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2 years ago

Write the equation of the parabola that has the vertex at point (1.5,0) and passes through the point (3,3).

Mathematics

1 answer:

astra-53 [7]2 years ago

4 0

Answer:

3y = 4(x - 1.5)²

Step-by-step explanation:

The equation of the parabola in the vertex form is:

y = a (x-h)² + k

Where: (h,k) the coordinates of the vertex & a is a multiplier

The parabola has a vertex at ( 1.5 , 0 )

So, h = 1.5 , k = 0

∴ y = a (x - 1.5)² + 0

∴ y = a (x - 1.5)²

The parabola passes through points ( 3 , 3 )

∴ 3 = a (3 - 1.5)²

∴ 1.5² a = 3 ⇒ a = 3/1.5² = 3/2.25 = 4/3

∴ y = (4/3) (x - 1.5)²

mukitbly both sides by 3

∴ 3y = 4(x - 1.5)²

So, the equation of a parabola that has a vertex at ( 1.5 , 0 ) and passes through points ( 3 , 3 ) is 3y = 4(x - 1.5)²

See the attached figure.

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Given: △ABC, AB=5sqrt2 m∠A=45°, m∠C=30° Find: BC and AC

Marysya12 [62]

BC is 10 units and AC is $5+5\sqrt{3}$ units

Step-by-step explanation:

Let us revise the sine rule

In ΔABC:

$\frac{AB}{sin(C)}=\frac{BC}{sin(A)}=\frac{AC}{sin(B)}$
AB is opposite to ∠C
BC is opposite to ∠A
AC is opposite to ∠B

Let us use this rule to solve the problem

In ΔABC:

∵ m∠A = 45°

∵ m∠C = 30°

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

∵ m∠A + m∠B + m∠C = 180

∴ 45 + m∠B + 30 = 180

- Add the like terms

∴ m∠B + 75 = 180

- Subtract 75 from both sides

∴ m∠B = 105°

∵ $\frac{AB}{sin(C)}=\frac{BC}{sin(A)}$

∵ AB = $5\sqrt{2}$

- Substitute AB and the 3 angles in the rule above

∴ $\frac{5\sqrt{2}}{sin(30)}=\frac{BC}{sin(45)}$

- By using cross multiplication

∴ (BC) × sin(30) = $5\sqrt{2}$ × sin(45)

∵ sin(30) = 0.5 and sin(45) = $\frac{1}{\sqrt{2}}$

∴ 0.5 (BC) = 5

- Divide both sides by 0.5

∴ BC = 10 units

∵ $\frac{AB}{sin(C)}=\frac{AC}{sin(B)}$

- Substitute AB and the 3 angles in the rule above

∴ $\frac{5\sqrt{2}}{sin(30)}=\frac{AC}{sin(105)}$

- By using cross multiplication

∴ (AC) × sin(30) = $5\sqrt{2}$ × sin(105)

∵ sin(105) = $\frac{\sqrt{6}+\sqrt{2}}{4}$

∴ 0.5 (AC) = $\frac{5+5\sqrt{3}}{2}$

- Divide both sides by 0.5

∴ AC = $5+5\sqrt{3}$ units

BC is 10 units and AC is $5+5\sqrt{3}$ units

Learn more:

You can learn more about the sine rule in brainly.com/question/12985572

#LearnwithBrainly

6 0

3 years ago

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Arisa [49]

Answer:

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Step-by-step explanation:

To determine if (1,2) is a solution to both equations, substitute into the equation and see if it is true

2x+y =4

2(1) + 2 =4

2+2 =4

4=4

true

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Since both statements are true

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4 0

2 years ago

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koban [17]

Answer:

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Step-by-step explanation:

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2 years ago