MATHEMATICS HIGH SCHOOL

The circles below are concentricWhat is the measure of the angle formed by the two secants?
What is the value of x?

Answers

Answer 1

Answer:

Given:

Intercepted arcs of small circle:

78° and x°

Intercepted arcs of large circle:

57° and 121°

To find:

The measure of angle formed by two secants and the value of x.

Solution:

Consider a large circle:

The angle made by two secants intersecting outside a circle is half the difference between the measure of intercepted arcs.

$$\Rightarrow \text{ angle} =(1)/(2)(121^\circ-57^\circ)$

$$\Rightarrow \text{ angle} =(1)/(2)(64^\circ)$

$$\Rightarrow \text{ angle} =32^\circ$

The measure of the angle formed by two secants is 32°.

Two circles are concentric circles.

Therefore 32° is also the angle made by small circle arcs.

$$\Rightarrow 32^\circ=(1)/(2)(x^\circ-78^\circ)$

Multiply by 2 on both sides.

$$\Rightarrow 2* 32^\circ= 2* (1)/(2)(x^\circ-78^\circ)$

$$\Rightarrow 64^\circ= x^\circ-78^\circ$

Add 78° on both sides.

$$\Rightarrow 64^\circ+78^\circ= x^\circ-78^\circ+78^\circ$

$$\Rightarrow 142^\circ= x^\circ$

The value of x is 124.

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Anna is watching a space shuttle launch 6 miles from Cape Canaveral in Florida. When the angle of elevation from her viewpoint to the shuttle is 80 degrees, how high is the shuttle if it is going straight up? (Round your answer to the nearest degree.)

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120% of it is 24. What is the number

Answers

Answer:

20

Step-by-step explanation:

1.2x = 24

x = 20

Answer:

20

Step-by-step explanation:

1.2x = 24

x = 20

Step-by-step explanation:

One term of (x+y)^m is 31,824x^18y^11
What is the value of m ?

Answers

Answer: The value of m is 29.

Step-by-step explanation:

Given that, One term of $(x+y)^m$ is $31,824x^(18)y^(11)$ ...(i)

We know that that (r+1)th term in $(a+b)^n$ is given by :-

$T_(r+1)=^nC_ra^(n-r)b^r$ ...(ii)

On comparing (i) with (ii) , we get

$a= x \text{ and } b= y \nn-r =18 \text{ and } r=11\nn=m$

i.e.

$m-r=18\Rightarow\ m-11=18\n\n\Rightarrow\ m=18+11=29$

Hence, the value of m is 29.

Helpppppp. (the other one cut out is multiplication property of equality)

Answers

Answer:

The second step is Distributive Property and the third is Subtraction Property of Equality

Step-by-step explanation:

The 1/2 is being distributed in the second step making the 8x to 4x and the 6 to 3.

The third step involves the subtraction of "x" from the right hand side and the left hand side.

The solution of an equation with two variables X and y is

Answers

Answer:

The solution of an equation with two variables (x and y) is an ordered pair (x, y).

Step-by-step explanation:

Solve for x.
25/60 = 30/x

25

36

50

72

Answers

25/60 = 30/x
x = 30/25 * 60
x = 1800/25
x = 72

So, option D is your answer.

Hope this helps!

Answer:

d

Step-by-step explanation:

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