If the radius of the planet is given by R, and the height above the surface is given by h, use the figure below, and the Pythagorean Theorem to derive the formula for the distance, d, to the horizon tangent point, assuming that the triangle is a right triangle.

Please answer the second one too

The center of the circle is (7,8) and the equation of the given circle is (x- 7)^2 + (y - 8)^2 = 16

The given parameters are:

Center (a,b) = (7,8)

Point (x,y) = (11,8)

Calculate the radius (r) using:

[tex]r = \sqrt{(x- a)^2 + (y - b)^2}[/tex]

So, we have:

[tex]r= \sqrt{(11- 7)^2 + (8 - 8)^2}[/tex]

Evaluate the expression

[tex]r = 4[/tex]

The circle equation is then calculated using:

[tex](x- a)^2 + (y - b)^2 =r^2[/tex]

So, we have:

[tex](x- 7)^2 + (y - 8)^2 = 4^2[/tex]

Evaluate the exponent

[tex](x- 7)^2 + (y - 8)^2 = 16[/tex]

Hence, the equation of the given circle is (x- 7)^2 + (y - 8)^2 = 16

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Answer:

b=20°, c=160°

Step-by-step explanation:

b=20° [vertically opposite angle]

c+b=180° [angle at same line ]

c=180° - 20°

c = 160°

Equations are expressions separated by equal sign. The value of x that make the expression equal is 2

Given the equation expressed as:

3^2x = 9^3x - 4

This can be further simplified as:

3^2x = 3^2(3x-4)

2x = 2(3x - 4)

x = 3x - 4

x - 3x = -4
-2x = -4

x = 2

Hence the value of x that make the expression equal is 2

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Answer: its 2

Step-by-step explanation: just took test on chrome 2022, and got 100%

Answer:

Step-by-step explanation:

The interquartile range = Third quartile - First quartile = 22 - 15 = 7

The range = 25 - 12 = 13

Range = largest data value - the least data value

Interquartile range = Q3 - Q1

Given the following weekly allowance of Sean's classmates as, 15, 15, 22, 14, 12, 24, 16, 25, 15, 15:

Third quartile (Q3) = 22

First quartile (Q1) = 15

Interquartile range = 22 - 15 = 7

Range = 25 - 12 = 13

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Answer:

80

Step-by-step explanation:

profit = revenue - expenses

revenue = $15 per hour = $15 * number of hours (n) = $15 * n

expenses = $490 + $45 + $65 = $600

we want profit to be 600 or more

15 * n - 600 = profit

profit ≥ 600

15 * n - 600 ≥ 600

add 600 to both sides to isolate the variable and its coefficient

15 * n ≥ 1200

divide both sides by 15 to isolate the variable

n ≥ 80

Jose must therefore work 80 or more hours, for a minimum of 80

Answer:eht sistep 2 and step 4 is the correct answer

Step-by-step explanation:

Answer:

the answer is (b), because

Step-by-step explanation:

rise over run

Answer:

B

because I

saw someone else say it was b

Step-by-step explanation:

I'm smart

Answer: 48

Step-by-step explanation:

Answer:

(2,5)

Step-by-step explanation:

-3+5=2 and 4+1=5

Answer:

w ≤ 5

Step-by-step explanation:

-2w ≥ -10

-2w / -2 ≥ -10 / -2

The -2 cancels each other out and -10 divided by -2 is 5. When divding an inequality by a negative number you MUST flip the sign.

w ≤ 5

Answer:

See below

Step-by-step explanation:

[tex]1.\:\:\overline{BD}||\overline{AE}[/tex]

(By Midsegment theorem)

[tex]2.\:\:m\angle 1=48\degree\implies m\angle 4=48\degree [/tex]

([tex]\angle 1\: \&\:\angle 4[/tex] are alternate angles)

[tex]3.\:\:m\angle 3=25\degree\implies m\angle 2=25\degree [/tex]

([tex]\angle 2\: \&\:\angle 3[/tex] are vertical angles)

[tex]4.\:\:\overline {AE}=17\: cm\implies BD = 8.5\: cm [/tex]

(By midsegment theorem: [tex]BD=\frac{1}{2}AE[/tex]

[tex]5.\:\: BD=\frac{1}{2}AE\\\\\implies (3x+10)=\frac{1}{2}\times (12x+2)\\\\\implies 2(3x +10) = 12x+2\\\\\implies 6x +20= 12x+2\\\\\implies 6x - 12x = 2-20\\\\\implies -6x =-18\\\\\implies x =\frac{-18}{-6}\\\\\implies x = 3\\\\\implies \overline{BD}= (3\times 3 + 10)\\\\=(9+10)\\\\\implies \overline{BD}= (9 + 10)\\\\\implies \huge{\purple{\overline{BD}=19}}[/tex]

Geometric series have the same ratio. The series which is a geometric series is 1, 3, 9, 27.

A series of numbers is a geometric series if the quotient of any two consecutive numbers is the same.

A series of numbers is a geometric series if the quotient of any two consecutive numbers is the same.

A.) 0.1 0.3 0.5 0.7

To check if the series is geometric series, find the quotient.

[tex]r_1=\dfrac{0.3}{0.1} = 3\\\\r_2 = \dfrac{0.5}{0.3} = 1.66[/tex]

Since the ratio is different this is not a geometric series.

B.) 1 3 9 27

To check if the series is geometric series, find the quotient.

[tex]r_1=\dfrac{3}{1} = 3\\\\r_2 = \dfrac{9}{3} = 3[/tex]

Since the ratio is the same this is a geometric series.

C.) 19 17 15 13

To check if the series is geometric series, find the quotient.

[tex]r_1=\dfrac{17}{19} = 0.8947\\\\r_2 = \dfrac{15}{17} = 0.8823[/tex]

Since the ratio is different this is not a geometric series.

D.) 0.4 0.9 1.5 2.2

To check if the series is geometric series, find the quotient.

[tex]r_1=\dfrac{0.4}{0.9} = 0.4444\\\\r_2 = \dfrac{0.9}{1.5} = 0.6[/tex]

Since the ratio is different this is not a geometric series.

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Answer:

its b 1 + 3 + 9 + 27

Step-by-step explanation:

Answer:

slope = 3/2

the plant grows 3 centimeters every 2 weeks

Step-by-step explanation:

Answer:

9 in.

Step-by-step explanation:

a^2 + 5.6^2 = 10.6^2

a^2 + 31.36 = 112.36

Subtract 31.36 from both sides

a^2 = 81

Squart Root both sides

a = 9 inches

Answer:

a = 11.9883 in

Step-by-step explanation:

Sides:

a = 5.6 in

b = 11.9883 in

c = 10.6 in

Angles:

A = 27.8476 °

B = 90 °

C = 62.1524 °

Other:

P = 28.1883 in

s = 14.0942 in

K = 29.68 in2

r = 2.10584 in

R = 5.99416 in

SAS is Side, Angle, Side

Given the size of 2 sides (c and a) and the size of the angle B that is in between those 2 sides, you can calculate the sizes of the remaining 1 side and 2 angles. Use The Law of Cosines to solve the remaining side.

Law of Cosines

If a, b and c are the lengths of the legs of a triangle opposite to the angles A, B and C respectively; then the law of cosines states:

a^2 = c^2 + b^2 - 2bc cos A,   solving for cos A,   cos A = ( b^2 + c^2 - a^2 ) / 2bc

b^2 = a^2 + c^2 - 2ca cos B,   solving for cos B,   cos B = ( c^2 + a^2 - b^2 ) / 2ca

c^2 = b^2 + a^2 - 2ab cos C,   solving for cos C,   cos C = ( a^2 + b^2 - c^2 ) / 2ab

Solving, for example, for an angle, A = cos^-1 [ ( b^2 + c^2 - a^2 ) / 2bc ]

The statement which is true about the function is the range of the function is all real numbers less than or equal to 9.​

The Domain of a function is the set of all the possible input values which are valid for that function.

Range of a function is the set of all the possible output values which are valid for that function.

The function shown in the graph can be given as,

[tex]f(x)=-x^2-4x+5[/tex]

The one coordinate point of this equation is -2, 9, which is shown in the graph. At the value of x as -2, the value of f(x) is 9,

[tex]f(-2)=-(-2)^2-4(-2)+5\\f(-2)=-4+8+5\\f(-2)=9[/tex]

Here, the input value is -2 and the output value is 9. The domain for this function is all real number, but the range of this function is (-∞,9).

Hence, the statement which is true about the function is the range of the function is all real numbers less than or equal to 9.​

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Answer:

its literally D bro on edge

Step-by-step explanation:

DDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDD

Answer:

10/12 is greater and for the second one, 4/11 is greater and 5/8 is greater

Answer:

13/20

Step-by-step explanation:

Note that:
Difference is the same meaning as subtract.

Given:

1 ¼ - ⅗

We first have to change 1 ¼ into a improper fraction:

1 ¼ = 5/4

5/4 - ⅗

Since the denominator are different we have to find common denominator.

25/20 - 12/20

Subtracting: 25 - 12 = 13

13/20

Hence, the different of these fractions is 13/20

Kavinsky

Answer:

a. +34 b. +46 c. +45 d. +31

Step-by-step explanation: use a number line

Answer:

the height is 5 and the base is 17.

Step-by-step explanation:

X + 1 is the height and 4x + 1 is the base, so we can substitute this into an equation:

( x + 1 ) (4x + 1) = 85

{apply the distributive law}

4x² + x + 4x + 1 =

4x² + 5x + 1 = 85

Take 85 to the other side by -85 each side:

4x² + 5x + 1 - 85 = 85 - 85

4x² + 5x - 84 = 0

{Now we have a quadratic equation}

The roots are either -5.25 or 4. X must be 4 since it must be positive as it is a side length.

Substitute x into the base and height to get the answers.

X + 1 = 4 + 1 = 5

4x + 1 = 16 + 1 = 17

Therefore the height is 5 and the base is 17.

1/8 is in it 3/2 if that is it

Answer:

(A) mK = 37° and n = 31.

Step-by-step explanation:

The following are A of ed.

The equation of a hyperbola with directrices at x = ±2 and foci at (6, 0) and (−6, 0) is y squared over 48 minus x squared over 12 equals 1.

The equation of the hyperbola is the equation which is used to represent the hyperbola in the algebraic equation form, with the value of center point in the coordinate plane and foci.

The standard form of the equation of the hyperbola can be given as,

[tex]\dfrac{(y-k)^2}{b^2}-\dfrac{(x-h)^2}{a^2}=r^2[/tex]

Here (h,k) is the center of the hyperbola, (b) is the transverse axis, and (a) is the conjugate axis.

The foci of the hyperbola is,

[tex](h,k\pm c)[/tex]

The directrix is,

[tex]y=k\pm \dfrac{a^2}{c}[/tex]

A hyperbola is given with directrices at x = ±2 and foci at (6, 0) and (−6, 0). Thus, the directrix is,

[tex]y=k\pm \dfrac{a^2}{c}\\\pm 2=k\pm \dfrac{a^2}{c}\\\dfrac{a^2}{6}=2\\a^2=12\\[/tex]

It is known that,

[tex]a^2+b^2=c^2\\[/tex]

Put the value of a and c,

[tex](12)+b^2=6^2\\b^2=36-12\\b^2=24[/tex]

The value of center is (0,0). Thus, the equation of hyperbola is,

[tex]\dfrac{(y-0)^2}{24^2}-\dfrac{(x-0)^2}{12^2}=1\\\dfrac{y^2}{24^2}-\dfrac{x^2}{12^2}=1[/tex]

Thus, the equation of a hyperbola with directrices at x = ±2 and foci at (6, 0) and (−6, 0) is y squared over 48 minus x squared over 12 equals 1.

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Answer:

m=1

Step-by-step explanation:

y2-y1/x2-x1

-4+3/-4+3

-1/-1

1

Answer:40

Step-by-step explanation:

Your correct and final answer for this question is 40

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