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4 years ago

1. What is the value of x? Identify the missing justifications.

Mathematics

1 answer:

Scrat [10]4 years ago

7 0

Answer:

x= 45°

Properties (B).

Angle addition postulate
Subtraction property of Equality

Step-by-step explanation:

Given

mPOR = x + 7,

mSOR =x+3

mPOR + mSOR = mzPOS = 100--------Apply Angle addition postulate

mPOR + m_SOR = m_POS

x+7+x+3=100-------------------------------apply addition property of equality

2x+10=100----------------------------------apply subtraction property of equality

2x=100-10

2x=90----------------------apply division property of equality

2x/2=90/2

x=45°

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Recursive & Explicit Definitions

natali 33 [55]

Answer:

$T_{15} = 9565938$

Step-by-step explanation:

Given

Sequence: 2, 6, 18, 54, 162,

Required

Determine the 15th term

The above sequence is a geometric sequence. So, first, we calculate the common ratio (r)

$r = \frac{T_2}{T_1}$

$r = \frac{6}{2}$

$r = 3$

The 15th term is calculated as thus:

$T_n = ar^{n-1}$

Where

$a = 2$ and $n = 15$

$T_n = 2 * 3^{15-1}$

$T_n = 2 * 3^{14}$

$T_{15} = 2 * 4782969$

$T_{15} = 9565938$

3 0

3 years ago

The height of a cone is two times its base diameter. What is the volume of the cone in terms of its base radius r? V = r2 V = r3

Gnom [1K]

So hmm check the picture below

the radius "r" is half the diameter, meaning, the diameter is 2r long
now, if the height "h" is twice "d" or 2d, then that means h = 2(2r)

thus $\bf \textit{volume of a cone}\\\\
V=\cfrac{\pi r^2 h}{3}\qquad 
\begin{cases}
h=height\\
r=radius\\
------\\
h=2(2r)
\end{cases}\implies V=\cfrac{\pi r^2[2(2r)]}{3}
\\\\\\
V=\cfrac{4\pi r^3}{3}$

8 0

3 years ago

A parabola can be drawn given a focus of ( 6 , − 5 ) (6,−5) and a directrix of y = 1 y=1. Write the equation of the parabola in

Pani-rosa [81]

Answer:

y = -(1/12)(x -6)² -2

Step-by-step explanation:

The vertex of the parabola is halfway between the focus and the directrix, so has y-coordinate (-5+1)/2 = -2. The difference in the y-coordinates between the focus and the vertex is ...

p = -5 -(-2) = -3

An equation of the parabola with vertex (h, k) and focus-vertex distance p can be written:

y = 1/(4p)(x -h)² +k

For (h, k) = (6, -2) and p = -3, the equation is ...

y = (-1/12)(x -6)² -2

4 0

3 years ago

Which of the following represents the solution of the inequality 2x2 + 7x - 45 0?

Stolb23 [73]

Not c I think but I’m not 100%

5 0

3 years ago

Read 2 more answers

Find the radius of a circle with the given circumference. 6√2pi in. r =

Juli2301 [7.4K]

Answer:

r = 3sqrt*2

Step-by-step explanation:

We'll need the formula for the circumference of a circle: C = 2*pi*r

This can be solved for r:

r = -----------

2*pi

Here, with C = 6sqrt(2)*pi,

6sqrt(2)*pi

r = ------------------ = 3sqrt*2

2*pi

7 0

4 years ago