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3 years ago

What’s the standard form of the quadratic equation

Mathematics

1 answer:

Finger [1]3 years ago

6 0

y = ax^2 + bx + 7 because when x = 0 y = 7

when x = -1 y = 14 so we have
14 = a - b + 7
so a - b = 7...............(1)
when x = 1 y = 4
so 4 = a + b + 7
a + b = -3.................(2)
Adding equations (1) and (2) we eliminate b so:-
2a = 4
a = 2
Substitute a = 2 in equation (1)
2 - b = 7
b = -5

so our equation is y = 2x^2 - 5x + 7

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Convert the Cartesian equation (x 2 + y 2)2 = 4(x 2 - y 2) to a polar equation.

SashulF [63]

<u>ANSWER</u>

${r}^{2} = 4 \cos2\theta$

<u>EXPLANATION</u>

The Cartesian equation is

${( {x}^{2} + {y}^{2} )}^{2} = 4( {x}^{2} - {y}^{2} )$

We substitute

$x = r \cos( \theta)$

$y = r \sin( \theta)$

and

${x}^{2} + {y}^{2} = {r}^{2}$

This implies that

${( {r}^{2} )}^{2} = 4(( { r \cos\theta) }^{2} - {(r \sin\theta) }^{2} )$

Let us evaluate the exponents to get:

${r}^{4} = 4({ {r}^{2} \cos^{2}\theta } - {r}^{2} \sin^{2}\theta)$

Factor the RHS to get:

${r}^{4} = 4{r}^{2} ({ \cos^{2}\theta } - \sin^{2}\theta)$

Divide through by r²

${r}^{2} = 4 ({ \cos^{2}\theta } - \sin^{2}\theta)$

Apply the double angle identity

$\cos^{2}\theta -\sin^{2}\theta= \cos(2 \theta)$

The polar equation then becomes:

${r}^{2} = 4 \cos2\theta$

7 0

3 years ago

Which of these is an irrational number?

Ilia_Sergeevich [38]

Answer:

$\sqrt{15}$

Step-by-step explanation:

6 0

3 years ago

Read 2 more answers

Can you help with both questions 4 and 5?

cupoosta [38]

Well since the triangle is split into 2 triangles and they both are the same size so BD on the bottom is 15 which means naturally BC must be 30. Five I'm not sure about

8 0

3 years ago

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Please answer all part correct

insens350 [35]

Answer:

a). We want to know how much each point was worth.

b). $12x+5=41$

c). Each problem worth 3 points.

Step-by-step explanation:

a). We want to know how much each problem was worth. Because we have the total points of the test, and how much was the bonus. But we still don't know the worth of each problem.

b). We know that the total points of the test were 41, and the bonus 5 points. There were 12 problems on the test and we are going to use "x" for the unknown part (how many points each problem was worth).

The equation is :

$12x+5=41$

Why 12x? Because if you multiply the twelve problems of the test with the worth of each one and then add the 5 points of the bonus you will obtain the total points of the test (41).

c). Now we have to solve the equation, this means that we have to clear "x":

$12x+5=41$

Subtract 5 from both sides.

$12x+5-5=41-5\\12x=36$

Finally divide in 12 both sides of the equation:

$\frac{12x}{12}=\frac{36}{12} \\\\x=3$

Then each problem worth 3 points.

7 0

3 years ago

93, 94, 95, 89, 85, 82, 87, 85, 84, 80, 78, 78, 84, 87, 90.

artcher [175]

Answer:

86 is the mean and the median is 85

Step-by-step explanation:

To calculate the mean all u gotta do is add all the numbers then divide by how many numbers there is and to calculate the median all u gotta do is put them in order 78-95 then mark 1 on each side til you reach the middle and the number in the middle is the answer.

6 0

3 years ago

Read 2 more answers