MATHEMATICS HIGH SCHOOL

Holly has watched 39% of a movie that is 122 minutes long. Which is the best estimate for the number of minutes of the movie that Holly has watched? 36 minutes 39 minutes 48 minutes 52 minute

Answers

Answer 1

Answer:

Answer:

48 minutes

Step-by-step explanation:

Answer 2

Answer:

Answer:

Step-by-step explanation:48

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What is the solution of x - 13 =5
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A circle is described by the equation x2 + y2 + 14x + 2y + 14 = 0. What are the coordinates for the center of the circle and the length of the radius?a. (-7, -1), 36 units
b. (7, 1), 36 units
c. (7, 1), 6 units
d. (-7, -1), 6 units

Answers

Answer:

option d is correct.

center = (-7, -1)

r = 6

Step-by-step explanation:

The general equation of the circle is given by;

$(x-h)^2+(y-k)^2 = r^2$

where;

(h, k) is the center of the circle

r is the radius of the circle respectively.

As per the statement:

A circle is described by the equation $x^2 + y^2 + 14x + 2y + 14 = 0$

then;

$(x^2+14x)+(y^2 + 2y) + 14 = 0$

Using the completing the square:

$(x^2+14x+7^2-7^2)+(y^2 + 2y+1^2-1^2) + 14 = 0$

⇒ $(x+7)^2 - 49 + (y+1)^2 - 1 + 14 = 0$

⇒ $(x+7)^2+(y+1)^2 -36 = 0$

Add 36 to both sides we have;

$(x+7)^2+(y+1)^2=36$

On comparing with the general equation of circle:

we get;

h = -7 , k = -1 and $r^2 = 36$

⇒ $r = 6$

Therefore, the coordinate of the center of the circle is (-7, -1) and length of the radius of the circle is 6

The equation of a circle:
$(x-h)^2+(y-k)^2=r^2$
(h,k) - the coordinates of the center
r - the radius

$x^2+y^2+14x+2y+14=0 \nx^2+14x+49+y^2+2y+1+14-49-1=0 \n(x+7)^2+(y+1)^2+14-49-1=0 \n(x+7)^2+(y+1)^2-36=0 \n(x+7)^2+(y+1)^2=36 \n(x-(-7))^2+(y-(-1))^2=6^2 \n \Downarrow \nh=-7 \nk=-1 \nr=6$

The center is (-7,-1), the length of the radius is 6 units.
The answer is D.

A man walks along a straight path at a speed of 4ft/s. A searchlight is located on the ground 20ft from the path and is kept focused on the man. At what rate is the searchlight rotating when the man is 15 ft from the point on the path closest to the searchlight.

Answers

Now note that tan(y) = x=20,
so that sec^2y *dy/dt=1/20 dx/dt
At the instant describedin the problem,
x = 15 and the hypotenuse of the above triangle
thus has length25,
so we compute:(25/20)^2 dy/dt=1/20*4 ==>dy/dt=1/2*400/625

=16/125 rad/sec

Where does the irrational number 1.8693… fall?

Answers

if you want just round to 1.9

To decrease an amount by 23% multiply by

Answers

Use the Formula x-(x*23)/100

If you want to decrease an amount by 23% then you should use the formula,

x - (x *23)/100

What is the area of this circle? (Express your answer using π.)
(Note: The diameter is 10ft.)

Answers

The area is πr².
The radius r is half the diameter. The diameter is 10 ft so the radius is 5 ft.

$A=\pi * 5^2=25 \pi$

The area is 25π ft².

Area of a circle is:

A = pi * r^2

If the diameter is 10 feet, the radius will be half of that or 5.

So:

A = 3.14 * 5^2

Simplify exponent:

A = 3.14 * 25

Multiply:

A = 78.5

You owe some friends $25 and pay them back $18. Which number sentence shows this situation?25 + 18
-25 + 18
-18 + 25
-25 + (-18)

Answers

If you would like to know which number sentence shows the following situation, you can find this like this:

$25 - $18 = $7

You still owe your friends $7.
The correct result would be 25 - 18 = - 18 + 25.

Answer:

-18 + 25

Step-by-step explanation:

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