Which expression does not factor?
O m³+1
m³-1
0 m² +1
m² - 1
O
DONE

The two bodies are being drawn together by a force of 10812 N, according to Newton's Law of Gravitation.

Every particle in the universe is drawn to every other particle with a force that is directly proportional to the product of their masses and inversely proportional to their separation from one another, according to Newton's Law of Universal Gravitation.

Symbolically, Newton came to the following conclusion on the strength of the gravitational force:

F = G(m₁ × m₂) / r²

F is the gravitational force between two bodies, m1 and m2 are the bodies' masses, r is the distance between their centres, and G is the gravitational constant of the universe.

According to the query,

satellite's mass is m1 = 1100 kg.

mass of earth = 5.98 ×10²⁴ kg

Radius of the earth = 6.37 × 10⁶ m

G = 6.67 × 10⁻¹¹ Nm² / kg²

Force = G(m₁ × m₂) / r²

Substituting the values,

F = 6.67 × 10⁻¹¹( 1100 × 5.98 ×10²⁴)  /( 6.37 × 10⁶)²

=> F = 6.67 × 1100 × 5.98 × 10¹³ / 40.58 × 10¹²

=> F = 43,875.26 × 10 / 40.58

=> F = 10812 N

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The interval notation of the number line is [-3, ∝) while that of the inequality is  called x >= 3

One can use interval notation to represent real numbers that are continuous by specifying the values that define their boundaries. Written intervals appear somewhat akin to ordered pairs.

The way to know the interval notation of the graph is:

Based on the number line in the question, one can see:

The rule that applies is that a closed line tells us that the number at that endpoint is one that is part of the solution set.

So this tells us that the interval notation of the number line is [-3, ∝). When depicted as an inequality, One can have x >= 3

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Answer:  you would need to cross the bridge 5 times

Step-by-step explanation:

costing a total of $42.50 for each option.

hope this helps

Answer:

\(x = 5(5) + 5\); \(x = 30 + 5 = 35\)

Step-by-step explanation:

Let the 1st number be x and the second number y.

1st equation: \(x = 5y + 5\)

2nd equation: \((x + y) + 2 = 37\)

Taking the 2nd equation: \((x + y) = 35\).

Substitute the value of X (from 1st equation into the 2nd): Since x = ( 5y + 5)

\((5y + 5) + y =35\)

\(6y + 5 = 35\)

\(6y = 30\)

\(y = 5\)

\(x = 5(5) + 5;\) \(x = 30 + 5 = 35\)

Smaller number 5 and larger number 30

Note to moderators: Please don't delete this answer because I just trying to help others.

Answer: The area of the floor of the hall is approximately 599.2448 square meters.

Step-by-step explanation: Let's assume the breadth of the hall be x meters. Then, the length of the hall will be 2x meters and the height will be 3x meters.

The volume of the hall can be found as follows:

Volume = Length × Breadth × Height

36000 = 2x × x × 3x

36000 = 6x³

x³ = 6000

x = ∛6000 ≈ 17.32 meters

Therefore, the breadth is approximately 17.32 meters, the length is 2 × 17.32 = 34.64 meters, and the height is 3 × 17.32 = 51.96 meters.

The area of the floor can be found by multiplying the length and breadth:

Area = Length × Breadth

Area = 34.64 × 17.32

Area = 599.2448 m²

Therefore, the area of the floor of the hall is approximately 599.2448 square meters.

Answer:

24.6 units

Step-by-step explanation:

\(tan \: 72 \degree = \frac{x}{8} \\ \\ 3.0776835372 = \frac{x}{8} \\ \\ x = 3.0776835372 \times 8 \\ \\ x = 24.6214683 \\ \\ x \approx \: 24.6 \: units\)

Answer:

x=2

Step-by-step explanation:

Step 2: Subtract 7x from both sides.

−8x+32−7x=7x+2−7x

−15x+32=2

Step 3: Subtract 32 from both sides.

−15x+32−32=2−32

−15x=−30

Step 4: Divide both sides by -15.

−15x

−15

=

−30

−15

x=2

Answer:

I love algebra anyways  

the ans is in the picture with the steps  

(hope it helps can i plz have brainlist :D hehe)

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

First, we can determine what type of relationship we are dealing with by examining the table.

From x = 1 to x = 2, the y-value increased by 14/4 (25/4-11/4).

From x = 2 to x = 3, the y-value also increased by 14/4 (39/4-25/4)

And from x = 3 to x = 4, the y-value still increased by 14/4 (53/4-39/4).

Therefore, we can conclude that our table represents a linear relationship.

And since it increases by 14/4 or 7/2 for every x, this means that our slope is 7/2.

The only choice that represents a linear equation with a slope of 7/2 is D. So, the correct answer is D.

However, we can confirm our answer by writing our equation. We can use the point-slope form:

\(y-y_1=m(x-x_1)\)

Where m is the slope and (x₁, y₁) is a point.

Let's substitute 7/2 for m. We can pick any point, so I'm going to use (1, 11/4) for (x₁, y₁).

Substitute:

\(\displaystyle y-\frac{11}{4}=\frac{7}{2}(x-1)\)

Distribute:

\(\displaystyle y-\frac{11}{4}=\frac{7}{2}x-\frac{7}{2}\)

Add 11/4 to both sides. Note that 7/2 is the same as 14/4. So:

\(\displaystyle y=\frac{7}{2}x-\frac{14}{4}+\frac{11}{4}\)

Add:

\(\displaystyle y=\frac{7}{2}x-\frac{3}{4}\)

So, our answer is D.

And we're done!

Step-by-step explanation:

(3h - 5)(5h + 4) =   3h * 5h    +   3h * 4     - 5*5h    - 5 *4

                              =    15h^2        - 13h    -20

\((3h-5)(5h+4)\)

\(=(3h+-5)(5h+4)\)

\(=(3h)(5h)+(3h)(4)+(-5)(5h)+(-5)(4)\)

\(=15h^2+12h-25h-20\)

Answer:

To plot the point, we can draw a horizontal number line, label the origin as 0, and then mark a point 4.472 units to the right of 0.

 |---------------------|---------------------|

 0                                            4.472

We have,

To plot the point representing the approximation of √(20), we need to first find the approximate value of √(20):

√(20) ≈ 4.472

This means that the point we want to plot is located approximately 4.472 units to the right of the origin on the number line.

To plot the point, we can draw a horizontal number line, label the origin as 0, and then mark a point 4.472 units to the right of 0.

The resulting point represents the approximation of √(20).

Thus,

A rough sketch of what the plot could look like:

 |---------------------|---------------------|

 0                                            4.472

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Answer:

hey, the answer is A I'm 100% for sure:)

Step-by-step explanation:

:)

Answer:

what exactly do i need to do ?????

Step-by-step explanation:

Answer:

sold 120 chocolate bars

sold 140 peanut butter bars

Step-by-step explanation:

x = peanut butter bars

y = chocolate bars

x + y = 260, total lbs

0.25x + 0.30y = 71, money

solve double variable equation

multiply -4 on both sides for 2nd equation

-x + -1.2y = -284

add both equations together

-0.2y = -24

y = 120

x = 260 - 120

x = 140

sold 120 chocolate bars

sold 140 peanut butter bars

Answer:

y=21 X=39

Step-by-step explanation:

expand brackets on first equation: 2x+2y=120

now divide the second equation by 2 on both sides:

2x+y/3=85

then subtract the second equation from the first equation

so (2x+2y) - (2x+y/3)

the 2x on both sides cancel out and you get 5/3 y

this is equal to the sum of the first equation subtract the second equation which is 35

divide both sides by 5/3 and you get

y=21

substitute y in the first equation and you get X=39

Answer:

B

Step-by-step explanation:

The exact solutions of the Quadratic equation x^2 - 3x - 5 = 0 are:

x = (3 + √29) / 2 ,x = (3 - √29) / 2. The correct answer choice is:

x = the quantity of 3 plus or minus the square root of 29 all over 2.

The exact solutions of the quadratic equation x^2 - 3x - 5 = 0 using the quadratic formula, we can identify the values of a, b, and c, and substitute them into the formula:

a = 1

b = -3

c = -5

Now, we can apply the quadratic formula:

x = (-b ± √(b^2 - 4ac)) / (2a)

Substituting the values into the formula:

x = (-(−3) ± √((−3)^2 - 4(1)(−5))) / (2(1))

x = (3 ± √(9 + 20)) / 2

x = (3 ± √29) / 2

Therefore, the exact solutions of the quadratic equation x^2 - 3x - 5 = 0 are:

x = (3 + √29) / 2

x = (3 - √29) / 2

The correct answer choice is:

x = the quantity of 3 plus or minus the square root of 29 all over 2.

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Answer:

\(\frac{dy}{dx}=\frac{8(xsec^2(x)-tan(x)+3)}{(3-tan(x))^2}\)

Step-by-step explanation:

\(y=\frac{8x}{3-tan(x)}\\ \\\frac{dy}{dx}=\frac{(3-tan(x))(\frac{d}{dx}8x)-(\frac{d}{dx}(3-tan(x)))(8x)}{(3-tan(x))^2}\\ \\ \frac{dy}{dx}=\frac{(3-tan(x))(8)-(-sec^2(x))(8x)}{(3-tan(x))^2}\\ \\ \frac{dy}{dx}=\frac{24-8tan(x)+8xsec^2(x)}{(3-tan(x))^2}\\ \\ \frac{dy}{dx}=\frac{8xsec^2(x)-8tan(x)+24}{(3-tan(x))^2}\\\\ \frac{dy}{dx}=\frac{8(xsec^2(x)-tan(x)+3)}{(3-tan(x))^2}\)

Remember to use the Quotient Rule

The y-intercept of the function is (0, c)

The coefficients b determine the horizontal shift of the parabola compared to the parent function

If a is negative, the parabola opens downward

The y-intercept of the function is (0, c).

This means that when x = 0, the y-value is equal to c.

The constant term c represents the y-coordinate of the point where the parabola intersects the y-axis.

The coefficient b determines the horizontal shift of the parabola compared to the parent function.

The value of b affects the position of the vertex and determines if the parabola is shifted to the left or right.

A positive value of b shifts the parabola to the left, while a negative value of b shifts it to the right.

If a is negative, the parabola opens downward.

The coefficient a determines the shape of the parabola.

If a is positive, the parabola opens upward, and if a is negative, the parabola opens downward. The sign of a determines the direction in which the parabola faces.

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Answer:

Option D is the correct answer

Step-by-step explanation:

D. Yes, because it passes the vertical line test.

The Equation of bisector 5x-7y+3=0 which is a straight line.

A straight line that divides an angle of a triangle in equal value.

The line that lies perpendicular to a side and goes through the midpoint of its length.

Given, coordinate H (-7,2), K (3, -4) and L (5,4)

we plot a triangle HKL with this point.

midpoint of side HK is found by (-7+3)/2 and (2-4)/2

hence, midpoint of HK is (-2,-1) is denoted by P

the perpendicular bisector of side HK means a straight line from the midpoint of HK to the point L(5,4). The bisector line PL divide the angle HLK.

so, the equation of bisector is y-y₁ = (y₂-y₁)/(x₂-x₁)[x-x₁] because the bisector line passes through the point P(-2,-1) and L(5,4)

  y-(-1) = [4-(-1)]/[5-(-2)]× [x-(-2)]

y+1 = 5/7×(x+2)

7y+7= 5x+10

5x-7y+3=0

hence, the equation of bisector is 5x-7y+3=0

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Answer/Step-by-step explanation:

Since ∆PHS ≅ ∆CNF, therefore:

<P ≅ <C,

<H ≅ <N

<S ≅ <F

Thus:

Since, <P ≅ <C, therefore,

36° = (4z - 32)°

36 = 4z - 32

Add 32 to both sides

36 + 32 = 4z

68 = 4z

Divide both sides by 4

68/4 = z

17 = z

z = 17

Since <H ≅ <N, therefore:

6x - 29 = 115°

Add 29 to both sides

6x = 115 + 29

6x = 144

Divide both sides by 6

x = 114/6

x = 24

m<F + m<C + m<N = 180° (sum of ∆)

(3y - 1) + (4z - 32) + 115 = 180 (substitution)

Plug in the value of z and solve for y

3y - 1 + 4(17) - 32 + 115 = 180

3y - 1 + 68 - 32 + 115 = 180

3y + 150 = 180

Subtract 150 from both sides

3y = 180 - 150

3y = 30

y = 10

The value of x, y and z are 24, 10 and 17 respectively.

PHS≅CNF

Therefore,

∠P ≅ ∠C

∠H ≅ ∠N

∠S ≅ ∠F

36 = 4z - 32

36 + 32 = 4z

4z = 68

z = 68 / 4

z = 17

6x - 29 = 115

6x = 115 + 29

x = 144 / 6

x = 24

3y - 1 = 180 - 115 - (4z - 32)

3y - 1 = 180 - 115 - 4z + 32

3y - 1 = 97 - 4(17)

3y - 1 = 29

3y = 30

y = 30 / 3

y = 10

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Answer:

x²+y²+6x+2y = -8

Step-by-step explanation:

The given equation is:

(x+3)²+(y+1)²=2

We know that, (a+b)² = a²+b²+2ab

Using above property

x²+9+6x+y²+1+2y = 2

x²+y²+6x+2y+10 = 2

x²+y²+6x+2y = -8

Hence, this is the required solution.

5x-3x=5-1

2x=2

x=1

Step-by-step explanation:

make the xes one side and the numb one side first and solve:

Answer: Step by Step Explanation Step 1: take 3x to the right side of equals to whereas 1 to the left side of it i.e. 5x-3x=5-1

Step2: Apply arithmetic operations now, it comes as 2x=4

Step3: Now x will stay at the left side, 1 goes to the divide 4 i.e. X=4/2 which equals to 2

Answer

The calculated price per video game for store A is $1.79 per game

From the question, we have the following parameters that can be used in our computation:

The price per video game for store A is calculated as

Price per video game = Total price/Number of games

using the above as a guide, we have the following:

Price per video game = 8.95/5

Evaluate the quotient

So, we have

Price per video game = 1.79

Hence, the price per video game for store A is $1.79 per game

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Answer:

y = 6/5x - 1

Step-by-step explanation:

y = mx + b

y = Slope * x + Y-intercept

the slope is found by the rise of 1 point to the other (Change in Y's) and the run of the the points (Change of X's)

this makes the slopw 6/5

y = 6/5x + b

the Y intercept is at (0,-1) or just -1

so Its now y = 6/5x + - 1

or rewritten as

Y = 6/5 x - 1

-- Gage Millar, Algebra 1/2 tutor

Answer:

-0.65 or -13/20

Step-by-step explanation:

The derivative of the function  f(x)= csch⁻¹(x²) is -2/x√1+x⁴

The given function is f(x)= csch⁻¹(x²)

We have to find the derivation of the hyperbolic function

d/dx f(x)= d/dx csch⁻¹(x²)

f(x)=csch⁻¹(x²)

We know that the derivative csch⁻¹x is -1/|x|√1+x²

Differentiate and apply the chain rule

=-1/|x²|√1+x⁴ d/dx (x²)

We know that d/dx (x²) = 2x as d/dx (xⁿ)=nxⁿ⁻¹

Apply these on the above function

= 2x/x²√1+x⁴

= -2/x√1+x⁴

Hence, the derivative of the function  f(x)= csch⁻¹(x²) is -2/x√1+x⁴

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Answer:

\(\text{A.} \quad \dfrac{-2}{x\sqrt{x^4+1}}\)

Step-by-step explanation:

Given inverse hyperbolic function:

\(f(x)=\text{csc\:h}^{-1}(x^2)\)

To find the derivative of the function, we can use the chain rule:

\(\boxed{\begin{minipage}{5.4 cm}\underline{Chain Rule for Differentiation}\\\\If $y=f(u)$ and $u=g(x)$ then:\\\\$\dfrac{\text{d}y}{\text{d}x}=\dfrac{\text{d}y}{\text{d}u}\times\dfrac{\text{d}u}{\text{d}x}$\\\end{minipage}}\)

\(\textsf{Let}\;\;y = \text{csch}^{-1}(u)\;\; \textsf{where}\;\;u=x^2.\)

Differentiate the two parts separately.

Differentiate u with respect to x:

\(u = x^2 \implies \dfrac{\text{d}u}{\text{d}x}=x\)

Use the following derivative of hyperbolic functions to differentiate y with respect to u:

\(\boxed{\dfrac{\text{d}}{\text{d}x}\left(\text{csch}^{-1}x\right)=\dfrac{-1}{|x|\sqrt{x^2+1}}, \quad x \neq 0}\)

Therefore:

\(y = \text{csch}^{-1}(u)\implies \dfrac{\text{d}y}{\text{d}u}=\dfrac{-1}{|u|\sqrt{u^2+1}}\)

Put everything into the chain rule formula:

\(\begin{aligned}\dfrac{\text{d}y}{\text{d}x}&=\dfrac{\text{d}y}{\text{d}u}\times\dfrac{\text{d}u}{\text{d}x}\\\\&=\dfrac{-1}{|u|\sqrt{u^2+1}} \times 2x\\\\&=\dfrac{-2x}{|u|\sqrt{u^2+1}} \\\\&=\dfrac{-2x}{|x^2|\sqrt{(x^2)^2+1}} \\\\&=\dfrac{-2x}{|x^2|\sqrt{x^4+1}}\\\\&=\dfrac{-2x}{|x^2|\sqrt{(x^2)^2+1}} \\\\&=\dfrac{-2}{x\sqrt{x^4+1}}\end{aligned}\)

Therefore, the derivative of the given inverse hyperbolic function is:

\(\boxed{-\dfrac{2}{x\sqrt{x^4+1}}}\)

Answer:   \(y=-\dfrac{16}{9}(x+3)^2+4\)

Step-by-step explanation:

Use the vertex formula:  y = a(x - h)² + k    where

We can see that the vertex of the curve is (-3, 4)  -->  h = -3, k = 4

and it is a reflection over the x-axis --> a-value is negative

We need to find the a-value. Choose another point on the curve and plug it into the vertex formula for (x, y) and then solve for a.

I will choose (x, y) = (-3/2, 0)

\(0=a\bigg(\dfrac{-3}{2}+3\bigg)^2+4\\\\\\-4=a\bigg(\dfrac{3}{2}\bigg)^2\\\\\\-4\bigg(\dfrac{2}{3}\bigg)^2=a\\\\\\-\dfrac{16}{9}=a\)

Now that we know the vertex and the a-value, we can input them into the vertex formula:

                         \(\large\boxed{y=-\dfrac{16}{9}(x+3)^2+4}\)

Answer:

Answer:  

Step-by-step explanation:

Use the vertex formula:  y = a(x - h)² + k    where

a is the vertical stretch

-a is a reflection over the x-axis

(h, k) is the vertex

We can see that the vertex of the curve is (-3, 4)  -->  h = -3, k = 4

and it is a reflection over the x-axis --> a-value is negative

We need to find the a-value. Choose another point on the curve and plug it into the vertex formula for (x, y) and then solve for a.

I will choose (x, y) = (-3/2, 0)

Now that we know the vertex and the a-value, we can input them into the vertex formula:

The probability of the baseball player getting exactly 4 hits out of 10 times at bat is approximately 0.161, or 16.1%.

To calculate the probability of a baseball player getting exactly 4 hits out of 10 times he was up at bat, we need to use the binomial probability formula.

The binomial probability formula is given by:P(X = k) = C(n, k) * p^k * (1 - p)^(n - k)

Where:

P(X = k) is the probability of getting exactly k hits

n is the total number of trials (in this case, the player's 10 times at bat)

k is the number of successful trials (in this case, 4 hits)

p is the probability of success in a single trial (in this case, the player's batting average, 0.298)

(1 - p) is the probability of failure in a single trial

Plugging in the values:

P(X = 4) = C(10, 4) * (0.298)^4 * (1 - 0.298)^(10 - 4)

Using the combination formula C(n, k) = n! / (k! * (n - k)!):

P(X = 4) = 10! / (4! * (10 - 4)!) * (0.298)^4 * (1 - 0.298)^(10 - 4)

Calculating the values:

P(X = 4) ≈ 0.161

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