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aleksley [76]
2 years ago
12

What's the correct answer and why?

Mathematics
1 answer:
alexandr402 [8]2 years ago
4 0
3x^4 becomes 3(3x)^4=3*3^4*x^4
y^2 becomes (3y)^2=3^2y²
the new z=3² the old z, so b is correct.
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Which equation represents the equation of the parabola with focus (-3 3) and directrix y=7?
Artemon [7]

Answer:

The equation y=\frac{-x^2-6x+31}{8} represents the equation of the parabola with focus (-3, 3) and directrix y = 7.

Step-by-step explanation:

To find the equation of the parabola with focus (-3, 3) and directrix y = 7. We start by assuming a general point on the parabola (x, y).

Using the distance formula d = \sqrt {\left( {x_1 - x_2 } \right)^2 + \left( {y_1 - y_2 } \right)^2 }, we find that the distance between (x, y) is

\sqrt{(x+3)^2+(y-3)^2}

and the distance between (x, y) and the directrix y = 7 is

\sqrt{(y-7)^2}.

On the parabola, these distances are equal so, we solve for y:

\sqrt{(x+3)^2+(y-3)^2}=\sqrt{(y-7)^2}\\\\\left(\sqrt{\left(x+3\right)^2+\left(y-3\right)^2}\right)^2=\left(\sqrt{\left(y-7\right)^2}\right)^2\\\\x^2+6x+y^2+18-6y=\left(y-7\right)^2\\\\x^2+6x+y^2+18-6y=y^2-14y+49\\\\y=\frac{-x^2-6x+31}{8}

6 0
3 years ago
What is the value of x in the equation 0.7 x - 1.4 = -3.5
Daniel [21]

Answer:

x=12.5

Step-by-step explanation:

0.7x times (-1.4)=-3.5

-0.28x=-3.5 (divide both sides)

Ans:12.5

4 0
3 years ago
Express in exponential form.<br><br> x = logby
Lunna [17]
X = log (base b) y
The base of the log becomes the base of the exponent.
The x and y switch.
b^x = y
6 0
3 years ago
Read 2 more answers
Given: 2x + 3y= 6.<br>What is the y-intercept?<br>(0,3)<br>(2,0)<br>(0,2)<br>no intercept<br><br>​
nirvana33 [79]
Answer: (0,2) Explanation: You plug in the coordinates into the equation and find which points make the equation true. Plugging in (0,2) turns the equations into (2•0) + (3•2) = 6. Simplify it and you get 6 = 6 which is true.
4 0
3 years ago
Find the solution to the system of equations
Neko [114]

Answer:

x=1

y=-4

Step-by-step explanation:

Since -x-3=y subsitue that in at the top equation

- x - 3 =  - 7x + 3

- x =  - 7x + 6

6x = 6

x = 1

Plug x=1 back into the equation to solve for y.

y =  - 7(1) + 3

y =  - 4

3 0
3 years ago
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