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solmaris [256]
3 years ago
9

the cost in dollars of a one day car rental is given by C=25+0.15x where x is the number of miles driven

Mathematics
1 answer:
AveGali [126]3 years ago
3 0
What do you want? It isn't a question but a statement
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Can anyone do these problems it’s for my daughter in law
Naya [18.7K]

Classwork:

Given f(x) = x^2 - 1 and g(x)=2x+5, we have

(1) (f\circ g)(x) = f(g(x)) = f(2x+5) = (2x+5)^2 - 1 = \boxed{4x^2+20x+24}

Using the composition found in (1), we have

(2) (f\circ g)(-2) = 4\cdot(-2)^2+20\cdot(-2)+24 = \boxed{0}

(3) (g\circ f)(x) = g(f(x)) = g(x^2-1) = 2(x^2-1) + 5 = \boxed{2x^2 + 3}

Using the composition found in (3),

(4) (g\circ f)(1) = 2\cdot1^2+3 = \boxed{5}

Homework:

Now if f(x)=x^2-3x+2, we would have

(1) (f\circ g)(x) = f(2x+5) = (2x+5)^2-3(2x+5)+2 = \boxed{4x^2+14x+12}

For (2), we could explicitly find (g\circ f)(x) then evaluate it at <em>x</em> = -1 like we did in the classwork section, but we don't need to.

(2) (g\circ f)(-1) = g(f(-1)) = g((-1)^2-3\cdot(-1)+2) = g(6) = 2\cdot6+5 = \boxed{17}

(3) We can demonstrate that both methods work here:

• by using the result from (1),

(f\circ g)(2) = 4\cdot2^2+14\cdot2+12 = \boxed{56}

• by evaluating the inner function at <em>x</em> = 2 first,

(f\circ g)(2) = f(g(2)) = f(2\cdot2+5) = f(9) = 9^2-3\cdot9+2 = \boxed{56}

4 0
3 years ago
If a car traveling at the constant rate of 67x=y , how far will it have traveled in 8.4 hours ?
lukranit [14]
Dedhamhdjdjjdjdjejrkrmdjxx
3 0
3 years ago
I need help this Question
Delicious77 [7]

Using the combination formula, it is found that the number of ways to choose the presenters is given by:

C. 462.

The order in which the presents are chosen is not important, hence the <em>combination formula</em> is used to solve this question.

<h3>What is the combination formula?</h3>

C_{n,x} is the number of different combinations of x objects from a set of n elements, given by:

C_{n,x} = \frac{n!}{x!(n-x)!}

In this problem, 6 students are chosen from a set of 11, hence the number of ways is given by:

C_{11,6} = \frac{11!}{6!5!} = 462

More can be learned about the combination formula at brainly.com/question/25821700

#SPJ1

8 0
2 years ago
Prove each of the following statements below using one of the proof techniques and state the proof strategy you use.
pochemuha

Answer:

See below

Step-by-step explanation:

a) Direct proof: Let m be an odd integer and n be an even integer. Then, there exist integers k,j such that m=2k+1 and n=2j. Then mn=(2k+1)(2j)=2r, where r=j(2k+1) is an integer. Thus, mn is even.

b) Proof by counterpositive: Suppose that m is not even and n is not even. Then m is odd and n is odd, that is, m=2k+1 and n=2j+1 for some integers k,j. Thus, mn=4kj+2k+2j+1=2(kj+k+j)+1=2r+1, where r=kj+k+j is an integer. Hence mn is odd, i.e, mn is not even. We have proven the counterpositive.

c) Proof by contradiction: suppose that rp is NOT irrational, then rp=m/n for some integers m,n, n≠. Since r is a non zero rational number, r=a/b for some non-zero integers a,b. Then p=rp/r=rp(b/a)=(m/n)(b/a)=mb/na. Now n,a are non zero integers, thus na is a non zero integer. Additionally, mb is an integer. Therefore p is rational which is contradicts that p is irrational. Hence np is irrational.

d) Proof by cases: We can verify this directly with all the possible orderings for a,b,c. There are six cases:

a≥b≥c, a≥c≥b, b≥a≥c, b≥c≥a, c≥b≥a, c≥a≥b

Writing the details for each one is a bit long. I will give you an example for one case: suppose that c≥b≥a then max(a, max(b,c))=max(a,c)=c. On the other hand, max(max(a, b),c)=max(b,c)=c, hence the statement is true in this case.

e) Direct proof: write a=m/n and b=p/q, with m,q integers and n,q nonnegative integers. Then ab=mp/nq. mp is an integer, and nq is a non negative integer. Hence ab is rational.

f) Direct proof. By part c), √2/n is irrational for all natural numbers n. Furthermore, a is rational, then a+√2/n is irrational. Take n large enough in such a way that b-a>√2/n (b-a>0 so it is possible). Then a+√2/n is between a and b.

g) Direct proof: write m+n=2k and n+p=2j for some integers k,j. Add these equations to get m+2n+p=2k+2j. Then m+p=2k+2j-2n=2(k+j-n)=2s for some integer s=k+j-n. Thus m+p is even.

7 0
3 years ago
A dog is standing 12 feet from a tree looking at a bird in the tree. the angle of elevation from the dog to the bird is 50°. how
jasenka [17]
The distance of the bird from the ground will be given by:
tan θ=opposite/adjacent
θ=50°
opposite=h
adjacent=12 ft
plugging in the values in the formula we get:
tan 50=h/12
thus
h=12tan50
h=14.301 ft
=14.3 ft 
5 0
3 years ago
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