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2 years ago

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Function f is a linear function with an initial value of 17 and a rate of change of –3. Some values for the linear function g ar

e shown in the table below. By how much does g exceed f when x = 5?

1 answer:

tia_tia [17]2 years ago

3 0

Answer:

g(x) exceed f(x) by $10$ when $x=5$

Step-by-step explanation:

step 1

Find the equation of function f(x)

we know that

The initial value is the y-intercept of the linear function (value of y when the value of x is equal to zero)

so

$b=17$

The rate of change is equal to the slope

so

$m=-3$

therefore

$f(x)=-3x+17$

step 2

Find the equation of function g(x)

Let

$A(0,-8),B(2,0)$

Find the slope

$m=(0+8)/(2-0)=4$

$b=-8$ ----> point A

therefore

$g(x)=4x-8$

step 3

Find the value of f(x) and g(x) for $x=5$

$f(5)=-3(5)+17=2$

$g(5)=4(5)-8=12$

Find the difference

$g(5)-f(5)=12-2=10$

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2 years ago

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A group of campers is going to occupy 3 campsites at a campground. There are 17 campsites from which to choose. In how many ways

Alexeev081 [22]

Answer:

Campsites be chosen in 680 ways.

Step-by-step explanation:

Given:

Number of campsites= 17

Number of campsites that are to be occupied=3

To Find:

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Solution:

Combination:

In mathematics, a combination is a way of selecting items from a collection where the order of selection does not matter. Suppose we have a set of three numbers P, Q and R. Then in how many ways we can select two numbers from each set, is defined by combination.

nCr = n(n - 1)(n - 2) ... (n - r + 1)/r! = n! / r!(n - r)!

No of ways in which campsites can be chosen= $\frac{17!}{3!(17-3)!}$ 17C3

=> $\frac{17!}{3!(14!)}$

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2 years ago

Mustafa, Heloise, and Gia have written more than a combined total of 22 articles for the school newspaper.

Ghella [55]

Answer: The required inequality is $x+\dfrac{1}{4}x+\dfrac{3}{2}x>22.$ and its solution is $x>8.$

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We are to write an inequality to determine the number of articles, m, Mustafa could have written for the school newspaper. Also, to solve the inequality.

Since m denotes the number of articles that Mustafa could have written. Then, according to the given information, we have

$x+\dfrac{1}{4}x+\dfrac{3}{2}x>22.$

And the solution of the above inequality is as follows :

$x+\dfrac{1}{4}x+\dfrac{3}{2}x>22\\\\\\\Rightarrow \dfrac{4x+x+6x}{4}>22\\\\\\\Rightarrow 11x>88\\\\\Rightarrow x>\dfrac{88}{11}\\\\\Rightarrow x>8.$

Thus, the required inequality is $x+\dfrac{1}{4}x+\dfrac{3}{2}x>22.$ and its solution is $x>8.$

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2 years ago

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Answer:

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Hope this helps!

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2 years ago

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Nadusha1986 [10]

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First, break it up into two fractions:

$\frac{ 8\sqrt{6mn} + 6\sqrt{8mn} }{ 2\sqrt{2mn}} = \frac{8\sqrt{6mn}}{ 2\sqrt{2mn}} + \frac{6\sqrt{8mn}}{ 2\sqrt{2mn}}$

Next, you can simplify the numbers outside of the square root:

$\frac{8\sqrt{6mn}}{ 2\sqrt{2mn}} + \frac{6\sqrt{8mn}}{ 2\sqrt{2mn}} = \frac{4\sqrt{6mn}}{\sqrt{2mn}} + \frac{3\sqrt{8mn}}{\sqrt{2mn}}$

Since the values are being acted by the same function, being under a radical, you can simplify these too:

$\frac{4\sqrt{6mn}}{\sqrt{2mn}} + \frac{3\sqrt{8mn}}{\sqrt{2mn}} = {4\sqrt{3}} + {3\sqrt{4}}$

Finally, the square root of 4 is 2, so it would be expressed like this:

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Your answer should be A.

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2 years ago