10x + 6 = -2x + 18 solve for x​

The simplified expression for \((m/3m^2-9m+6) - (2m+1/3m^2+3m-6)\) is \((3m-1)/(3m^2+3m-6)\). The variable m is restricted such that m cannot be equal to -1 or 2.

To simplify the given expression, we need to find a common denominator for the fractions. The denominators in this case are \(3m^2-9m+6\) and \(3m^2+3m-6\). The common denominator is obtained by multiplying these two expressions, resulting in \((3m^2-9m+6)(3m^2+3m-6)\).

Next, we can simplify the numerator by subtracting the fractions. Distributing the negative sign to the second fraction gives us \(-(2m+1) = -2m-1\). Now, we have (m - 2m - 1) as the numerator, which simplifies to (-m - 1).

Combining the simplified numerator and the common denominator, the expression becomes \((-m - 1)/(3m^2+3m-6)\). We can further simplify this expression by factoring the denominator, which gives us (3m-1)(m+2)/(3m-1)(m+2). Notice that the factor (3m-1) appears in both the numerator and the denominator, so we can cancel it out, resulting in the simplified expression: \((m+2)/(3m^2+3m-6)\).

However, we should note that the factor (3m-1) cannot be equal to zero, as it would result in division by zero. Therefore, the variable m is restricted such that m ≠ 1/3. Additionally, we canceled out the factor (3m-1) during the simplification process, which means m cannot be equal to 1/3 even if it was a solution to the original equation. Hence, the restrictions on the variable m are m ≠ -1 and m ≠ 2.

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A. The speed at which blood is travelling through the plaque-constricted region is approximately 31.62 cm/s. and B. P2 - P1 ≈ -405,431.58 kg/\((m*s^2)\) = -405,431.58 Pa (approximately).

(a) To determine the speed at which blood is travelling through the plaque-constricted region, we can apply the principle of continuity, which states that the flow rate of an incompressible fluid remains constant in a closed system.

The flow rate (Q) is given by the product of the cross-sectional area (A) and the velocity (v): Q = A * v.

Since the flow rate remains constant, we can write:

Q1 = Q2

A1 * v1 = A2 * v2

The cross-sectional area of the artery can be approximated as A = π * \(r^2\), where r is the radius of the artery.

Given that the diameter decreases from 1.16 cm to 0.70 cm, the initial radius (r1) is 0.58 cm (0.58 cm = 1.16 cm / 2) and the final radius (r2) is 0.35 cm (0.35 cm = 0.70 cm / 2).

Using these values, we can find the ratio of the cross-sectional areas:

A1/A2 = (π * \(r1^2\)) / (π * \(r2^2\)) =\((r1^2) / (r2^2).\)

Substituting the given values:

A1/A2 = \((0.58 cm)^2 / (0.35 cm)^2\) ≈ 2.108.

Since the cross-sectional areas are inversely proportional to the velocities, we have:

v2 = (A1/A2) * v1 = 2.108 * 15.0 cm/s ≈ 31.62 cm/s.

Therefore, the speed at which blood is traveling through the plaque-constricted region is approximately 31.62 cm/s.

(b) To determine the pressure change within the plaque-constricted region, we can use Bernoulli's equation, which relates the pressure, velocity, and height of a fluid in a flowing system.

Bernoulli's equation is given by:

P1 + (1/2) * ρ * \(v1^2\) + ρ * g * h1 = P2 + (1/2) * ρ * \(v2^2\) + ρ * g * h2.

Where P1 and P2 are the pressures, v1 and v2 are the velocities, ρ is the density of blood, g is the acceleration due to gravity, h1 is the initial height, and h2 is the final height.

In this case, we can assume that the height remains constant, so the terms ρ * g * h1 and ρ * g * h2 cancel out.

Since we are interested in the pressure change, we can rewrite Bernoulli's equation as:

P2 - P1 = (1/2) * ρ * \((v1^2 - v2^2).\)

Substituting the given values:

\(P2 - P1 = (1/2) * 1050 kg/m^3 * [(15.0 cm/s)^2 - (31.62 cm/s)^2].\\P2 - P1 = (1/2) * 1050 kg/m^3 * [225 cm^2/s^2 - 1000.2244 cm^2/s^2].\)

\(P2 - P1 ≈ (1/2) * 1050 kg/m^3 * (-775.2244 cm^2/s^2).\\P2 - P1 ≈ -405,431.58 kg/(m*s^2) = -405,431.58 Pa (approximately).\)

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Answer:

C

Step-by-step explanation:

Integers are only positive and negative numbers:)

also 0

fractions are not integers

Answer:

1/2

Step-by-step explanation:

c is the correct answer

The derivative of g(y) evaluated at 7 is approximately -1.62.

To use part 1 of the fundamental theorem of calculus to find the derivative of the function g(y) = y t² sin(6t) dt evaluated at 7, we first need to define a new function F(t) as the antiderivative of g(y) with respect to t.
F(t) = ∫ g(y) dt = ∫ y t² sin(6t) dt
To evaluate this integral, we can use u-substitution with u = 6t, du/dt = 6, dt = du/6:
F(t) = ∫ y (u/6)² sin(u) (du/6)
F(t) = (y/216) ∫ u² sin(u) du
Using integration by parts with u = u² and dv = sin(u) du, we get:
F(t) = (y/216) [-u² cos(u) - 2u sin(u) + 2 ∫ sin(u) du]
F(t) = (y/216) [-u² cos(u) - 2u sin(u) - 2 cos(u)] + C
where C is the constant of integration.
Now, we can apply part 1 of the fundamental theorem of calculus, which states that if F(x) is the antiderivative of f(x), then the derivative of ∫ a to b f(x) dx is F(b) - F(a).
Therefore, the derivative of g(y) evaluated at 7 is:
g'(7) = d/dy [F(t)] evaluated at t = 7
g'(7) = d/dy [(y/216) [-u² cos(u) - 2u sin(u) - 2 cos(u)] + C] evaluated at t = 7
g'(7) = (1/216) [-u² cos(u) - 2u sin(u) - 2 cos(u)] evaluated at t = 7
g'(7) = (1/216) [-294 cos(42) - 84 sin(42) - 2 cos(42)]
Therefore, the derivative of g(y) evaluated at 7 is approximately -1.62.

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Answer:

Same I'll help you all if you guys try to help me with my recent question.

Step-by-step explanation:

Answer:

\(x^{3}\)

Step-by-step explanation:

multiply x by x

\(x^{2}\) · \(x\)

Multiply \(x^{2}\)    by \(x\)    by adding the exponents.

Raise  \(x\) to the power of  1

\(x^{2}\) · \(x^{1}\)

Use the power rule \(a^{m} a^{n} = a^{m+n}\) to combine exponents.

\(x^{2+1}\)

add 2 and 1

\(x^{3}\)

Answer

it can also be x^3...........

According to the SAS theorem, two triangles are equal if their two sides and the angle between them are both equal. The included angle is another name for the angle formed by the two sides. The side angle side is referred to as SAS.

More about SAS(Side Angle Side) theorem:

This geometric theorem gave rise to the SAS area formula, which is used in trigonometry. If you know the length of two triangle sides and the included angle, you can use the SAS area formula to determine the triangle's area. In particular, if the included angle is designated as A and the sides of the included angle are denoted by the letters b and c, then

Triangle ABC's area is (b*c*sin A) / 2.

It is crucial that the angle you use to calculate the area of the object lies between the two sides that you utilize.

So basically when the two sides and the angle between them are both equals then the SAS theorem can be used to determine whether the two triangles are also equal.

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Answer: 1 4/8 or 1 1/2

Step-by-step explanation:

1 5/8

-1/8

5/8 - 1/8 = 4/8  

add 1.....  1 4/8

So the estimated value of √6.02 using differentials is approximately 2.4556.

The change in g(x,y,z) can be estimated using partial derivatives and differentials.

We can start by finding the partial derivatives of g(x,y,z) with respect to x, y, and z:∂g/∂x = 3 + cos(z)∂g/∂y = -sin(z) + 1∂g/∂z = -x sin(z) - y cos(z)Next, we can use the point P0(1,-3,0) and the distance ds = 0.1 to find the differentials dx, dy, and dz:dx = -2/√6 dsdy = 2/√6 dsdz = 1/√6 dsUsing these values, we can estimate the change in g:Δg ≈ (∂g/∂x) dx + (∂g/∂y) dy + (∂g/∂z) dzΔg ≈ (3 + cos(0)) (-2/√6 ds) + (-sin(0) + 1) (2/√6 ds) + (-1 sin(0) - (-3) cos(0)) (1/√6 ds)Δg ≈ (3 - 2/√6) dsPlugging in ds = 0.1, we get:Δg ≈ (3 - 2/√6) (0.1)Δg ≈ 0.389

Therefore, the change in g(x,y,z) is estimated to be approximately 0.389 units if the point P(x,y,z) moves from P0(1,-3,0) a distance of ds = 0.1 unit toward the point P1(-1,-1,2).

Suppose we want to estimate the value of √6.02 using differentials. We can start by choosing x = 6 and Δx = 0.02. Then, we need to find the derivative of f(x) = √x with respect to x:

f(x) = √x

f'(x) = 1/(2√x)

Using these values, we can estimate Δy:

Δy ≈ dy = f'(x) Δx

dy ≈ (1/(2√6)) (0.02)

dy ≈ 0.005

This means that a small change of 0.02 in x produces a small change of approximately 0.005 in y. To estimate the value of √6.02, we can add this change to the known value of √6:

√6.02 ≈ √(6 + 0.02) ≈ √6.04 ≈ 2.4556

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x = 15 is in fact a solution of the given inequality.

Here we have the inequality:

x + 9 > 21

We want to see if it is true for x = 15, to check it, we need to repace the value:

15 + 9 > 21

24 > 21

This is true, 24 is larger than 21, then we conclude that x = 15 is a solution of the given inequality.

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Answer:

27

Step-by-step explanation:

The triangle shown is an isoceles triangle. This means that there are two congruent base angles and a vertex angle. In this case, angle X and angle Y are the base angles, so we can set up an equation to first find the value of t.

5t - 13 = 3t + 3

2t - 13 = 3              (Subtract 3t from both sides)

2t = 16                   (Add 13 to both sides)

t = 8                      (Divide both sides by 2)

Now that we have the value of t, we can plug it back in to the expression for angle X to find its measure.

5(8) - 13

40 - 13

27

So, the measure of angle X is 27

The answer is C. 1/10 of a centimeter.

The amount he would pay to purchase a laptop today that is the same value as the one he saw in the ad is $390.

Cost price: Cost prize is the price at which the goods and services were purchased.

It is given that,

projected price: $400.00, and the laptop will be out on the market in about one year with 2.5% inflation.

Now, if he pays today for a laptop of the same value as the one in the advertisement, his cost will be 2.5% of $400 less, or as follows:

cost price of laptop = $400 - 2.5& x 400

cost price of laptop = 97.5% x $400

cost price of laptop = $390

As a result, the laptop that he needs right now will cost $390.

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9 can be expressed as 3² where value larger than the base.

Exponents and powers are ways used to represent very large numbers or very small numbers in a simplified manner.

Given:

A power with a positive base and a positive integer exponent will always have a value larger than the base.

We can take example as

5³ = 125

Here the base is 5 and value is 125 which is larger than base.

So, to express 9 as such form is

3² = 9

Here Base (3) < Value (9)

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Answer:

18 miles= how many feet

____95,040_____feet

Step-by-step explanation:

happy to help ya:)

The equilateral triangle ΔGH with sides 1/2 a units long can be positioned and labeled on the coordinate plane. However, without specific information about the vertex points or additional constraints, we cannot determine the exact positioning or labeling of the triangle.

To position and label the equilateral triangle on the coordinate plane, we need information about the vertex points or specific constraints such as the coordinates of one vertex or the center of the triangle. Without such information, we cannot determine the exact positioning of the triangle.

Additionally, labeling the triangle typically involves assigning letters or symbols to each vertex to uniquely identify them. However, without specific information or context, we cannot provide a specific labeling scheme for the equilateral triangle.

Therefore, to accurately position and label the equilateral triangle on the coordinate plane, we require additional information such as the coordinates of one vertex or the center of the triangle. With this information, we can determine the positioning and labeling of the equilateral triangle on the coordinate plane.

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Therefore, the solution to the differential equation with the given initial condition is: u(t) = -1/4 ln(6t² + e⁻⁶⁸)) - 1/4 ln(2).

Initial value problems are another name for differential equations with initial conditions. The example dydx=cos(x)y(0)=1 is used in the video up above to demonstrate a straightforward starting value issue. You get y=sin(x)+C by solving the differential equation without the initial condition.

For the separable differential equation to be solved:

\(u du/dt = e^(4u) 6t\)

The variables can be rearranged and divided:

\(u du e^(-4u) du = 6t dt\)

Integrating both sides, we get:

\((1/2)e^(-4u) = 3t^2 + C\)

where C is the integration constant. We utilise the initial condition u(0) = 17 to determine C:

\((1/2)e^(-4(17)) = 3(0)^2 + CC = (1/2)e^(-68)\)

When we put this C value back into the equation, we get:

\((1/2)e^(-4u) = 3t^2 + (1/2)e^(-68)\)

After taking the natural logarithm and multiplying both sides by 2, we arrive at:

\(-4u = ln(6t^2 + e^(-68)) + ln(2)\)

Simplifying, we have:

\(u = -1/4 ln(6t^2 + e^(-68)) - 1/4 ln(2)\)

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Answer:

d > -2

Step-by-step explanation:

-2d-2 < 3d+8

3d+8 > -2d-2

3d + 2d > -2 -8

5d > -10

d > -2

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a) The histogram for given data is as shown below.

b)From the box and whisker plot we can see that there is no outlier for given data.

c) mean = 47.48

standard deviation = 22.61

IQR = 44

In this question, we have been given the data on the number of contacts for a random sample of 30 elderly adults with smartphones in a large city.

7,20,24,25,25,28,28,30,32,35,42,43,44,45,46,47,48,48,50,51,72,75,77,78,79,83,87,88,13,51,51

a) the histogram for given data is as shown below.

b) From the box and whisker plot we can see that there is no outlier for given data.

c) the mean of the given data is:

m = 47.48

the standard deviation for given data is:

s = 22.61

the First quartile:  

Q1 =  28

the median = 46

the Third quartile:  

Q3 = 72

the Interquartile range:  

IQR = Q3 - Q1

IQR = 72 - 28

IQR = 44

Therefore, for given data:

a)  the histogram for given data is as shown below.

b) there is no outlier for given data.

c) mean = 47.48

standard deviation = 22.61

IQR = 44

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Answer:

x = -37.5

Step-by-step explanation:

Set up a proportion so -5/12.5 = 15/x

Solve for x so -5x = 15(12.5) so -5x = 187.5 so x = -37.5

Answer:

x = -1 1/2 , x = 1.5

Step-by-step explanation:

Answer:x=12

Step-by-step explanation:

Subtract

3x

from both sides of the equation.

4x−5−3x=7

Subtract

3x from 4x.x−5=7Move all terms not containing x to the right side of the equation.

Add 5

to both sides of the equation.

x=7+5Add 7and 5

.

x=12

Answer:

3/9

Step-by-step explanation:

15/45

divide both sides by a factor of each number; I'll be using 5.

3/9

It didn't have to be 5, I could have used 3, but in that case It wouldn't have been it's simplest form and I would have to divide again by another factor.

Answer:

64

Step-by-step explanation:

16 times 4

If the probability that Mary will win a game is 0.03, and loosing game is 0.97 then the excepted value of game is equals to -$1.11.

Expected Value of the game is the mean of the probability distribution of the payout values, denoted by E(X). It is equal to the sum of the products of each possible payout value and its corresponding probability, that is\(E( x) = \sum_{i } x_i p( x_i) \\\)

where, xᵢ --> payouts

p(xᵢ) --> probability for corresponding to payouts. Let's consider X be a variable denotes the payouts ( the amount the player wins for a particular outcome of the game). Here possible value of x are $60 and -$3. Now, determine probabilities corresponding to payouts.

Probability that Mary will win a game= 0.03

Probability that marry will not win a game

= 1 - 0.03 = 0.97

So, Probability distribution table is

x $60 -$3

P(x) 0.03 0.97

Now, using formula of excepted value,

E(X) = - (prize for winning game × (Probability of winning) + (Prize for loosing game)×(Probability of loosing the game or \(E( x)= \sum_{i } x_i p( x_i)\\ \) Substitute all known values

= $60× 0.03 - $3× 0.97

= $1.80 - $2.91

= -$1.11

Hence required value is -$1.11.

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Answer:

1/2x=40

Step-by-step explanation:

This problem can be solved using the concept of the expected value of a random variable. Let X be the random variable representing the number of boxes a person needs to buy to get all four prizes.

To calculate the expected value E(X), we can use the formula:

E(X) = 1/p

where p is the probability of getting a new prize in a single box. In the first box, the person has a 4/4 chance of getting a new prize. In the second box, the person has a 3/4 chance of getting a new prize (since there are only 3 prizes left out of 4). Similarly, in the third box, the person has a 2/4 chance of getting a new prize, and in the fourth box, the person has a 1/4 chance of getting a new prize. Therefore, we have:

p = 4/4 * 3/4 * 2/4 * 1/4 = 3/32

Substituting this into the formula, we get:

E(X) = 1/p = 32/3

Therefore, the average number of boxes a person needs to buy to get all four prizes is 32/3, or approximately 10.67 boxes.

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Answer:

Step-by-step explanation:

Answer:

23a + 9b + 9c

Step-by-step explanation:

9a + 6b + 3b + 14a + 9c ( collect like terms )

= (9 + 14)a + (6 + 3)b + 9c

= 23a + 9b + 9c

Answer:

Graph B

Step-by-step explanation:

Rearrange in the form y > mx + c :

    2. x + y < 2

Graph which shows this inequality is : Graph B

B. is the correct graph.

Answer:

What Is Your Dogs Name. - Don't have one :(

Or If You Dont Have One And When You Get It What Will You Name It. - I would name it Beau :3

Answer:

x= -2

Step-by-step explanation:

Hope this helps.

Answer:

-102 = (-8×6 -8×-4x) -5x ( this is only for explanation write only this way as given below)

-102 = -48+32x -5x

-102 = -48+27x

-102+48= 27x

-54 = 27x

x = -54/27

x = -2 Ans

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