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Molodets [167]
3 years ago
12

Elizabeth wants to ride her bicycle 28.6 miles this week. She has already ridden 19 miles. If she rides for 3 more days, write a

nd solve an equation which can be used to determine mm, the average number of miles she would have to ride each day to meet her goal.
Mathematics
1 answer:
8090 [49]3 years ago
5 0

Answer: The average number of miles she would have to ride each day to meet her goal = 3.2 miles.

Step-by-step explanation:

Given: Elizabeth wants to ride her bicycle 28.6 miles this week.

She already ridden 19 miles.

Number of days she will ride more =3

Let m = average number of miles ridden in a day.

Then,

Total distance = initial distance + (m) (Number of days)

i.e. 28.6 = 19+3m   (Required equation)

Subtract 19 from both sides , we get

9.6=3m\\\\\Rightarrow\ m=\dfrac{9.6}{3}\\\\\Rightarrow\ m=3.2\ miles

Hence, the average number of miles she would have to ride each day to meet her goal = 3.2 miles.

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Write the equation of a parabola having the vertex (1, −2) and containing the point (3, 6) in vertex form. Then, rewrite the equ
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PART A

The equation of the parabola in vertex form is given by the formula,

y - k = a {(x - h)}^{2}

where

(h,k)=(1,-2)

is the vertex of the parabola.

We substitute these values to obtain,


y  + 2 = a {(x - 1)}^{2}

The point, (3,6) lies on the parabola.

It must therefore satisfy its equation.


6  + 2 = a {(3 - 1)}^{2}


8= a {(2)}^{2}


8=4a


a = 2
Hence the equation of the parabola in vertex form is


y  + 2 = 2 {(x - 1)}^{2}


PART B

To obtain the equation of the parabola in standard form, we expand the vertex form of the equation.

y  + 2 = 2{(x - 1)}^{2}

This implies that

y + 2 = 2(x - 1)(x - 1)


We expand to obtain,


y + 2 = 2( {x}^{2}  - 2x + 1)


This will give us,


y + 2 = 2 {x}^{2}  - 4x + 2


y =  {x}^{2}  - 4x

This equation is now in the form,

y = a {x}^{2}  + bx + c
where

a=1,b=-4,c=0

This is the standard form
7 0
3 years ago
What is the constant of proportionality of the relationship shown in the graph?
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There is no graph to figure this out...
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3 years ago
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WILL GIVE BRAINLIEST! PLEASE HELP ASAP!
sergejj [24]

Answer:

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Step-by-step explanation:

I'll it explain it as soon as it sends

20 x 4 - 100 ÷ 5

Pemdas First parenthesis then multiplica or division and the addition or subtraction. Everything from left to right

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80 - 100 ÷ 5

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7 0
2 years ago
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what is the slope of the line that passes through the points (-4,-4) and (-4,-9)? Write your answer in simplest form
Aneli [31]

Answer:

undefined

Step-by-step explanation:

We can find the slope of a line using two points by

m = (y2-y1)/(x2-x1)

   = (-9- -4)/(-4 -  -4)

    = (-9+4)/(-4+4)

   = -5/0

When we divide by zero, our solutions is undefined

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3 0
3 years ago
The Acme Company manufactures widgets. The distribution of widget weights is bell-shaped. The widget weights have a mean of 43 o
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Answer:

a) 95% of the widget weights lie between 29 and 57 ounces.

b) What percentage of the widget weights lie between 12 and 57 ounces? about 97.5%

c) What percentage of the widget weights lie above 30? about 97.5%

Step-by-step explanation:

The empirical rule for a mean of 43 and a standard deviation of 7 is shown below.  

a) 29 represents two standard deviations below the mean, and 57 represents two standard deviations above the mean, so, 95% of the widget weights lie between 29 and 57 ounces.  

b) 22 represents three standard deviations below the mean, and the percentage of the widget weights below 22 is only 0.15%. We can say that the percentage of widget weights below 12 is about 0. Equivalently we can say that the percentage of widget weights between 12 an 43 is about 50% and the percentage of widget weights between 43 and 57 is 47.5%. Therefore, the percentage of the widget weights that lie between 12 and 57 ounces is about 97.5%

c) The percentage of widget weights that lie above 29 is 47.5% + 50% = 97.5%. We can consider that the percentage of the widget weights that lie above 30 is about 97.5%

3 0
2 years ago
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