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3 years ago

Which of the following relations represents a function?

Mathematics

2 answers:

liraira [26]3 years ago

6 0

Answer:

Step-by-step explanation:

Each function needs to have a unique output... i.e: plugging in a value for x, you get a unique value of y. D is the only one where that occurs :)

Aleks04 [339]3 years ago

6 0

Answer:

Step-by-step explanation:

A is the only one that has an x-value that has a unique y-value. C b and d have multiple x-values that have multiple y-values. For example, c has an x-value of 1 which has 2 outputs, which are 3 and 4.

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If f(x) = 3x + 2 and g(x) = 2x – 2, what is (f – g)(x)?

DiKsa [7]

I hope this helps you

4 0

3 years ago

Spring stretches by 21.0 cm when a 135 n object is attached. what is the weight of a fish that would stretch the spring by 62.1

Marta_Voda [28]

Caution: you need to use the same units of measurement throughout. If the spring stretches by 21 cm when a 135 newton object is attached, then you must ask for the mass (in newtons) of a fish that would stretch the spring by 62.1 cm.

We will need to assume that the spring is not stretched at all if and when no object is attached to the spring.

Write the ratio

21.0 cm 135 newtons
------------- = --------------------
62.1 cm x

Solve this for x. This x value represents the mass of a fish that would stretch the spring by 62.1 cm. You can cancel "cm" in the equation above:

21.0 135 newtons
------ = --------------------
62.1 x

Then 21.0x = (62.1)(135 newtons). Divide both sides of this equation by 21.0 to solve it for x.

7 0

3 years ago

Read 2 more answers

Jon earns $77 per week. Choose the expression below to help him find out how much he'll earn after x weeks.

Damm [24]

Answer:The equation is $77 x ? =x

8 0

3 years ago

Read 2 more answers

A 100 gallon tank initially contains 100 gallons of sugar water at a concentration of 0.25 pounds of sugar per gallon suppose th

Vsevolod [243]

At the start, the tank contains

(0.25 lb/gal) * (100 gal) = 25 lb

of sugar. Let $S(t)$ be the amount of sugar in the tank at time $t$ . Then $S(0)=25$ .

Sugar is added to the tank at a rate of P lb/min, and removed at a rate of

$\left(1\frac{\rm gal}{\rm min}\right)\left(\dfrac{S(t)}{100}\dfrac{\rm lb}{\rm gal}\right)=\dfrac{S(t)}{100}\dfrac{\rm lb}{\rm min}$

and so the amount of sugar in the tank changes at a net rate according to the separable differential equation,

$\dfrac{\mathrm dS}{\mathrm dt}=P-\dfrac S{100}$

Separate variables, integrate, and solve for S.

$\dfrac{\mathrm dS}{P-\frac S{100}}=\mathrm dt$

$\displaystyle\int\dfrac{\mathrm dS}{P-\frac S{100}}=\int\mathrm dt$

$-100\ln\left|P-\dfrac S{100}\right|=t+C$

$\ln\left|P-\dfrac S{100}\right|=-100t-100C=C-100t$

$P-\dfrac S{100}=e^{C-100t}=e^Ce^{-100t}=Ce^{-100t}$

$\dfrac S{100}=P-Ce^{-100t}$

$S(t)=100P-100Ce^{-100t}=100P-Ce^{-100t}$

Use the initial value to solve for C :

$S(0)=25\implies 25=100P-C\implies C=100P-25$

$\implies S(t)=100P-(100P-25)e^{-100t}$

The solution is being drained at a constant rate of 1 gal/min; there will be 5 gal of solution remaining after time

$1000\,\mathrm{gal}+\left(-1\dfrac{\rm gal}{\rm min}\right)t=5\,\mathrm{gal}\implies t=995\,\mathrm{min}$

has passed. At this time, we want the tank to contain

(0.5 lb/gal) * (5 gal) = 2.5 lb

of sugar, so we pick P such that

$S(995)=100P-(100P-25)e^{-99,500}=2.5\implies\boxed{P\approx0.025}$

5 0

3 years ago

There are 50 cupcakes and 160 cookies to be sold at the school bake sale. What is the greatest number of packages of baked items

Sav [38]

The greatest number of packages of baked items that can be sold is 10

Solution:

Given that there are 50 cupcakes and 160 cookies to be sold at the school bake sale

To find: greatest number of packages of baked items that can be sold

Each package has the same number of cupcakes and same number of cookies with none left over

So, we have to find the greatest common factor of 50 and 160

The greatest number that is a factor of two (or more) other numbers.

When we find all the factors of two or more numbers, and some factors are the same ("common"), then the largest of those common factors is the Greatest Common Factor.

Greatest common factor of 50 and 160:

The factors of 50 are: 1, 2, 5, 10, 25, 50

The factors of 160 are: 1, 2, 4, 5, 8, 10, 16, 20, 32, 40, 80, 160

Then the greatest common factor is 10

So the greatest number of packages sold is 10

Each package will contain:

Given that there 50 cupcakes and 160 cookies

Number of cupcakes in 1 package:

$\rightarrow \frac{50}{10} = 5$

Number of cookies in 1 package:

$\rightarrow \frac{160}{10} = 16$

So each package has the same number of cupcakes and same number of cookies with none left over

7 0

4 years ago