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Tamiku [17]
3 years ago
7

Consider the system: y = 3x + 5 y = ax + b What values for a and b make the system inconsistent? What values for a and b make th

e system consistent and dependent? Explain.
Mathematics
2 answers:
AnnyKZ [126]3 years ago
7 0
<span>When a = 3 and b ≠ 5, the system will be inconsistent because the lines will be parallel. When a = 3 and b = 5, the system will be consistent and dependent because they represent the same line.</span>
marishachu [46]3 years ago
3 0

Answer:

When a = 3 and b ≠ 5, the system will be inconsistent because the lines will be parallel. When a = 3 and b = 5, the system will be consistent and dependent because they represent the same line.

Step-by-step explanation:

edg 2020

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Solve the equations shown above. Show your work by using the inverse operation.​
sergeinik [125]
X=12 and x=7 hope this helps !
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2 years ago
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Which is the approximate solution for the system of equations x + 5= 10 and 3x + y = 1?
zheka24 [161]

Answer: The approximate solution is (-0.36, 2.08).

Given system of equations : x+5y=10 and 3x+y=1

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2 years ago
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1. Derive the half-angle formulas from the double
lilavasa [31]

1) cos (θ / 2) = √[(1 + cos θ) / 2], sin (θ / 2) = √[(1 - cos θ) / 2], tan (θ / 2) = √[(1 - cos θ) / (1 + cos θ)]

2) (x, y) → (r · cos θ, r · sin θ), where r = √(x² + y²).

3) The point (x, y) = (2, 3) is equivalent to the point (r, θ) = (√13, 56.309°). The point (r, θ) = (4, 30°) is equivalent to the point (x, y) = (2√3, 2).

4) The <em>linear</em> function y = 5 · x - 8 is equivalent to the function r = - 8 / (sin θ - 5 · cos θ).

<h3>How to apply trigonometry on deriving formulas and transforming points</h3>

1) The following <em>trigonometric</em> formulae are used to derive the <em>half-angle</em> formulas:

sin² θ / 2 + cos² θ / 2 = 1                      (1)

cos θ = cos² (θ / 2) - sin² (θ / 2)           (2)

First, we derive the formula for the sine of a <em>half</em> angle:

cos θ = 2 · cos² (θ / 2) - 1

cos² (θ / 2) = (1 + cos θ) / 2

cos (θ / 2) = √[(1 + cos θ) / 2]

Second, we derive the formula for the cosine of a <em>half</em> angle:

cos θ = 1 - 2 · sin² (θ / 2)

2 · sin² (θ / 2) = 1 - cos θ

sin² (θ / 2) = (1 - cos θ) / 2

sin (θ / 2) = √[(1 - cos θ) / 2]

Third, we derive the formula for the tangent of a <em>half</em> angle:

tan (θ / 2) = sin (θ / 2) / cos (θ / 2)

tan (θ / 2) = √[(1 - cos θ) / (1 + cos θ)]

2) The formulae for the conversion of coordinates in <em>rectangular</em> form to <em>polar</em> form are obtained by <em>trigonometric</em> functions:

(x, y) → (r · cos θ, r · sin θ), where r = √(x² + y²).

3) Let be the point (x, y) = (2, 3), the coordinates in <em>polar</em> form are:

r = √(2² + 3²)

r = √13

θ = atan(3 / 2)

θ ≈ 56.309°

The point (x, y) = (2, 3) is equivalent to the point (r, θ) = (√13, 56.309°).

Let be the point (r, θ) = (4, 30°), the coordinates in <em>rectangular</em> form are:

(x, y) = (4 · cos 30°, 4 · sin 30°)

(x, y) = (2√3, 2)

The point (r, θ) = (4, 30°) is equivalent to the point (x, y) = (2√3, 2).

4) Let be the <em>linear</em> function y = 5 · x - 8, we proceed to use the following <em>substitution</em> formulas: x = r · cos θ, y = r · sin θ

r · sin θ = 5 · r · cos θ - 8

r · sin θ - 5 · r · cos θ = - 8

r · (sin θ - 5 · cos θ) = - 8

r = - 8 / (sin θ - 5 · cos θ)

The <em>linear</em> function y = 5 · x - 8 is equivalent to the function r = - 8 / (sin θ - 5 · cos θ).

To learn more on trigonometric expressions: brainly.com/question/14746686

#SPJ1

4 0
2 years ago
As part of a study of the association between smoking and risk of squamous cell carcinoma, a logistic regression model was estim
AlekseyPX

Answer:

0.44

Step-by-step explanation:

Given the estimated logistic regression model on risk of having squamous cell carcinoma

-4.84 + 4.6*(SMOKER)

SMOKER = 0 (non-smoker) ; 1 (SMOKER)

What is the predicted probability of a smoker having squamous cell carcinoma?

exp(-4.84 + 4.6*(SMOKER)) / 1 + exp(-4.84 + 4.6*(SMOKER))

SMOKER = 1

exp(-4.84 + 4.6) / 1 + exp(-4.84 + 4.6)

exp^(-0.24) / (1 + exp^(-0.24))

0.7866278 / 1.7866278

= 0.4402863

= 0.44

3 0
2 years ago
Which value of x makes the following equation true? <br> 6(x - 1) = -2x + 50
lakkis [162]

Answer:

x=7

Step-by-step explanation:

Step 1: Simplify both sides of the equation.

6(x−1)=−2x+50

(6)(x)+(6)(−1)=−2x+50(Distribute)

6x+−6=−2x+50

6x−6=−2x+50

Step 2: Add 2x to both sides.

6x−6+2x=−2x+50+2x

8x−6=50

Step 3: Add 6 to both sides.

8x−6+6=50+6

8x=56

Step 4: Divide both sides by 8.

8x /8 = 56 /8

x=7

7 0
3 years ago
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