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RideAnS [48]
3 years ago
11

Use the definition of absolute value to write f as a piecewise-defined function

Mathematics
1 answer:
ycow [4]3 years ago
7 0

we are given

any absolute function

Let's assume that function as

f(x)=|x|

now, we can write it in piecwise form

we know that value of f(x) will always be positive

so, we write function such that it results in positive value

so, we can write as

f(x)=-x;....x\leq 0

f(x)=x;....x>0

...........Answer

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3 packs of 10 with 3 left over or 2 packs of 10 and 7 singles
6 0
3 years ago
If the flare is launched with an initial velocity of 144 feet per second, find the height after 2 seconds. The answer is not 288
salantis [7]

Answer:

The height = 223.6 ft

Step-by-step explanation:

∵ Initial velocity (u) = 144 ft/sec

∵ t = 2 sec

∵ a = - 32.2 ft/sec²

∵ h = ut + 1/2 at²

∴ h = 144(2) +1/2 (-32.2 × 4) = 288 + 1/2( -128.8) = 223.6 ft

6 0
3 years ago
Consider the following equation.
Natali [406]

\\ \tt\longmapsto 6(-x)+4=3x+1

\\ \tt\longmapsto -6x+4=3x+1

\\ \tt\longmapsto -6x-3x=1-4

\\ \tt\longmapsto -9x=-3

\\ \tt\longmapsto x=\dfrac{1}{3}

7 0
3 years ago
1. The Cajun Heartland State Fair charges $1.25 per ticket for the rides. Johnny bought 25 tickets for the rides and spent a tot
vladimir1956 [14]

<u>Part (a)</u>

The variable y is the dependent variable and the variable x is the independent variable.

<u>Part (b)</u>

The cost of one ticket is $1.25. Therefore, the cost of 25 tickets will be: .

Now, we know that Johnny spent his money only on ride tickets and fair admission and that he spent a total of $43.75.

Therefore, the price of the fair admission is: $43.75-$31.25=$12.5

If we use y to represent the total cost and x to represent the number of ride tickets, the linear equation that can be used to determine the cost for anyone who only pays for ride tickets and fair admission can be  written as:

y=1.25x+12.5......Equation 1

<u>Part (c)</u>

The above equation is logical because, in general, the total cost of the rides will depend upon the number of ride tickets bought and that will be 1.25x. Now, even if one does not take any rides, that is when x=0, they still will have to pay for the fair admission, and thus their total cost, y=$12.5.

Likewise, any "additional" cost will depend upon the number of ride tickets bought as already suggested. Thus, the total cost will be the sum of the total ride ticket cost and the fixed fair admission cost. Thus, the above Equation 1 is the correct representative linear equation of the question given.

7 0
3 years ago
Determine if the two figures are congruent and explain your answer using transformations.
Maslowich

The coordinate A(-1, 1) reflected over y-axis is (1, 1) is the coordinate of E, hence the two figures are congruent

  • The given figures are quadrilaterals, in order to determine whether they are similar, we need to check if they are reflections of each other.

  • For the Quadrilateral ABCD, the coordinate of A is at A(-1, 1)  and for the Quadrilateral DEFG, the coordinate of E is at E(1, 1).

  • Note that if an object is reflected over the y-axis the transformation is (x, y)->(-x, y)

  • We need to check whether if we reflect the coordinate A over the y-axis we will get coordinate E

Since the coordinate A(-1, 1) reflected over y-axis is (1, 1) is the coordinate of E, hence the two figures are congruent

Learn more on reflections here:brainly.com/question/1908648

7 0
3 years ago
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