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storchak [24]
3 years ago
6

Tadeo Volunteered at the library six times as many hours over the weekend as Dylan. Together they volunteer at a total of 14 hou

rs. How many hours did each person volunteer over the weekend?
Mathematics
1 answer:
LuckyWell [14K]3 years ago
4 0

Answer:

<em>Tadeo Volunteered for 12 hours while Dylan volunteered for 2 hours</em>

Step-by-step explanation:

Let the total number of hours Tadeo volunteered be x

Let the total number of hours Dylan volunteered be y

If together they volunteer at a total of 14 hours, then;

x + y = 14 ...... 1

If<em> </em>Tadeo Volunteered at the library six times as many hours over the weekend as Dylan, then;

x = 6y

Substitute x = 6y into 1;

6y + y = 14

7y = 14

y = 14/7

y = 2

Since x = 6y

x = 6(2)

x = 12

<em>Hence Tadeo Volunteered for 12 hours while Dylan volunteered for 2 hours</em>

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\stackrel{\begin{array}{llll} \textit{"y" directly}\\ \textit{proportional to }\sqrt{x} \end{array}}{y = k\sqrt{x}}\qquad \textit{we know that} \begin{cases} y = 56\\ x = 49 \end{cases}\implies 56=k\sqrt{49} \\\\\\ 56=7k\implies \cfrac{56}{7}=k\implies 8=k~\hfill \boxed{y=8\sqrt{x}} \\\\\\ \textit{when x = 81, what is "y"?}\hfill y=8\sqrt{81}\implies y=8(9)\implies y=72

7 0
2 years ago
If f and g are differentiable functions for all real values of x such that f(1) = 4, g(1) = 3, f '(3) = −5, f '(1) = −4, g '(1)
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Answer:

h'(1)=0

Step-by-step explanation:

We use the definition of the derivative of a quotient:

If h(x)=\frac{f(x)}{g(x)}, then:

h'(x)=\frac{f'(x)*g(x)-f(x)*g'(x)}{(g(x))^2}

Since in our case we want the derivative of h(x) at the point x = 1, which is indicated by: h'(1), we need to evaluate the previous expression at x = 1, that is:

h'(1)=\frac{f'(1)*g(1)-f(1)*g'(1)}{(g(1))^2}

which, by replacing with the given numerical values:

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h'(1)=\frac{f'(1)*g(1)-f(1)*g'(1)}{(g(1))^2}=\\=\frac{-4*3-4*(-3)}{(3)^2}=\frac{-12+12}{9} =\frac{0}{9} =0

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3 years ago
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The first to simplify the expression would be C. Distributive
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Answer:

Step-by-step explanation:

D={ 6  , -9  , 1 }

R={  0  ,-3 }

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3 years ago
Storage locker A is 6 feet wide, 6 feet deep, and has a height of 9 feet. Storage locker B has a volume of 306 cubic feet. Which
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Answer:

Storage locker A is 6 feet wide, 6 feet deep, and has a height of 9 feet. Storage locker B has a volume of 306 cubic feet.

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Step-by-step explanation:

4 0
3 years ago
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