In the underlined section, what do the colonists promise to do?

Answer:

For F=GMm/r^2

[tex]F = \frac{GMm}{r^{2} }[/tex]

a. [tex]M = \frac{Fr^{2} }{Gm}[/tex]

b. [tex]r = \sqrt{\frac{GMm}{F}}[/tex]

M=kxa^3/p^2

[tex]M = \frac{kxa^{3} }{p^{2} }[/tex]

a. [tex]p = \sqrt{\frac{kxa^{3} }{M}}[/tex]

b. [tex]a = \sqrt[3]{\frac{Mp^{2} }{kx}}[/tex]

Step-by-step explanation:

To solve for the unknown quantity, we will make the unknown quantity the subject of the given equation.

For F=GMm/r^2

a. M =

F=GMm/r^2

[tex]F = \frac{GMm}{r^{2} }[/tex]

The first thing to do is cross multiply, so that the equation gives

[tex]Fr^{2} = GMm[/tex]

Now, divide both sides of the equation by [tex]Gm[/tex], we then get

[tex]\frac{Fr^{2} }{Gm} = \frac{GMm}{Gm}[/tex]

Then, [tex]\frac{Fr^{2} }{Gm} = M[/tex]

Hence,

[tex]M = \frac{Fr^{2} }{Gm}[/tex]

b. r =

F=GMm/r^2

[tex]F = \frac{GMm}{r^{2} }[/tex]

Likewise, we will first cross multiply, we then get

[tex]Fr^{2} = GMm[/tex]

Now, divide both sides by [tex]F[/tex], so that the equation becomes

[tex]\frac{Fr^{2} }{F} = \frac{GMm}{F} \\[/tex]

∴ [tex]r^{2} = \frac{GMm}{F} \\[/tex]

Then,

[tex]r = \sqrt{\frac{GMm}{F}}[/tex]

For M=kxa^3/p^2

a. P =

M=kxa^3/p^2

[tex]M = \frac{kxa^{3} }{p^{2} }[/tex]

The first thing to do is cross multiply, so that the equation becomes

[tex]Mp^{2} = kxa^{3} \\[/tex]

Now, divide both sides by M, we then get

[tex]\frac{Mp^{2} }{M} = \frac{kxa^{3} }{M}[/tex]

∴ [tex]p^{2} = \frac{kxa^{3} }{M}[/tex]

Then,

[tex]p = \sqrt{\frac{kxa^{3} }{M}}[/tex]

b. a =

M=kxa^3/p^2

[tex]M = \frac{kxa^{3} }{p^{2} }[/tex]

Also, we will first cross multiply to get

[tex]Mp^{2} = kxa^{3} \\[/tex]

Then, divide both sides of the equation by [tex]kx[/tex] to get

[tex]\frac{Mp^{2} }{kx}= \frac{kxa^{3} }{kx}\\[/tex]

[tex]\frac{Mp^{2} }{kx}= a^{3}[/tex]

∴ [tex]a^{3} = \frac{Mp^{2} }{kx}[/tex]

Then,

[tex]a = \sqrt[3]{\frac{Mp^{2} }{kx}}[/tex]

Answer:

⅓y

Step-by-step explanation:

[tex] \frac{1}{3} \times y \\ = \frac{1}{3} y[/tex]

Step-by-step explanation:

Hey, there!!

It's so simple, you just use the formula as given and put the values in it.

Radius of a circle (r) = 13 cm.

pi= 3.14

Now,

Circumference = 2× pi × r

= (2× 3.14 × 13) cm

= 81.64 cm

Therefore, the answer is 82 cm.

Hope it helps..

Answer:

The answer = 82 cm.

Step-by-step explanation:

By using the formula,

C=2×3.14×13

C= 81.64

then,

The nearest hundredth = 82 cm.

Answer: Maximum of 5 days

Step-by-step explanation: To find that conclusion, you subtract the "610" from "1,800" getting "1,190". But to find the amount of days you would need to divide "1,190" by "238" to get your 5 days.

An equation is formed of two equal expressions. The maximum number of days Wayne can stay at a resort within his budget is 5.

An equation is formed when two equal expressions are equated together with the help of an equal sign '='.

Given that Wayne's budget for the vacation is $1,800. Therefore, the total amount spent by Wayne during the vacation should be equal to his budget.

Also, it is given that the airfare for the vacation is $610. also, the cost of staying in a hotel for a day is $238. Therefore, the expression for x days staying can be written as,

Total cost = $610 + $238(x days)

Since the total cost or expenses should be equal to the budget, therefore, we can write,

Total cost = budget

610 + 238x = 1800

238x = 1800 - 610

238x = 1190

x = 1190 / 238

x = 5

Hence, the maximum number of days Wayne can stay at a resort within his budget is 5.

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14

(a + b)² = a² + 2ab + b²

x² + _x + 49

a = x

b = 7

2ab = 2×x×7 = 14x => 2b = 14

Answer:

[tex]\Huge \boxed{\mathrm{14}}[/tex]

[tex]\rule[225]{225}{2}[/tex]

Step-by-step explanation:

Square of a sum formula:

[tex](a + b)^2 = a^2 + 2ab + b^2[/tex]

x² + ___ x + 49

The value of a is x.

The value of b is 7, since 7² = 49.

[tex]x^2 +2(x)(7)+7^2[/tex]

[tex]x^2 +14x+49[/tex]

The missing coefficient is 14.

[tex]\rule[225]{225}{2}[/tex]

Step-by-step explanation:

[tex] \frac{1}{4} \boxed{?} \frac{3}{8} \\ \\ \frac{1}{4} = \frac{2}{8} \\ \\ \because \: 2 < 3 \\ \therefore \: \frac{1}{4} \boxed{ < } \frac{3}{8} [/tex]

Answer:

[tex]\Huge \boxed{\mathrm{16 \ marbles}}[/tex]

Step-by-step explanation:

Let the number of marbles that Charlotte has be x.

Let the number of marbles that Vinny has be y.

[tex]x+y=20[/tex]

[tex]x=4y[/tex]

Substitute for x.

[tex]4y+y=20[/tex]

Combine like terms.

[tex]5y=20[/tex]

Divide both sides by 5.

[tex]y=4[/tex]

Vinny has 4 marbles.

Let y = 4.

[tex]x=4(4) \\ \\ \\ x=16[/tex]

Charlotte has 16 marbles.

Answer:

x+y=20

x=4yx=4y

Substitute the given equation for x.

4y+y=20

4y+y=20

Collect all like terms.

5y=20

Divide both sides by 5.

y=4y=4

Vinny has 4 marbles.

Let y = 4.

x=4(4)

x=16

Answer: B

Step-by-step explanation:

To find the inverse function, you switch x with y and y with x. Then, you solve for y.

[tex]y=(x-1)^{2} -4[/tex]                                  [switch x with y, and y with x]                        

[tex]x=(y-1)^2-4[/tex]                                  [add both sides by 4]

[tex]x+4=(y-1)^2[/tex]                                  [square root both sides]

[tex]\sqrt{x+4} =y-1[/tex]                                    [add both sides by 1]

[tex]\sqrt{x+4} +1=y[/tex]

[tex]f^-^1(x)=1+\sqrt{x+4}[/tex]

Now that we know the inverse function, we can actually tell that the answer is B. We know this because of the restriction that f(x) is x≤1. This makes it positive, and B the answer.

Answer:

a.  [tex]P(Both) = \frac{1}{60}[/tex]

b.   [tex]P(None) = \frac{3}{4}[/tex]

c.  [tex]P(At least 1) = \frac{1}{4}[/tex]

Step-by-step explanation:

Given

A fair 6-sided die

A fair 10-sided die

Both have an ace side

For the 6-sided die;

Probability of landing on Ace: P(A)

[tex]P(A) = \frac{1}{6}[/tex]

Probability of not landing on Ace: P(A')

[tex]P(A') = \frac{5}{6}[/tex]

For the 10-sided die;

Probability of landing on Ace: P(B)

[tex]P(B) = \frac{1}{10}[/tex]

Probability of not landing on Ace: P(B')

[tex]P(B') = \frac{9}{10}[/tex]

Solving (a): Both landing on Ace

This is calculated as thus;

[tex]P(Both) = P(A) * P(B)[/tex]

[tex]P(Both) = \frac{1}{6} * \frac{1}{10}[/tex]

[tex]P(Both) = \frac{1}{60}[/tex]

Solving (b): None landing on Ace

This is calculated as thus;

[tex]P(None) = P(A') * P(B')[/tex]

[tex]P(None) = \frac{5}{6} * \frac{9}{10}[/tex]

[tex]P(None) = \frac{1}{6} * \frac{9}{2}[/tex]

[tex]P(None) = \frac{1}{2} * \frac{3}{2}[/tex]

[tex]P(None) = \frac{3}{4}[/tex]

Solving (c): At least one landing on Ace

This is calculated as thus;

[tex]P(At least 1) = 1 - P(None)[/tex]

[tex]P(At least 1) = 1 - \frac{3}{4}[/tex]

[tex]P(At least 1) = \frac{4 - 3}{4}[/tex]

[tex]P(At least 1) = \frac{1}{4}[/tex]

The required probabilities are,

(a):[tex]P(A)=\frac{1}{60}[/tex]

(b):[tex]P(B)=\frac{3}{4}[/tex]

(c):[tex]P(C)=\frac{59}{60}[/tex]

Given that the die having the 6 sides.

The formula for finding the expected probability is,

[tex]P(A)=\frac{m}{n}[/tex]

Where m= Number of expected observation

n= Number of total observation

Part(a):

P(Both landed on ace) is,

[tex]P(A)=\frac{1}{6} \times\frac{1}{10} \\=\frac{1}{60}[/tex]

Part(b):

P(Neither landed on ace) is,

[tex]P(B)=[1-\frac{1}{6} ][1-\frac{1}{10} ]\\=\frac{3}{4}[/tex]

Part(c):

P(At least one not land on ace) = 1 - P(Both landed on ace)

[tex]1-\frac{1}{60} =\frac{59}{60}[/tex]

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Answer:

the value of M angle 3 is 70° and M angle 1 is (90-70)=20° and angle 3 - angle 1 is 70° - 20° is 50°

Answer:

x<6/5, x>14/5

Step-by-step explanation:

Steps

$5\left|x-2\right|+4>8$

$\mathrm{Subtract\:}4\mathrm{\:from\:both\:sides}$

$5\left|x-2\right|+4-4>8-4$

$\mathrm{Simplify}$

$5\left|x-2\right|>4$

$\mathrm{Divide\:both\:sides\:by\:}5$

$\frac{5\left|x-2\right|}{5}>\frac{4}{5}$

$\mathrm{Simplify}$

$\left|x-2\right|>\frac{4}{5}$

$\mathrm{Apply\:absolute\:rule}:\quad\mathrm{If}\:|u|\:>\:a,\:a>0\:\mathrm{then}\:u\:<\:-a\:\quad\mathrm{or}\quad\:u\:>\:a$

$x-2<-\frac{4}{5}\quad\mathrm{or}\quad\:x-2>\frac{4}{5}$

Show Steps

$x-2<-\frac{4}{5}\quad:\quad x<\frac{6}{5}$

Show Steps

$x-2>\frac{4}{5}\quad:\quad x>\frac{14}{5}$

$\mathrm{Combine\:the\:intervals}$

$x<\frac{6}{5}\quad\mathrm{or}\quad\:x>\frac{14}{5}$

Answer:

Option C

Step-by-step explanation:

There should be no difference ($0). This is  true about a balanced budget. Therefore, the correct option is option C among all the given options.

When your expenses are equivalent or lower than to your income, you have a balanced budget. In other words, your ability to live within your means will be shown by a balanced budget.

Any period during that a budget is not in deficit is sometimes referred to as a balanced budget. In other words, your budget is balanced if it is at a profit and has income left over. There should be no difference ($0). This is  true about a balanced budget.

Therefore, the correct option is option C among all the given options.

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Answer:

C=0,10E+5

Step-by-step explanation:

La respuesta es que la expresión que indica el costo mensual "C" en función de la energía "E" consumida es:

C=0,10E+5

Esto teniendo en cuenta que se indica que hay una tarifa fija de $5 por mes y que a esto se debe sumar el resultado de multiplicar la energía consumida por el valor del kilowatt-hora.

Answer:

Coterminal angles are angles with the same terminal side.

When we have an angle A, the coterminal angles can be written as:

A + k*(360°)

where k can be any integer number. (Notice that when we have k = 0, means that A is coterminal with itself)

Then the set of all the coterminal angles to -225° is:

{-225° + k*360°I k ∈ Z}

where Z is the set of integer numbers.

Answer:

Hey there!

2x+3y=18

2(3)+3(4)=18

6+12=18

18=18, so this is a valid ordered pair.

Let me know if this helps :)

Answer:

65

Step-by-step explanation:

5(6 + 7)

5 • 6 = 30

5 • 7 = 35

30 + 35 = 65

Answer:

x >3

Step-by-step explanation:

2(2x - 3) > 6

Divide each side by 2

2/2(2x - 3) > 6/2

2x-3 > 3

Add 3 to each side

2x-3+3 > 3+3

2x>6

Divide by 2

2x/2 > 6/2

x >3

Answer:

x > 3

Step-by-step explanation:

First, you're going to divide both sides by two

2( 2x - 3) / 2 and 6/2

After that, you will simplify that into....

2x - 3 > 3

Then you want to add three to both sides like so

2x - 3 + 3 > 3 + 3

Once you're done with that, go ahead and simplify the problem

2x > 6

Then, divide by two on each side

2x/2 > 6/2

Lastly, simplify your answer and that's the solution

x > 3

I hope this helped! :)

Answer:

35000

Step-by-step explanation:

Answer:

Step-by-step explanation:

f 35 = 100 % as a whole number then 50% = 17.5

50 % more than 35 must be 35 + 17.5 = 52.5

Answer:

Hey!

Your answer is 52.5

Step-by-step explanation:

50% x 35=

(50/100) x 35=

(50 x 35) / 100=

1750 / 100 = 17.50

NOW...

35+17.5=52.5

ANSWER: 52.5

Answer:

Second option.

Step-by-step explanation:

In a mathematical sense, all real values of x are possible, as no real values of x will make it undefined.

However, in a reasonable sense, the length and width of a rectangle should be positive, so 0.5x -2 > 0.

Therefore, in a reasonable sense, x > 4.

Answer:

Quadrant 1:

(6,4) and (3,2)

Quadrant 2:

(-3,4)

Quadrant 3:

(-2,-8) and (-1,-12)

Quadrant 4:

(6,-5)

HOPE THIS HELPS!!!!!! :)

<3333333333

Answer:

Natural numbers < Whole Numbers < Rational numbers < Integers

Step-by-step explanation:

Natural numbers are the numbers that are called counting numbers.They are numbers you can count. But Zero is not among them. Basically, Natural numbers are numbers you can count with the exception of Zero.

Whole numbers are a bit more than natural numbers. Unlike Natural numbers, whole numbers contain Zero. As a result, we can say they're counting numbers Zero inclusive.

Rational numbers are numbers that are written as ratio. They can be written as a fraction, but then, both the denominator and the numerator would have to be whole numbers.

Integers are whole numbers including negative numbers. Remember, whole numbers are an extension of natural numbers? Well then, Integers are an extension of Whole numbers.

Answer:

see attachement

Step-by-step explanation:

Solve for x:

8 x + 26 - 3/x + 6/x^2 = 0

Hint: | Write the left hand side as a single fraction.

Bring 8 x + 26 - 3/x + 6/x^2 together using the common denominator x^2:

(8 x^3 + 26 x^2 - 3 x + 6)/x^2 = 0

Hint: | Multiply both sides by a polynomial to clear fractions.

Multiply both sides by x^2:

8 x^3 + 26 x^2 - 3 x + 6 = 0

Hint: | Look for a simple substitution that eliminates the quadratic term of 8 x^3 + 26 x^2 - 3 x + 6.

Eliminate the quadratic term by substituting y = x + 13/12:

6 - 3 (y - 13/12) + 26 (y - 13/12)^2 + 8 (y - 13/12)^3 = 0

Hint: | Write the cubic polynomial on the left hand side in standard form.

Expand out terms of the left hand side:

8 y^3 - (187 y)/6 + 799/27 = 0

Hint: | Write the cubic equation in standard form.

Divide both sides by 8:

y^3 - (187 y)/48 + 799/216 = 0

Hint: | Perform the substitution y = z + λ/z.

Change coordinates by substituting y = z + λ/z, where λ is a constant value that will be determined later:

799/216 - 187/48 (z + λ/z) + (z + λ/z)^3 = 0

Hint: | Transform the rational equation into a polynomial equation.

Multiply both sides by z^3 and collect in terms of z:

z^6 + z^4 (3 λ - 187/48) + (799 z^3)/216 + z^2 (3 λ^2 - (187 λ)/48) + λ^3 = 0

Hint: | Find an appropriate value for λ in order to make the coefficients of z^2 and z^4 both zero.

Substitute λ = 187/144 and then u = z^3, yielding a quadratic equation in the variable u:

u^2 + (799 u)/216 + 6539203/2985984 = 0

Hint: | Solve for u.

Find the positive solution to the quadratic equation:

u = (17 (9 sqrt(157) - 188))/1728

Hint: | Perform back substitution on u = (17 (9 sqrt(157) - 188))/1728.

Substitute back for u = z^3:

z^3 = (17 (9 sqrt(157) - 188))/1728

Hint: | Take the cube root of both sides.

Taking cube roots gives 1/12 17^(1/3) (-(188 - 9 sqrt(157)))^(1/3) times the third roots of unity:

z = 1/12 17^(1/3) (-(188 - 9 sqrt(157)))^(1/3) or z = -1/12 (-1)^(2/3) 17^(1/3) (188 - 9 sqrt(157))^(1/3) or z = -1/12 17^(1/3) (188 - 9 sqrt(157))^(1/3)

Hint: | Perform back substitution with y = z + 187/(144 z).

Substitute each value of z into y = z + 187/(144 z):

y = 1/12 (-17 (188 - 9 sqrt(157)))^(1/3) - (11 (-17)^(2/3))/(12 (188 - 9 sqrt(157))^(1/3)) or y = 11/12 17^(2/3) ((-1)/(188 - 9 sqrt(157)))^(1/3) - 1/12 (-1)^(2/3) (17 (188 - 9 sqrt(157)))^(1/3) or y = -(11 17^(2/3))/(12 (188 - 9 sqrt(157))^(1/3)) - 1/12 (17 (188 - 9 sqrt(157)))^(1/3)

Hint: | Simplify each solution.

Bring each solution to a common denominator and simplify:

y = 1/12 (153 sqrt(157) - 3196)^(1/3) - (11 (-17)^(2/3))/(12 (188 - 9 sqrt(157))^(1/3)) or y = 1/12 17^(1/3) (11 ((-17)/(188 - 9 sqrt(157)))^(1/3) - (-1)^(2/3) (188 - 9 sqrt(157))^(1/3)) or y = -1/12 17^(1/3) (1/(188 - 9 sqrt(157)))^(1/3) ((188 - 9 sqrt(157))^(2/3) + 11 17^(1/3))

Hint: | Perform back substitution on the three roots.

Substitute back for x = y - 13/12:

Answer: x = -13/12 - (11 (-17)^(2/3))/(12 (188 - 9 sqrt(157))^(1/3)) + 1/12 (153 sqrt(157) - 3196)^(1/3) or x = 1/12 17^(1/3) (11 (-17/(188 - 9 sqrt(157)))^(1/3) - (-1)^(2/3) (188 - 9 sqrt(157))^(1/3)) - 13/12 or x = -1/12 (17/(188 - 9 sqrt(157)))^(1/3) (11 17^(1/3) + (188 - 9 sqrt(157))^(2/3)) - 13/12

Answer:

The correct answer is, "8x + 2x^2 + 21 / (x + 5)(x - 3)"

Step-by-step explanation:

This is 100% correct! :)

Answer:

Its either 1.98 percentage or 51.

Step-by-step explanation:

Divison?

Answer:2%

Step-by-step explanation: 38.76-0.76=38

38(1+r)=38.76

__________

38

1+r=1.02

R=0.02 (2%)

Answer:

yes because

Step-by-step explanation:

this point, we pause to see if it makes sense that we actually have two viable cases to consider. As we have discussed, both candidates for are ‘compatible’ with the given angle-side pair ( ;a) = (30 ;3) in that both choices for can t in a triangle with and both have a sine of 2 3. The only other given piece of information is that c= 4 units.

Answer:

The correct option is;

b. Simpsons Rule

Step-by-step explanation:

The midpoint rule involves the estimation of the area under the curve with the aid of rectangular shaped approximations

The trapezoidal rule, involved the approximation of the curve by linear approximations by using piece by piece linear functions

In the Simpson's rule the curve is approximated using piece by piece quadratic functions. The intervals are partitioned into even numbered smaller intervals having the same width and we approximate the resulting integrals of the intervals.

Answer:

5 cases

Step-by-step explanation:

you'll need at least five cases to fulfill the requirement of 60

Answer:

5 cases are needed

Step-by-step explanation:

Answer:

8

Step-by-step explanation: