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EastWind [94]
3 years ago
12

Solve and graph the inequality. 8 + k < 5

Mathematics
2 answers:
Gnom [1K]3 years ago
4 0
K < -3 Have a circle on the -3 and the arrow pointing to the left

omeli [17]3 years ago
3 0
K< -3 hope this helps :)))

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A square has a rotational symmetry of how many degrees?
anyanavicka [17]
Answer: C
all shapes must equal 360 degrees
90 x the 4 angles of the square equals 360 degrees
4 0
3 years ago
Read 2 more answers
Solve the system using either Gaussian elimination with back-substitution or Gauss-Jordan elimination. (If there is no solution,
Gnom [1K]

Answer:

x1=-4/5, x2=18/5 and x3=7/5

Step-by-step explanation:

\left[\begin{array}{ccc|c}1&0&-3&-5\\3&1&2&4\\2&2&1&7\end{array}\right]

you can do linear combination between the rows:

2nd row=R2-3R1 and 3th row=R3-2R1

\left[\begin{array}{ccc|c}1&0&-3&-5\\0&1&11&19\\0&2&7&17\end{array}\right]

3th row=(3R2-R3)/15

\left[\begin{array}{ccc|c}1&0&-3&-5\\0&1&11&19\\0&0&1&\frac{7}{5} \end{array}\right]

1st row=R1+3R3 and R2-11R3

\left[\begin{array}{ccc|c}1&0&0&-4/5 \\0&1&0&18/5 \\0&0&1&7/5\end{array}\right]

x1=-4/5, x2=18/5 and x3=7/5

6 0
3 years ago
The curve given by x=sin(t),y=sin(t+sin(t)) has two tangent lines at the point (x,y)=(0,0). List both of them in order of increa
SOVA2 [1]

Answer:

y = 0

y =2x

Step-by-step explanation:

Given parametric equations:

x (t) = sin (t)

y (t) = sin (t + sin (t))

The slope of the curve at any given point is given by dy / dx we will use chain rule to find dy / dx

(dy / dx) * (dx / dt) = (dy / dt)

(dy / dx) = (dy / dt) / (dx / dt)

Evaluate dx / dt and dy / dt

dx / dt = cos (t)

dy / dt = cos (t + sin (t)) * (1+cos (t))

Hence,

dy / dx = (1+cos(t))*cos(t + sin (t))) / cos (t)

@Given point (x,y) = 0 we evaluate t

0 = sin (t)

t = 0 , pi

Input two values of t and compute dy / dx

@ t = 0

dy / dx = (1 + cos (0))*cos (0 + sin (0))) / cos (0)

dy / dx = (1+1)*(1) / (1) = 2 @ t = 0

@t = pi

dy / dx = ( 1 + cos (pi))* cos (pi + sin (pi)) / cos (pi)

dy / dx = (1-1) * (-1) / (-1) = 0 @ t = pi

The corresponding gradients are 0 and 2 in increasing order and their respective equations are:

y = 2x

y = 0

5 0
3 years ago
Find a solution to the linear equation y equals 8x-32
Lerok [7]

Answer:

(4, 0).

Step-by-step explanation:

y = 8x - 32

There are many solutions that we can choose from, since any set of coordinates that fit in the equation counts as a solution.

We can have (0, -32), (1, -24), (2, -16), (3, -8), (4, 0), and many more.

Hope this helps!

4 0
3 years ago
Read 2 more answers
1.This circle is centered at the origin and contains the points two units away. Write the equation for this circle.
denis-greek [22]

Answer:

1. The location of the center of the given circle = The origin (0, 0)

The given points on the circumference of the circle = (1, √3), and (0, -2)

The general form of the equation of a circle, is presented as follows

(x - h)² + (y - k)² = r²

Where;

(h, k) = The coordinates of the center of the circle

r = The radius of the circle

∴ (h, k) = (0, 0)

The radius of the given equation is the distance from the center (0, 0) to either the point (0, -2) or (1, √3)

The distance from the center (0, 0) to the point (0, -2), which are points on the same ordinate,  r = y₂ - y₁

∴ r =  0 - (-2) = 2

r = 2

The equation of the circle is therefore;

(x - 0)² + (y - 0)² = 2²

∴ x² + y² = 2²

2. When x = 1, and y = √3, we have;

(1 - 0)² + (√3 - 0)² = 1 + 3 = 4 = 2²

When x = 0, and y = -2, we have;

(0 - 0)² + ((-2) - 0)² = (-2)² = 4 = 2²

Therefore, the points shown on the circle (1, √3), and (0, -2) satisfy the equation of the circle, x² + y² = 2² and are solutions to the equation of the circle

Step-by-step explanation:

3 0
3 years ago
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