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BartSMP [9]
3 years ago
14

Wayne needs to drive 470 miles to reach Milwaukee. Suppose he drives at a constant speed of 50 miles per hour. Which function re

presents Wayne’s distance i
n miles from Milwaukee in terms of the number of hours he drives?
Answer choices:
A y = 420x
B y = 470 + 50x
C y = 50 - 470x
D y = 50 + 470x
E y = 470 - 50x
Mathematics
1 answer:
Savatey [412]3 years ago
5 0
B: Because your slope is 50 because it says "per hour" so this leaves out answers A,C, and D. Now you only answers B and E. E is wrong because its a negitve slope and there's nothing in this problem that makes it a negative, so your answer is B
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Would each of them be able to be the side lengths of a triangle?
ratelena [41]
Pythagoras Theorem:
hipotenuse²=leg₁²+leg₂²

First posible triangle:
hypotenuse=13    (13²=169)
leg₁=12                ( 12²=144)
leg₂=5                  (5²=25)

13³=144 + 25


Answer:can be side lengths of a triangle

Second triangle:
 hypotenuse=12.6    (12.6²=158.76)
leg₁=6.7                ( 6.7²=44.89)
leg₂=6.5                  (6.5²=42.25)

leg₁²+leg₂²=44.89+42.25=87.14≠158.76

Answer: cannot be side lenghts of a triangle.

third triangle:
hypotenuse=13    (13²=169)
leg₁=12                ( 12²=144)
leg₂=11                  (11²=121)

leg₁²+leg₂²=144+121=265≠169

Answer: cannot be side lenghts of a triangle.

fourth triangle:
hypotenuse=13   (13²=169)
leg₁=6                ( 6²=36)
leg₂=4                  (4²=16)

leg₁²+leg₁²=36+16=52≠169

Answer: cannot be side lenghts of a triangle.
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Chose the correct property
vodka [1.7K]

Answer:

B) Associative Property of Multiplication

Step-by-step explanation:

The associative property states you can change where the parentheses (grouping terms) are in a multiplication statement, and you'll get the same product.

More generally:

(a * b) * c = a * (b * c)

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Consider functions of the form f(x)=a^x for various values of a. In particular, choose a sequence of values of a that converges
sleet_krkn [62]

Answer:

A. As "a"⇒e, the function f(x)=aˣ tends to be its derivative.

Step-by-step explanation:

A. To show the stretched relation between the fact that "a"⇒e and the derivatives of the function, let´s differentiate f(x) without a value for "a" (leaving it as a constant):

f(x)=a^{x}\\ f'(x)=a^xln(a)

The process will help us to understand what is happening, at first we rewrite the function:

f(x)=a^x\\ f(x)=e^{ln(a^x)}\\ f(x)=e^{xln(a)}\\

And then, we use the chain rule to differentiate:

f'(x)=e^{xln(a)}ln(a)\\ f'(x)=a^xln(a)

Notice the only difference between f(x) and its derivative is the new factor ln(a). But we know  that ln(e)=1, this tell us that as "a"⇒e, ln(a)⇒1 (because ln(x) is a continuous function in (0,∞) ) and as a consequence f'(x)⇒f(x).

In the graph that is attached it´s shown that the functions follows this inequality (the segmented lines are the derivatives):

if a<e<b, then aˣln(a) < aˣ < eˣ < bˣ < bˣln(b)  (and below we explain why this happen)

Considering that ln(a) is a growing function and ln(e)=1, we have:

if a<e<b, then ln(a)< 1 <ln(b)

if a<e, then aˣln(a)<aˣ

if e<b, then bˣ<bˣln(b)

And because eˣ is defined to be the same as its derivative, the cases above results in the following

if a<e<b, then aˣ < eˣ < bˣ (because this function is also a growing function as "a" and "b" gets closer to e)

if a<e, then aˣln(a)<aˣ<eˣ ( f'(x)<f(x) )

if e<b, then eˣ<bˣ<bˣln(b) ( f(x)<f'(x) )

but as "a"⇒e, the difference between f(x) and f'(x) begin to decrease until it gets zero (when a=e)

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It will cost 387 for 3 nights
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