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Elza [17]
3 years ago
7

Select the correct equations in the image.

Mathematics
1 answer:
ladessa [460]3 years ago
3 0

Answer:

The equations of the parabolas whose focus and vertex lie in different quadrants are;

The third equation x=-\frac{y^{2}}{16}-\frac{y}{4}+\frac{11}{4} and the sixth equationy=-\frac{x^{2}}{24}-\frac{5x}{12}+\frac{95}{24}

Step-by-step explanation:

We analyse each of the equations as follows

h =\frac{-b}{2a}

k = \frac{4ac-b^2}{4a}

Vertex = V(h, k)

Focus = F(h, k+p)

First equation

a = -1/8

b = 1/4

c = 23/8

k = 3

h = 1 Hence same quadrant

Second equation

a = 1/32

b = 1/4

c = -13/2

h = -4

k = -7 same quadrant

Third equation

a = -1/16

b = -1/4

c = 11/4

k = 3

h = -2 Hence different quadrants

Fourth equation

a = 1/16

b = 1/4

c = -19/4

h = -2

k = -5 The same quadrant

Fifth equation

a = -1/36

b = -5/18

c = 299/36

k = 620.56

h = 149.5 The same quadrant and

Sixth equation

a = -1/24

b = -5/12

c = 95/24

h = -5

k ≈ 5   Hence different quadrants

Hence the equations of the parabolas whose focus and vertex lie in different quadrants are the third and sixth equations presented as follows;

Third equation:

x=-\frac{y^{2}}{16}-\frac{y}{4}+\frac{11}{4}

Sixth equation:

y=-\frac{x^{2}}{24}-\frac{5x}{12}+\frac{95}{24}.

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Yes what do you need help with
8 0
3 years ago
A rectangle has a perimeter of 204 feet. It's length is six feet longer than twice it's width. If L stands for the length of the
Ratling [72]

Answer:

L = 70

W = 32

Step-by-step explanation:

P = 2L + 2W

P 204 feet

W = x

L  = 2x + 6

P = 2L + 2W

P = 2*(2x + 6) + 2*x

P = 4x + 12 + 2x

P = 6x + 12

But we know that P = 204  So 6x + 12 = 204

6x + 12 = 204                    Subtract 12 from both sides

6x + 12 - 12 = 204 - 12       Collect like terms on the right

6x = 192                             Divide by 6

x = 192/6

x = 32

Answer

W = 32

L = 2*W + 6

L = 2*32 + 6

L = 64 + 6

L = 70


7 0
3 years ago
(x+1)^1/2
Step2247 [10]

Answer:

Step-by-step explanation:

L.C.M. of 2 and 3=6

Raise to the power 6

8 0
3 years ago
The parents' club will need 100 of the same item for international night. They have a budget of $250. The choices are 100 baseba
Nuetrik [128]

Answer:

The parents' club can afford to buy 100 Baseball hats or 100 sports bottles.

Step-by-step explanation:

Given:

Item to be bought = 100

Total Budget = $250

Cost of each Baseball Hat = $2.45

Cost of each sports bottles = $2.50

Cost of each flag = $2.75

We need to find which items can they afford to buy.

Solution:

each Baseball Hat = $2.45

100 Baseball Hat = Cost of 100 Baseball Hat

Using Unitary method we get;

Cost of 100 Baseball Hat  = 2.45\times 100 =\$245

each sports bottles = $2.50

100 sports bottles = Cost of 100 sports bottles

Using Unitary method we get;

Cost of 100 sports bottles  = 2.5\times 100 =\$250

each flag = $2.75

100 flags = Cost of 100 flags

Using Unitary method we get;

Cost of 100 flags  = 2.75\times 100 =\$275

Hence from above we can see that;

Cost of 100 Base ball hat and 100 sports bottles are within the budget while Cost of 100 flags exceed the budget.

So we can say that;

The parents' club can afford to buy 100 Baseball hats or 100 sports bottles.

6 0
3 years ago
Would you rather (A) Run for 12 minutes at least 10 miles and hour; ... OR ... (B) 20 minutes at 6 miles per hour?
vlabodo [156]
Its actually the same length. I will choose B so that i can run slower
5 0
3 years ago
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