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lorasvet [3.4K]
2 years ago
14

5y + 2 + 6 + 2y 5y + 2(y + 3) + 2 combining like terms 6y − y + 2y + 10 − 4 + 2 Commutative Property Distributive Property arrow

Both arrowBoth arrowBoth
Mathematics
1 answer:
Paraphin [41]2 years ago
4 0

Answer:

Distributive Property

Step-by-step explanation:

5y + 2 + 6 + 2y

= 5y + 2(y + 3) + 2 This is the distributive property of multiplication w.r.t. addition

= 6y − y + 2y + 10 − 4 + 2

The distributive property of multiplication with respect to addition  is the one  which separates each term by using multiplication and then addition.

So we see that 2 is multiplied with y and 3 and then added with the like terms. If there was a minus sign the property would be distributive over subtraction.

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its 76 degrees fahrenheit at the 6000-foot level of a mountain, and 49 degrees Fahrenheit at the 12000-foot level of the mountai
brilliants [131]

T = \frac{-9}{2}x + 103 is the linear equation to find the temperature T at an elevation x on the mountain, where x is in thousands of feet.

<em><u>Solution:</u></em>

The linear equation in slope intercept form is given as:

T = cx + k ------ (i)

Where "t" is the temperature at an elevation x

And x is in thousands of feet

<em><u>Given that its 76 degrees fahrenheit at the 6000-foot level of a mountain</u></em>

Given, when c = 6 thousand ft and T = 76^{\circ} fahrenheit

This implies,

From (i)

76 = c(6) + k

76 = 6c + k

⇒ k = 76 - 6c  ----- (ii)

<em><u>Given that 49 degrees Fahrenheit at the 12000-foot level of the mountain</u></em>

Given, when c = 12 thousand ft and T = 49^{\circ} fahrenheit

This implies,

From (i)

49 = c(12) + k

49 = 12c + k

Substitute (ii) in above equation

49 = 12c + (76 - 6c)

49 = 12c + 76 - 6c

49 - 76 = 6c

6c = -27

c = \frac{-9}{2}

Substituting the value of c in (ii) we get

k = 76 - 6( \frac{-9}{2})\\\\k = 76 + 27 = 103

Substituting the value of c and k in (i)

T = \frac{-9}{2}x + 103

Where "x" is in thousands of feet

Thus the required linear equation is found

5 0
2 years ago
The sum of 3 consecutive
Troyanec [42]
The three numbers are 52, 53, 54.

52+53=105 105+54=159
7 0
1 year ago
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Body fat percentage was found to be 16.5% and the person weighs 124 pounds what part in pounds of the body weight is fat
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Answer:

20.46 pounds

Step-by-step explanation:

  1. Since 16.5% of their body is fat you need to multiply the weight by that percentage
  2. you can do this by multiplying 124 by .165 which equals 20.46 pounds
7 0
3 years ago
Suppose a river flows south to north at a velocity of 1 m/s, and a motorboat traverses the river from east to west at a speed of
irina1246 [14]

Answer: 24^{\circ}

Step-by-step explanation:

Given

River is flowing from south to North with a velocity of u=1\ m/s

Motor boat traverses the river from east to west at a speed of v=2.5\ m/s

South component of boat velocity must compensate the river velocity in order to travel in west direction.

\therefore v\sin \theta=u\\\\\Rightarrow 2.5\sin \theta=1\\\\\Rightarrow \sin \theta=\dfrac{2}{5}\\\\\Rightarrow \theta=23.57^{\circ}\approx 24^{\circ} \text{south of west}

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Children pick their favorite sports team 35% pick basketball 28% pick hockey what percent pick football
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37% pick football

35+28=63
100-63=37
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