Answer:
Step-by-step explanation:
n + d = 12
0.05n + 0.1d = 1 ║ × ( - 10 )
n + d = 12 ..... <em>(1)</em>
- 0.5n - d = - 10 ..... <em>(2)</em>
<em>(1)</em> + <em>(2)</em>
0.5n = 2 ⇒ n = 4
d = 12 - 4 = 8
There are <em>4 nickels</em> and <em>8 dimes</em> in the pocket.
Recognize that the student used k = –5 instead of k = 5.
Recognize that the student did not use a placeholder zero for the x2 term.
Conclude that x – 5 is a factor because there is no remainder when the division is performed correctly.
1. 4(2+3c) = 56
c = 4
3. -29 = 5(2a-1)+2a
a = -2
5 . 7p-(3p+4) = -2(2p-1)+10
p=2
7. 1/2 (-4+6x) = 1/3x + 2/3*(x+9)
x=4
Step-by-step explanation:
1. 4(2+3c) = 56

Subtracting 8 from both sides

Dividing both sides by 12

<u>Checking: </u>
![4[2+3(4)] = 56\\4(2+12) = 56\\4(14) = 56\\56 = 56](https://tex.z-dn.net/?f=4%5B2%2B3%284%29%5D%20%3D%2056%5C%5C4%282%2B12%29%20%3D%2056%5C%5C4%2814%29%20%3D%2056%5C%5C56%20%3D%2056)
3. -29 = 5(2a-1)+2a
Simplifying

Adding 5 on both sides

Dividing both sides by 12

<u>Checking:</u>
![-29 = 5(2a-1)+2a\\-29 = 5[2(-2)-1]+2(-2)\\-29 = 5(-4-1) -4\\-29 = 5(-5) -4\\-29 = -25-4\\-29 = -29](https://tex.z-dn.net/?f=-29%20%3D%205%282a-1%29%2B2a%5C%5C-29%20%3D%205%5B2%28-2%29-1%5D%2B2%28-2%29%5C%5C-29%20%3D%205%28-4-1%29%20-4%5C%5C-29%20%3D%205%28-5%29%20-4%5C%5C-29%20%3D%20-25-4%5C%5C-29%20%3D%20-29)
5 . 7p-(3p+4) = -2(2p-1)+10
Simplifying

Adding 4 on both sides

Adding 4p on both sides

Dividing both sides by 8

<u>Checking:</u>
![7p-(3p+4) = -2(2p-1)+10\\7(2)-[3(2)+4] = -2[2(2)-1] +10\\14 - (6+4) = -2 (4-1) +10\\14 - 10 = -2(3) +10\\4 = -6+10\\4=4](https://tex.z-dn.net/?f=7p-%283p%2B4%29%20%3D%20-2%282p-1%29%2B10%5C%5C7%282%29-%5B3%282%29%2B4%5D%20%3D%20-2%5B2%282%29-1%5D%20%2B10%5C%5C14%20-%20%286%2B4%29%20%3D%20-2%20%284-1%29%20%2B10%5C%5C14%20-%2010%20%3D%20-2%283%29%20%2B10%5C%5C4%20%3D%20-6%2B10%5C%5C4%3D4)
7. 1/2 (-4+6x) = 1/3x + 2/3*(x+9)
Simplifying

Adding 6 on both sides

Subtracting 3x from both sides

Dividing both sides by 6

<u>Checking:</u>
![\frac{1}{2} [-4+6(4)] = \frac{1}{3}(4)+\frac{2}{3}(4+9)\\\frac{1}{2}(-4+24) = \frac{4}{3}+\frac{2}{3}(13)\\\frac{1}{2}(20) = \frac{4}{3} +\frac{26}{3}\\15 = \frac{4+26}{3}\\15 = \frac{30}{3}\\15=15](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B2%7D%20%5B-4%2B6%284%29%5D%20%3D%20%5Cfrac%7B1%7D%7B3%7D%284%29%2B%5Cfrac%7B2%7D%7B3%7D%284%2B9%29%5C%5C%5Cfrac%7B1%7D%7B2%7D%28-4%2B24%29%20%3D%20%5Cfrac%7B4%7D%7B3%7D%2B%5Cfrac%7B2%7D%7B3%7D%2813%29%5C%5C%5Cfrac%7B1%7D%7B2%7D%2820%29%20%3D%20%5Cfrac%7B4%7D%7B3%7D%20%2B%5Cfrac%7B26%7D%7B3%7D%5C%5C15%20%3D%20%5Cfrac%7B4%2B26%7D%7B3%7D%5C%5C15%20%3D%20%5Cfrac%7B30%7D%7B3%7D%5C%5C15%3D15)
Keywords: Linear equations
Learn more about linear equations at:
#LearnwithBrainly
Function F goes in the first one, G goes in the second one, and H goes in the last one. Hope this helps :)
Answer:

Step-by-step explanation:
Let the greater number be x and the smaller number be y.
So,
<u>Condition # 1:</u>
x - y = 7 --------------(1)
<u>Condition # 2:</u>
3x = 72 --------------(2)
Taking Eq. (2)
3x = 72
Divide both sides by 3
x = 72 / 3
x = 24
Now, Put x = 24 in Eq. (1)
24 - y = 7
Subtract 24 to both sides
-y = 7 - 24
-y = -17
y = 17
![\rule[225]{225}{2}](https://tex.z-dn.net/?f=%5Crule%5B225%5D%7B225%7D%7B2%7D)
Hope this helped!
<h3>~AH1807</h3>