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3 years ago

5

Miss. Joyce has $72 to spend on parking and admission to the theater.the parking will cost $10, and the mission tickets will cos

t 15.50 dollars per person, including tax. write and solve an equation that can be used to determine the number of people that she can bring to the theater, including including herself.

1 answer:

leonid [27]3 years ago

6 0

Step-by-step explanation:

15.50n +10=72

15.50×4+10=72

62+10=72

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A jumping spider's movement is modeled by a parabola. The spider makes a single jump from the origin and reaches a maximum heigh

Stella [2.4K]

A parabola is a mirror-symmetrical U-shape.

The equation of the parabola is $\mathbf{y = -\frac{1}{640}(x - 80)^2 + 10}$
The focus is $\mathbf{Focus = (80, -1760)}$
The directrix is $\mathbf{y = \frac{1}{640}}$
The axis of the symmetry of parabola is: $\mathbf{x = 80}$

From the question, we have:

$\mathbf{Vertex: (h,k) = (80,10)}$

$\mathbf{Origin: (x,y) = (0,0)}$

The equation of a parabola is:

$\mathbf{y = a(x - h)^2 + k}$

Substitute the values of origin and vertex in $\mathbf{y = a(x - h)^2 + k}$

$\mathbf{0 = a(0 - 80)^2 + 10}$

$\mathbf{0 = a(- 80)^2 + 10}$

$\mathbf{0 = 6400a + 10}$

Collect like terms

$\mathbf{6400a =- 10}$

Solve for a

$\mathbf{a =- \frac{1}{640}}$

Substitute the values of a and the vertex in $\mathbf{y = a(x - h)^2 + k}$

$\mathbf{y = -\frac{1}{640}(x - 80)^2 + 10}$

The focus of a parabola is:

$\mathbf{Focus = (h, \frac{k+1}{4a})}$

Substitute the values of a and the vertex in $\mathbf{Focus = (h, \frac{k+1}{4a})}$

$\mathbf{Focus = (80, \frac{10+1}{4 \times -\frac{1}{640}})}$

$\mathbf{Focus = (80, -\frac{11}{\frac{1}{160}})}$

$\mathbf{Focus = (80, -11\times 160)}$

$\mathbf{Focus = (80, -1760)}$

The equation of the directrix is:

$\mathbf{y = -a}$

So, we have:

$\mathbf{y = \frac{1}{640}}$ ----- the directrix

The axis of symmetry is:

$\mathbf{x = -\frac{b}{2a}}$

We have:

$\mathbf{y = -\frac{1}{640}(x - 80)^2 + 10}$

Expand

$\mathbf{y = -\frac{1}{640}(x^2 -160x + 6400) +10}$

Expand

$\mathbf{y = -\frac{1}{640}x^2 +\frac{1}{4}x - 10 +10}$

$\mathbf{y = -\frac{1}{640}x^2 +\frac{1}{4}x }$

A quadratic function is represented as:

$\mathbf{y = ax^2 + bx + c}$

So, we have:

$\mathbf{a = -\frac{1}{640}}$

$\mathbf{b = \frac{1}{4}}$

Recall that:

$\mathbf{x = -\frac{b}{2a}}$

So, we have:

$\mathbf{x = -\frac{1/4}{2 \times -1/640}}$

$\mathbf{x = \frac{1/4}{1/320}}$

This gives

$\mathbf{x = \frac{320}{4}}$

$\mathbf{x = 80}$

Hence, the axis of the symmetry of parabola is: $\mathbf{x = 80}$

Read more about parabola at:

brainly.com/question/21685473

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3 years ago

Which is greater 7/8 or 2/3

andrew11 [14]

Answer:

7/8 is greater.

Step-by-step explanation:

In decimal form, 7/8 is greater than 2/3.

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0.667 (2/3)

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2 years ago

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Answer plzz tell the truth

Tanzania [10]

Answer:

Is there any choices? I'd either say 3/5 or 60/100.

Step-by-step explanation:

The reason being, both would equal around 60% I believe. 60% is 3/5th's of a 100, and 60/100 is simply 60 out of 100. Unless your going farther than I'm not entirely sure. I'm sorry.

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3 years ago

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Y=2x-5<br> 4x-y=7 what is the value of x

amid [387]

Answer:

x=1 and y=-3

Step-by-step explanation:

hope this helped :)

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3 years ago

What is x ? please help :)

bekas [8.4K]

Answer:

x =12

Step-by-step explanation:

The two angles are complementary, so the add to 90 degrees

5x+1/2x +24 = 90

Combine like terms

5 1/2 x +24 = 90

Subtract 24 from each side

5 1/2 x = 90-24

Change the mixed number to an improper fraction

11/2 x = 66

Multiply by the reciprocal 2/11 on each side

2/11 *11/2 x = 66*2/11

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3 years ago