Two interior angles of a polygon are equal and each is of measure 90°, while all the others are 170° each. Find the number of si
des of the polygon.
2 answers:
Answer:
2
Step-by-step explanation:
2
Answer: 2
Step by step explanation: 2
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Answer:
answer is in explanation
Step-by-step explanation:
Computing the rate we get:
![\frac{300}{10}\frac{cameras}{\text{hour}}=30\frac{cameras}{\text{hour}}](https://tex.z-dn.net/?f=%5Cfrac%7B300%7D%7B10%7D%5Cfrac%7Bcameras%7D%7B%5Ctext%7Bhour%7D%7D%3D30%5Cfrac%7Bcameras%7D%7B%5Ctext%7Bhour%7D%7D)
Then, when the assembly line runs at the same rate for 24 hours they will produce:
![24\text{hour}\cdot30\frac{cameras}{\text{hour}}=720\text{ cameras}](https://tex.z-dn.net/?f=24%5Ctext%7Bhour%7D%5Ccdot30%5Cfrac%7Bcameras%7D%7B%5Ctext%7Bhour%7D%7D%3D720%5Ctext%7B%20cameras%7D)
Answer: Option C) 720.
Answer:
5
Step-by-step explanation:
The equation says y equals 5. I attached a graph below:
<h2>✒️VALUE</h2>
![\\ \quad \begin{array}{c} \qquad \bold{Distance \: \green{ Formula:}}\qquad\\ \\ \boldsymbol{ \tt d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}} \end{array}\\ \begin{array}{l} \\ 1.)\: \bold{Given:}\: \begin{cases}\tt D(- 5,6), E(2.-1),\textsf{ and }F(x,0) \\ \tt DF = EF \end{cases} \\ \\ \qquad\bold{Required:}\:\textsf{ value of }x \\ \\ \qquad \textsf{Solving for }x, \\ \\ \tt \qquad DF = EF \\ \\ \implies\small \tt{\sqrt{(x -(- 5))^2 + (0 - 6)^2} = \sqrt{(x - 2)^2 + (0 - (-1))^2}} \\ \\ \implies\tt\sqrt{(x + 5)^2 + 36 } = \sqrt{(x - 2)^2 + 1 } \\ \\ \textsf{Squaring both sides yields} \\ \\ \implies\tt (x + 5)^2 + 36 = (x - 2)^2 + 1 \\ \\ \implies\tt x^2 + 10x + 25 + 36 = x^2 - 4x + 4 + 1 \\ \\ \implies \tt x^2 + 10x + 61 = x^2 - 4x + 5 \\ \\ \implies\tt10x + 4x = 5 - 61 \\ \\ \implies\tt14x = -56 \\ \\ \implies \red{\boxed{\tt x = -4}}\end{array} \\ \\ \\ \\\begin{array}{l} \\ 2.)\: \bold{Given:}\: \begin{cases}\tt P(6,-1), Q(-4,-3),\textsf{ and }R(0,y) \\ \tt PR = QR \end{cases} \\ \\ \bold{Required:}\:\textsf{ value of }y \\ \\ \qquad\textsf{Solving for }y, \\ \\ \qquad\tt PR = QR \\ \\ \implies \tt\small{\sqrt{(0 - 6)^2 + (y - (-1))^2} = \sqrt{(0 - (-4))^2 + (y - (-3))^2}} \\ \\ \implies\tt\sqrt{36 + (y + 1)^2} = \sqrt{16 + (y + 3)^2 } \\ \\ \textsf{Squaring both sides yields} \\ \\ \implies \tt \: 36 + (y + 1)^2 = 16 + (y + 3)^2 \\ \\ \implies\tt 36 + y^2 + 2y + 1 = 16 + y^2 + 6y + 9 \\ \\ \implies \tt \: y^2 + 2y + 37 = y^2 + 6y + 25 \\ \\ \implies \tt \: 2y - 6y = 25 - 37 \\ \\ \implies \tt -4y = -12 \\ \\ \implies\red{\boxed{ \tt y = 3}} \end{array} \\ \\ \\ \begin{array}{l} \\ 3.)\: \bold{Given:}\: \begin{cases}\: A(4,5), B(-3,2),\textsf{ and }C(x,0) \\ \: AC = BC \end{cases} \\ \\ \bold{Required:}\:\textsf{ value of }x \\ \\ \qquad\textsf{Solving for }x, \\ \\ \qquad\tt AC = BC \\ \\ \implies\tt\small{\sqrt{(x - 4)^2 + (0 - 5)^2} = \sqrt{(x - (-3))^2 + (0 - 2)^2}} \\ \\ \implies\tt\sqrt{(x - 4)^2 + 25} = \sqrt{(x + 3)^2 + 4} \\ \\ \textsf{Squaring both sides yields} \\ \\ \implies\tt\:(x - 4)^2 + 25 = (x + 3)^2 + 4 \\ \\ \implies\tt\:x^2 - 8x + 16 + 25 = x^2 + 6x + 9 + 4 \\ \\ \implies\tt\:x^2 - 8x + 41 = x^2 + 6x + 13 \\ \\ \implies\tt-8x - 6x = 13 - 41 \\ \\\implies\tt -14x = -28 \\ \\ \implies\red{\boxed{\tt\:x = 2}} \end{array}](https://tex.z-dn.net/?f=%20%5C%5C%20%5Cquad%20%20%5Cbegin%7Barray%7D%7Bc%7D%20%5Cqquad%20%5Cbold%7BDistance%20%5C%3A%20%5Cgreen%7B%20Formula%3A%7D%7D%5Cqquad%5C%5C%20%5C%5C%20%5Cboldsymbol%7B%20%5Ctt%20d%20%3D%20%5Csqrt%7B%28x_2%20-%20x_1%29%5E2%20%2B%20%28y_2%20-%20y_1%29%5E2%7D%7D%20%5Cend%7Barray%7D%5C%5C%20%20%5Cbegin%7Barray%7D%7Bl%7D%20%5C%5C%201.%29%5C%3A%20%5Cbold%7BGiven%3A%7D%5C%3A%20%5Cbegin%7Bcases%7D%5Ctt%20D%28-%205%2C6%29%2C%20E%282.-1%29%2C%5Ctextsf%7B%20and%20%7DF%28x%2C0%29%20%5C%5C%20%5Ctt%20DF%20%3D%20EF%20%5Cend%7Bcases%7D%20%5C%5C%20%5C%5C%20%20%5Cqquad%5Cbold%7BRequired%3A%7D%5C%3A%5Ctextsf%7B%20value%20of%20%7Dx%20%5C%5C%20%5C%5C%20%5Cqquad%20%5Ctextsf%7BSolving%20for%20%7Dx%2C%20%5C%5C%20%5C%5C%20%20%5Ctt%20%20%5Cqquad%20DF%20%3D%20EF%20%5C%5C%20%5C%5C%20%20%5Cimplies%5Csmall%20%5Ctt%7B%5Csqrt%7B%28x%20-%28-%205%29%29%5E2%20%2B%20%280%20-%206%29%5E2%7D%20%3D%20%5Csqrt%7B%28x%20-%202%29%5E2%20%2B%20%280%20-%20%28-1%29%29%5E2%7D%7D%20%5C%5C%20%5C%5C%20%20%20%5Cimplies%5Ctt%5Csqrt%7B%28x%20%2B%205%29%5E2%20%2B%2036%20%7D%20%3D%20%5Csqrt%7B%28x%20-%202%29%5E2%20%2B%201%20%7D%20%5C%5C%20%5C%5C%20%5Ctextsf%7BSquaring%20both%20sides%20yields%7D%20%5C%5C%20%5C%5C%20%20%5Cimplies%5Ctt%20%28x%20%2B%205%29%5E2%20%2B%2036%20%3D%20%28x%20-%202%29%5E2%20%2B%201%20%5C%5C%20%5C%5C%20%20%5Cimplies%5Ctt%20x%5E2%20%2B%2010x%20%2B%2025%20%2B%2036%20%3D%20x%5E2%20-%204x%20%2B%204%20%2B%201%20%5C%5C%20%5C%5C%20%5Cimplies%20%5Ctt%20x%5E2%20%2B%2010x%20%2B%2061%20%3D%20x%5E2%20-%204x%20%2B%205%20%5C%5C%20%5C%5C%20%20%20%5Cimplies%5Ctt10x%20%2B%204x%20%3D%205%20-%2061%20%5C%5C%20%5C%5C%20%20%20%5Cimplies%5Ctt14x%20%3D%20-56%20%5C%5C%20%5C%5C%20%20%5Cimplies%20%5Cred%7B%5Cboxed%7B%5Ctt%20x%20%3D%20-4%7D%7D%5Cend%7Barray%7D%20%20%5C%5C%20%20%5C%5C%20%20%5C%5C%20%20%5C%5C%5Cbegin%7Barray%7D%7Bl%7D%20%5C%5C%202.%29%5C%3A%20%5Cbold%7BGiven%3A%7D%5C%3A%20%5Cbegin%7Bcases%7D%5Ctt%20P%286%2C-1%29%2C%20Q%28-4%2C-3%29%2C%5Ctextsf%7B%20and%20%7DR%280%2Cy%29%20%5C%5C%20%5Ctt%20PR%20%3D%20QR%20%5Cend%7Bcases%7D%20%5C%5C%20%5C%5C%20%5Cbold%7BRequired%3A%7D%5C%3A%5Ctextsf%7B%20value%20of%20%7Dy%20%5C%5C%20%5C%5C%20%20%5Cqquad%5Ctextsf%7BSolving%20for%20%7Dy%2C%20%5C%5C%20%5C%5C%20%20%5Cqquad%5Ctt%20PR%20%3D%20QR%20%5C%5C%20%5C%5C%20%20%5Cimplies%20%5Ctt%5Csmall%7B%5Csqrt%7B%280%20-%206%29%5E2%20%2B%20%28y%20-%20%28-1%29%29%5E2%7D%20%3D%20%5Csqrt%7B%280%20-%20%28-4%29%29%5E2%20%2B%20%28y%20-%20%28-3%29%29%5E2%7D%7D%20%5C%5C%20%5C%5C%20%20%20%5Cimplies%5Ctt%5Csqrt%7B36%20%2B%20%28y%20%2B%201%29%5E2%7D%20%3D%20%5Csqrt%7B16%20%2B%20%28y%20%2B%203%29%5E2%20%7D%20%5C%5C%20%5C%5C%20%5Ctextsf%7BSquaring%20both%20sides%20yields%7D%20%5C%5C%20%5C%5C%20%20%5Cimplies%20%5Ctt%20%5C%3A%2036%20%2B%20%28y%20%2B%201%29%5E2%20%3D%2016%20%2B%20%28y%20%2B%203%29%5E2%20%5C%5C%20%5C%5C%20%20%5Cimplies%5Ctt%2036%20%2B%20y%5E2%20%2B%202y%20%2B%201%20%3D%2016%20%2B%20y%5E2%20%2B%206y%20%2B%209%20%5C%5C%20%5C%5C%20%20%5Cimplies%20%5Ctt%20%5C%3A%20y%5E2%20%2B%202y%20%2B%2037%20%3D%20y%5E2%20%2B%206y%20%2B%2025%20%5C%5C%20%5C%5C%20%20%5Cimplies%20%5Ctt%20%5C%3A%202y%20-%206y%20%3D%2025%20-%2037%20%5C%5C%20%5C%5C%20%5Cimplies%20%5Ctt%20-4y%20%3D%20-12%20%5C%5C%20%5C%5C%20%20%20%5Cimplies%5Cred%7B%5Cboxed%7B%20%5Ctt%20y%20%3D%203%7D%7D%20%5Cend%7Barray%7D%20%20%5C%5C%20%20%5C%5C%20%20%5C%5C%20%5Cbegin%7Barray%7D%7Bl%7D%20%5C%5C%203.%29%5C%3A%20%5Cbold%7BGiven%3A%7D%5C%3A%20%5Cbegin%7Bcases%7D%5C%3A%20A%284%2C5%29%2C%20B%28-3%2C2%29%2C%5Ctextsf%7B%20and%20%7DC%28x%2C0%29%20%5C%5C%20%5C%3A%20AC%20%3D%20BC%20%5Cend%7Bcases%7D%20%5C%5C%20%5C%5C%20%5Cbold%7BRequired%3A%7D%5C%3A%5Ctextsf%7B%20value%20of%20%7Dx%20%5C%5C%20%5C%5C%20%20%5Cqquad%5Ctextsf%7BSolving%20for%20%7Dx%2C%20%5C%5C%20%5C%5C%20%20%20%5Cqquad%5Ctt%20AC%20%3D%20BC%20%5C%5C%20%5C%5C%20%5Cimplies%5Ctt%5Csmall%7B%5Csqrt%7B%28x%20-%204%29%5E2%20%2B%20%280%20-%205%29%5E2%7D%20%3D%20%5Csqrt%7B%28x%20-%20%28-3%29%29%5E2%20%2B%20%280%20-%202%29%5E2%7D%7D%20%5C%5C%20%5C%5C%20%5Cimplies%5Ctt%5Csqrt%7B%28x%20-%204%29%5E2%20%2B%2025%7D%20%3D%20%5Csqrt%7B%28x%20%2B%203%29%5E2%20%2B%204%7D%20%5C%5C%20%5C%5C%20%5Ctextsf%7BSquaring%20both%20sides%20yields%7D%20%5C%5C%20%5C%5C%20%5Cimplies%5Ctt%5C%3A%28x%20-%204%29%5E2%20%2B%2025%20%3D%20%28x%20%2B%203%29%5E2%20%2B%204%20%5C%5C%20%5C%5C%20%5Cimplies%5Ctt%5C%3Ax%5E2%20-%208x%20%2B%2016%20%2B%2025%20%3D%20x%5E2%20%2B%206x%20%2B%209%20%2B%204%20%5C%5C%20%5C%5C%20%5Cimplies%5Ctt%5C%3Ax%5E2%20-%208x%20%2B%2041%20%3D%20x%5E2%20%2B%206x%20%2B%2013%20%5C%5C%20%5C%5C%20%5Cimplies%5Ctt-8x%20-%206x%20%3D%2013%20-%2041%20%5C%5C%20%5C%5C%5Cimplies%5Ctt%20-14x%20%3D%20-28%20%5C%5C%20%5C%5C%20%5Cimplies%5Cred%7B%5Cboxed%7B%5Ctt%5C%3Ax%20%3D%202%7D%7D%20%5Cend%7Barray%7D%20)
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#5-MinutesAnswer
Make a table with two columns, to find the ordered pair. This is an example.