Factor completely. -3x^2+6x+9 =

|x| + 2 is always greater than |x| because |x| is always positive or zero.

Absolute value of a number is defined as the positive value of the number. even the number is negative, the absolute value is the positive value of that number.

Consider |x| for any number x.

The possibilities of x are positive number, zero or negative number.

If x is a positive number, |x| is also the same positive number.

2 adding to |x| is also positive number.

So |x| + 2 > |x|

If x is a negative number, |x| is the positive value of that negative number.

So |x| + 2 > |x|.

If x is 0, the |x| = 0

|x| + 2 = 0 + 2 = 2 > |x| = 0

Hence in all cases, |x| + 2 > |x|.

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The response to the given question would be that Hence, 2 is the proportionality constant between y and x.

Partnerships that have the same ratio across time are said to be proportional. For instance, how many trees there are in an orchard and how many apples there are in a harvest of apples are determined by the average number of apples per tree. Proportional in mathematics refers to a linear connection between two numbers or variables. As the first quantity doubles, so does the other. When one of the variables drops to 1/100th of its previous value, the other also decreases. When two quantities are proportional, it means that as one rises, the other rises as well, and the ratio between the two quantities stays the same at all levels. As an example, consider the diameter and circumference of a circle.  

We must calculate the ratio of the change in y to the change in x in order to discover the constant of proportionality between two variables, x and y. The slope of the line that depicts the connection between x and y is another name for this.

The slope of the line, which is the change in y divided by the change in x, is therefore equal to the constant of proportionality between y and x. As we can see from the graph, y grows by 2 units for every unit rise in x. Hence, the line's slope is 2/1, or only 2.

Hence, 2 is the proportionality constant between y and x.

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The scientific notation or representation of expression (2.5 X 1/10²)(4.2 X 10⁶) is equal to 10.5×10⁴.

Scientific notation is a way of writing very large or very small numbers. Numbers are written in scientific notation as a number from 1 to 10 multiplied by a power of 10.For example, 650,000,000 can be written in scientific notation as 6.5 ✕ 10⁸. 

Scientific notation is utilized by scientists, mathematicians, and engineers whilst they may be operating with very huge or very small numbers

Solution for scientific notation according to the information given:

(2.5 X 10^-2)(4.2 X 10⁶) = 2.5 ×(1/10²) × 4.2 × 10⁶

                                        = 2.5 × 4.2 × 10⁴

                                        = 10.5 × 10⁴

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it definitely should be (-2,3)

The function to represent the total charges for your hotel and car rental is C,) p(x) = 45 + 214x

In other terms, an equation is a mathematical statement stating that "this is equivalent to that." It appears to be a mathematical expression on the left, an equal sign in the center, and a mathematical expression on the right.

Given that hotel, you are going to stay at charge $135 per night. It can be represented by the function p(x) = 135x.

Also, car rental company charges a $45 insurance fee plus $79 per day.

It can be represented by the function p(x) = 45 + 79x.

Daily rental fee = $135 per night,

Write the equation for the total fees

p(x) = 45 + 214x

Thus, x represents the number of days.

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Answer:

Traduction:

Ann and Barbara are comparing their ages. They find that Barbara is the age that Ann was when Barbara was the age that Ann was when Barbara was half the age that Ann is today. If the sum of their current ages is 44 years, what is Ann's age today?

Soit x l'âge d'Ann aujourd'hui.

On sait que l'âge de Barbara est x - (x/2) = x/2 (car Barbara avait la moitié de l'âge d'Ann lorsque l'écart d'âge entre elles était de x/2).

On sait également que l'âge d'Ann lorsque Barbara avait x/2 ans est (x/2 - x) = -x/2 ans de moins que son âge actuel.

Donc, l'âge d'Ann lorsque Barbara avait l'âge qu'avait Ann à ce moment-là est x - (x/2) - (-x/2) = 2x/2 = x ans.

Ainsi, l'âge de Barbara aujourd'hui est également x ans.

La somme de leurs âges actuels est 44 ans, donc :

x + x = 44

2x = 44

x = 22

Donc, l'âge d'Ann aujourd'hui est 22 ans.

Answer:

[tex]y=\frac{2}{3}x+1[/tex]

Step-by-step explanation:

Slope-Intercept Line Equation:

[tex]y=mx+b[/tex]

Where [tex]m[/tex] is the slope and [tex]b[/tex] is the y-intercept.

From the graph, we can see that the y-intercept is (0, 1). This means that the equation is currently:

[tex]y=mx+1[/tex]

To find the slope, we can use a point on the line to replace the x and y variables. The point that we use cannot have x equal to zero. If we use the x-intercept [tex](-1.5, 0)[/tex], the new equation will be:

[tex]0=m(-1.5)+1[/tex]

Then, we must find m:

[tex]0=m(-1.5)+1[/tex]

[tex]-1=m(-1.5)[/tex]

[tex]\frac{-1}{-1.5}=m[/tex]

[tex]m=\frac{2}{3}[/tex]

Now we can find the equation of the line:

[tex]y=\frac{2}{3}x+1[/tex]

Answer:

1286.3934 kg

Step-by-step explanation:

Convert 153% to a decimal:

153 / 100 = 1.53

Multiply 840.78 by 1.53:

840.78 * 1.53 = 1286.3934

The augmented matrix for the given system of equations is [[-2, 5, 2, 0], [3, 4, -8, 6], [-6, -6, 3, 0]]

An augmented matrix is a matrix that includes the coefficients of the variables and the constants in a system of equations. Each row of the matrix corresponds to one equation, and each column corresponds to one variable or the constant.

To write the augmented matrix for the given system of equations, we can start by rearranging the equations so that the variables are on the left side and the constants are on the right side:

5x + 2z = 2
3x + 4y - 8z = -6
-6x + 6y - 3z = 0

Next, we can write the coefficients of the variables and the constants in a matrix, with each row corresponding to one equation:

[5, 0, 2, 2]
[3, 4, -8, -6]
[-6, 6, -3, 0]

Finally, we can combine these rows into a single matrix to get the augmented matrix:

[[-2, 5, 2, 0], [3, 4, -8, 6], [-6, -6, 3, 0]]

This is the augmented matrix for the given system of equations.

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Answer:It will hit the ground when 84 - 16t^2 = 0

Step-by-step explanation:

16t^2 = 84

t^2 = 5.25

t = 2.29

Answer:

C is the answer

we have proved that H ◃ G ↔ N(H) = G.

Given G = (G;*) is a group and H ≤ G, and given set N(H) = {g ∈ G | gHg^-1 = H}, we need to prove that H ◃ G ↔ N(H) = G.

First, let's assume that H ◃ G. This means that H is a normal subgroup of G. By definition, a normal subgroup is a subgroup that is invariant under conjugation by any element of the group. In other words, for any g ∈ G and h ∈ H, we have gHg^-1 = H. This is exactly the condition for an element to be in N(H), so we can conclude that N(H) = G.

Now, let's assume that N(H) = G. This means that every element of G is in N(H), which means that for any g ∈ G and h ∈ H, we have gHg^-1 = H. This is the definition of a normal subgroup, so we can conclude that H ◃ G.

Therefore, we have proved that H ◃ G ↔ N(H) = G.

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About 71 % of the residents in a town say that they are making an effort to conserve water or electricity. 110 residents are randomly selected. The mean is 0.71. Standard Deviation is 0.043. The probability that the proportion of sampled residents who are making an effort to conserve water or electricity is greater than 80% is 0.0183.

1) Mean:
The mean of a proportion is simply the proportion itself, so the mean is 0.71.

2) Standard Deviation:
The standard deviation of a proportion is given by the formula:
σ = √(p(1-p)/n)
where p is the proportion, and n is the sample size. Plugging in the values given in the question:
σ = √(0.71(1-0.71)/110)
σ = 0.043

3) To find this probability, we need to use the normal distribution. We will use the z-score formula:
z = (x - μ) / σ
where x is the proportion we are interested in (0.8), μ is the mean (0.71), and σ is the standard deviation (0.043). Plugging in the values:
z = (0.8 - 0.71) / 0.043
z = 2.09
Using a z-table, we find that the probability of getting a z-score greater than 2.09 is 0.0183. So the probability that the proportion of sampled residents who are making an effort to conserve water or electricity is greater than 80% is 0.0183.

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Step-by-step explanation:

the perimeter of a rectangle is

2×length + 2×width

simply because the perimeter means to go along every side the shape has.

I don't see any answer options. you did not provide any. I can only give you the approach of how to solve this.

so, that means for us

2(6x + 5) + 2×3x = 100

12x + 10 + 6x = 100

18x = 90

x = 90/18 = 5

Answer:4/5 and y = 9/5.

Step-by-step explanation:We can start by substituting the second equation into the first equation, replacing y with 1/2x+8:

3x + 4(1/2x+8) = 36

Simplifying, we get:

3x + 2x + 32 = 36

Combining like terms, we get:

5x + 32 = 36

Subtracting 32 from both sides, we get:

5x = 4

Dividing both sides by 5, we get:

x = 4/5

Now that we have found x, we can substitute it back into the second equation to find y:

y = 1/2x + 8 = 1/2(4/5) + 8 = 9/5

Therefore, the solution to the system of equations is x = 4/5 and y = 9/5.

The shortest distance Jose can ride to park is 5 miles.

The Pythagoras theorem which is also referred to as the Pythagorean theorem explains the relationship between the three sides of a right-angled triangle. According to the Pythagoras theorem, the square of the hypotenuse is equal to the sum of the squares of the other two sides of a triangle.

Given that, Jose can follow the roads getting to the park- first heading south 3 miles, then heading west 4 miles.

Let the shortest root Jose can choose be x miles.

By using Pythagoras theorem, we get

x²=3²+4²

x²=9+16

x²=25

x= 5 miles

Therefore, the shortest distance is 5 miles.

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Answer:

x to the power of 67000 to the 5th power.

Step-by-step explanation:

The mean of the values will be 9.4, the median will be 3 points and the mode will be 4

It should be noted that mean in mathematics simply means the total added values of all the data in a set of divided by the number of days in a set.

The mean of the values will be:

= (10 + 8 + 11 + 12 + 6) / 5

= 47 / 5

= 9.4

The median of the set of numbers is the number on the middle when arranged ascending or in a descending manner. This is 3 points. The mode is 4.

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The answer to this question is C) 0.8. This can be determined using the Pythagorean Theorem.

What is Pythagorean theorem?

The Pythagorean Theorem is one of the most important theorems in mathematics, and it has been used for centuries to solve various mathematical problems. It is a fundamental tool for measuring distances and calculating angles in Euclidean geometry.

The theorem can be expressed as an equation, a^2 + b^2 = c^2, where a and b are the lengths of the sides of the triangle, and c is the length of the hypotenuse. This equation can be used to calculate the lengths of the sides of a right-angled triangle if two of the sides are known.

The theorem states that the sum of the squares of the lengths of the two legs of the triangle is equal to the square of the length of the hypotenuse. In this case, the legs of the triangle are AB and BC, each of which is 10 units long. Therefore, the formula for this triangle is 10² + 10² = 12², or 100 + 100 = 144. Solving this equation shows that the length of the hypotenuse, AC, is equal to 12 units, which is a ratio of 0.8 compared to the lengths of the two legs. Therefore, the correct answer is C) 0.8.

The value of sin can then be determined using the sine formula, which states that the ratio of the length of the side opposite the angle to the length of the hypotenuse is equal to the sine of the angle. In this case, the side opposite the angle is AB, which is 10 units long. The hypotenuse is AC, which is 12 units long. Therefore, the sine of the angle is equal to 10/12, or 0.8. Therefore, the value of sin is 0.8.

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The value for the quadratic equation is C(t) = t² + 3.

When two lines or rays intersect and cross at one endpoint or vertex, a vertex angle is created. This angle, which is expressed in degrees, is occasionally confused with face angle. Two intersecting lines at the corner of a 2D object, such a polygon, generate a vertex angle. In 3D forms, however, multiple angles are conceivable since there are more than two lines.

The standard form of the quadratic function is given as:

C(t) = at² + bt + c

Using different values of t from the table we have:

a(-2)² + b(-2) + c = 7

a(-1)² + b(-1) + c = 4

a(0)² + b(0) + c = 3

Simplifying the equations we have:

4a - 2b + c = 7

a - b + c = 4

c = 3

Substituting the value of c = 3 in equation 2:

a - b = 1

Further solving the equation for a and b we have:

a = 1

b = 0

Hence, the equation for the quadratic equation is C(t) = t² + 3.

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There is no unit vector with a positive first component that is orthogonal to both u and v.

The unit vector we are looking for is (1/√14, √13/14, √15/14, -√12/14). To find this vector, we need to solve the equation 0 = u1 + v1, where u1 and v1 are the first components of u and v. From the given vectors, u1 = 1 and v1 = 6. So 0 = 1 + 6, which simplifies to -6 = 0, which is a contradiction, meaning there is no unit vector with a positive first component that is orthogonal to both u and v.

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No, a negative solution such as (-5, -10) would not be acceptable in this situation.

Coordinates are a set of values that indicate a position on a two-dimensional grid. The most common type of coordinates are known as Cartesian coordinates, which have an x-axis and a y-axis. Coordinates can also be used to describe points in three-dimensional space, such as a latitude and longitude on a map. Coordinates are used by scientists, engineers, and navigators to pinpoint exact locations and make calculations.

This is because a negative solution would imply that the acts were running for a negative amount of time, which is impossible. Additionally, the intersection point of the two equations should be a point of equilibrium where both acts are running for the same amount of time. A negative solution would indicate that one of the acts is running for more time than the other, which defeats the purpose of the equations. Therefore, a negative solution would not be an acceptable answer for this situation.

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The ferry travels at constant rate is 7/18 miles/hour

Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications.

For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.

As per the data given in the question we have to find the ferry travels at a constant rate.

As per the question it is given that a ferry traveled 1/6 of the distance between two ports in 3/7 hour.

Now, Ferry travelled 1/6 miles of distance between two ports in 3/7 hours  

Hence, Rate of Ferry is equal to distance travelled over time taken.  

Rate of ferry = 1/6 ÷ 3/7

Now we calculate it.  

Rate of ferry = 1/6 × 7 / 3 miles/hour

Rate of Ferry = 7/18 miles/hour

Hence, The ferry travels at constant rate is, 7/18 miles/hour.

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The solution for the inequality in this problem is problem is given as follows:

v ≤ 81.

The four inequality symbols, along with their meaning, are presented as follows:

The inequality is given as follows:

5v/9 ≤ 45.

v ≤ 45 x 9/5

v ≤ 9 x 9

v ≤ 81.

Hence the solution is composed by the numbers to the left of 81, with a closed interval at x = 81.

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Answer:

If applying the 20% off coupon and the 10% coupon it would be separate. This would be different than a 30% coupon

Step-by-step explanation:

Let's say you are taking 20% off of $100, doing that would reduce the price to $80 because you took off $20, after this you would apply the 10% off coupon to the $80, your total would be 72 now because 10% of 80 is 8. The 20% Coupon and the 10% coupon stacked would bring your total to $72. If you flat out took 30% out of 100 dollars you would be left with $70 compared to the $72 that you got with the 20% coupon and the 10% coupon.

20% + 10% would remove less than a 30% coupon because after applying the 20% coupon, your 10% coupon would remove less because of the lower number being subtracted. Hope this helps

The simplified form of the left side of the equation is $2 \tan x$.

The left side of the equation can be simplified using the quotient and reciprocal identities. The quotient identity states that $\tan x = \frac{\sin x}{\cos x}$ and the reciprocal identity states that $\sec x = \frac{1}{\cos x}$ and $\csc x = \frac{1}{\sin x}$. By substituting these identities into the equation, we can simplify the left side:

\[ \begin{aligned} \frac{\sec x+\tan x \csc x}{\csc x} & =\frac{\frac{1}{\cos x}+\frac{\sin x}{\cos x} \cdot \frac{1}{\sin x}}{\frac{1}{\sin x}} \\ & =\frac{\frac{1}{\cos x}+\frac{1}{\cos x}}{\frac{1}{\sin x}} \\ & =\frac{2 \cdot \frac{1}{\cos x}}{\frac{1}{\sin x}} \\ & =\frac{2}{\cos x} \cdot \frac{\sin x}{1} \\ & =\frac{2 \sin x}{\cos x} \\ & =2 \tan x \end{aligned} \]

Therefore, the simplified form of the left side of the equation is $2 \tan x$.

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The minimum cost per pupil is $7,500 when 250 students are enrolled.

To find the minimum cost per pupil, we need to find the vertex of the parabola C = 70,000 − 500n + n². The vertex of a parabola in the form y = ax² + bx + c is given by the formula x = -b/2a. In this case, a = 1, b = -500, and c = 70,000.

Plugging these values into the formula, we get:
x = -(-500)/2(1) = 500/2 = 250

So the minimum cost per pupil occurs when n = 250 students are enrolled.

To find the minimum cost, we can plug n = 250 back into the equation for C:
C = 70,000 − 500(250) + (250)² = 70,000 - 125,000 + 62,500 = 7,500

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Answer: 20

Step-by-step explanation:

49 ÷ 245 %

convert the percentage to decimals

49 ÷ 2.455

calculate the product or quotient

20

                   Please give me brainliest

Answer:20

Step-by-step explanation:

Let's denote the number we are looking for as "x".

We can set up the equation:

245% of x = 49

We can convert 245% to the decimal form by dividing by 100:

2.45 * x = 49

To solve for x, we can divide both sides of the equation by 2.45:

x = 49 / 2.45

x = 20

Therefore, 245% of 20 is equal to 49.

If the stone dropped by Maria falls 2 meter in 1st second, then the stone would have fallen 30 meter after 10 seconds.

The distance that the stone falls in the first second is = 2 meters;

The distance that the stone falls in the 50th second is = 149 meters;

So, the rate of fall of the stone can be calculated as:

⇒ (149 - 2)/(50 - 1);

⇒ 147/49;

⇒ 3.

So , the stone is falling at the rate of 3 meter per second,

The distance fall by the stone after 10 second can be calculated as :

⇒ 10×3

⇒ 30 meter.

Therefore, After 10 seconds the stone would have fallen 30 meter.

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