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The general formula for the parabola is [tex]x^{2}+y^{2}-21\cdot x +51\cdot y +548 = 0[/tex].

We need the knowledge of three distinct points to determine all coefficients of the vertical parabola based on the following general formula:

[tex]x^{2} + y^{2} + D\cdot x + E\cdot y + F = 0[/tex] (1)

If we know that [tex](x_{1}, y_{1}) = (-2, -18)[/tex], [tex](x_{2}, y_{2}) = (3,-13)[/tex] and [tex](x_{3}, y_{3}) = (5,-39)[/tex], then we have the following system of linear equations:

[tex]-2\cdot D -18\cdot E + F = -328[/tex] (2)

[tex]3\cdot D -13\cdot y + F = -178[/tex] (3)

[tex]5\cdot D -39\cdot E + F = -1546[/tex] (4)

The solution of the system of equations is: [tex]D = -21[/tex], [tex]E = 51[/tex], [tex]F = 548[/tex].

The general formula for the parabola is [tex]x^{2}+y^{2}-21\cdot x +51\cdot y +548 = 0[/tex].

We kindly invite to check this question on parabolae: https://brainly.com/question/4074088

Answer:

the value of a = 7..............

Answer:

[tex]h(x) = 3x + 8 \\ h(a) =3 a + 8 [/tex]

But, it is given that

[tex]h(a) = 29[/tex]

Therefore,

[tex]3a + 8 =29 \\ 3a = 29 - 8 \\ 3a = 21 \\ a = \frac{21}{3} \\ \boxed{ a = 7}[/tex]

Hence, the value of a is 7

Answer:

C. Action: Divide both sides by 3.

F. Property: Division property of equality

Step-by-step explanation:

you are trying to get x by itself so if you divide by 3 you are taking the 3 from x, and what you do to one side you do to the other.

Answer:

C. Action: Divide both sides by 3.

F. Property: Division property of equality.

Step-by-step explanation:

Isolate the variable, x. Note the equal sign, what you do to one side, you do to the other.

First, divide 3 from both sides of the equation:

(3x)/3 = (12)/3

x = 12/3

x = 4

C. Action: Divide both sides by 3.

F. Property: Division property of equality.

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Answer:

90 degrees

Step-by-step explanation:

please say thanks

Answer:

2inch=1 foot

Step-by-step explanation:

so 2 to 1       2:1

Answer:

$ 80,000

Step-by-step explanation:

2/5 + 1/3 = (6 + 5)/15 = 11/15

15/15 - 11/15 = 4/15

4/15 of 300,000

4/15 x 300,000 = 1,200,000/15 = 80,000

Answer:

159.29-159.29(5/100)=151. 3255

Answer:

Step-by-step explanation:

Two of the legs will be at right angles to each other and have negative reciprocal slopes. Area will be half of the product of these two legs.

slope of DE (-3 - (-1)) / (1 - (-6)) = -2/7

slope of EF (4 - (-3)) / (3 - 1) = 7/2

so these two are perpendicular

check the DF line to be certain

slope of DF (4 - (-1)) / (3 - (-6)) = 5/9

Length of DE =  √(-2² + 7²) = √53

Length of EF = √(7² + 2²) = √53

Area of triangle

A = ½√53√53 = 26.5 units²

Answer:

The answer is 570 feet.

Step-by-step explanation:

First, the bird is 520 feet HIGH.

The diver is 50 feet BELOW sea level, which is also -50.

To find the difference, you would SUBTRACT right?

So 520 - -50 OR 520 + 50 (This is because two negatives make a positive, and you are also subtracting negatives, which in turn means adding).

520 + 50 = 570 - HOPE THIS HELPED!

Answer:

yes bti dsnin s

Step-by-step explanation:

Answer:

1 1/45

Step-by-step explanation:

Hello there I think the measure of EBC is 58 degrees.

That's because angles EBC and DBE are complementary. it means that they add up to 90 degrees.

We are given that

DBE=32 degrees.

And we know that angles EBC and DBE add up to 90 degrees.

So we take 90 and subtract the measure of angle DBE (32 degrees)

90-32=58

Hope this helps!

Answer:

I don't know sorry.....

Answer:

D

Step-by-step explanation:

We are given the function:

[tex]\displaystyle f(x) = \frac{1}{3} x + 2[/tex]

And we want to find its inverse h.

To find the inverse of a function, we can switch the y and x variables and solve for the new y. This will be our inverse.

We begin with:

[tex]\displaystyle f(x) = y = \frac{1}{3} x+ 2[/tex]

Switching the variables yield:

[tex]\displaystyle x = \frac{1}{3}y + 2[/tex]

And solving for y yields that:

[tex]\displaystyle y = h(x) = 3x - 6[/tex]

In conclusion, the inverse function to f is 3x - 6. Our answer is D.

To understand why we switch the variables, recall that by the definition of inverse functions, if f(a) = b, then f⁻¹(b) = a. So, by switching the variables, we are essentially solving for f⁻¹(x).

Answer:

3.98%

Step-by-step explanation:

R = $17,300/$435,000 = .0398, or 3.98%

Answer:

Step-by-step explanation:

If you like my answer than please mark me brainliest thanks

Answer:

$437.58

Step-by-step explanation:

15% + 28%

= 43%

43/100 × 306

= $131.58

$131.58 + $306

= $437.58

d/dx cot(x) = -csc²(x)

d/dx sin(x) = cos(x)

So, if f(x) = 4 cot(x) + 10 sin(x), then

f '(x) = -4 csc²(x) + 10 cos(x)

Answer:

The sum is about 22

Step-by-step explanation:

When you round the values at the ones place, you get:

7 + 6 + 9 = 22

Answer:22

Step-by-step explanation:

Answer:

Step-by-step explanation:

x² + 5x - 5 =  (-6)² + 5*(-6) - 5

                 = 36 - 30 - 5  

                 = 36 - 35

                 = 1

Answer:

1

Step-by-step explanation:

-6^(2)+5(-6)-5

36 + 5(-6) -5

36- 30- 5

6 - 5

1

Answer:

13.6 - x = -64.2

Step-by-step explanation:

x = 77.8

13.6 - 77.8 = -64.2 True!

Answer:

x=77.8

Step-by-step explanation:

13.6-x=-64.2

-13.6. -13.6

---------------------

since there is already -x it wouldn't be -77.8 bc that would cancel it out

Answer:

8.61

Step-by-step explanation:

Answer:

8.61 I think try that okay

[tex]▪ ▪ ▪ ▪ ▪ ▪ ▪ ▪ ▪ ▪ ▪ ▪ ▪ { \huge \mathfrak{Answer}}▪ ▪ ▪ ▪ ▪ ▪ ▪ ▪ ▪ ▪ ▪ ▪ ▪ ▪ [/tex]

The value of given expression is 2

Solution is in attachment ~

You should first recognize the shape of the curve - it's an exponential function, so its equation takes the form [tex]y(x)=a\cdot b^{cx}[/tex] for some constants a, b, and c.

The curve lies above the x-axis, so a must be positive.

The curve is defined everywhere (there are no discontinuities), so b must be positive.

As you move left to right, the function is increasing, so c must also be positive. But to make things simpler, let's assume c = 1.

When x = 0, the curve passes through the point (0, 1). In our equation, we have

[tex]y(0) = a\cdot b^0 = a[/tex]

so it follows that a = 1.

When x = 1, the curve approximately passes through the point (1, 4); so

[tex]y(1) = b^1 = 4[/tex]

so b = 4.

Then the equation of the curve might be [tex]\boxed{y = 4^x}[/tex].

Answer:

2.222

Step-by-step explanation:

Hope this helps :)  

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Answer:

2 2/9

Step-by-step explanation:

so if we want to be able to substract, we're gonna multiply the 1/3 times three so the result come out to 3/9 and now we are able to substract, so 6 3/9 - 4 1/9 is equal to 2 2/9

Answer:

f(x)=4x2−2x+8,

or, f(2)=4*2*2-2*2+8

or,f(2)=16-4+8

or,f(2)=20....

f(2)=20