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Scorpion4ik [409]
3 years ago
14

Find the equation for the line passing through the point (−1,1) ( − 1 , 1 ) and parallel to the line whose equation is y=2x+12.

Mathematics
1 answer:
tekilochka [14]3 years ago
7 0
So, parallel lines have the same slope, therefore a parallel line to 2x+12, will have the same slope as that one, so which is it?   \bf y=\stackrel{slope}{2}x\stackrel{y-intercept}{+12}

so, we're really looking for the equation of a line whose slope is 2, and runs through -1,1.

\bf \begin{array}{lllll}
&x_1&y_1\\
%   (a,b)
&({{ -1}}\quad ,&{{ 1}})
\end{array}
\\\\\\
% slope  = m
slope = {{ m}}= \cfrac{rise}{run} \implies 2
\\\\\\
% point-slope intercept
\stackrel{\textit{point-slope form}}{y-{{ y_1}}={{ m}}(x-{{ x_1}})}\implies y-1=2[x-(-1)]
\\\\\\
y-1=2(x+1)\implies y-1=2x+2\implies y=2x+3
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A line with a slope of 0 passes through the point (9,5). What is its equation in slope-intercept form?
shepuryov [24]

Answer:

y = 5      

Step-by-step explanation:

Any line with a slope of 0 is horizontal, represented by the equation y = a number. That number is the y-value of all the points the line intersects.

We know that that the line intersects (9,5). So, take the y-value of that point and write it into the equation of y = a number. Thus, the answer is y =5.

8 0
3 years ago
In the complex number system, which of the following is equal to
pogonyaev

Answer:

C) 122+154i

Step-by-step explanation:

(14-2i)(7+12i)\\\\(14)(7)+(14)(12i)+(-2i)(7)+(-2i)(12i)\\\\98+168i-14i-24i^2\\\\98+154i-24(-1)\\\\98+154i+24\\\\122+154i

Therefore, C is correct. Recall that i^2=-1

3 0
2 years ago
Read 2 more answers
The outside diameter of the igloo is 12 feet. The thickness of each block of ice that was used to construct the igloo is 1.5 fee
mojhsa [17]
The first thing we are going to do for this case is to model the igloo as a hemisphere.
 The volume of the hemisphere is:
 V = ((4/3) * (pi) * (r ^ 3)) / 2
 Where,
 r: sphere radio
 We have then that the internal diameter is:
 di = 12-1.5
 di = 10.5 feet
 So the radio is:
 r = di / 2
 r = 10.5 / 2
 r = 5.25 feet
 Substituting values:
 V = ((4/3) * (pi) * ((5.25) ^ 3)) / 2
 V = 303.1 feet ^ 3
 Answer:
 
the amount of space of the living area inside the igloo is:
 
V = 303.1 feet ^ 3
6 0
3 years ago
What is 3/4f + 5 = -5
anyanavicka [17]
<span>3/4f + 5 = -5
Subtract 5 from both sides
3/4f= -10
Divide both sides by 3/4 so that the only thing remaining on the left side is the variable f.
Final Answer: f= 40/3 or 13 1/3 *Both answers are equivalent to each other.</span>
5 0
3 years ago
Read 2 more answers
Suppose the discrete random variable X has the probability distribution below:
Talja [164]

(a) P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2) = 0.11 + 0.52 + 0.19 = 0.82

(b) P(X ≥ 1) = P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) = 0.52 + 0.19 + 0.12 + 0.06 = 0.89

(c) µ = 0×0.11 + 1×0.52 + 2×0.19 + 3×0.12 + 4×0.06 = 1.5

(d) σ² = (0²×0.11 + 1²×0.52 + 2²×0.19 + 3²×0.12 + 4²×0.06) - µ² = 1.07

σ = √(σ²) ≈ 1.03

4 0
3 years ago
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