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Anvisha [2.4K]
3 years ago
7

akio buys scissors for 3.79, tape for 2.57, and pens for 5.80.the sales tax is 6.25percent what is the amount of tax for akios p

urchases
Mathematics
1 answer:
nasty-shy [4]3 years ago
8 0
The answer is:  " $0.76 "  .
________________________________________________
or, write as:  " 76<span>¢" .
</span>________________________________________________
Explanation:
________________________________________________
The answer is:  What is  6.25% of  "{ $ 3.79 + 2.57 + 5.80}" ?
________________________________________________
  $ 3.79
+   2.57
 <u>    5.80    </u>
  $ 12.16
________________________________________________
So, what is:  6.25 %  of   $12.16 ? 

    6.25% = 6.25 / 100 = 6.25 ÷ 100 = 0.0625 ;

6.25% of $12.16 = 0.0625 * $12.16 =  19/25 = $0.76 .
________________________________________________
The answer is:  " $0.76 "  .
________________________________________________
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The red graph is the result of a vertical translation, 4 units down, of the black graph.

This means that, whenever the black graph associates

x\mapsto f(x)

The red graph must associate 4 less to the same input:

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So, the equation for the red graph is

y=f(x)-4

or, equivalently,

y+4=f(x)

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Nolan watched a beetle on the sidewalk. It crawled 7/12 of a yard, then rested for a bit, and then crawled 1/4 of a yard farther
liberstina [14]
D, because 1/4 is equivalent to 4/12 and 7/12+4/12=11/12 which is equivalent to 5/6
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2 years ago
Can someone help me with this? I need to find the points of discontinuity/limits for each of these. I think one point is 4, but
Debora [2.8K]
The answers are shown in the attached image

-------------------------------------------------------------------------

Explanation:

Set the denominator x^4-8x^3+16x^2 equal to zero and solve for x

x^4-8x^3+16x^2 = 0
x^2(x^2-8x+16) = 0
x^2(x-4)^2 = 0
x^2 = 0 or (x-4)^2 = 0
x = 0 or x-4 = 0
x = 0 or x = 4

The x values 0 and 4 make the denominator zero

These x values lead to asymptote discontinuities because the numerator 8x-24 = 8(x-3) has no common factors which cancel with the denominator factors.

There are two vertical asymptotes

Let's see what happens when we plug in a value to the left of x = 0, say x = -1, we'd get
f(x) = (8x-24)/(x^4-8x^3+16x^2)
f(-1) = (8(-1)-24)/((-1)^4-8(-1)^3+16(-1)^2)
f(-1) = -1.28
So as x gets closer and closer to x = 0 from the left side, the f(x) is heading to negative infinity

Now plug in some value to the right of x = 0. I'm going to pick x = 1
f(x) = (8x-24)/(x^4-8x^3+16x^2)
f(1) = (8(1)-24)/((1)^4-8(1)^3+16(1)^2)
f(1) = -1.78 (approximate)
So as x gets closer and closer to x = 0 from the right side, the f(x) is heading to negative infinity

Overall, as x approaches 0 from either the left or right side of x = 0, the y value is heading off to negative infinity

---------------------

Repeat for values to the left and right of x = 4
We can't use x = 1 as it turns out that x = 3 is a root
But we can use something like x = 3.5 to find that...
f(x) = (8x-24)/(x^4-8x^3+16x^2)
f(3.5) = (8(3.5)-24)/((3.5)^4-8(3.5)^3+16(3.5)^2)
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So as x gets closer to x = 4 from the left, y is getting closer to positive infinity

Plug in x = 5 to find that
f(x) = (8x-24)/(x^4-8x^3+16x^2)
f(5) = (8(5)-24)/((5)^4-8(5)^3+16(5)^2)
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which has the same behavior as the left side

So overall, as we approach x = 4, the y value is heading off to positive infinity

Again everything is summarized in the image attachment

Note: you could make a table of more values but they would effectively say what has already been said. It would be redundant busy work. However, its always good practice for function evaluation. 

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lakkis [162]
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