</span>θ = <span>4.91718592528713</span>
3 0
3 years ago
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