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2 years ago

11

Clinton earns $12 per hour cutting grass. he earned a total of $162 last week cutting grass. exactly how msny hours did he spend

cutting grass last week?

1 answer:

professor190 [17]2 years ago

6 0

Answer:13.5

Step-by-step explanation:

12•13.5=162

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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

6 0

2 years ago

X=3y+10 x=-8y-12<br><br> can u guys help me find the steps to solve this equations

Natalija [7]

Answer:

x=4, y=-2

Step-by-step explanation:

$x = 3y + 10 \\ x = - 8y -12\\ now \\ 3y + 10 = - 8y - 12 \\ 3y + 8y = - 12 - 10 \\ 11y = - 22 \\ y = \frac{ - 22}{11} \\ y = - 2 \\ again \: putting \: the \: value \:of \: y \\ x = 3y + 10 \\ x = 3( - 2) + 10 \\ x = - 6 + 10 \\ x = 4$

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1 year ago

6/36 reduce to simplest form

likoan [24]

Answer: 1/6

Step-by-step explanation: because 6/6=1 and 36/6 = 6 sp it will be 1/6

6 0

2 years ago

What is the median of the data set represented by the dot plot?

Butoxors [25]

So ur numbers are : 3,3,4,5,5,5,6,8,8

and the median (middle number) is 5 <==

because 2 dots above the 3 means u have 2 threes....and 1 dot above the 4 means there is 1 four..and so on

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3 years ago

Read 2 more answers

The Hu family goes out for lunch, and the price of the meal is $58. The sales tax on the meal is 7%, and the family also leaves

Alexxx [7]

58 plus tip of .20

so

58 times 0.2 = 11.6 is the tip

now we add tax (Presuming we son't tax the tip)

58 times 0.07 = 4.06 the tax

so its

58 + 11.6 + 4.06 = $73.66 total cost

8 0

2 years ago