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e-lub [12.9K]
3 years ago
12

Write the equation of the line that passes through the point ( -6 , 2 ) and is parallel to the line y = 1/2x + 4.

Mathematics
1 answer:
SashulF [63]3 years ago
8 0
Parallel lines need the same slope, and for y = 1/2x + 4, it is 1/2.

Let's solve for b.

2 = 1/2(-6) + b
2 = -3 + b
Add 3 on both sides.
5 = b

y = 1/2x + 5
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Answer:

36+4h=60

36+4h-36=60-36

4h=24

4h÷4=24÷4

h=6

So, after the move they can spend 6 hours there. (6×4=24, 24+36=60, they will spend $60 if they spend 6 hours there, $56 if they spend 5 hours there and don't want to spend $60).

Step-by-step explanation:

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F(x) =2x^2+12x-6 Does this function have a minimum or maximum value? What is this minimum or maximum value?
Alex777 [14]

Let's compare the given function with the model for a quadratic equation:

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Since the value of a is positive, the parabola has its concavity upwards, and the function has a minimum value.

The minimum value can be found calculating the y-coordinate of the vertex:

\begin{gathered} x_v=-\frac{b}{2a}=-\frac{12}{4}=-3 \\  \\ y_v=2\cdot(-3)^2+12\cdot(-3)-6 \\ y_v=2\cdot9-36-6^{} \\ y_v=-24 \end{gathered}

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Answer:

c = 13.2

Step-by-step explanation:

* Lets explain how to solve the problem

- In Δ ABC

# Side a is opposite to ∠A

# Side b is opposite to ∠B

# Side c is opposite to ∠C

- The sine rule is:

# \frac{a}{sinA}=\frac{b}{sinB}=\frac{c}{sinC}

* Lets solve the problem

- In Δ ABC

∵ m∠A = 16°

∵ m∠B = 49°

∵ The sum of the measures of the interior angles of a triangle is 180°

∴ m∠A + m∠B + m∠C = 180°

∴ 16° + 49° + m∠C = 180°

∴ 65° + m∠C = 180° ⇒ subtract 65° from both sides

∴ m∠C = 115°

- Lets use the sine rule to find c

∵ a = 4 and m∠A = 16°

∵ m∠C = 115°

∵ \frac{4}{sin(16)}=\frac{c}{sin(115)}

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∴ c=\frac{4(sin115)}{sin16}=13.2

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The proportion looks like this
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