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grandymaker [24]
3 years ago
9

A lifeguard received 15 hours of first aid training and 10 hours of cardiopulmonary resuscitation training what is the ratio of

hours of cpr training to hours of first aid training
Mathematics
1 answer:
aivan3 [116]3 years ago
5 0

Answer:

The ration of 15 to 10 is 3/2

Step-by-step explanation:

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Plz help, I'm taking an Advanced class (Algebra) Will give brainliest ✔✔✔✔✔✔✔✔✔
bija089 [108]

Part A:

The average rate of change refers to a function's slope. Thus, we are going to need to use the slope formula, which is:

m = \dfrac{y_2 - y_1}{x_2 - x_1}

  • (x_1, y_1) and (x_2, y_2) are points on the function

You can see that we are given the x-values for our interval, but we are not given the y-values, which means that we will need to find them ourselves. Remember that the y-values of functions refers to the outputs of the function, so to find the y-values simply use your given x-value in the function and observe the result:

h(0) = 3(5)^0 = 3 \cdot 1 = 3

h(1) = 3(5)^1 = 3 \cdot 5 = 15

h(2) = 3(5)^2 = 3 \cdot 25 = 75

h(3) = 3(5)^3 = 3 \cdot 125 = 375


Now, let's find the slopes for each of the sections of the function:

<u>Section A</u>

m = \dfrac{15 - 3}{1 - 0} = \boxed{12}

<u>Section B</u>

m = \dfrac{375 - 75}{3 - 2} = \boxed{300}


Part B:

In this case, we can find how many times greater the rate of change in Section B is by dividing the slopes together.

\dfrac{m_B}{m_A} = \dfrac{300}{12} = 25


It is 25 times greater. This is because 3(5)^x is an exponential growth function, which grows faster and faster as the x-values get higher and higher. This is unlike a linear function which grows or declines at a constant rate.

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X^2+y^2+14x+10y=7 <br> center and radius
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(x-a)^2+(y-b)^2=r^2\\\\(a;\ b)-the\ coordinates\ of\ the\ center\\r-the\ radius\\\\==================================\\Use:(k+l)^2=k^2+2kl+l^2\ (*)\\==================================

x^2+y^2+14x+10y=7\\\\x^2+14x+y^2+10y=7\\\\x^2+2x\cdot7+y^2+2y\cdot5=7\\\\\underbrace{x^2+2x\cdot7+7^2}_{Use\ (*)}-7^2+\underbrace{y^2+2y\cdot5+5^2}_{Use\ (*)}-5^2=7\\\\(x+7)^2-49+(y+5)^2-25=7\\\\(x+7)^2+(y+5)^2-74=7\ \ \ \ |add\ 74\ to\both\ sides\\\\(x+7)^2+(y+5)^2=81\\\\(x+7)^2+(y+5)^2=9^2

Answer:\\\boxed{(-7;-5)-center;\ 9-radius}
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