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adelina 88 [10]

3 years ago

9

Given circle X with radius 10 units and chord AB with length 12 units, what is the length of segment CX, which bisects the chord

? A. 10 units B. 8 units C. 6 units D. 16 units

1 answer:

andrew-mc [135]3 years ago

7 0

Consider the circle with center X, as shown in the figure.

Draw the diameter of the circle which is parallel to cherd AB, as shown in the figure.

Since the diameter and AB are parallel, then the line segment XC which bisects AB at C, will be perpendicular to AB.

SO triangle XCB is a right triangle. Thus the length of CX, by the Pythagorean theorem is

$\sqrt{ XB^{2}- CB^{2}} = \sqrt{ 10^{2}- CB^{6}}= \sqrt{100-36}= \sqrt{64}=8$ units.

Answer: 8 units

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Which is the solution set of the inequality<br> -15y+9<-36

liraira [26]

Answer:

$-15y+93\:\\ \:\mathrm{Interval\:Notation:}&\:\left(3,\:\infty \:\right)\end{bmatrix}$

Therefore, the first choice is correct.

The graph of the inequality is also attached below.

Step-by-step explanation:

Considering the inequality

$-15y+9$

solving

$-15y+9$

$\mathrm{Subtract\:}9\mathrm{\:from\:both\:sides}$

$-15y+9-9$

$-15y$

$\mathrm{Multiply\:both\:sides\:by\:-1\:\left(reverse\:the\:inequality\right)}$

$\left(-15y\right)\left(-1\right)>\left(-45\right)\left(-1\right)$

$15y>45$

$\mathrm{Divide\:both\:sides\:by\:}15$

$\frac{15y}{15}>\frac{45}{15}$

$y>3$

In other words,

$-15y+93\:\\ \:\mathrm{Interval\:Notation:}&\:\left(3,\:\infty \:\right)\end{bmatrix}$

Therefore, the first choice is correct.

The graph of the inequality is also attached below.

6 0

3 years ago

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Anon25 [30]

Trapezoid, plot the points down on a graph

8 0

3 years ago

Driving 25 miles total. Already driven 11 miles. What fraction of the way have we driven?

-BARSIC- [3]

Answer:25-11=14 so the fraction would be 11/25

Step-by-step explanation:

25-11=14

11/25 miles

7 0

3 years ago

Read 2 more answers

A space telescope on a mountaintop is housed inside of a cylindrical building with a hemispheric dome. If the circumference of t

Vlad1618 [11]

Answer:

$185553.7\text{ feet}^3$

Step-by-step explanation:

GIVEN: A space telescope on a mountaintop is housed inside of a cylindrical building with a hemispheric dome. If the circumference of the dome is $84\text{ feet}$ , and the total height of the building up to the top of the dome is $91\text{ feet}$ .

TO FIND: what is the approximate total volume of the building.

SOLUTION:

let the height of the mountaintop be $h\text{ feet}$

As the dome hemispherical.

circumference of a hemisphere $=\frac{1}{2}\times2\pi\times radius$

$=\pi\times radius$

$\frac{22}{7}\times radius=84$

$radius=26.75\text{ feet}$

total height of the building up to the top of the dome $=\text{radius of hemisphere}+\text{height of mountaintop}$

$=26.75+h=91$

$h=64.25\text{ feet}$

Volume of building $=\text{volume of cylindrical mountaintop}+\text{volume of dome}$

$=\pi(radius)^2h+\frac{2}{3}\pi(radius)^3$

as radius of mountain top is same as dome

putting values

$=3.14(26.75)^264.75+\frac{2}{3}3.14(26.75)^3$

$=145484.6+40069.1$

$185553.7\text{ feet}^3$

Hence the total volume of the building is $185553.7\text{ feet}^3$

5 0

3 years ago

What is the equation of the following graph?

nignag [31]

Answer:

${y}^{2} = 24x$

Step-by-step explanation:

This is horizontal parabola.

It has a directrix at x=-6.

The vertex is (0,0).

The focus is (6,0)

The equation of this parabola is of the form

${y}^{2} = 4px$

Where (p,0) is the focus

By comparison, p=6

Therefore the equation of the parabola is

${y}^{2} = 4 \times 6x$

This implies that

${y}^{2} =2 4 x$

6 0

3 years ago