Simplify (a^2-7a+12)/(a^2-2a-8) if a cannot be 4

Given linear inequalities is solved using graph paper line will pass through (6,0) and (-0,4) Area where required linear inequalities is satisfied is towards origin.

let's first try to understand  what is linear inequalities?

A linear inequality in mathematics is an inequality involving a linear function. One of the symbols for inequality is found in a linear inequality. It displays non-equal data in graph style.

the linear inequality's graph Since the inequality is severe and the shaded region points in the direction of the origin, 2 x-3 y < 12 is a straight line passing through the points (6, 0) and (0, -4), with the line being dot-dotted.

x - coordinate of the given line 2x - 3y =12

y =0 2x = 12 x = 6 (6,0)

y - coordinate of the given line -3y = 12 y = -4  (0,-4)

line passes through (6,0) and (0,-4).

Given Question is incomplete complete Question here:

How do you graph linear inequalities 2x - 3y< 12?

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The number of ways in which Kristen can rank her favorite four from 8 using permutations is 1680.

The permutation is a way of finding the number of ways of selecting a set of articles from a larger set of articles, with the order of selection being significant.

If we want to choose r items from n items, where the order of selection is significant, then we can find the number of ways of doing this using the permutation as follows:

nPr = n!/{(n - r)!}.

In the question, we are asked to find the number of ways Kristen can rank her favorite four investments from the 8 potential investments that her financial advisor has given her.

Thus, using permutations, we need to select 4 items from 8 items, with order of selection being significant.

Substituting n = 8, and r = 4 in the formula, we get:

8P4 = 8!/{(8 - 4)!}

= 8!/4!

= 5 * 6 * 7 * 8

= 1680.

Thus, the number of ways in which Kristen can rank her favorite four from 8 using permutations is 1680.

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Answer:

2 quarts

Step-by-step explanation:

He originally had 8 quarts, then he sold a total of 18+6 which is 24 cups of lemonade. 4 cups is one quart, so he sold 6 quarts. 8-6 is 2, so he is left with 2 quarts.

Answer:

2 quarts left

Step-by-step explanation:

Kirk started out with 8 quarts of lemonade. He then sold 6 cups and 18 cups.

6+18=24

So now with 24 total cups sold, we convert that to quarts by dividing by 4 since there are 4 cups in a quart.

24/4=6

Since we know he sold 3 quarts, we can subtract that from the original amount to find the amount of lemonade he has left.

8-6=2

Now we know he has 5 quarts of lemonade left.

HTH :)

Answer:

y= 3/2x -14

Step-by-step explanation:

The formula to solve this problem is y- y1 = m(x-x1), so plug in the coordinates according to the formula: y-(-8)= m(x-4). Then, find the reciprocal of the slope, which is 3/2. Plug 3/2 to where the slope belongs: y+8=3/2(x-4). Calculate to solve the rest: y =3/2x -14

It is False that based only on the r and p values listed above you can come to the conclusion that age is a moderator of the bivariate relationship between the amount of texting and the number of accidents.

In the given scenario, it is not completely true that based only on the r and p values listed above, you can come to the conclusion that age is a moderator of the bivariate relationship between the amount of texting and the number of accidents.

Let's first understand what is meant by the term "moderator.

"Moderator: A moderator variable is a variable that changes the strength of a connection between two variables. If there is a statistically significant bivariate relationship between the amount of texting during driving and the number of accidents, scientists investigate whether this bivariate relationship is moderated by age.

Therefore, based on the values of r and p, it is difficult to determine if age is a moderator of the bivariate relationship between the amount of texting and the number of accidents.

As we have to analyze other factors also to determine whether the age is a moderator or not, such as the sample size, the effect size, and other aspects to draw a meaningful conclusion.

So, it is False that based only on the r and p values listed above you can come to the conclusion that age is a moderator of the bivariate relationship between the amount of texting and the number of accidents.

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\( \sf = 6(3a - 8b + 2)\)

\( \sf = 18a - 48b + 12\)

Opsi : B

Answer:

Step-by-step explanation:

Distribute 6 to all terms in (3a - 8b + 2 )

6(3a  - 8b + 2) = 6*3a - 6*8b + 6*2

                        = 18a - 48b + 12

Hence, in response to the provided question, we can say that As a result,  equation the inequality representing the amount of copies you can produce is: x ≤ 41.

A math equation is a mechanism for connecting statements and indicating equivalence with both the equals symbol (=). An equation is an algebraic claim that asserts the equivalency of two formulae in algebra. In the calculation 3x + 5 = 14, for example, the equivalence sign separates the numbers 3x + 5 and 14. To explain the relationship among the two words on each surface of a letter, a formula can really be employed. The software and the logo are usually interchangeable. For instance, 2x - 4 equals 2.

Let x represent the number of copies that can be made. The cost of x copies is $0.30x.

$0.30x ≤ $12.50

To find x, we must divide both sides by $0.30:

x ≤ $12.50 ÷ $0.30

x ≤ 41.67

Because you cannot manufacture a fraction of a copy, the most you can afford to make is 41 copies.

As a result, the inequality representing the amount of copies you can produce is:

x ≤ 41.

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Answer:

A

Step-by-step explanation:

5/18 = 0.2777 = 0.27° so when you divided thd no. it is 0.277777 and 7 is repeat .

The solution to the equation is (a) -2.

To solve the equation log(3x) = log(2) + log(x - 1), we can use the properties of logarithms.

According to the logarithmic property log(a) + log(b) = log(ab), we can rewrite the equation as:

log(3x) = log(2(x - 1))

Since the logarithm function is one-to-one, we can equate the expressions inside the logarithms:

3x = 2(x - 1)

Expanding the equation:

3x = 2x - 2

Bringing all terms to one side:

3x - 2x = -2

x = -2

Therefore, the solution to the equation is x = -2.

The correct answer is (a) -2.

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Answer:

102055290485752224 /125

Step-by-step explanation:

(5)(95524.36)+(854793.8888)(955133552.2) + 9/100 (7) / 100 + 6^2/ 12^2

= 477621.8 + (854793.8888)(955133552.2) + 9/100 (7) / 100 + 6^2 / 12^2

= 477621.8 + 816442323408395.75 + 9/100 (7) / 100 + 6^2 /12 ^2

= 816442323886017.5 +  9/100 (7) / 100 + 6^2 /12 ^2

= 816442323886017.5 + 63 / 100 /100 + 6^2 /12 ^2

= 816442323886017.5 + 63/10000 + 6^2 /12 ^2

= 102055290485752192/125 + 36/12^2

= 102055290485752192/125 + 36/144

= 102055290485752192/125 + 1/4

= 102055290485752224/125

Answer:

4567890,1234567890

Step-by-step explanation:

Answer:

\(-5120\)

Step-by-step explanation:

From the geometric sequence, we find that the first term is a=10 and the common ratio is r= -2.

So, the 10th term is:

\(a_{n}=ar^{n-1}\\a_{10}=10\cdot(-2)^{10-1}\\a_{10}=-5120\)

Answer:

280 Pineapple Slices

Step-by-step explanation:

To set this up, we put the fraction 7/3 next to our assumed fraction, x/120. X being the number of pineapple slices in the shopping bag.  Then, we multiply 7 x 120 (840) and divide that by 3. Our answer comes out to 280, which we can prove by seeing that 3 x 4 = 120 and 7 x 4 = 280. This is also a similar way to solve the problem.

The odds ratio is \(1.36\) (option b) based on the given table. The odds ratio is a measure of the strength and direction of the association between two categorical variables.

In more detail, the odds ratio is obtained by taking the ratio of the odds of an event in one group (e.g., exposed) to the odds of the event in another group (e.g., unexposed). It provides information on how much more likely (or less likely) the event is to occur in one group compared to the other. An odds ratio greater than 1 indicates a positive association, where the event is more likely in the exposed group. Conversely, an odds ratio less than 1 suggests a negative association, indicating that the event is less likely in the exposed group.

To determine the odds ratio from the given table, you would need to look at the values in the table that represent the exposed and unexposed groups and their respective event frequencies. Without the specific data in the table, it is not possible to provide a more detailed explanation for why option b (\(1.36\)) is the correct answer.

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Answer:

AC = 9

Step-by-step explanation:

We solve using Pythagoras Theorem

The formula is given as:

a² + b² = c²

Where:

AC = a = ?

AD = b= 12

DB = c = 15

Hence,

a² + 12² = 15²

a² = 15² - 12²

a² = 225 - 144

a² = 81

Square root both sides

√a² = √81

a = 9

Hence, AC = 9

we first found the antiderivative of (3x-8)/9, which allowed us to write the general solution to the differential equation. We then used the initial condition y(-1) = -6 to find the specific value of the constant of integration. Finally, we obtained the function y(x) that satisfies the differential equation dy/dx = (3x-8)/9 and y(-1) = -6.

To find the function y(x) that satisfies the differential equation dy/dx = (3x-8)/9 and y(-1) = -6, we need to integrate both sides of the equation with respect to x.

The antiderivative of (3x-8)/9 is (3/18)x^2 - (8/27)x + C, where C is an arbitrary constant of integration. Therefore, we have:

y(x) = (3/18)x^2 - (8/27)x + C

To determine the value of the constant C, we use the initial condition y(-1) = -6. Substituting x = -1 and y = -6 into the equation above, we get:

-6 = (3/18)(-1)^2 - (8/27)(-1) + C

Simplifying this expression, we get:

C = -5

Therefore, the function y(x) that satisfies the differential equation dy/dx = (3x-8)/9 and y(-1) = -6 is:

y(x) = (1/6)x^2 - (8/27)x - 5

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At a rate of 2 m³ per minute, it would take 212.5 minutes to fill this swimming pool.

Based on the information provided, we can logically deduce that the shape of this pool is a prism because it is deep (2.2 m) at one end and shallow (1.2 m) at the other end.

First of all, we would determine the volume of this swimming pool as follows:

Volume = 1/2 × (1.2 + 2.2) × 10 × 25

Volume = 1/2 × (3.4) × 250

Volume = 1.7 × 250

Volume = 425 m³.

For the time, we have:

Time = volume/rate

Time = 425/2

Time = 212.5 minutes.

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Answer:

(1/3)x + 3 >= 3

<=> (1/3)x >= 0

<=> x >= 0

=> The only value from set satisfies, that is 0.

Hope this helps!

:)

Answer:

0

Step-by-step explanation:

⅓x + 3 》3

⅓x 》0

x 》0

After the sixth drop is added, the liquid level in the test tube will be between two marks that are 0.84 mL apart. Thus, the liquid level after the sixth drop is added will be between two marks that are 0.84 mL apart on the test tube.

Given that each drop contains 0.14 mL, we can find the total volume of liquid added by multiplying the number of drops by the volume per drop. In this case, the sixth drop corresponds to 6 * 0.14 mL = 0.84 mL.

Since the test tube has marks every mL, the liquid level will fall between two adjacent marks. The distance between each mark is 1 mL. Therefore, after the sixth drop is added, the liquid level will be between the mark corresponding to the total volume added (0.84 mL) and the mark below it.

For example, if the initial mark on the test tube represents 0 mL, the liquid level after the sixth drop would be between the mark representing 0.84 mL and the mark representing 1 mL. The liquid level will be closer to the mark representing 0.84 mL since it has not reached the next mark at 1 mL.

Thus, the liquid level after the sixth drop is added will be between two marks that are 0.84 mL apart on the test tube.

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Answer:

The number 3 represents the fixed cost in the equation which is the flat charge.

Considering the definition of zeros of a function, the zeros of the function f(t)= (t-5)² - 9 are 2 and 8.

The points where a polynomial function crosses the axis of the independent term (x) represent the so-called zeros of the function.

That is, the zeros of a function are those values ​​of x for which the expression is equal to 0. Graphically, the roots correspond to the abscissa of the points where the parabola intersects the x-axis.

Considering the function f(t)= (t-5)² - 9, if the zeros of a function are those values ​​of x for which the expression is equal to 0, you get:

(t-5)² - 9= 0

Solving:

(t-5)² = 9

t-5 = √9

t-5= ±3

Then:

t-5= 3

t= 3 +5

t= 8

and

t-5= -3

t= -3 +5

t= 2

Finally, the zeros of the function are 2 and 8.

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Answer:

Stephen spent $4 on milk, $6 on eggs, and $11 on cereal. He wrote the ratio 6

11

to describe some of his purchases

Step-by-step explanation:

The expression c|a + b| = |ca + cb| is always equal by the multiplicative additive property.

An element that in a particular mathematical system leaves any element by which it is multiplied intact. An example of an identity element is 1 in the group of rational numbers without a 0.

Given expression is c|a + b| = |ca + cb|.

For example, let a = 2, b = 3, and c = 4 put the values in the expression whether it is satisfying or not.

4 x | 2 + 3 | = | ( 4 x 2 ) + ( 4 x 3 ) |

4  x 5 = ( 8 + 12 )

20 = 20

Therefore, the expression c|a + b| = |ca + cb| is always equal by the multiplicative additive property.

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The total cost of importing this four-wheel drive vehicle would be $41,000.

To calculate the total costs of importing a four-wheel drive vehicle with a customs value of $30,000, you'll need to consider various factors such as import duties, taxes, and other fees.

Please note that these values may vary depending on the country and specific regulations.

1. Import Duty: This is a tax levied on imported goods, usually calculated as a percentage of the customs value. For example, if the import duty rate is 10%, the duty would be $3,000 (10% of $30,000).

2. Taxes: These are additional charges imposed by the government on imported goods, such as VAT or sales tax. The percentage varies depending on the country. Assuming a 20% tax rate, the tax would be $6,000 (20% of $30,000).

3. Other fees: These may include costs related to customs clearance, shipping, insurance, and other import-related expenses.

Let's say these fees total $2,000.

To calculate the total cost of importing the vehicle, simply add the customs value, import duty, taxes, and other fees:

$30,000 (customs value) + $3,000 (import duty) + $6,000 (taxes) + $2,000 (other fees) = $41,000.

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Answer:

8b

Step-by-step explanation:

You can factor the b-term out since b-term exists for all terms in the expression. By factoring out, you are basically dividing the factored term off and put it outside of the bracket, thus:

\(\displaystyle{16b-8b=\left(16-8\right)b}\)

Then evaluate and simplify:

\(\displaystyle{\left(16-8\right)b=8\cdot b}\\\\\displaystyle{=8b}\)

Answer:

Step-by-step explanation:

1/6

Answer:

(67x+90) / 10

Step-by-step explanation:

hope this will help you

By using sum or difference formulas, cos(-a) can be written as - cos(a). Explanation: We know that cosine is an even function of x, therefore,\(cos(-x) = cos(x)\) .Then, by using the identity \(cos(a - b) = cos(a) cos(b) + sin(a) sin(b)\), we can say that:\(cos(a - a) = cos²(a) + sin²(a).\)

This simplifies to:\(cos(0) = cos²(a) + sin²(a)cos(0) = 1So, cos(a)² + sin(a)² = 1Or, cos²(a) = 1 - sin²\)(a)Similarly,\(cos(-a)² = 1 - sin²(-a)\) Since cosine is an even function, \(cos(-a) = cos(a)\) Therefore, \(cos(-a)² = cos²(a) = 1 - sin²(a)cos(-a) = ±sqrt(1 - sin²(a))'.\)

This is the general formula for cos(-a), which can be written as a combination of sine and cosine. Since cosine is an even function, the negative sign can be written inside the square root: \(cos(-a) = ±sqrt(1 - sin²(a)) = ±sqrt(sin²(a) - 1) = -cos\).

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The null hypothesis to test for instruments' relevance is option D) H0:π2=0 or π3=0 or π4=0.In order to test the relevance of the instrument, the first stage equation's null hypothesis should be stated as: H0: π2 = 0 or π3 = 0 or π4 = 0.The relevance requirement will be fulfilled if we can refute the null hypothesis.

The null hypothesis will not be rejected if the F-statistic is less than 10.0. However, if the F-statistic is greater than 10.0, the null hypothesis will be rejected, indicating that the variables are relevant and that the instrument satisfies the relevance requirement.In summary, to test for instruments' relevance in TSLS, the null hypothesis of the first stage equation is stated as H0: π2 = 0 or π3 = 0 or π4 = 0.

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Answer:

600ft^2

Step-by-step explanation:

Because we are rounding the dimensions to the nearest ten this means the length of 29ft because 30ft and the width of 22ft is 20ft

Area = l X w

Area = 30 X 20

Area = 600

Therefore an estimate for the area of the wall is 600ft^2

Answer:

area =length x width

20 is the length and 30 is the width

So, area=20x30

=600ft^2