Answer:
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Step-by-step explanation:
- When two straight lines intersect each other, then the pairs of angles so formed without any common arm are called vertically opposite angles.
- Vertically opposite angles are equal to each other.
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So,
![{\longrightarrow \it\qquad { \ { (6n - 4) {}^{ \circ} = {(5n + 7)}^{ \circ} }}}](https://tex.z-dn.net/?f=%7B%5Clongrightarrow%20%5Cit%5Cqquad%20%7B%20%5C%20%7B%20%286n%20%20%20-%204%29%20%7B%7D%5E%7B%20%5Ccirc%7D%20%20%20%3D%20%20%7B%285n%20%2B%207%29%7D%5E%7B%20%5Ccirc%7D%20%7D%7D%7D)
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Removing the brackets,
![{\longrightarrow \it\qquad { \ { 6n - 4{}^{ \circ} = {5n + 7 \: }^{ \circ} }}}](https://tex.z-dn.net/?f=%7B%5Clongrightarrow%20%5Cit%5Cqquad%20%7B%20%5C%20%7B%206n%20%20%20-%204%7B%7D%5E%7B%20%5Ccirc%7D%20%20%20%3D%20%20%7B5n%20%2B%207%20%5C%3A%20%7D%5E%7B%20%5Ccirc%7D%20%7D%7D%7D)
![{\longrightarrow \it\qquad { \ { 6n - 5n = { 7 \: }^{ \circ} +4{}^{ \circ} }}}](https://tex.z-dn.net/?f=%7B%5Clongrightarrow%20%5Cit%5Cqquad%20%7B%20%5C%20%7B%206n%20%20%20-%205n%20%20%20%3D%20%20%7B%20%207%20%5C%3A%20%7D%5E%7B%20%5Ccirc%7D%20%2B4%7B%7D%5E%7B%20%5Ccirc%7D%20%7D%7D%7D)
![{\longrightarrow \it\qquad { \pmb{ n = { 11 \: }^{ \circ} }}}](https://tex.z-dn.net/?f=%7B%5Clongrightarrow%20%5Cit%5Cqquad%20%7B%20%5Cpmb%7B%20n%20%20%20%3D%20%20%7B%20%2011%20%5C%3A%20%7D%5E%7B%20%5Ccirc%7D%20%20%7D%7D%7D)
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Therefore,
Answer:becayse djr d,mstud bdn dhg furfhtb-=gvg
Step-by-step explanation:
Answer:
Here's what I get
Step-by-step explanation:
Total cost = equipment cost + monthly fee × number of months
Let C = total cost
and e = equipment cost
and f = monthly fee
and x = number of months. Then
C = e + f·x
The condition is that C ≤ $175 or
e + f·x ≤ $175
1. NetGear
e = $99; f = $5/mo
The condition is
99 + 5x ≤ 175
![\begin{array}{rcll}99 + 5x & \leq & 175 &\\5x & \leq &76 & \text{Subtracted 99 from each side}\\x & \leq & \dfrac{76}{5} & \text{Divided each side by 5}\\\\x & \leq & \mathbf{15.2} & \text{Simplified}\\\end{array}\\](https://tex.z-dn.net/?f=%5Cbegin%7Barray%7D%7Brcll%7D99%20%2B%205x%20%26%20%5Cleq%20%26%20175%20%26%5C%5C5x%20%26%20%5Cleq%20%2676%20%20%26%20%5Ctext%7BSubtracted%2099%20from%20each%20side%7D%5C%5Cx%20%26%20%5Cleq%20%26%20%5Cdfrac%7B76%7D%7B5%7D%20%26%20%5Ctext%7BDivided%20each%20side%20by%205%7D%5C%5C%5C%5Cx%20%26%20%5Cleq%20%26%20%5Cmathbf%7B15.2%7D%20%26%20%5Ctext%7BSimplified%7D%5C%5C%5Cend%7Barray%7D%5C%5C)
The centre could rent the games for 15 mo.
They would pay $99 for the equipment.
Fifteen months rental at $5/mo = $75.
Total cost = $174.
2. Anytime Games
e = $19; f = $19/mo
The condition is
19 + 19x ≤ 175
![\begin{array}{rcll}19 + 19x & \leq & 175&\\19x& \leq & 156 & \text{Subtracted 19 from each side}\\x & \leq & \dfrac{156}{19} & \text{Divided each side by 19}\\\\x & \leq & \mathbf{8.2} & \text{Simplified}\\\end{array}\\](https://tex.z-dn.net/?f=%5Cbegin%7Barray%7D%7Brcll%7D19%20%2B%2019x%20%26%20%5Cleq%20%20%26%20175%26%5C%5C19x%26%20%5Cleq%20%26%20156%20%20%26%20%5Ctext%7BSubtracted%2019%20from%20each%20side%7D%5C%5Cx%20%26%20%5Cleq%20%26%20%5Cdfrac%7B156%7D%7B19%7D%20%26%20%5Ctext%7BDivided%20each%20side%20by%2019%7D%5C%5C%5C%5Cx%20%26%20%5Cleq%20%26%20%5Cmathbf%7B8.2%7D%20%26%20%5Ctext%7BSimplified%7D%5C%5C%5Cend%7Barray%7D%5C%5C)
The centre could rent the games for eight months.
They would pay $19 for the equipment.
Eight months rental at $19/mo = $152.
Total cost = $171.
3. Recommendation
The Community Centre should rent from NetGear.
They can rent for 15 mo without going over the budget.
With the other company, they can rent for only eight months.
The graphs below show how the costs for the two companies vary with the number of months.
Anything above the horizontal orange line at C = $175 is beyond the Community Centre's budget.
Range, Maximum, and y-intercept
Answer:
x = 6 units
Step-by-step explanation:
By geometric mean property:
![x = \sqrt{9 \times 4} \\ \\ x = \sqrt{36} \\ \\ x = 6 \: units](https://tex.z-dn.net/?f=x%20%3D%20%20%5Csqrt%7B9%20%5Ctimes%204%7D%20%20%5C%5C%20%20%5C%5C%20x%20%3D%20%20%5Csqrt%7B36%7D%20%20%5C%5C%20%20%5C%5C%20x%20%3D%206%20%5C%3A%20units)