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vova2212 [387]
3 years ago
9

Find the axis of symmetry and what direction the parabola opens. -1/4(y+4)=(x-3)²

Mathematics
2 answers:
ioda3 years ago
8 0
Equation of parabola ==> (y-k) = a(x-h)²

To find te direction of this parabola, multiply both sides by (-1) ==>
1/4(y+4) - (x+3)². Since "a" is negative, the parabola opens downward & hence it's Vertex is a MAXIMUM.

Let's calculate this Maximum:
Vertex (h , k) and Axis of symmetry x=h

The given function: -1/4(y+4)=(x-3)², where k=- 4 & h= +3

Hence the axis of symmetry is x=3 & the vertex is at (3, -4)

MariettaO [177]3 years ago
7 0
First, convert the equation to the standard equation of a parabola.
-1/4(y+4)=(x-3)^2     ---multiply -4 on both sides   
y+4=-4(x-3)^2           ---subtract 4 on both sides
y=-4(x-3)^2-4
From the equation, we know that the parabola was moved by 3 to the right, because of (x-3)^2. So the axis of symmetry is x=3. Now look at the number in front of (x-3)^2. It is -4. Since it is negative, the parabola opens downwards. 

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−7y−4x=1 ​7y−2x=53 Solve the system of equations​​
Reptile [31]
-7y-4x=17y-2x=53
-4x=24y-2x=53
-2x=24y=53
24y+2x=53

You would have to solve one at a time.
y=53/24 
y=2.21
x=53/2
x=26.5
3 0
3 years ago
If it takes 4 gallons of gas to drive 92 miles how many miles can be driven using 6 gallons
AVprozaik [17]

Answer:

138

Step-by-step explanation:

as 92÷4 = 23 and 23x6 = 148

4 0
2 years ago
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You have two exponential functions. One function has the formula g(x) = 5 ^x . The other function has the formula h(x) = 5^-x .
Shkiper50 [21]
We are given with two functions here: h(x) is 5^-x and g(x) is 5^x . we are asked in the problem to determine the value of the expression (g-h)(x). In this case, we just have to employ subtraction to the given functions. That is 

(g-h)(x) = 5^x - 5^-x
             = 5^x -1/5^x
             = (5^2x -1)/5^x


 
4 0
3 years ago
Read 2 more answers
I am once again asking for your help with solving this problem.
densk [106]

Answer:

why does this hurt my head so much

Step-by-step explanation:

5 0
3 years ago
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Help,anyone can help me do quetion.​
lorasvet [3.4K]

Answer:

C2- 65° C3- 84°

Step-by-step explanation:

for C2:

the 2 parallel lines and the one cutting fully through form a transversal.

One of the rules for this is that co-interior angles (the 2 on the same side of the intersecting line) add to 180°.

This means that the angle at the top left (still within the triangle) should be 50° (180-121).

The other angle within the triangle (not the x one) is vertically opposite (opposite or "diagonal") with the 65°.

Vertically opposite angles have the same value, meaning the second angle is 65°.

In a triangle, the 3 angles add to 180. In this case, 50+65+x=180, which can be simplified to 115+x=180. Subtracting 115 from both sides gives x=65°.

For C3-

Imagine a parallel line is going through the angle x, splitting it into 2 angles (let's call them a and b).

With a being the top half, you can use the 133° given to help you. Like before, vertically opposite angles are the same, so the value "diagonal" to 133° should also be 133°. Using the co-interior rule, a should be 180-133, which gives 47°.

For b, we can skip this first step entirely. Since 143 and b are co-interior, 180-143=b, therefore b=37°.

To use these, remember a+b=x, which by subbing in the values gives 47+37=x, simplified to x=84°.

** I suggest revising the types of transversal relationships (corresponding, alternate, vertically opposite and co-interior). It's difficult explaining this without diagrams, but if you need more clarification, I'm happy to help!

7 0
2 years ago
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