how many solutions does this system of equations have y=2x y=x^2+2

Answer:3.5

Step-by-step explanation:

The rate at which air is being pumped in when the radius of the sphere is 10 cm and increasing at a rate of 2 cm/s is 400π/3 cm³/s.

The volume V of a sphere with radius r is given by V = (4/3)πr³. Taking the derivative of this expression with respect to time t, we get dV/dt = 4πr²(dr/dt). This equation relates the rate of change of volume to the rate of change of the radius. We are given that the radius is increasing at a rate of 2 cm/s, so dr/dt = 2 cm/s.

At the instant when the radius is 10 cm, we can find the rate at which air is being pumped in by substituting r = 10 cm and dr/dt = 2 cm/s into the equation for dV/dt. Thus, we have dV/dt = 4π(10)²(2) = 800π cm³/s.

Therefore, when the radius of the spherical balloon is 10 cm and is increasing at a rate of 2 cm/s, the rate at which air is being pumped in is 400π/3 cubic centimeters per second.

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Using substitution method, the cost of hotel per night is $ 85

Let hotel cost per night = x

Let car rental per day = y

4x + 2y = 500 ____(1)

4x + 5y = 740 ____(2)

Solving for x in the equation

Equation (1) - (2)

-3y = - 240

y = 80

Substitute the value of y in (1)

4x + 2(80) = 500

4x + 160 = 500

4x = 500-160

4x = 340

x = $85

Therefore, hotel cost per night is $85

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Answer: 66.548

Step-by-step explanation: 26.2 in = 66.548 so that is how I got my elegant marvelous answer

To determine the true fraction of voters who support the proposal to pay $200 more a year in taxes for improved schools, we can calculate a 95% confidence interval based on the survey results. Additionally, to estimate the required sample size to obtain an estimate with a 95% confidence interval.

To find the 95% confidence interval for the true fraction of voters who support the proposal, we can use the formula:

Confidence Interval = Sample Proportion ± Margin of Error

The sample proportion is calculated by dividing the number of voters willing to pay $200 more in taxes (885) by the total sample size (1500). The margin of error is determined using the critical value associated with a 95% confidence level.

To estimate the required sample size, we can use the formula:

Sample Size = (Z-score * Standard Deviation / Margin of Error)²

In this case, we want the margin of error to be at most one percentage point. The Z-score corresponds to the desired confidence level of 95%. The standard deviation can be estimated using the sample proportion (from the previous question) and the formula for standard deviation of a sample proportion.

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The Gauss-Jacobi method is an iterative technique used to solve systems of linear equations. Here are the general steps:

1. Write down the system of linear equations derived from the mesh analysis of the circuit.

2. Rearrange the equations so that the variables appear on one side and the constant terms on the other side.

3. Initialize the variables to some initial values.

4. For each equation, calculate the new value of the variable based on the previous values of the other variables. Repeat this step for each equation.

5. Check the error for each variable by comparing the new value with the previous value. If the error is below a specified threshold (such as Ea ≤ 0.00001), terminate the iteration. Otherwise, go back to step 4 and repeat the process.

6. Once the iteration is terminated, you will have the approximate values of the variables.

Now, let's consider an example to illustrate the Gauss-Jacobi method:

Suppose we have the following system of linear equations derived from a mesh analysis of a circuit:

Equation 1: 4x - y + z = 10

Equation 2: x + 5y - 2z = -4

Equation 3: 2x + y + 7z = 6

Let's initialize the variables:

x = 0, y = 0, z = 0

We can start the iterative process as follows:

Iteration 1:

New value of x: (10 + y - z) / 4

New value of y: (-4 - x + 2z) / 5

New value of z: (6 - 2x - y) / 7

Iteration 2:

New value of x: (10 + y - z) / 4

New value of y: (-4 - x + 2z) / 5

New value of z: (6 - 2x - y) / 7

Continue the iterations until the errors for each variable are below the specified threshold (Ea ≤ 0.00001).

Finally, you can tabulate the results, including the values of x, y, z at each iteration until convergence.

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Answer:

B hope this helps

Step-by-step explanation:

Answer: it’s (A)

Step-by-step explanation:

Answer:

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

Each coordinate of the midpoint is the average of endpoints:

Therefore M is (13, 14).

Answer: X = 2

Step-by-step explanation:

2x + 7 = -9 - 6x

subtract 7 from both sides

2x = - 16 - 6x

add 6x to both sides

8x = 16

divide 16 by 8

x = 2

Answer:

x=-2

Step-by-step explanation:

add the 6x to the other side & combine the 2x+6x then subtract the 7 to the other side so combine the -7--9

so you would get 8x=-16 then divide by 8 & you get x=-2

Answer:

9x^2 + 21x + 12

Step-by-step explanation:

(3x+4)(x+2x+3)

Combine x and 2x to get 3x.

(3x+4)(3x+3)

Apply the distributive property by multiplying each term of 3x+4 by each term of 3x+3.

9x^2 + 9x + 12x + 12

Combine 9x and 12x to get 21x.

9x^2 + 21x + 12

Answer:

see below

Step-by-step explanation:

7. (4-4). K =0

d+12-8/4+5 = d+12-2+5 =d+15

The total distance if Pete walks from A to B to C is 40 yards, the direct distance from A to C is more than 10 yards, and an inequality w < 30

It is defined as the expression in mathematics in which both sides are not equal they have mathematical signs either less than or greater than known as inequality.

We have:

Points A, B, and C, form a triangle. The distance between point A and point B is 15 yards. The distance between point B and point C is 25 yards.

Total distance if Pete walks from A to B to C:

= 15 + 25 = 40 yards

As we know in the triangle the sum of the two sides is greater than the third side.

25 + 15 > AC

40 > AC

or

AC < 40

The direct distance from A to C is more than 10(25-15) yards.

The inequality w < 30 represents the distance, w, that Pete might save by taking the direct path.

Thus, the total distance if Pete walks from A to B to C is 40 yards, the direct distance from A to C is more than 10 yards, and an inequality w < 30

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Answer:

40, 10, 30
see picture

Step-by-step explanation:

Let the number be "x" , then according to the question :

• 2x - 12 = -8

Further solving

→ 2x = -8 + 12

→ 2x = 4 .

→ x = 2

★ Solution :

Let number be n.

\(\rule{130}{1}\)

☯ \(\underline{\boldsymbol{According\: to \:the\: Question\:now :}}\)

\(:\implies\sf 2n - 12 = -8 \\\\\\:\implies\sf 2n = -8 + 12\\\\\\:\implies\sf 2n = 4\\\\\\:\implies\sf n = \dfrac{4}{2}\\\\\\:\implies\underline{\boxed{\sf n = 2}}\:\:\:\:\:\Bigg\lgroup\bf{Required\: number}\Bigg\rgroup\)

\(\therefore\:\underline{\textsf{The required number is \textbf{2}}}.\)

The pair of 1st line is vertical opposite angle and 2nd one is adjacent angles.

What is vertical opposite angle ?

When 2 lines meet one another, then the other angles, shaped thanks to intersection ar known as vertical angles or vertically opposite angles. A try of vertically opposite angles ar continuously adequate to one another. Also, a angle and its adjacent angle are supplementary angles, i.e., they add up to a hundred and eighty degrees.

Main body:

1st pair of line intersect each other , so ∠1 = ∠2 by using vertical opposite angle.

2nd pair of line also intersect each other , so ∠3 ,∠4 are adjacent angles.

Hence ,pair of 1st line is vertical opposite angle and 2nd one is adjacent angles.

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Answer:

See below

Step-by-step explanation:

I think you meant

  y= a (x-h)^2  +k

       this is the vertex form of a parabola with vertex  (h,k)

Answer:

A D E

Step-by-step explanation:

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Answer:

-1.25 or -10/8

Step-by-step explanation:

the additive inverse of a number is the number that would make it zero when added

ex. the inverse of 5 is -5 because 5+(-5)=0

so the inverse of -5/8 is 5/8 because -5/8+5/8=0. The question said to subtract the additive inverse.

-5/8-(5/8)=

-5/8-5/8=

-10/8 or -1.25

Answer:

No

Step-by-step explanation:

A parallelogram has opposite angels equal and opposite sides equal. in this case, only a single pair of angels are equal.

Answer:

At x = -2 the graph of this polynomial will touch the x-axis.

Step-by-step explanation:

Recall the behavior difference between power functions of even and odd power. Odd powers are associated with the crossing of the x-axis, while even powers are associated with "touching" of the x axis.

in this cases, since they give you the function in factor form, the actual roots (x-values where the function adopts value zero) of the function are evident :

\(f(x)=(x-5)^3\, (x+2)^2\)

It has a root at x = 5 [notice that at such x-value the factor (x-5) becomes zero], and this root is of multiplicity "3" (given by the power associated with the binomial factor for this root)

and has another root at x = -2  [notice that at such x-value the factor (x+2) becomes zero], and this root is of multiplicity "2" (given by the power associated with the binomial factor for it)

It is just the second root analyzed the one that shows an even power (2) associated to its binomial factor, and therefore it is at x= -2 that the graph of this function will show as "touching" the x axis.

The probability of approximately 48% that a player will have a height between 5'2" and 5'6".

To calculate the probability of a player being between 5'2" and 5'6" given that historically, the members of the chess club have had an average height of 5'6" with a standard deviation of 2", we can use the standard normal distribution.

First, we need to convert the heights to z-scores using the formula:

z = (x - μ) / σ

where x is the height we want to find the probability for, μ is the mean height, and σ is the standard deviation.

For 5'2":

z = (62 - 66) / 2 = -2

For 5'6":

z = (66 - 66) / 2 = 0

Next, we can use a standard normal distribution table or calculator to find the area under the curve between these two z-scores.

Using a standard normal distribution table, we can find that the area to the left of z = -2 is 0.0228 and the area to the left of z = 0 is 0.5. Therefore, the area between z = -2 and z = 0 is:

0.5 - 0.0228 = 0.4772

Multiplying this by 100 gives us a probability of approximately 48% that a player will have a height between 5'2" and 5'6".

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Answer:

v=7

Step-by-step explanation:

You want to write your equation and it should look like this:

12 - 3V+ 12Y = 4

next you wanna plug in y which in this case it is 3 now your equation should look like this:

12 - 3V+ 12(3) = 4

next you wanna multiply 12 and 3 so keep everything the same your new equation should look like this:

12 - 3V+ 36 = 4

now you wanna combine like terms and the like terms here would be 12 and 36 so you wanna subtract 12 from 36 to get you 24 and your new equation should look like this:

3V+ 24 = 4

next you want to subtract 24 from 4 and it should look like this:

3V= -20

now you want to get the variable by itself and you can do that by dividing 3 from -30 and your new equation should look like this:

v=-6.666666666666667

but you cant submit that so you wanna say v=7

it will go far as 231 km in 45 mins

Answer:

5 + 2x

Step-by-step explanation:

Called the unknown number "x"

The problem essentially says;

5 + 2x

Answer:

Graham: -50x + 14,040

Max:  20x + 12,500

  Graham = Max

-50x + 14,040 = 20x + 12,500

   +50x +50x              

       14,040 = 70x + 12,500

          -12,500-12.500

            1,540  = 70x

               220 = x

Answer: 220 minutes (3 hours 40 minutes)

PLZ MARK AS BRAINILEST:-)

Answer:

Here now he can get brainliest

Step-by-step explanation:

Chuggy

Answer:

y = 63

Step-by-step explanation:

A straight line is equal to 180 degrees.

180 = 2y - 18 + y + 9

180 = 3y -9

189 = 3y

189/3

y = 63

Answer:

63

Step-by-step explanation:

2y-18+y+9=180 degrees

3y-9=180 degrees

3y=189 degrees

y=63 degrees

Answer:

You:If it’s was 6 cups of citric I’d be to 32 water

Your friend: if it was 4 cups it’d be 12 water

Step-by-step explanation:

I believe your friends is more acidic because your Is being diluted more

Answer:

-12 is the answer

Step-by-step explanation:

Substitute 1/4 for a and 6 for b in the equation

-8ab

-8(1/4)(6) Multiply

-8(1.5) Multiply

-12

The half of the time that Arnold skied without falling is 712 as 2 x 356=712>223 .

Inequality is a mathematical statement that illustrates the connection between two expressions by using the inequality symbol. The phrases on both sides of an inequality sign are distinct. It indicates that the left expression should be larger or smaller than the right expression, or vice versa. When the link between two algebraic expressions is expressed using inequality symbols, literal inequalities arise.

The discrepancy represents the incident in which Kelvin skied for more than twice as long as anybody else in his family:

2f < 223

Here 223 is the time for Kelvin.

Check for Lori as follows:

2f < 223

2 x 55=110 < 223

Kelvin skied without falling more than twice as long as Lori.

Check for Vanessa as follows:

2f < 223

2 x 265=530>223

Check for Arnold as follows:

2f < 223

2 x 356=712>223

Kelvin skied without falling less than twice as long as Arnold.

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Complete question:

Kelvin wants to know whether he skied without falling more than twice as long as anyone else in his family. His dad tells him that he can check by using the inequality 2f < 223, where f is the time skied in seconds for each person. Plug the values for the time skied by each person into the inequality to find the answer.

Lori 55

Vanessa 265

Devon 172

Celia 112

Arnold 356