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Keith_Richards [23]
3 years ago
10

Find all the square roots of x2 ≡ 53 (mod 77)

Mathematics
1 answer:
Nikolay [14]3 years ago
3 0

Answer:

x=\pm\sqrt{77n+53}

Step-by-step explanation:

We have been given an equivalence equation x^2\equiv 53\text{ (mod } 77). We are asked to find all the square root of the given equivalence equation.

Upon converting our given equivalence equation into an equation, we will get:

x^2-53=77n

Add 53 on both sides:

x^2-53+53=77n+53

x^2=77n+53

Take square root of both sides:

x=\pm\sqrt{77n+53}

Therefore, the square root for our given equation would be x=\pm\sqrt{77n+53}.

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Answer:

∠E = ∠F = 41°

Step-by-step explanation:

The sum of the 3 angles in a triangle = 180°

Sum the 3 given angles and equate to 180

x + x + 98 = 180 ( subtract 98 from both sides )

2x = 82 ( divide both sides by 2 )

x = 41

Hence

∠E = ∠F = 41°

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3 years ago
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Step-by-step explanation:

Just did it and got the answers wrong so these are the correct ones

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4 0
3 years ago
3. Try It #3 Write the point-slope form of an equation of a line with a slope of -2 that passes through the point (-2,2). Then r
vova2212 [387]

Answer:

Point-slope form of equation given as $y-2=-2(x+2)$.

Slope-intercept form of equation is given as $y=-2 x-2$.

Step-by-step explanation:

In the question, it is given that the slope of a line is -2 and it passes from (-2,2).

It is asked to write the point-slope form of the equation and rewrite it as slope-intercept form.

To do so, first find the values which are given in the question and put it in the formula of point-slope form. Simplify the equation to rewrite as slope-intercept form.

Step 1 of 2

Passing point of the line is (-2,2).

Hence, $x_{1}=-2$ and

$$y_{1}=2 \text {. }$$

Also, the slope of the line is -2.

Hence, m=-2

Substitute the above values in point-slope form of equation given by $y-y_{1}=m\left(x-x_{1}\right)$

$$\begin{aligned}&y-y_{1}=m\left(x-x_{1}\right) \\&y-2=-2(x-(-2) \\&y-2=-2(x+2)\end{aligned}$$

Hence, point-slope form of equation given as y-2=-2(x+2).

Step 2 of 2

Solve y-2=-2(x+2) to write it as slope-intercept form given by y=mx+c.

$$\begin{aligned}&y-2=-2(x+2) \\&y-2=-2 x-4 \\&y=-2 x-4+2 \\&y=-2 x-2\end{aligned}$$

Hence, slope-intercept form of equation is given as y=-2x-2.

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2 years ago
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liubo4ka [24]

Answer:

B

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