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DENIUS [597]
3 years ago
9

Li walks at a constant rate of 7 ft. in 4 seconds. The table shows the relationship of feet to seconds. What is the constant of

proportionality for the relationship of feet to minutes? (1 minute=60 seconds) *
10 points
Mathematics
1 answer:
Kisachek [45]3 years ago
4 0

Answer:

The rate is 1.75 feet/seconds or 105 feet/minute.

Step-by-step explanation:

Given that,

Li walks at a constant rate of 7 feet in 4 seconds

To find the constant of proportionality, divide 7 feet by 4 seconds.

So,

k=\dfrac{7\ \text{feet}}{4\ \text{seconds}}\\\\k=1.75\ \text{ft/s}

1.75 ft/s is the constant of proportionality

We know that, 1 minute = 60 seconds

k = 105 feet/minute

So, the rate is 1.75 feet/seconds or 105 feet/minute.

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<u>Given</u>:

Given that the graph of the quadratic function.

We need to determine the value of a in the function's equation.

<u>Value of a:</u>

The value of a can be determined using the formula,

y=a(x-h)^2+k

where (h,k) is the vertex and a is a constant.

From the graph, it is obvious, that the vertex of the parabola is (0,9).

Thus, substituting the vertex (h,k) = (0,9) in the above formula, we get;

y=a(x-0)^2+9

y=ax^2+9  -------- (1)

Let us substitute any one of the coordinate that the graph passes through to determine the value of a.

Let us substitute the point (3,0) in the equation (1), we have;

  0=a(3)^2+9

  0=9a+9

-9=9a

-1=a

Thus, the value of a is -1.

Hence, Option B is the correct answer.

3 0
3 years ago
Lisa wears 10 rings in her hand. Each ring weights 250 grams. Find the
Gnom [1K]

Answer:

2.5 kilograms

Step-by-step explanation:

10 rings times each weight ring(250)=2500

2500 grams to kilograms is 2.5

7 0
3 years ago
Given the foci of (8,0) and the difference of the focal radii = 6, find the equation of the hyperbola
k0ka [10]

Given :

The foci of hyperbola are (8,0) and (-8,0) .

The difference of the focal radii = 6.

To Find :

The equation of the hyperbola.

Solution :

We know, distance between foci is given by :

2c = 8 - (-8)

c = 8

Also, difference between the foci or focal distance is given by :

2a = 6

a = 3

Now, we know for hyperbola :

b^2 +a^2 = c^2\\\\b^2={c^2-a^2}\\\\b^2 = 64-9\\\\b^2 = 55

General equation of hyperbola is :

\dfrac{x^2}{a^2}+\dfrac{y^2}{b^2}=1\\\\\dfrac{x^2}{9}+ \dfrac{y^2}{55}=1

Hence, this is the required solution.

3 0
3 years ago
A side of an equilateral triangle is 2/8 cm long. Draw a picture that shows the triangle
lianna [129]
Here you go. I hope this will help

7 0
4 years ago
The sum of the three numbers in 2003,two of the numbers are 814 and 519 what is the third number​
KonstantinChe [14]

Answer:

670

Step-by-step explanation:

2003-814=1189

1189-519=670

8 0
3 years ago
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