Solve 2x2 + x − 4 = 0

The ordered pair (2,3) is not a solution of the system

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

−8x + 4y > 3

6x - 7y < −5

The solution is given as

(2, 3)

Next, we test this value on the system

So, we have

−8(2) + 4(3) > 3

-4 > 3 --- false

This means that (2,3) is not a solution of the system

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It's 12 because if you divide 6 by 0.5 you should get 12, so basically use the opposite operation.

Hope that helps!

To make the 2% solution of tetracaine hydrochloride isotonic, a 0.9% solution of sodium chloride should be used.

The amount of the 0.9% sodium chloride solution needed can be calculated by setting up a proportion based on the concentration percentages.

Let's assume x represents the volume of the 0.9% sodium chloride solution needed in milliliters.

Since the 0.9% solution is isotonic, it means that the concentrations of tetracaine hydrochloride and sodium chloride should be equal. Therefore, the proportion can be set up as follows:

(0.9 / 100) = (2 / 100) * (x / 30)

Simplifying the proportion, we have:

0.009 = 0.02 * (x / 30)

To solve for x, we can multiply both sides of the equation by 30 and divide by 0.02:

x = (0.009 * 30) / 0.02

x ≈ 13.5 mL

Therefore, approximately 13.5 milliliters of the 0.9% sodium chloride solution should be used in compounding the prescription to make the 2% tetracaine hydrochloride solution isotonic.

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Answer:

6,7

Step-by-step explanation:

the squre root of 41 is 6.403

Answer:

151.2

Step-by-step explanation:

7x12=84

84/3=28

28x5.4=151.2

Answer:

the blue one but not sure

Answer:

the third one i think

Step-by-step explanation:

Answer: 5/4

Step-by-step explanation: That should be right because I have big brain. Mark brainlist please :)

Therefore, the probability of exactly one card being jack when a hand of four cards is drawn from a standard deck of playing cards with replacement is 0.073 or 7.3%.

Suppose a hand of four cards is drawn from a standard deck of playing cards with replacement, the probability of exactly one card being jack can be determined using the following steps:Step 1: Determine the total number of possible outcomes when four cards are drawn from a standard deck of 52 cards with replacement. The total number of possible outcomes = 52 × 52 × 52 × 52 = 7,311,616.Step 2: Determine the total number of ways in which exactly one card can be a jack. There are four jacks in a standard deck of 52 cards, so the total number of ways in which exactly one card can be a jack = 4 × 48 × 48 × 48 = 53,333,632.Step 3: Determine the probability of exactly one card being jack. Probability of exactly one card being jack = Total number of ways in which exactly one card can be a jack / Total number of possible outcomes= 53,333,632/ 7,311,616 = 7.28 ≈ 0.073 or 7.3%.Therefore, the probability of exactly one card being jack when a hand of four cards is drawn from a standard deck of playing cards with replacement is 0.073 or 7.3%.

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Answer:

60 degrees

Step-by-step explanation:

Each triangle needs to add up to 180 total degrees.  70+50=120,

180

-

120

___

60

(a) `dy/dx = (2y - 2x)/(3y - 2x)`.

(b) The slope of the tangent line at points where x = 6 is 0.

(c) the curve has a vertical tangent line when x = (3/2)y.

(a) To show that `dy/dx = (2y - 2x)/(3y - 2x)`, we need to find the derivative of `y` with respect to `x`. We can do this by implicitly differentiating the given equation.

Differentiating both sides of the equation with respect to `x`, we get:

4x(dx/dx) + 6y(dy/dx) - 4[(dx/dx)y + x(dy/dx)] = 0

Simplifying the equation, we have:

4x + 6y(dy/dx) - 4xy - 4xy - 4x(dy/dx) = 0

Rearranging the terms and combining like terms, we get:

(6y - 4x)(dy/dx) = 8x - 8xy

Dividing both sides by (6y - 4x), we obtain:

dy/dx = (8x - 8xy)/(6y - 4x)

Simplifying further, we have:

dy/dx = (2x(4 - 4y))/(2(3y - 2x))

Canceling out the common factors, we get:

dy/dx = (2y - 2x)/(3y - 2x)

Therefore, `dy/dx = (2y - 2x)/(3y - 2x)`.

(b) To find the slope of the tangent line at the points where x = 6, substitute x = 6 into the expression we found for `dy/dx` in part (a):

dy/dx = (2(6) - 2(6))/(3y - 2(6))

      = 0/(3y - 12)

      = 0

The slope of the tangent line at points where x = 6 is 0.

(c) To find the value of x at which the curve has a vertical tangent line, we need to find the point(s) where the slope `dy/dx` is undefined. In other words, we need to find the values of x where the denominator of `dy/dx` becomes zero.

Setting the denominator equal to zero and solving for x:

3y - 2x = 0

2x = 3y

x = (3/2)y

So, the curve has a vertical tangent line when x = (3/2)y.

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Answer: Joe earns a monthly salary of 250 plus a commission on his total sales. Last month his total sales were $7,289 and he earned a total of $1,275. What is his commission rate?

Step-by-step explanation:  

250 + $7,289 + $1,275 = 8814

The potential that satisfies the given boundary conditions in part (a) and (b) is: [tex]\[u(r, \theta) = \sin(\theta)\][/tex] and [tex]\[u(r, \theta) = \sin(\theta)\][/tex] respectively.

Consider the circular annulus (a plane figure consisting of the area between a pair of concentric circles) specified by the range:

[tex]$1 \leq r \leq 2$.[/tex]

a) Find the potential that satisfies the following boundary conditions:

[tex]\[\begin{aligned}u(1,0) &= \sin(\theta) \\u(2,0) &= 0 \\u(\theta, 1) &= 1 + (1 - \cos(2\theta))\end{aligned}\][/tex]

b) Find the potential that satisfies the following boundary conditions:

[tex]\[\begin{aligned}u(1,0) &= \sin(\theta) \\u(2,0) &= 0 \\u(\theta, 1) &= 1 + (1 - \cos(20\theta))\end{aligned}\][/tex]

To solve this problem, we can use separation of variables and assume a solution of the form:

[tex]\[u(r, \theta) = R(r)\Theta(\theta)\][/tex]

Plugging this into Laplace's equation [tex]$\nabla^2u = 0$[/tex] and separating variables, we get:

[tex]\[\frac{1}{R}\frac{d}{dr}\left(r\frac{dR}{dr}\right) + \frac{1}{\Theta}\frac{d^2\Theta}{d\theta^2} = 0\][/tex]

Solving the radial equation gives us two solutions:

[tex]\[R(r) = A\ln(r) + B\quad \text{and} \quadR(r) = C\frac{1}{r}\][/tex]

For the angular equation, we have:

[tex]\[\Theta''(\theta) + \lambda\Theta(\theta) = 0\][/tex]

The general solution to this equation is given by:

[tex]\[\Theta(\theta) = D\cos(\sqrt{\lambda}\theta) + E\sin(\sqrt{\lambda}\theta)\][/tex]

To satisfy the boundary conditions, we can impose the following restrictions on [tex]$\lambda$[/tex] and choose appropriate constants:

For part (a)

[tex]\[\begin{aligned}R(1) &= 0 \implies B = -A\ln(1) = 0 \implies B = 0 \\R(2) &= 0 \implies A\ln(2) + B = 0 \implies A\ln(2) = 0 \implies A = 0 \\\Theta(0) &= \sin(0) \implies D = 0 \\\Theta(0) &= \sin(0) \implies E = 1\end{aligned}\][/tex]

Therefore, the potential that satisfies the given boundary conditions in part (a) is:

[tex]\[u(r, \theta) = \sin(\theta)\][/tex]

For part (b)

[tex]\[\begin{aligned}R(1) &= 0 \implies B = -A\ln(1) = 0 \implies B = 0 \\R(2) &= 0 \implies A\ln(2) + B = 0 \implies A\ln(2) = 0 \implies A = 0 \\\Theta(0) &= \sin(0) \implies D = 0 \\\Theta(0) &= \sin(0) \implies E = 1\end{aligned}\][/tex]

Therefore, the potential that satisfies the given boundary conditions in part (b) is:

[tex]\[u(r, \theta) = \sin(\theta)\][/tex]

Please note that in both parts (a) and (b), the radial solution does not contribute to the potential due to the boundary conditions at r=1 and r=2. Thus, the solution is purely dependent on the angular part.

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Answer:

∠1and∠5

Step-by-step explanation:

Hello There!

The image shown below shows an example of what corresponding angles look like

Properties of corresponding angles

angles 2 and 4 are on the same side of the transversal however they are supplementary angles not congruent

angles 2 and 4 are an example of adjacent angles therefore this is not the answer

angles 1 and 5 are on the same side of the transversal and they are most definitely congruent

This might be our answer but lets check the last answer just to be sure

Angles 3 and 6 are congruent but they are not on the same side of the transversal

angles 3 and 6 are an example of alternate interior angles therefore this is not the correct answer

So we can conclude that angles 1 and 5 are corresponding angles

Answer: 65

Step-by-step explanation:

8nn+7 is your given expression. Plug in 7 for n, the number of tickets: 8(7)+9=56+9=65

The school is not justified to make this claim because of the reasons defined.

The following is a statement that might be made about the high school to justify its claim No, because the z-score of Z = 1.06 is not uncommon because it does not fall within the range of a typical event, namely within 2 standard deviations of the sample mean.

It has been given to us that:

μ = 511

σ = 119

Sample size (n) = 55

and

s = 119 / √55

= 16.046

As we all know,

Only when z > 2 then, the high school's allegation is valid and warranted.

To locate,

Z's value is

So,

Z = ( X - μ )/σ

by applying the Central Limit Theorem to the values,

z = ( 528 - 511 ) / 16.046

= 1.06

Since, z < 2, as a result, the allegation is unjustified.

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Correct question:

The average math SAT score is 511 with a standard deviation of 119. A particular high school claims that its students have unusually high math SAT scores. A random sample of 55 students from this school was​ selected, and the mean math SAT score was 528. Is the high school justified in its​ claim? Explain. ▼ No Yes ​, because the​ z-score ​( nothing​) is ▼ unusual not unusual since it ▼ does not lie lies within the range of a usual​ event, namely within ▼ 1 standard deviation 2 standard deviations 3 standard deviations of the mean of the sample means. ​(Round to two decimal places as​ needed.)

The velocity of the train after 4 hours is 20 miles per hour.

To find the velocity of the train after 4 hours, we need to differentiate the given function s(t) with respect to t.

Velocity is the derivative of position with respect to time.

That is,v(t) = ds(t)/dtTo differentiate s(t) = –13 + 3t² – 4t – 4, we differentiate each term separately.v(t) = d/dt(-13) + d/dt(3t²) - d/dt(4t) - d/dt(4)v(t) = 0 + 6t - 4

The velocity of the train after 4 hours is given by substituting t = 4 in the above equation.v(4) = 6(4) - 4 = 20

The velocity of the train after 4 hours is 20 miles per hour.To sum up, the velocity of the train after 4 hours is 20 miles per hour.

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Given that the probability of event A is Pr(A) = 1/3 and the probability of the union of event A and event B, namely AUB, is Pr(AUB) = 5/6. The probability of event B is Pr(B) = 2/3.

Suppose that event A and event B are disjoint.

The probability of event B is Pr(B) = 1/2.

To find the probability of event B.

For disjoint events A and B, we know that A ∩ B = Φ (empty set).

Thus, we can express the union of A and B as: AUB = A + B, where A and B are disjoint.

In general, the probability of the union of two events can be expressed as: P(AUB) = P(A) + P(B) - P(A ∩ B).

For disjoint events, the intersection of the events is always an empty set.

Thus, P(A ∩ B) = 0.

Using this information, we can write:

P(AUB) = P(A) + P(B) - P(A ∩ B)

= P(A) + P(B) - 0

= P(A) + P(B)

Given P(A) = 1/3 and P(AUB) = 5/6, we can solve for P(B) as follows:

5/6 = P(A) + P(B)

=> P(B) = 5/6 - P(A)

=> P(B)  = 5/6 - 1/3

=> P(B)  = 2/3

Thus, the probability of event B is Pr(B) = 2/3.

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Answer:

x = 30

Step-by-step explanation:

2x + x = 90

3x = 90

x = 30

Answer:

d

Step-by-step explanation:

integer is a whole number

imagine the sum of the first set of 3 integers = 4 + 5 + 6

product = 4 x 5 x 6 = 120

imagine the sum of the 2nd set of 3 integers = 6 + 7 + 8 = 21

6 x 7 x 8 = 3364

Answer:

m=3/4

Step-by-step explanation:

First, let us remind ourselves of the slope formula: m=rise/run=([tex]y_{2}[/tex]-[tex]y_{1}[/tex])/([tex]x_{2}[/tex]-[tex]x_{1}[/tex])

Let's pick two points from the graph to work with. Let's do (3,-6) and (-1,-9).

And let 3=[tex]x_{1}[/tex], -6=[tex]y_{1}[/tex], -1=[tex]x_{2}[/tex], -9=[tex]y_{2}[/tex].

1. Substitute the values into the slope formula: [-9-(-6)]/(-1-3)

2. simplify the expression: [-9-(-6)]/(-1-3)=(-9+6)/-4=-3/-4=3/4

3. As a result, the slope of the line is 3/4

The coefficient matrix is a square matrix with dimensions equal to the number of variables in the system of equations.

The coefficient matrix is a matrix of the coefficients of the variables in a system of linear equations.

Now, we arrange these coefficients in a matrix format by placing them row-wise. This gives us the coefficient matrix:

[tex]2x + 3y + 3x3 = 20[/tex]

[tex]3x + 5y + 2x3 = 9[/tex]

[tex]-x + 3y + 5x3 = 4[/tex]

Each row of the coefficient matrix corresponds to an equation in the system, and each column represents the coefficients of a specific variable (x₁, x₂, x₃).

In summary, the coefficient matrix for the given system of equations is:

[tex]| 2 3 3 |[/tex]

[tex]| 3 5 2 |[/tex]

[tex]|-1 3 5 |[/tex]

This matrix provides a compact representation of the coefficients in the system, which can be further used for various operations and calculations.

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Answer:

c because 3.3.3.3 is 3 to the 4th power expanded

Answer:

I THINK it would be B.

Step-by-step explanation:

I’m very sorry if I’m wrong.

Answer:

16.3%

Step-by-step explanation:

21.5 times 0.163= 3.5

The composite functions fog and g • f are not equal to x. The function fog simplifies to 4x² - 20x + 25, while g • f simplifies to 45. Therefore, neither composite function equals x.

To determine whether the composite functions fog and g • f are equal to x, we need to evaluate each expression separately and compare the results.

1. fog (or f(g(x))):

f(g(x)) = f(2x - 5)

To compute f(2x - 5), we substitute (2x - 5) into the function f(x) = x²:

f(2x - 5) = (2x - 5)²

Expanding this expression, we get:

f(2x - 5) = 4x² - 20x + 25

Therefore, fog is not equal to x since f(2x - 5) simplifies to 4x² - 20x + 25, not x.

2. g • f (or g(f(x))):

g(f(x)) = g(25)

To compute g(25), we substitute 25 into the function g(x) = 2x - 5:

g(25) = 2(25) - 5

g(25) = 50 - 5

g(25) = 45

Therefore, g • f is not equal to x since g(25) evaluates to 45, not x.

In conclusion, neither fog nor g • f is equal to x. The composite functions do not simplify to x; fog simplifies to 4x²- 20x + 25, and g • f simplifies to 45.

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Answer:

a ≤ 9

Step-by-step explanation:

Closed circle means ≤ or ≥

Shading to the left means left direction < or ≤

The inequality sign that has both is: ≤

a ≤ 9

Answer:

The answer is C

Step-by-step explanation:

I took the test and I got it right

Answer:

85

Step-by-step explanation:

425 divided by 8= 85

Answer:

He as 85 race cars.

Step-by-step explanation:

Just divide 425 by 5 and you have your answer.

Answer:

69

Step-by-step explanation:

Answer:

Step-by-step explanation:

62.00

The Laplace transform of the function f on (0,0) defined by f(t) = i Se^4t is L(f)(s) = i S / (2s-4).

Given function is f(t) = i Se^4t

Here, Laplace transform of the function f is given by:

L(f)(s) = ∫[0,∞) e^(-st) f(t) dt

On substituting the given function in the above equation, we get:

L(f)(s) = ∫[0,∞) e^(-st) i Se^(4t) dt

L(f)(s) = i S ∫[0,∞) e^(t(4-s)) dt

We know that the Laplace transform of e^(at) is 1/(s-a).

Therefore, Laplace transform of e^(t(4-s)) = 1/(s - (4-s)) = 1/(2s - 4).

Therefore,L(f)(s) = i S * ∫[0,∞) e^(t(4-s)) dt

L(f)(s) = i S * 1/(2s-4) * [-e^(-(4-s)t)]_0^∞

L(f)(s) = i S * 1/(2s-4) * [0 - (-1)] (since the exponentials evaluated at ∞ is zero)

L(f)(s) = i S * 1/(2s-4) * 1

L(f)(s) = i S / (2s-4)

Therefore, the Laplace transform of the function f on (0,0) defined by f(t) = i Se^4t is  L(f)(s) = i S / (2s-4).

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