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aalyn
11 days ago
15

This past Saturday, Jack worked for 3 hours mowing the lawn and doing chores in the house. Mowing the lawn burns 352 calories pe

r hour and doing chores burns 136 calories per hour. If he burned a total of 570 calories, how long did it take him to mow the lawn?
Mathematics
1 answer:
AnnZ [12.3K]11 days ago
3 0
Let x represent the time invested in mowing the lawn, and y for the chores done. Then,
x + y = 3
Additionally, 352x + 136y = 570

From the first equation, we can express y as 3 - x, and substitute into the second equation:

352x + 136(3 - x) = 570
Solving gives us 216x = 570 - 136(3) = 162
Thus, x = 162/216 = 0.75 

This indicates he dedicated 0.75 hours (or 45 minutes) to mowing the lawn.

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Four times a number added to 3 times a larger number is 31. Seven subtracted from the larger number is equal to twice the smalle
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Answer:

y = negative four-thirds x + StartFraction 31 Over 3 EndFraction

y = 2 x + 7

Step-by-step explanation:

Let x denote the smaller number and y denote the larger number.

Part 1

The equation presented indicates that four times some number added to three times a larger number equals 31.

This translates to:

  • 4x + 3y = 31

From here, solving for y yields:

  • 4x + 3y=31 ⇒ 3y= -4x+31 ⇒ y= (-4x+31)/3 = - 4/3x + 31/3

    ⇒  y= - 4/3x + 31/3

This indicates the correct response for this scenario:

y = negative four-thirds x + StartFraction 31 Over 3 EndFraction

Part 2

The statement that seven subtracted from the larger number equals twice the smaller number translates to:

y-7= 2x

Further, solving for y yields:y-7= 2x ⇒

y= 2x+ 7

The correct answer for this equation is:

y = 2 x + 7
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27 days ago
Let an integer be chosen at random from the integers 1 to 30 inclusive. Find the probability that the integer chosen is not even
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Given that the sequence goes odd, even, odd, and even , there is an equal chance of drawing an odd (<span>not divisible by 2) number as there is for drawing an even number, so the correct option is C.

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How does the graph of g (x) = StartFraction 1 Over x + 4 EndFraction minus 6 compare to the graph of the parent function f (x) =
lawyer [12517]

The adjusted equation $g(x)=\frac{1}{x+4}-6$, indicating that the graph has been altered 4 units leftward and 6 units downward.

Clarification:

The parent equation is $f(x)=\frac{1}{x}$.

The transformed equation is $g(x)=\frac{1}{x+4}-6$.

Applying the function transformation rules, it's clear that the parent function $f(x)=\frac{1}{x}$ has been modified into the function $g(x)=\frac{1}{x+4}-6$.

According to the function transformation rules,

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Additionally, from the function transformation rules, we understand that,

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Consequently, the transformed function mirrors a shift of 6 units downward.

In summary, the adjusted equation $g(x)=\frac{1}{x+4}-6$, shows the graph shifted 4 units to the left and 6 units downward.

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