Solve for x
Solve for x give that the segments ST and SU are both
tangent to the circle.
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7X-3
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5x+1
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The distance from the center of the Earth to the point where the net gravitational force is zero is one-ninth the distance from the Earth to the Moon.

Let's assume that the distance from the center of the Earth to this point is denoted as x.

Given:

Mass of the Moon (M\(_{moon}\)) = 1/81 × M\(_{earth}\)

Distance from Earth to Moon (d\(_{moon}\)) = distance on center

According to the principle of gravitational equilibrium, the gravitational force from the Earth and the gravitational force from the Moon acting on an object at that point must balance out. Mathematically, we can express this as:

F\(_{earth}\) = F\(_{moon}\)

The gravitational force between two objects can be calculated using Newton's law of universal gravitation:

F \(_{gravity}\)= G × (m₁ × m₂) / r²

Where:

G is the gravitational constant (approximately 6.67430 x 10⁻¹¹m²/kg/s²)

m₁ and m₂ are the masses of the two objects

r is the distance between the centers of the two objects

Considering the gravitational forces involved:

F\(_{gravity}\)\(_{earth}\) = G ₓ (M\(_{EARTH}\)  ₓ m\(_{OBJECT}\)) / (d\(_{earth}\))²

F\(_{gravity}\) \(_{moon}\) = G ₓ (M \(_{moon}\) ₓ m\(_{object}\)) / (d \(_{moon}\))²

Since we are looking for the point where the net gravitational force is zero, we set these two forces equal to each other:

G × (M\(_{earth}\) × m\(_{object}\)) / (d\(_{earth}\))²   =     G × (M \(_{moon}\) × m\(_{object}\)) / (d \(_{moon}\))²

Canceling out the common factors of G and m\(_object}\), and substituting the given values:

(M\(_{earth}\) × 1) / (d\(_{earth}\))² = (M \(_{moon}\) × 1) / (d \(_{moon}\))²

Rearranging the equation:

(d\(_{earth}\))²/ (M\(_{earth}\)) = (d \(_{moon}\))² / (M \(_{moon}\))

Taking the square root of both sides:

d\(_{earth}\) / √(M \(_{moon}\))) = d_moon / √(M \(_{moon}\))

Substituting the given values:

d\(_{earth}\) /√(M\(_{earth}\)) = d\(_{moon}\) / √(1/81 × M\(_{earth}\))

Simplifying further:

d\(_{earth}\)  / √(M\(_{earth}\)) =d\(_{moon}\)  / (1/9 × √(M\(_{earth}\)))

Multiplying both sides by √(M\(_{earth}\)):

d\(_{earth}\) = (1/9) × d\(_{moon}\)

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\(x_{1} =-0.1705\\\\x_{2} =0.7330\).

\(5(\frac{3x}{2-4x} )+15=-12x+12\)

\(\frac{(5)(3x)}{2-4x} +15=-12x+12\\ \\\frac{15x}{2-4x} +15=-12x+12\)

\(\frac{15x}{2-4x} +15-15=-12x+12-15\\ \\\frac{15x}{2-4x}=-12x-3\)

\(\frac{15x}{2-4x} (2-4x)=(-12x-3)(2-4x)\\ \\15x=(-12x)(2)+(-12x)(-4x)+(-3)(2)+(-3)(-4x)\\ \\15x=(-24x)+(48x^{2} )+(-6)+(12x)\\ \\15x=-24x+48x^{2}-6+12x\\ \\15x=48x^{2}-12x-6\)

\(15x+12x=48x^{2}-12x-6+12x\\ \\27x=48x^{2}-6\)

\(-48x^{2}+27x+6=0\)

Check the attached image to see how to identify these coefficients.

a= -48;

b= 27;

c= 6.

\(x_{1} =\frac{-(27)+\sqrt{(27)^{2} -4(-48)(6)} }{2(-48)}\\ \\x_{1} =-0.1705\)

\(x_{2} =\frac{-(51)-\sqrt{(51)^{2} -4(36)(6)} }{2(36)}\\ \\x_{2} =0.7330\)

If the answers are correct, both sides of the equation should return the same value when substituting any of the x values and calculating.

\(5(\frac{3(\frac{-(27)+\sqrt{(27)^{2} -4(-48)(6)} }{2(-48)})}{2-4(\frac{-(27)+\sqrt{(27)^{2} -4(-48)(6)} }{2(-48)})} )+15=-12(\frac{-(27)+\sqrt{(27)^{2} -4(-48)(6)} }{2(-48)})+12\\\\14.04631211=14.04631211\)

That's correct.

\(5(\frac{3(\frac{-(27)-\sqrt{(27)^{2} -4(-48)(6)} }{2(-48)})}{2-4(\frac{-(27)-\sqrt{(27)^{2} -4(-48)(6)} }{2(-48)})} )+15=-12(\frac{-(27)-\sqrt{(27)^{2} -4(-48)(6)} }{2(-48)})+12\\ \\3.203687889=3.203687889\)

That's correct.

Check attached image 2 to see the proof of these calculations.

Hence, x₁=-0.1705 and x₂=0.7330 are the correct answers.

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Answer:

Sally does 1/5 of a room per hour.

Steve does 1/7 of a room per hour.

Together --> 1/5 + 1/7 = 12/35 rooms per hour.

The inverse is hours per room = 35/12

--------------

Parallel work is similar to parallel flow and parallel resistors.

----

PS 5*7/(5+7) = 35/12

Step-by-step explanation:

Answer: about 3 hours and 5 minutes

Step-by-step explanation:

Sally can paint \(\frac{1}{5}\) of the room in an hour while Steve is able to paint \(\frac{1}{8}\) in an hour.

To find how long it would take to paint the room together you add the two fractions together:

\(\frac{1}{5} + \frac{1}{8}\)

To add or subtract fractions we find a common denominator and add the numenators:

\(\frac{1}{5} = \frac{8}{40}\)   \(\frac{1}{8} = \frac{5}{40}\)

\(\frac{5}{40} + \frac{8}{40} = \frac{13}{40}\)

The inverse of the fraction is hours per room = \(\frac{40}{13}\)

\(\frac{40}{13}\) = 3.077 = about 3 hours and 5 minutes.

The new curriculum significantly affects the earning potential.

According to the question, Eight kids were chosen at random to take part in a brand-new educational program that emphasizes both academics and mental health education between middle school and high school. The average annual income is $29432. The standard deviation is unknown.

The probability level is given to be 5%.

When the p-value is less than or equal to your significance level, reject the null hypothesis. The alternative theory, which contends that the effect is widespread, is supported by your sample data.

A probability level of 0.05 means that the new curriculum significantly affects the earning potential.

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The Pythagoras theorem states that in a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides.

From the given Pythagoras theorem above, the mathematical representation of the theorem would be written below as follows;

C² = a²+b²

Where:

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Answer: 5/4

Step-by-step explanation: You go up five from point (-6,0) and across for to point (-2,4)

Given:

Lionfish are considered an invasive species, with an annual growth rate of 69%. A scientist estimates there are 9,000 lionfish in a certain bay after the first year.

The general equation of the growth is:

Given rate = r = 69% = 0.69

After 1 year, P = 9000

Substitute to find the initial number of Lionfish

So,

Part (A), we will write an explicit formula f(n) that represents the number of lionfish after n years

so, the formula will be:

Part (B): we will find the number of lionfish after 6 years

so, substitute with n = 6 into the equation of part (a)

So, after 6 years, the number of lionfish = 124,073

Part (C): The scientists remove 1400 fish per year after the first year

So, we the number of lionfish:

Then after 2 years, the number of lionfish

After 3 years:

So, after (n) years:

Angles in a triangle add up to 180 degrees

The value of x is 85 degrees

A triangle is a polygon which has  three sides and three vertices. It is one of the normal shapes in geometry. A triangle with vertices A, B, and C has three sides & three angles A, B, C.

here, we have,

How to determine the value of x

The total  sum of angles for a triangle is 180 degrees.

So, we have:

x + 35 + 60 = 180

Evaluate the sum

x + 95= 180

Subtract 95 from both sides

x = 85

Hence, the value of x is 85 degrees

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Full question: (SAT Prep) Find the value of x. 35° 60° X

x=?​

answer: the range is 41.

to find the range of this data set, we first need to find the minimum and maximum values - which are 59 and 100.

then we subtract the minimum from the maximum.

59 - 100 = 41.

Answer:

9

Step-by-step explanation:

Raising a number to the second means multiplying that number.  3 * 3 = 9

Answer:

no

Step-by-step explanation:

The logarithmic regression equation that models the situation is given as follows:

y = 242.9037 + 23.7097ln(x).

The estimated population in 2010 is of:

313.9 million

Which overestimates the actual amount by 5.2 million.

The prediction for when the population will be of 400 million is of:

Year of 2,744.

The logarithmic regression equation is obtained inserting the points of the data-set into a logarithmic regression calculator.

From the table given by the image at the end of the answer, the points are given as follows:

(0, 248.8), (10, 281.4), (20, 308.7), (30, 331.4), (31, 331.9).

Inserting these points into a calculator, the equation is given as follows:

y = 242.9037 + 23.7097ln(x).

2010 is 20 years after 1990, hence the estimate is given as follows:

y = 242.9037 + 23.7097 x ln(20) = 313.9 million.

The overestimate of the actual value, from the table, is of:

313.9 - 308.7 = 5.2 million.

The prediction for when the population will be of 400 million is obtained as follows:

400 = 242.9037 + 23.7097 x ln(x)

ln(x) = (400 - 242.9037)/23.7097

ln(x) = 6.6258.

x = e^(6.6258)

x = 754.

Hence during the year of 2,744.

The table is given by the image presented at the end of the answer.

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Answer:

Area of the base = 24 cm²

Height of the prism = 5 cm

Volume of the prism = 120 cm³

Answer:

the solution to the equation is m = 28/3, or approximately 9.3333

Step-by-step explanation:

To solve this equation, you need to get the variable, in this case "m," by itself on one side of the equation. To do this, you can start by isolating the fraction on the left side of the equation. You can do this by multiplying both sides of the equation by 2/3, which will cancel out the 2/3 on the left side:

3m/2/3 = 7

(2/3) * (3m/2/3) = (2/3) * 7

3m/2 = 7 * (2/3)

3m/2 = 14/3

Next, you can multiply both sides of the equation by 2 to get rid of the fraction on the left side:

(2) * (3m/2) = (2) * (14/3)

3m = 28/3

Finally, you can simplify the right side of the equation by dividing both sides by 3 to get the final solution:

(3m) / 3 = (28/3) / 3

m = 28/3

Therefore, the solution to the equation is m = 28/3, or approximately 9.3333.

Answer:

Maybe m = 14/9

Maybe m = 14

Step-by-step explanation:

It is not clear what you mean by the fraction on the left side.

Do you mean

3m/(2/3) = 7  ?

If so:

3m = 7 × 2/3

3m = 14/3

m = 14/9

Do you mean

(3m/2)/3 = 7   ?

If so:

3m/2 = 21

m = 21 × 2/3

m = 14

Do you mean something else?

Answer:

156.6

Step-by-step explanation:

Sorry for the messy handwriting.

Hope this helps!

Apollo Spas will need 46.035 liters of muriatic acid to service all 297 hot tubs.

What is Algebraic expression ?

Algebraic expression can be defined as combination of variables and constants.

To find the total amount of muriatic acid needed for all of the hot tubs, we can multiply the amount needed for one hot tub (155 mL) by the number of hot tubs (297) and convert the result to liters.

First, let's convert the volume of acid needed for one hot tub from milliliters to liters by dividing by 1000:

155 mL ÷ 1000 = 0.155 L

Now we can find the total amount of acid needed for all of the hot tubs:

0.155 L/hot tub x 297 hot tubs = 46.035 L

Therefore, Apollo Spas will need 46.035 liters of muriatic acid to service all 297 hot tubs.

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Answer:

$63

Step-by-step explanation:

Find out the total amount of units that Jack and Molly have.

5 + 6 = 11

11 units = $77

Find out 1 unit to be able to find out how much Evan receives.

1 unit = $77 ÷ 11 = 7

Evan has 9 units, so find out how much money is 9 units.

9 units = 7 x 9 = $63

The statements DF=EG, EF=DG and ∠DEG ≅ ∠FGE are true for parallelogram DEFG.

a quadrilateral is a four-sided polygon, having four edges and four corners.

DEFG is a parallelogram.

A parallelogram is a simple quadrilateral with two pairs of parallel sides.

The opposite or facing sides of a parallelogram are of equal length and the opposite angles of a parallelogram are of equal measure.

DF=FG is a true statement.

The diagonal passing through a parallelogram are equal in length.

EF=DG is a true statement

The opposite sides of a parallelogram are equal.

∠DEG ≅ ∠FGE are congruent angles.

Because the opposite angles of a triangle are equal in meausure.

Hence, the statements DF=EG, EF=DG and ∠DEG ≅ ∠FGE are true for parallelogram DEFG.

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Answer:

68.5

Step-by-step explanation:

Subtract 4 from 73.

You get 69.

Then, subtract 0.5 more.

Your answer is 68.5.

Hope it helps!

Answer:

aprx. 50.24 inches

Step-by-step explanation:

I hope this helps! :)

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Answer:

ur question doesnt make sense

Step-by-step explanation:

Step-by-step explanation:

Time = interest ×100/principle ×rate

time = (31250×100)/(2000000×6.25). [after calculation]

time = 0.25 yrs = ¼×12 = 3months.

hope this helps you.

Step-by-step explanation:

The mean is 6.6, the median is 5 and the mode is 4

The dataset is give as:

4, 4, 5, 8, 12

The mean is calculated as:

Mean = Sum/Count

So, we have:

Mean = (4 + 4 + 5 + 8 + 12)/5

Evaluate

Mean = 6.6

The median is the middle number.

Here, the middle number is 5

So, we have:

Median = 5

The mode is the number with the highest frequency

Here, 4 has the highest frequency

So, we have:

Mode = 4

Hence, the mean is 6.6, the median is 5 and the mode is 4

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Answer:

x = 3/2 or x = -1

Step-by-step explanation:

2x² - x - 3 = 0

2*(-3) = -6

Factors of -6:

(-1, 6), (1, -6), (-2, 3), (2, -3)

We need to find a pair that adds up to the co-eff of x which is (-1)

Factors :(2,-3)

2 - 3 = -1

so, 2x² - x - 3 = 0 can be written as:

2x² + 2x - 3x - 3 = 0

⇒ 2x(x + 1) -3(x + 1) = 0

⇒ (2x - 3)(x + 1) = 0

⇒ 2x - 3 = 0 or

x + 1 = 0

⇒ 2x = 3 or x = -1

⇒ x = 3/2 or x = -1

Answer:

y = 10

Step-by-step explanation:

calculate the slope m of the 2 points using the slope formula and equate to the given slope.

m = \(\frac{y_{2}-y_{1} }{x_{2}-x_{1} }\)

with (x₁, y₁ ) = (5, 6 ) and (x₂, y₂ ) = (10, y )

m = \(\frac{y-6}{10-5}\) = \(\frac{y-6}{5}\)

equate this expression for m to the given m of \(\frac{4}{5}\)

\(\frac{y-6}{5}\) = \(\frac{4}{5}\) ( cross- multiply )

5(y - 6) = 20 ( divide both sides by 5 )

y - 6 = 4 ( add 6 to both sides )

y = 10

When you have an interest compoounded semi anually. It means that it is 2 times in a year. If y ou have 1,3% of interest you receive the half every 6 months

Then in the first 6 months the interest is:

1.3$ /2 = 0.65%

Then to calculate the balance you calculate the 0.65% of the $6,500

Answer:

w = 120

x = 60

y = 120

z = 60

Step-by-step explanation:

w = 120 (vertically opposite angles)

sum of co interior angles is 180

⇒ w + x = 180 and x + y = 180

w + x = 180

⇒ 120 + x = 180

⇒ x = 180 - 120

⇒  x = 60

x + y = 180

⇒  60 + y = 180

⇒   y = 180 - 60

⇒   y = 120

z = x (corresponding angles)

z = 60

Answer:

slope=(y2-y1)÷ ( x2-x1)

where x1=3, x2=8 and y1=5, y2=9.

slope=(9-5)÷(8-3)

slope=4÷5....ans