In the following figure, BA≅CA, and D is on BC

Two cities have the same longitude .The latitude of the city a is 6 degree north and the latitude of city b is 30 degree north. Then the distance between two cities is 1658.844 miles

Two cities have the same longitude. the latitude of the city a is 6 degree north

and the latitude of city b is 30 degree north.

assume the radius of earth is 3960 miles.

find the distance between two cities.

City A = 6°   = 6°× π/180 =  0.1047 rad

City B = 30° = 30° × π /180= 0.5236 rad

multiply by π/180 to convert the degree to radian

radius of Earth = 3960 miles

to find out

distance between City A and City B

solution

we first get here central angle between A and B city is

central angle between A and B city = 0.5236rad - 0.1047 rad

and

now by arc length so  we get distance

distance = 3960 miles × (0.5236 rad - 0.1047rad )   as radius given 3960

distance = 1658.844 miles

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$4051.63 will be in the account after 18 years.

The formula to be used is given as follows :

               A(t) = a ( 1 + r )^t      (1)

 where,  A(t) = future value

                a = principal amount or amount initially deposited.

                r = annual interest rate

                t = time

According to the question we have been given that

             a = $2000

             r = 0.04

             t = 18 years

putting the required values in equation (1) we get

         A(t) = 2000 (1+0.04)^18

         A(t) = 2000 (1.04)^18

         A(t) = 2000*2.03

         A(t) = $4051.63

Thus $4051.63 will be in the account after 18 years.

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The inverse function of f(x) is; f-¹(x) = x³ + 5

To find the inverse of the function;

We should represent f(x) as y.

Now we have;

By taking the cube of both sides;

y³ = x - 5

By solving for x;

x = y³ + 5

By swapping x and y; we have;

y = x³ + 5

f-¹(x) = x³ + 5.

The inverse function of f(x) is; f-¹(x) = x³ + 5.

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A triangle is congruent, and Range of values for x is 5 < x < 29

According to the figure, if L(AB) is less than L(AD), the ∠ACB must be less than the ∠ACD. Take note of how these angles are opposite to the sides stated.

∴ ∠ACB < ∠ACD

⇒2x-10 < 48

At the same time, 2x-10 > 0.

∴ 0< 2x-10 < 48

0+10 < 2x < 48+10 , add 10 to both sides

10 < 2x < 58

10/2 < x < 58/2 , divide 2  by both the side

∴ 5 < x < 29

Range of values for x is 5 < x < 29

Complete question is

Enter the range of values for x:

AB =15, ∠BCA =( 2X-10)°, and AD=18 have angle ∠DCA= 48°

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Answer:

  2√2 -√6

Step-by-step explanation:

You want to know the surd representation of the irrational number that rounds to 0.378937382.

The plural "surds" suggests this is the difference of two irrational roots. Looking at √(n+1) -√n, we find that √3 -√2 is the nearest, but does not match.

Looking at √(n+2) -√n, we find that √8 -√6 matches all 9 digits when rounded to the 9th decimal place. 20 digits of that value are ...

  0.37893738196301199941

The given number approximately matches the irrational value ...

  2√2 -√6

__

Additional comment

We programmed a calculator to find the values of √(n+2) -√n for n = 1..10. The result is attached. The 6th value matches, and corresponds to n=6.

In general, finding a surd representation of an arbitrary value seems to be a matter of trial and error. Perhaps your curriculum materials offer an algorithm.

The following system of equations is solved to find how many minutes of each exercise type she should do now:

In which a is the amount of calories lost per minute running, and b is the amount of calories lost per minute jogging.

A system of equations is when two or more variables are related, and equations are built to find the values of each variable.

For this problem, the variables are given as follows:

She still wants to exercise for 40 min every other day, hence:

x + y = 40.

She wants to burn 460 calories during each session, hence:

ax + by = 460.

In which a is the amount of calories lost per minute running, and b is the amount of calories lost per minute jogging. (the problem is incomplete and I couldn't find it anywhere, hence I am speaking into general terms).

Then the following system of equations is solved to find how many minutes of each exercise type she should do now:

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Answer:

GD.

Step-by-step explanation:

Step-by-step explanation:

the X is always O when we talk about the y intercept and the Y id always O when we talk about the x intercept

Step-by-step explanation:

I can't draw here, but I can tell and explain to you what happens to the points (incl. N).

remember the slope of lines, and what happens when we have to create a perpendicular slope (90°) ?

x and y in the slope ratio y/x go upside down and the sign flips (that means it flips for one of them).

a rotation by 90° follows the same principles.

x and y trade places, and for one of them the sign flips.

the only "difficult" trick is to determine, if the sign of x or of y flips.

let's look at N first.

N = (-5, -4)

the rotation counterclockwise takes it over into the 4th (bottom right) quadrant, where x values are positive.

aha, so the sign of x flips after x and y trade places, and we get

N' = (4, -5)

now for the other points

X = (-3, -2)

the same principle as for N

X' = (2, -3)

B = (-4, 1)

this is now moving from the 2nd (where y values are positive) to the 3rd quadrant (where x and y are negative).

so, again the sign of x flips after x and y trade places

B' = (-1, -4)

with the new coordinates of the points you can now easily draw the new triangle'.

Answer: Sam has 7 quarters and 2 dimes

Step-by-step explanation: If you have 7 quarters you would have $1.75 and with the 2 dimes which make 20 cents more give you $1.95 in total! and every quarter is worth 25 cents multiplied by 7 gave me 175 but in decimal form would 1.75

Hope this helps! :D

Answer: $33

Step-by-step explanation: I've done it before Have a nice day <3

The coordinates of A are (3, 5).

According to the section formula-

If a point (x , y) divides a line in the ratio of m : n, where the two endpoints of the line are (x1, y1) and (x2, y2), then-

x = (nx1 + mx2)/ (m + n)

and y = (ny1 + my2)/ (m + n)

Here, M (4,6) is the midpoint of AB and B is (5,7)

Let the coordinates of A be (x2, y2)

Therefore,

x1 = 5, y1 = 7

x = 4, y = 6

Since, midpoint divides a line segment into two equal halves, m : n = 1 : 1

Now, substituting the values in the section formula we get-

4 = (5 + x2)/2

4 × 2 = 5 + x2

8 = 5 + x2

5 + x2 = 8

x2 = 8 - 5

x2 = 3

and 6 = (7 + y2)/2

6 × 2 = 7 + y2

12 = 7 + y2

7 + y2 = 12

y2 = 12 - 7

y2 = 5

Thus, the coordinates of A are (3, 5).

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The area of a rectangular patio with the dimensions of 18-3/4 feet and 12 feet will be determined by using the formula for the area of rectangle.

Area of rectangle is calculated by multiplying the length of the rectangle to the width of the rectangle. i.e.,

Area of rectangle= Length*Width

In the given situation,

Length= 18-3/4feet

Width=12 feet.

1. Convert the value of length to improper fraction:

18-3/4=75/4

2. Multiply the length and width to find the area:

Area=(75/4)x12

Solving the expression:

3. Area=75x3=225 sq. feet

The area of a 18-3/4 feet and 12 feet rectangular patio is 225 sq. feet.

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If the expression is log₄5 x,then the expansion of this will look like

(log 5+ log x)/log 4.

Given that the expression is log₄5 x.

We are required to find the expansion of the expression.

Base change theorem says that [tex]log_{a}b[/tex]=[tex]log_{x}b/log_{x}a[/tex]. We use the change of base formula to re-write a logarithm operation as a fraction of logarithms with a new base.

The expression is log₄5 x.

log₄5 x=(log 5+log x)/log 4

(We know that [tex]log_{a}b[/tex]= log b/ log a and log mn =log m +log n)

Hence if the expression is log₄5 x then the expansion of this will look like (log 5+ log x)/log 4.

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Answer:

The answer is 7

Step-by-step explanation:

The formula is y=mx+b so m=10 and b=7

Answer:

Hope this helps :)

The y-intercept is 7.

Step-by-step explanation:

This is because the in the slope-intercept form, y = mx + b, so the b in this case is 7.

Kyra wants the total length of the tree to the nearest inch it will be 193.68 inches.

The measurement couldn't have been added earlier because they're in different units

Kyra measures 4 feet. This in centimeters will be:

= 4 × 30.48 = 121.92 cm

Tai measures 3.5 yards. This in centimeters will be:

= 91.44 × 3.5

= 320.04 cm

Rodney measures 50 centimeters.

Therefore, the addition will be:

= 121.92 cm + 320.04 cm + 50cm

= 491.96 cm

The total length in inches will be:

1 inch = 24 cm

= 491.96 / 2.54

= 193.68 inches.

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Statements 2, 4 and 5 are true.

Let us check each statement one by one-

1. The square root of a positive number cannot be negative-

This statement is false. Let us take an example. If we take a number, say 4, 4 has 2 square roots- 2 and -2. This is because 2 × 2 = -2 × -2 = 4. Thus, the square root of a positive number can be negative.

2. All positive numbers have two square roots.

This statement is true. It follows from the example in 1 that any positive number has 2 square roots- one negative and one positive.

3. √18 = 9 because 9(2) = 18

The given statement is false. √18 ≠ 9. If √18 was equal to 9, then 9 × 9 must be 18. But 9 × 9 is 81. Hence, false.

4. √49 = 7 because 7(7) = 49

The given statement is true. √49 = 7 as 7 × 7 = 49

5. √25 = 5 because 5²= 25

The given statement is true. √25 = 5 as 5 × 5 = 25

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Answer:

y = x − 6

Step-by-step explanation:

Find slope: (y2-y1)/(x2-x1)

(6-3)/(1-0) = 3/1 = 3

Y = 3x + b, plug in point

3 = 3(0) + b, b = 3

Equation: y = 3x + 3

The slope intercept form of the equation of a line is:

y

=

m

x

+

b

where m is the slope and b is the value of y when x is 0.

We are given that the slope is 1 and the given point shows us that y is -6 when x is 0. Therefore, the equation of the line is:

y = x - 6

Answer:

[tex]x^2-8x+12[/tex]

Step-by-step explanation:

Knowing both intercepts we can write the equation in factored form:

[tex](x-2)(x-6)[/tex]

Now use distributive property to find the equation in standard form:

[tex](x-2)(x-6)\\x^2-6x-2x+12\\x^2-8x+12[/tex]

Answer: 38 and 24

Step-by-step explanation:

38 and 24

The odds in favor of selecting an ace then a face card is 3/52.

Probability is used to determine the odds in favor of an event happening. The odds in favor of an event happening lies between 0 and 1. The greater the odds in favor of the event happening, the closer to one, the probability value would be. In a deck of cards, there are 13 aces and there are 12 face cards

The odds in favor of selecting an ace then a face card = (number of ace cards / total number of cards) x (number of face cards / total number of cards)

(13 / 52) x (12 / 52)

1/4 x 3/13 = 3/52

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Answer: 7a

Step-by-step explanation:

Step-by-step explanation:

do sum of 3a and 4a your answer will be 7a

Answer:

x = 9

Step-by-step explanation:

Rearrange

[tex]\sf \rightarrow x^3 - 729 = 0[/tex]

Factor using (a-b) × (a^2 +ab +b^2)

a^3 + a^2b + ab^2 - ba^2 - b^2a - b^3 =

           a^3 + (a^2b-ba^2) + (ab^2-b^2a) - b^3 =

           a^3 + 0 + 0 - b^3 =

           a^3 - b^3

x^3 = x^1

Rearrange(Using polynomial/cube roots)

(x - 9) × (x2 + 9x + 81)  = 0

Subtract/Add

x - 9 = 0 = 9

x^2 + 9x = -81

-81 + 81/4

-243/4

x^2 + 9x + (81/4) = -243/4

(x + (9/2)) × (x + (9/2)) = (x + (9/2)) × 2

(x + (9/2))2 = -243/4

x^2 + 9x + 81 = 0

√243 = 3 × 3 × 3 × 3 × 3 = 3 × 3 × √3 = ±9 × √3

= ±9x  =  (-9 ± 9 × 1.732(i)) / 2

= ±9x

Divide by 9 (Absolute value: positive)

|9/9| = x

Reverse, re-arranging x (Assuming x = 1)

x = |9/x|

Thus,

x = 9

Hope this helped, let me know if anything confuses you, and I will try my best to address that. Have a good day!

Answer: The dimensions are 8 and 28

as i said i would go with 93-51=42

Step-by-step explanation:

8.7*10.6=92.22 and 8.7*10+6=93

4.8*10.3=49.44 and 4.8*10+3=51

so i am thinking that you would add 93+51 which equals 144...

or you could try 93*51 but your gunna get 4,743

or try 93-51 which is 42

or try 93 diveded by 51 which is 1.8235294117647058

I would go with 93-51=42!

if you really liked this answer, please rate thanks and award brainliest

hope this helped :)

The x-intercept will be 5 , y-intercept will be 4 and the coordinate will be (x , y) = (5 , 4).

What is an intercept ?

An intercept is a location on the y-axis where the line's slope passes. It is the y-coordinate of the location where a line or curve crosses the y-axis.

It is given that we have to find out the x and y intercepts from the given graph.

We know that , a function's x-intercept is the value of x at the point where the graph crosses the horizontal axis, or when y = 0. As a result, while examining the function's graph, we find out that the x-intercept is equal to 5.

Similarly , The value of y when the graph crosses the vertical axis, or the value of y when x = 0, is the y-intercept of a function. As a result, while examining the function's graph, we find out that the y-intercept is equal to 4.

So , the coordinate will be (x , y) = (5 , 4).

Therefore , the x-intercept will be 5 , y-intercept will be 4 and the coordinate will be (x , y) = (5 , 4).

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The minimum firing time for a stable orbit 300km above Earth is 25 seconds.

An orbit, in the context of celestial mechanics, is the curved path taken by an object, such as the trajectory of a planet around a star, a natural satellite around a planet, or an artificial satellite around an object or place in space, such as a planet, moon, asteroid, or Lagrange point.

Ordinarily, the term "orbit" denotes a trajectory that repeats itself on a regular basis, though it can also denote a non-repeating trajectory. Kepler's rules of planetary motion roughly describe the elliptic orbits that planets and satellites take, with the center of mass orbiting at a focal point of the ellipse.

We know that to achieve stable orbit 300 km above earth, the velocity must be ≈ 7.7 km/s

We will use the given formula

              v = -0.0098 t+c ln R

Here given that c = 2.5 km/s

                          R = 24

Apply the information in the equation we get,

7.7 = -0.0098t + 2.5  In  24

we can also write

t = [tex]\frac{7.7 - 2.5 In 24}{-0.0098}[/tex]  

 = [tex]\frac{7.7 - 7.945}{-0.0098}[/tex]

 = 25s

Hence, the minimum firing time for a stable orbit 300km above Earth is 25 seconds

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Answer:

= 4.875 × 105

(scientific notation)

= 4.875e5

(scientific e notation)

= 487.5 × 103

(engineering notation)

(thousand; prefix kilo- (k))

Step-by-step explanation:

hope this helps

Step-by-step explanation:

or, y° + 40° + y + 30° = 180 [Sum of angle of a triangle]

or, 2y°+ 70° = 180°

or, 2y° = 180° - 70°

or, y = 110°/2°

or. y = 55°

Therefore the value of y is 55°