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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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Karen purchased the DVD
9966 [12]

Answer:

Percent markdown = 14%

Step-by-step explanation:

Given:

Original price of DVD player = $175.90

Markdown price of DVD player =$153.77

To find percent markdown.

Amount of mark down =\textrm{Original price - Markdown price}=\$175.90-\$153.77=\$22.13

Percent markdown =\frac{Amount\ of\ markdown}{Markdown\ price}\times100=\frac{22.13}{153.77}\times 100=14.39\%\approx 14\%

4 0
3 years ago
A pair of shoes usually sells for $67. If the shoes are 40% off, and sales tax is 8%, what is the total price of the shoes, incl
Gekata [30.6K]
If it is 40% off, it means you have to pay 60% of its price.
$67 × 60/100 = $40.20
the 8% of sales tax is added from the $40.20
$40.20 × 8/100 = $3.22
total price = $40.20 + $3.22 = $43.42
5 0
3 years ago
Jen Butler has been pricing​ Speed-Pass train fares for a group trip to New York. Three adults and four children must pay $ 79.
xxMikexx [17]

<u>Answer:</u>

Price of the​ adult's ticket = $13

Price of a​ child's ticket = $ 10

<u>Step-by-step explanation:</u>

Given:

Cost of train fares for Three adults and four children = $79

Cost of train fares Two adults and three children  = $ 56

To Find:

Price of the​ adult's ticket and the price of a​ child's ticket =?

Solution:

Let the cost of one adult's ticket be x  and

Let the cost of one child's ticket be y

Then

Three adults and four children must pay $ 79 be

3x + 4y = 79-----------------------------------------------(1)

Two adults and three children must pay $56

2x + 3y = 56----------------------------------------------(2)

multiply  eq(1) by 2, we get

6x + 8y = 158----------------------(3)

multiply  eq(2) by 3, we get

6x + 9y = 168----------------------(4)

Subracting (3) from (4)

 6x + 9y = 168

 6x + 8y = 158

(-)      (-)       (-)

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

0x +  y = 10

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

y=10

Now substitute the value of y in eq (1) to get the value of x

3x + 4(10)= 79

3x +  40 = 79

3x = 79 - 40

3x = 39

x = \frac{39}{3}

x= 13

3 0
3 years ago
Enter product in simplest form<br>1/4×7 4/5​
grigory [225]

Answer:

i believe the answer is 39/20 which could also be 13/7

Step-by-step explanation:

8 0
3 years ago
Read 2 more answers
A company that makes boxes finds that 6 out of 8 boxes are damaged.What percent of the boxes are damage?
Elanso [62]
8 boxes is 100%, 6 out of 8 is 6/8 x 100% = 75%
7 0
3 years ago
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