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3 years ago

The functions below represent the amounts of water released from two reservoirs over x weeks:

Mathematics

1 answer:

solong [7]3 years ago

6 0

Answer:

h(x) = -2x^2 -x +3
Reservoir A releases the same amount of water as Reservoir B over 1 week

Step-by-step explanation:

Given:

f(x) = x^2 -7x +5

g(x) = 3x^2 -6x +2

h(x) = f(x) -g(x)

Find:

h(x)

h(1)

Solution:

The expression for h(x) is found by evaluating its definition:

h(x) = (x^2 -7x +5) -(3x^2 -6x +2)

h(x) = x^2(1 -3) +x(-7 -(-6)) +(5 -2)

h(x) = -2x^2 -x +3

Then h(1) is found by substituting 1 for x:

h(1) = -2(1^2) -(1) +3 = -2 -1 +3

h(1) = 0 . . . . difference in release amounts after 1 week is 0

The true statements are ...

h(x) = -2x^2 -x +3
Reservoir A releases the same amount of water as Reservoir B over 1 week

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Blake rows his boat against a current 90 yards in 15 minutes. With a current, he rows 90 yards in 9 minutes. What is the rate at

Anna71 [15]

Answer:

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90 yards in 9 minutes =10 yds/min

x = current rate

r = rowing rate

r + x = 10

r - x = 6 Adding both equations

2 r = 16

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Step-by-step explanation:

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3 years ago

Which is a true statement?

myrzilka [38]

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3 years ago

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Which shows the expression below simplified? 0.00048 - (3.4 × 10-5) A. 4.46 × 10-4 B. 3.39952 × 10-5 C. 4.46 × 10-5 D. 1.4 × 10-

MakcuM [25]

Option C

The simplified form of given expression is $4.46 \times 10^{-4}$

Solution:

Given that we have to simplify the expression shown below

$0.00048 - (3.4 \times 10^{-5})$

Let us first convert 0.00048 to scientific notation

Steps to follow:

Move the decimal point in your number until there is only one non-zero digit to the left of the decimal point. The resulting decimal number is a.

Count how many places you moved the decimal point. This number is b.

If you moved the decimal to the left b is positive.

If you moved the decimal to the right b is negative.

If you did not need to move the decimal b = 0.

Write your scientific notation number as a x 10^b and read it as "a times 10 to the power of b."

Remove trailing 0's only if they were originally to the left of the decimal point.

$0.00048 = 4.8 \times 10^{-4}$

So the given expression becomes,

$\rightarrow 4.8 \times 10^{-4} - 3.4 \times 10^{-5}$

Let us make the exponent of second term as -4

$\rightarrow 4.8 \times 10^{-4} - 0.34 \times 10^{-4}$

Take $10^{-4}$ as common term,

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Thus option C is correct

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3 years ago

A recursive rule for a sequence is given. Find the first four terms of the sequence.

tigry1 [53]

Answer:

So...

a0 = -2

a1 = (a0)2 - 4 = 4 - 4 = 0

a2 = (a1)2 - 4 = ((a0)2-4)2 - 4 =...= 02 - 4 = -4

For an+1, you may use the previous term (an) if you have just calculated it, rather than calculating it recursively again

a3 = (-4)2 - 4 = 12

The first four terms in the sequence are -2, 0, -4, 12.

Step-by-step explanation:

This recursive sequence is defined as follows:

a0 = -2 [the first term]

an+1 = an2 - 4 [for all other terms, n≥0; note that you cannot find a0 using this line]

Note that this is not "BASE" for a number base, but it is "SUB" for subscript, indicating the term. Sometimes, sequences are written with the first term being a1 and sometimes sequences are written with the first term being a0. This is because there are situations that make one or the other more convenient (for example, starting with elapsed time t=0 makes sense).

To find the value of later terms, a recursive definition requires that you find the value of the previous term, which requires that you find the value of the previous term, which requires that you find the value of the previous term, which requires that you find the value of the previous term, ... which requires that use the value of the first term.

That's why (joke) that the dictionary definition of "recursive" is "see recursive."

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Y_Kistochka [10]

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