Answer:
7) m = 6
8) k = 15
9) a = -12
10) x = 1
11) n = 4
12) r = 11
Step-by-step explanation:
<h3><u>Solution</u> : </h3>
Solving all the questions step by step!
7) 1 = 6+m/12
![\longmapsto{\tt{1 = \dfrac{6 + m}{12}}}](https://tex.z-dn.net/?f=%20%5Clongmapsto%7B%5Ctt%7B1%20%3D%20%20%5Cdfrac%7B6%20%2B%20m%7D%7B12%7D%7D%7D)
![\longmapsto{\tt{6 + m = 1 \times 12}}](https://tex.z-dn.net/?f=%20%5Clongmapsto%7B%5Ctt%7B6%20%2B%20m%20%3D%201%20%5Ctimes%2012%7D%7D)
![\longmapsto{\tt{6 + m = 12}}](https://tex.z-dn.net/?f=%20%5Clongmapsto%7B%5Ctt%7B6%20%2B%20m%20%3D%2012%7D%7D)
![\longmapsto{\tt{m = 12 - 6}}](https://tex.z-dn.net/?f=%20%5Clongmapsto%7B%5Ctt%7Bm%20%3D%2012%20-%206%7D%7D)
![\longmapsto{\tt{m = 6}}](https://tex.z-dn.net/?f=%20%5Clongmapsto%7B%5Ctt%7Bm%20%3D%206%7D%7D)
![\bigstar\: \:\underline{\boxed{\tt{\pink{m = 6}}}}](https://tex.z-dn.net/?f=%5Cbigstar%5C%3A%20%5C%3A%5Cunderline%7B%5Cboxed%7B%5Ctt%7B%5Cpink%7Bm%20%3D%206%7D%7D%7D%7D)
- Hence, the value of m is 6.
![\begin{gathered}\end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%5Cend%7Bgathered%7D)
8) 8 = 3 + k/3
![\implies{\tt{8 = 3 + \dfrac{k}{3}}}](https://tex.z-dn.net/?f=%5Cimplies%7B%5Ctt%7B8%20%3D%203%20%2B%20%20%5Cdfrac%7Bk%7D%7B3%7D%7D%7D)
![\implies{\tt{ \dfrac{k}{3} = 8 - 3}}](https://tex.z-dn.net/?f=%5Cimplies%7B%5Ctt%7B%20%5Cdfrac%7Bk%7D%7B3%7D%20%3D%208%20-%203%7D%7D)
![\implies{\tt{ \dfrac{k}{3} = 5}}](https://tex.z-dn.net/?f=%5Cimplies%7B%5Ctt%7B%20%5Cdfrac%7Bk%7D%7B3%7D%20%3D%205%7D%7D)
![\implies{\tt{k = 5 \times 3}}](https://tex.z-dn.net/?f=%5Cimplies%7B%5Ctt%7Bk%20%3D%205%20%5Ctimes%203%7D%7D)
![\implies{\tt{k = 15}}](https://tex.z-dn.net/?f=%5Cimplies%7B%5Ctt%7Bk%20%3D%2015%7D%7D)
![\bigstar \: \: \underline{\boxed{\tt{\red{k = 15}}}}](https://tex.z-dn.net/?f=%5Cbigstar%20%5C%3A%20%20%5C%3A%20%5Cunderline%7B%5Cboxed%7B%5Ctt%7B%5Cred%7Bk%20%3D%2015%7D%7D%7D%7D)
- Hence, the value of k is 15.
![\begin{gathered}\end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%5Cend%7Bgathered%7D)
9) -4(-8+a) = 80
![\longmapsto{\tt{ - 4( - 8 + a) = 80}}](https://tex.z-dn.net/?f=%20%5Clongmapsto%7B%5Ctt%7B%20-%204%28%20-%208%20%2B%20a%29%20%3D%2080%7D%7D)
![\longmapsto{\tt{( - 8 + a) = \dfrac{80}{ - 4}}}](https://tex.z-dn.net/?f=%20%5Clongmapsto%7B%5Ctt%7B%28%20-%208%20%2B%20a%29%20%3D%20%5Cdfrac%7B80%7D%7B%20-%204%7D%7D%7D)
![\longmapsto{\tt{( - 8 + a) = - 20}}](https://tex.z-dn.net/?f=%20%5Clongmapsto%7B%5Ctt%7B%28%20-%208%20%2B%20a%29%20%3D%20%20-%2020%7D%7D)
![\longmapsto{\tt{a = - 20 - ( - 8)}}](https://tex.z-dn.net/?f=%20%5Clongmapsto%7B%5Ctt%7Ba%20%3D%20%20-%2020%20-%20%28%20-%208%29%7D%7D)
![\longmapsto{\tt{a = - 20 + 8}}](https://tex.z-dn.net/?f=%20%5Clongmapsto%7B%5Ctt%7Ba%20%3D%20%20-%2020%20%20%2B%208%7D%7D)
![\longmapsto{\tt{a = -12}}](https://tex.z-dn.net/?f=%20%5Clongmapsto%7B%5Ctt%7Ba%20%3D%20%20-12%7D%7D)
![\bigstar \: \: \underline{\boxed{\tt{\purple{a = - 12}}}}](https://tex.z-dn.net/?f=%5Cbigstar%20%5C%3A%20%20%5C%3A%20%5Cunderline%7B%5Cboxed%7B%5Ctt%7B%5Cpurple%7Ba%20%3D%20%20-%2012%7D%7D%7D%7D)
- Hence, the value of a is -12.
![\begin{gathered}\end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%5Cend%7Bgathered%7D)
10) 8(x-1) = 0
![\implies\tt{8(x - 1) = 0}](https://tex.z-dn.net/?f=%20%5Cimplies%5Ctt%7B8%28x%20-%201%29%20%3D%200%7D)
![\implies\tt{8x - 8 = 0}](https://tex.z-dn.net/?f=%20%5Cimplies%5Ctt%7B8x%20-%208%20%3D%200%7D)
![\implies\tt{8x = 0 + 8}](https://tex.z-dn.net/?f=%20%5Cimplies%5Ctt%7B8x%20%3D%200%20%2B%208%7D)
![\implies\tt{8x = 8}](https://tex.z-dn.net/?f=%20%5Cimplies%5Ctt%7B8x%20%3D%208%7D)
![\implies\tt{x = \dfrac{8}{8}}](https://tex.z-dn.net/?f=%20%5Cimplies%5Ctt%7Bx%20%3D%20%5Cdfrac%7B8%7D%7B8%7D%7D)
![\implies\tt{x = 1}](https://tex.z-dn.net/?f=%20%5Cimplies%5Ctt%7Bx%20%3D%201%7D)
![\bigstar \: \: \underline{\boxed{\tt{\blue{x = 1}}}}](https://tex.z-dn.net/?f=%5Cbigstar%20%5C%3A%20%20%5C%3A%20%5Cunderline%7B%5Cboxed%7B%5Ctt%7B%5Cblue%7Bx%20%3D%201%7D%7D%7D%7D)
- Hence, the value of x is 1.
![\begin{gathered}\end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%5Cend%7Bgathered%7D)
11) n/2 - 1 = 1
![\longmapsto{\tt{\dfrac{n}{2} - 1 = 1}}](https://tex.z-dn.net/?f=%20%5Clongmapsto%7B%5Ctt%7B%5Cdfrac%7Bn%7D%7B2%7D%20-%201%20%3D%201%7D%7D)
![\longmapsto{\tt{\dfrac{n}{2} = 1 + 1}}](https://tex.z-dn.net/?f=%20%5Clongmapsto%7B%5Ctt%7B%5Cdfrac%7Bn%7D%7B2%7D%20%3D%201%20%2B%201%7D%7D)
![\longmapsto{\tt{\dfrac{n}{2} = 2}}](https://tex.z-dn.net/?f=%20%5Clongmapsto%7B%5Ctt%7B%5Cdfrac%7Bn%7D%7B2%7D%20%3D%202%7D%7D)
![\longmapsto{\tt{n = 2 \times 2}}](https://tex.z-dn.net/?f=%20%5Clongmapsto%7B%5Ctt%7Bn%20%3D%202%20%5Ctimes%202%7D%7D)
![\longmapsto{\tt{n = 4}}](https://tex.z-dn.net/?f=%20%5Clongmapsto%7B%5Ctt%7Bn%20%3D%204%7D%7D)
![\bigstar \: \: \underline{\boxed{\tt{\orange{n = 4}}}}](https://tex.z-dn.net/?f=%5Cbigstar%20%5C%3A%20%20%5C%3A%20%5Cunderline%7B%5Cboxed%7B%5Ctt%7B%5Corange%7Bn%20%3D%204%7D%7D%7D%7D)
- Hence, the value of n is 4.
![\begin{gathered}\end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%5Cend%7Bgathered%7D)
12) 1 = r-3/8
![\implies{\tt{1 = \dfrac{r - 3}{8}}}](https://tex.z-dn.net/?f=%20%5Cimplies%7B%5Ctt%7B1%20%3D%20%20%5Cdfrac%7Br%20-%203%7D%7B8%7D%7D%7D)
![\implies{\tt{r - 3 = 1 \times 8}}](https://tex.z-dn.net/?f=%20%5Cimplies%7B%5Ctt%7Br%20-%203%20%3D%201%20%5Ctimes%208%7D%7D)
![\implies{\tt{r - 3 = 8}}](https://tex.z-dn.net/?f=%20%5Cimplies%7B%5Ctt%7Br%20-%203%20%3D%208%7D%7D)
![\implies{\tt{r = 8 + 3}}](https://tex.z-dn.net/?f=%20%5Cimplies%7B%5Ctt%7Br%20%20%3D%208%20%2B%203%7D%7D)
![\implies{\tt{r = 11}}](https://tex.z-dn.net/?f=%20%5Cimplies%7B%5Ctt%7Br%20%20%3D%2011%7D%7D)
![\bigstar \: \: \underline{\boxed{\tt{\green{r = 11}}}}](https://tex.z-dn.net/?f=%5Cbigstar%20%5C%3A%20%20%5C%3A%20%5Cunderline%7B%5Cboxed%7B%5Ctt%7B%5Cgreen%7Br%20%3D%2011%7D%7D%7D%7D)
- Hence, the value of r is 11.
![\rule{300}{2.5}](https://tex.z-dn.net/?f=%5Crule%7B300%7D%7B2.5%7D)
Answer:
1
Step-by-step explanation:
Answer:
17.50
Step-by-step explanation:
you really don't need to know the tax amount.
20% of x = 3.50
(20/100) x = 3.50 Divide top and bottom of the left number by 20
(20÷20) / (100÷20) * x = 3.50
(1/5) x = 3.50 Multiply both sides by 5
x = 3.50 * 5
x = 17.50
The meal cost 17.50
HOPE THIS HELPS
Answer:
![\boxed{131}](https://tex.z-dn.net/?f=%5Cboxed%7B131%7D)
Step-by-step explanation:
→ We know that co-interior angles add up to 180°, so we can set up an equation
x + 17 + 4x + 3 = 180
→ Collect the x terms
5x + 17 + 3 = 180
→ Collect the integers
5x + 20 = 180
→ Minus 20 from both sides to isolate 5x
5x = 160
→ Divide both sides by 5 to isolate x
x = 32
⇒ Now we know the value of x, we can substitute it in back into m∠f because we know angles on a straight line add up to 180°
4x + 3 when x = 32 ⇔ 4 × 32 + 3 ⇔ 128 + 3 ⇔ 131