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3 years ago

Is the sum of 4.2 and square root of 2 rational or irrational

1 answer:

3 0

The sum of an irrational number and a rational one
is always irrational. There's nothing you can add to
an irrational number to make it behave better.

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Which of the following could be a mirror line on a coordinate plane?

denis-greek [22]

Answer: D

Step-by-step explanation:

This is the only option that is a line.

6 0

3 years ago

When making a long distance call from a certain pay phone, the first three minutes of a call cost $3.00. afterthat, each additio

motikmotik

3 + 0.45*M<=8,40. Notice the equal, because you may use all the money. Then, rearranging: M<=(8.40-3)/0.45= 12, so M<=12. Now, obviously time is positive, so you may end saying 0<=M<=12, with M=0 meaning no call! :)

4 0

3 years ago

9. Two points in the plane, A(−3,8) and ????(17,8), represent the endpoints of the diameter of a circle.

kherson [118]

Answer:

a) (7,8)

b) r = 10

c) $(x-7)^2+(y-8)^2=100$

Step-by-step explanation:

a) Given the endpoints the diameter of the circle as A(-3,8) and B(17,8)

we should realize that the center of the circle lies exactly at the midpoint of these two points. let's denote the midpoint as $(x_m,y_m)$

$(x_m, y_m) = \left(\dfrac{x_1+x_2}{2},\dfrac{y_1+y_2}{2}\right)$

$(x_m, y_m) = \left(\dfrac{-3+17}{2},\dfrac{8+8}{2}\right)$

$(x_m, y_m) = (7,8)$

this is the coordinate of the center of the circle.

b) The radius of the circle can be easily found by using the distance formula between the center point and either of the two endpoints of the diameter.

the general distance formula is:

$r = \sqrt{(x_1-x_2)^2+(y_1-y_2)^2}$

in our case the equation changes to: (selecting the centre and point B)

$r = \sqrt{(x_m-x_2)^2+(y_m-y_2)^2}$

$r = \sqrt{(7-17)^2+(8-8)^2}$

$r = 10$

side note: there are more alternate ways to find the radius for e.g (you can use the distance formula between the points A and B and that'll give you the length of the diameter which you can divide by 2 to get the radius) OR (you don't need to use the distance formula at all <u>since in this particular case</u> all the coordinates lie on the same horizontal line, so by simply subtracting the two x-coordinates of the center and either of A or B)

c) the ingredients needed to make the equation of the circle are the

coordinates of the center: $(x_m,y_m) = (7,8)$
radius of the circle: $r = 10$

we can put this in the formula of the circle:

$(x-a)^2+(y-b)^2=r^2$

in our case the equation changes to:

$(x-x_m)^2+(y-y_m)^2=r^2$

$(x-7)^2+(y-8)^2=(10)^2$

$(x-7)^2+(y-8)^2=100$

this is the equation of the circle!

6 0

3 years ago

Larry wants to buy some carpet for his living room. The length of the room is 3 times the width and the total area of the room i

TiliK225 [7]

Answer:

the width is 2 and the length is 6

7 0

3 years ago

Read 2 more answers

How do i solve this?

Law Incorporation [45]

Answer:

$\large\boxed{x$

Step-by-step explanation:

$-\dfrac{1}{2}x+\dfrac{1}{3}>\dfrac{3}{5}\\\\\text{Find common denominator of the fractions}\\\\2,\ 3,\ 5\to2\cdot3\cdot5=30\\\\-\dfrac{1}{2}x+\dfrac{1}{3}>\dfrac{3}{5}\qquad\text{multiply both sides by 30}\\\\30\!\!\!\!\!\diagup^{15}\left(-\dfrac{1}{2\!\!\!\!\diagup_1}x\right)+30\!\!\!\!\!\diagup^{10}\left(\dfrac{1}{3\!\!\!\!\diagup_1}\right)>30\!\!\!\!\!\diagup^{6}\left(\dfrac{3}{5\!\!\!\!\diagup_1}\right)\\\\-15x+10>(6)(3)\\\\-15x+10>18\qquad\text{subtract 10 from both sides}$

$-15x>8\qquad\text{change the signs}\\\\15x$

4 0

4 years ago