Give the slope of the graph and the unit rate. Express your answers as simplified fractions, if necessary.


Jorge: 7 miles every 9 hours

Answer:

22/3=8/3=2.66

if 12 servings =2.6 cup of flour

...18 servings=???????

18×2.6/12=3.9

the answer is 3.9

Answer:

1) x=1/2-y/2-3z

2)x= 16/3- 2y/3- 5z/3

3)x= 11/7- 3y/7+ 4z/7

Step-by-step explanation:

isolate the variable, to do that divide each side by the factors that don't contain the variable

The final cubic equation we are trying to find is \(x^{3}-5x^{2} -12x-12\)

What is equation of degree n?

The highest power of x appearing in the equation is called the degree say n and polynomial is of degree n

\(3x/(x-2)+ 2x/(x+3)= 30/(x^2-3x-18)\)

this is question lets start

\(\frac{3x(x+3) + 2x(x-2)}{(x-2)(x+3)} = \frac{30}{x^{2} -3x-18}\)

\(\frac{3x^{2} +9x + 2x^{2} -4x}{(x-2)(x+3)} = \frac{30}{x^{2} -3x-18}\)

we can factorize \(x^{2} -3x-18 = (x-6)(x+3)\)

In next few steps we are going to get a cubic equation

\(\frac{5x^{2} +5x}{(x-2)(x+3)} = \frac{30}{(x-6)(x+3)}\)

\(\frac{5(x^{2} +x)}{x-2} = \frac{30}{x-6} \\\\\\\frac{x^{2}+x }{x-2} = \frac{6}{x-6}\\ (x^{2} +x)(x-6) = 6(x-2)\\\\x^{3} -5x^{2} -12x-12 = 0\)

which is our required cubic equation we were trying to find

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Answer:

1:8

Step-by-step explanation:

Answer:

1:8

Step-by-step explanation:

Here , 2.5:20

or 25/10:20

or 25:200(Multiplying by 10)

or 1:8(Dividing both sides with 25)

Step-by-step explanation:

hope you can understand

Answer:

a) 2y

b) 69

Step-by-step explanation:

Answer:

z < 4 or z > -6

Step-by-step explanation:

5z < 20

z < 4

or

z > -6

z < 4 or z > -6

\(\tan(\beta) = -\frac{\sqrt{5}}{2}\) in the third quadrant (\(270^\circ < \beta < 360^\circ\)), the exact value of \(\tan\left(\frac{\beta}{2}\right)\) is \(2\sqrt{5} + 5\).

To find the exact value of the function \(\tan\left(\frac{\beta}{2}\right)\), given \(\tan(\beta) = -\frac{\sqrt{5}}{2}\), and \(\beta\) is in the third quadrant (\(270^\circ < \beta < 360^\circ\)), we can use the half-angle identity for tangent.

The half-angle identity for tangent is given by:

\[\tan\left(\frac{\theta}{2}\right) = \frac{\sin(\theta)}{1 + \cos(\theta)}\]

In this case, we are given \(\tan(\beta) = -\frac{\sqrt{5}}{2}\), which implies:

\[\frac{\sin(\beta)}{\cos(\beta)} = -\frac{\sqrt{5}}{2}\]

Since \(\beta\) is in the third quadrant, we know that \(\cos(\beta) < 0\) and \(\sin(\beta) < 0\). Let's introduce a positive constant \(k\) to represent the magnitudes of the sine and cosine:

\[\frac{-k}{-k} = -\frac{\sqrt{5}}{2}\]

Simplifying, we have:

\[k = \frac{\sqrt{5}}{2}\]

Now, we can determine the values of \(\sin(\beta)\) and \(\cos(\beta)\):

\[\sin(\beta) = -k = -\frac{\sqrt{5}}{2}\]

\[\cos(\beta) = -k = -\frac{\sqrt{5}}{2}\]

Next, we can substitute these values into the half-angle identity for tangent:

\[\tan\left(\frac{\beta}{2}\right) = \frac{\sin(\beta)}{1 + \cos(\beta)} = \frac{-\frac{\sqrt{5}}{2}}{1 - \frac{\sqrt{5}}{2}}\]

Simplifying the expression:

\[\tan\left(\frac{\beta}{2}\right) = \frac{-\sqrt{5}}{2 - \sqrt{5}}\]

To rationalize the denominator, we can multiply both the numerator and denominator by the conjugate of the denominator:

\[\tan\left(\frac{\beta}{2}\right) = \frac{-\sqrt{5}}{2 - \sqrt{5}} \times \frac{2 + \sqrt{5}}{2 + \sqrt{5}}\]

Expanding and simplifying:

\[\tan\left(\frac{\beta}{2}\right) = \frac{-\sqrt{5}(2 + \sqrt{5})}{4 - 5}\]

\[\tan\left(\frac{\beta}{2}\right) = \frac{-2\sqrt{5} - 5}{-1}\]

Finally, we have the exact value of the function:

\[\tan\left(\frac{\beta}{2}\right) = 2\sqrt{5} + 5\]

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Developing strategies for remembering facts is essential for children before they engage in drill and practice activities to develop fluency. By establishing these strategies, children can effectively learn, retain, and recall information, ultimately enhancing their performance during practice sessions.

Yes, it is important for children to develop strategies for remembering facts before engaging in drills and practice to develop fluency. By doing so, children can enhance their ability to recall information more quickly and accurately, making it easier for them to perform well on tests and assignments. Strategies such as visualizing, chunking, and using mnemonic devices can help children remember information more effectively. Once these strategies are established, drill and practice can then be used to further reinforce their understanding and speed up their recall time. This approach can ultimately lead to improved academic performance and a stronger foundation for learning.

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The statement that best proves that <XWY ≅ <ZYW is that two parallel lines are cut by a transversal, then the alternate interior angles are congruent

To determine the correct statement, we need to know the properties of a parallelogram.

These properties includes;

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Answer:

V|, V||, V|||, |X, X, because the other ones where 1,2,3,4,5 in roman numerals.

Step-by-step explanation:

The value of f(5) is 37. This can be answered by the use the fundamental theorem of calculus.

This states that the integral of the derivative of a function equals the difference between the value of the function at the upper limit and the lower limit of the integral.

In this case,

the integral from 3 to 5 of f'(x)dx is equal to 24.

Therefore, f(5) = f(3) + 24. As f(3) is 13, f(5) is 37.

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Hope you could understand.

If you have any query, feel free to ask.

Answer:

The perimeter is 80

Answer:

P = 80

Step-by-step explanation:

w = 10

L = 10 x 3

L = 30

P = L + L + w + w

P = 30 + 30 + 10 + 10

P = 80

Answer: Where is the triangle?

Step-by-step explanation: Brainliest pls:)

The inequality is x ≤ 35, where x represents the amount of gas in gallons.

This question means by the statement that we have been given that the number of gallons cannot exceed 35 so it actually means that they are either 35 or less than 35. so will use < = sign to come up with this equation.

You can have up to 35 gallons of gas at a time at the gas station. The inequality x ≤ 35 represents the fact that x (the amount of gas in gallons) is less than or equal to 35.

This means that the equation will be x≤35

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The probability of falling while skiing is 0.025, or 2.5%.

Multiplying the probability of a ski accident if the resort sells out by the probability of a ski accident if the resort sells out (0.25% or 10%) yields the probability of a ski accident.

We must use conditional probability to determine the likelihood of a ski accident. We start with the way that there's a 25% likelihood of the ski resort selling out, and a 10% likelihood of a ski mishap assuming it sells out. We can involve the equation for contingent likelihood:

P(A|B) = P(A and B) / P(B), where A represents the occurrence of the "ski accident" and B represents the "ski resort sells out"

P(ski mishap) = P(sells out) * P(accident | sells out) = 0.25 * 0.10 = 0.025 or 2.5%.

As a result, there is a 2.5% chance of an accident while skiing.

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Product of two polynomials can be done by distribution of multiplication over addition. The product of \((x+5)^2\) is \(x^2 + 10x + 25\)

Suppose a, b and c are three numbers. Then we have:

\(a(b + c) = a\times b + a\times c\)

(a(b+c) means a multiplied to (b+c). The sign of multiplication is usually hidden when using symbols and both quantities which are in multiplication are written together without space)

They are mathematical expressions involving variables raised with non negative integers and coefficients(constants who are in multiplication with those variables) and constants with only operations of addition, subtraction, multiplication and non negative exponentiation of variables involved.

Example:

\(x^3 + 4x + 3\)

is a polynomial.

Using both above facts, as the given expression is \((x+5)^2\)

Its product result is obtained as

\((x+5)^2 = (x+5)(x+5) = x(x+5) + 5(x+5) = x^{1+1} + 5x + 5x + 25\\\\(x+5)^2 = x^2 + (5+5)x + 25 \text{\:(Addition of coefficients of like terms)}\\\\(x+5)^2 = x^2 + 10x + 25\)

It is a fact that result of a polynomial product is polynomial. Thus, the obtained product is a polynomial since x + 5 was a polynomial.

Thus,

The product of \((x+5)^2\) is \(x^2 + 10x + 25\)

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Answer: 4.2 and above.

4.2 would make it equal and anything above would be greater

Answer:

3(t - 3.6) ≥ 1.8

Distribute the 3

3t - 10.8 ≥ 1.8

Add 10.8 to both sides

3t ≥ 12.6

Divide both sides by 3

t ≥ 4.2

The product of the given expression is option C. 6x^3 - 33x^2 + 45x - 6.

The product of two or more numbers implies the final value that would be derived when the numbers are multiplied with each other.

The given expression in the question involves the expansion of brackets.

Thus it can be solved as;

(3x - 6) (2x^2 - 7x + 1)

Considering the first bracket, the first term is 3x and second term is -6. To solve the question thus require to first expand the second bracket by 3x, then by -6 to have;

(3x - 6) (2x^2 - 7x + 1)  = 6x^3 - 21x^2 + 3x - 12x^2 + 42x - 6

                      = 6x^3 - 33x^2 + 45x - 6

Therefore, the product of given brackets is 6x^3 - 33x^2 + 45x - 6. Thus option C.

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In a mathematical sense..

Not to make it too complicated, however, here's where we get on to the real mathematics.

There are infinite equations for 2 + 2. The gap between any number can be infinite if you keep giving it more numerical content. However, solving 2 + 2 can be very tricky.

1 + 1 + 1 + 1 = 4. Easy, right? Wrong. We can deduct from this equation that 1 + 1 = 2, so if we do 1 + 1 PLUS 1 + 1, (1 + 1 + 1 + 1 again), that equals four, because 1 + 1 is 2 and if we add another 1 to 2, 1 + 2, it equals 3, so 1 + 3 = 4. I'd like to remind you-- this works both ways, whether or not it's 3 + 1 or 1 + 3, it equals 4. If we carry the 1 from the three and put it in a separate number in an equation, said equation is now 1 + 1 + 2. It still equals 4, because 1 + 1 = 2 and if you take 2 and put it in 1 + 1's place, it's 2 + 2.

2 + 2 = 4.

(this was a joke answer, don't take anything said in this answer seriously.. OR you can if you want, because it's all true.. 2 + 2 = 4.)

Hope this helped!

- William.

The inequality that can be used to find w, the number of weeks it can take for the shelter to meet its goal, is: w ≥ 10

To find the inequality that can be used to determine the number of weeks it can take for the animal shelter to meet its fundraising goal, we need to consider the total expenses and donations.

Let's break down the expenses and donations:

Expenses:

Annual rental = $2,500

Weekly expenses = $450

Donations:

One-time donation = $125

Pledged donations per week = $680

Let w represent the number of weeks it takes for the shelter to meet its goal.

Total expenses for w weeks = Annual rental + Weekly expenses * w

Total expenses = $2,500 + $450w

Total donations for w weeks = One-time donation + Pledged donations per week * w

Total donations = $125 + $680w

To meet the goal, the total donations must be greater than or equal to the total expenses. Therefore, the inequality is:

Total donations ≥ Total expenses

$125 + $680w ≥ $2,500 + $450w

Simplifying the inequality, we have:

$230w ≥ $2,375

Dividing both sides of the inequality by 230, we get:

w ≥ $2,375 / $230

Rounding the result to the nearest whole number, we have:

w ≥ 10

Therefore, the inequality that can be used to find w, the number of weeks it can take for the shelter to meet its goal, is:

w ≥ 10

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The corrrect statements about angle are:

Please refer to the attached picture below for visualization of the angles.

Based on the attached picture, we can consider the relationship of each angle, such as:

Alternate interior angles and congruent:

Angle 4 and angle 5

Angle 3 and angle 6

Alternate exterior angles and congruent:

Angle 1 and angle 8

Angle 2 and angle 7

Consecutive interior angles and supplementary:

Angle 3 and angle 5

Angle 4 and angle 6

Corresponding angles and congruent:

Angle 1 and angle 5

Angle 2 and angle 6

Angle 3 and angle 7

Angle 4 and angle 8

Vertical angles and congruent:

Angle 1 and angle 4

Angle 2 and angle 3

Angle 5 and angle 8

Angle 6 and angle 7

Supplementary angles:

Angle 1 and angle 2

Angle 3 and angle 4

Angle 5 and angle 6

Angle 7 and angle 8

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A restricted lifestyle is not an advantage of renting.

Option D is the correct answer.

Renting a property has several advantages, such as ease of mobility, fewer responsibilities, and lower initial costs.

We have,

Ease of mobility is an advantage because it is easier for renters to move to a new location since they are not tied down to a specific property.

Fewer responsibilities are another advantage because the landlord is usually responsible for maintaining the property, making repairs, and paying for utilities.

This means that renters do not have to worry about these tasks or expenses.

Lower initial costs are also an advantage because renters do not have to pay for a down payment or closing costs, which can be a significant expense when purchasing a property.

A restricted lifestyle is not an advantage of renting.

This is because renters may be limited in terms of decorating, making changes to the property, or having pets.

Renters may also have to abide by certain rules set by the landlord or property management company.

This can limit their freedom and personalization of the space.

Thus,

A restricted lifestyle is not an advantage of renting.

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We proved the identities:

8.  tanxsinx+cosx = secx.

9.  1- sin²x/(1+cosx) = cosx.

8. We have to prove the identity tanxsinx+cosx = secx.

Let us consider the LHS side of the identity:  tanxsinx+cosx

Using the identity tanx=sinx/cosx.

sinx/cosx. sinx + cosx

sin²x+cos²x/cosx

We know that identity sin²x+cos²x =1

1/ cosx

secx

So,  tanxsinx+cosx = secx.

9. To establish the identity 1- sin²x/(1+cosx) = cosx:

Let us consider the LHS side of the identity 1- sin²x/(1+cosx)

Using the identity sin²x = 1-cos²x

1- (1-cos²x)/(1+cosx)

Combining the terms over a common denominator:

1+cosx-(1-cos²x)/(1+cosx)

1+cosx-sin²x/(1+cosx)

1+cosx-(1-cos²x)/ 1+cosx

Expanding the numerator:

1+cosx-1+cos²x/1+cosx

Combining like terms:

cos²x+cosx/1+cosx

Canceling out the common factor cosx+1:

We get cosx.

So,  1- sin²x/(1+cosx) = cosx.

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Answer:

1) n=±2\(\sqrt{5}\)

2) a=±3\(\sqrt{10}\)

Step-by-step explanation:

1) \(n^{2}\) =20

✰Take the square root of both sides n=±\(\sqrt{20\\}\)

✰ Simplify \(\sqrt{20\\}\) to 2\(\sqrt{5}\)

→ n=±2\(\sqrt{5}\)  

⋆⋆⋆⋆⋆⋆⋆⋆⋆⋆⋆⋆⋆⋆⋆⋆⋆⋆⋆⋆⋆⋆⋆⋆⋆⋆⋆⋆⋆⋆⋆⋆⋆⋆⋆⋆⋆⋆⋆⋆⋆⋆⋆⋆⋆⋆⋆⋆⋆⋆⋆⋆⋆⋆⋆⋆⋆⋆⋆⋆

2) \(a^{2}\) =90

✰ (Same as above) Take the square root of both sides ​a=±\(\sqrt{90\\}\)

✰ Simplify \(\sqrt{90}\) to 3\(\sqrt{10}\)

→ a=±3\(\sqrt{10}\)

Statistical power is a measure of the ability to reject the null hypothesis when it is false. It represents the probability of correctly identifying a true effect or relationship in a statistical hypothesis test.

A high statistical power indicates a greater likelihood of detecting a significant result if the null hypothesis is indeed incorrect. The power of a statistical test depends on several factors, including the sample size, the effect size (the magnitude of the true effect or difference), the chosen significance level (often denoted as α), and the variability or noise in the data. Increasing the sample size or effect size generally increases the statistical power, while a lower significance level or higher variability decreases it.

Power analysis is commonly used to determine an appropriate sample size for a study, ensuring that it is adequately powered to detect the desired effect. A higher power is desirable as it reduces the chances of a Type II error (failing to reject the null hypothesis when it is false) and increases the chances of correctly detecting real effects or relationships.

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The value of k for a first-order reaction with a half-life of 137 minutes is approximately 5.06×10^(-3) s^(-1).

If the half-life of a first-order reaction is given as 137 minutes, we need to determine the corresponding rate constant (k) for the reaction.

In a first-order reaction, the relationship between the half-life and the rate constant is given by the equation t_1/2 = (ln(2) / k), where t_1/2 represents the half-life.

Plugging in the given half-life value of 137 minutes, we can rearrange the equation to solve for the rate constant (k). Taking the natural logarithm of both sides, we have ln(2) / t_1/2 = k.

Substituting the value for t_1/2 as 137 minutes, we can calculate the rate constant.

Performing the calculation, we find that the rate constant (k) is approximately 5.06×10^(-3) s^(-1).

Therefore, the correct option is 5.06×10^(-3) s^(-1) as the value of k for the first-order reaction with a half-life of 137 minutes.

It's important to note that the rate constant represents the rate at which the reaction occurs, and in this case, it corresponds to the specific reaction with the given half-life.

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The graph of y = f(x) is shown below:graph{y=(x-6)x^2-12x-72 [-10, 10, -150, 50]}

The pertinent information obtained by applying the graphing strategy and sketching the graph of y=f(x) is explained below:y = f(x) = (x - 6) x^2 - 12x - 72 has two real roots,

which can be found by applying the quadratic formula. We have x = 9 and x = -2.f(x) is defined for all values of x except for x = 6 (due to the denominator) and x = ±∞.

So, the domain of f is {x | x ∈ R, x ≠ 6}.The y-intercept is given by f(0) = -72. And x-intercepts are given by (9, 0) and (-2, 0).Since the coefficient of x^2 is positive, the parabola opens upward.

The axis of symmetry is at x = (9 - 2)/2 = 3.5. And the vertex is (3.5, -99.25).The graph of y = f(x) is shown below:graph{y=(x-6)x^2-12x-72 [-10, 10, -150, 50]}

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Answer:

z = -1

Step-by-step explanation:

add like terms: 13z = -13

divide both sides by 13: z = -1

Answer:

z=-1

Step-by-step explanation:

Combine like terms: 11+2 ( 13z )

Divide: -13/13 ( -1 )