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3 years ago

What are all the common factors of 24,64 and 88

Mathematics

1 answer:

shutvik [7]3 years ago

8 0

A common factor for all of them is 8

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Is the given point interior , exterior, or on the circle k (x+2)2 + (y-3)2 =18 P (8,4)

Mnenie [13.5K]

One way would be to find the distance from the point to the center of the circle and compare it to the radius

for
$(x-h)^2+(y-k)^2=r^2$
the center is (h,k) and the radius is r

and the distance formula is
distance between $(x_1,y_1)$ and $(x_2,y_2)$ is
$D=\sqrt{(x_1-x_2)^2+(y_1-y_2)^2}$

r=radius
D=distance form (8,4) to center

if r>D, then (8,4) is inside the circle
if r=D, then (8,4) is on the circle
if r<D, then (8,4) is outside the circle

so
$(x+2)^2+(y-3)^2=18$
$(x-(-2))^2+(y-3)^2=(\sqrt{18})^2$
$(x-(-2))^2+(y-3)^2=(3\sqrt{2})^2$

the radius is $3\sqrt{2}$
center is (-2,3)

find distance between (8,4) and (-2,3)

$D=\sqrt{(8-(-2))^2+(4-3)^2}$
$D=\sqrt{(8+2)^2+(1)^2}$
$D=\sqrt{10^2+1}$
$D=\sqrt{100+1}$
$D=\sqrt{101}$

$r=3\sqrt{2}$ ≈4.2
$D=\sqrt{101}$ ≈10.04

do r<D

(8,4) is outside the circle

6 0

3 years ago

What is 5/8 to the lowest fraction?

neonofarm [45]

5/8 is the lowest fraction. It can not be simplified anymore

3 0

3 years ago

A submersible traveling at a depth of 250 feet dives at an angle of 15 degrees with respect to a

kipiarov [429]

Answer:

$\boxed{\text{652 ft}}$

Step-by-step explanation:

The submersible is diving at a down angle of 15° along the hypotenuse AC of triangle ABC.

Its horizontal track along the surface AB is 1500 ft.

$\begin{array}{rcl}\tan A & = &\dfrac{BC}{AC}\\\\\tan 15^{\circ} & = & \dfrac{a}{1500}\\\\0.2679 & = & \dfrac{a}{1500}\\\\a & = & 1500 \times 0.2679\\& = & \textbf{402 ft}\\\end{array}$

The submersible was already at a depth of 250 feet when it began the dive.

New depth = 250 + 402 = 652 ft

$\text{The depth after the dive is }\boxed{\textbf{652 ft}}$

6 0

3 years ago

A rectangle is 12m longer than it is wide. Its perimeter is 68m. Write and equation and show steps to find its length and width.

Galina-37 [17]

Answer:

length: 23 m; width: 11 m.

Step-by-step explanation:

The perimeter of a rectangle is twice the sum of its length and width, so that sum is 34 m. Then you can write two equations in length and width:

l + w = 34

l - w = 12

Adding these together gives you ...

2l = 46

l = 23 . . . . . . divide by 2

Then the width is

w = 23 -12 = 11

The length and width are 23 m and 11 m, respectively.

4 0

3 years ago

500000000000 in scientific notation

liraira [26]

5 x 108. The purpose of scientific notation is for scientists to write very large, or very small, numbers with ease.

4 0

3 years ago