SOLVE AND CHECK THESE EQUATIONS
14. x2 + 8x + 7 = 0
17. x3 – 9x = 0
18. (x + 6)(x – 3) = 10

Y = 4114/5114

3 (a) To solve 2557⋅X=457 for X∈Z57 using Euclid's algorithm, take the GCD of 2557 and 457. That is, the GCD is:

GCD(2557, 457) = GCD(2557 - 457, 457)

                  = GCD(2157, 457)

                  = GCD(757, 457)

                  = GCD(357, 457)

                  = GCD(157, 457)

                  = 457


Therefore, the GCD of 2557 and 457 is 457, and thus the solution to the equation is X = 457/2557.

3 (b) To find all solutions to the equation 50114⋅Y=8114 for Y∈Z114, we need to rewrite the equation in terms of ordinary integers, since the inverse of 50114 does not exist. The equation can be rewritten as Y = 8114/50114 = 8114/(5114⋅2114) = 4114/5114. This equation is the same as the one in part (a), with 25 replaced by 5. Thus, the solution to this equation is Y = 4114/5114, which is the same solution found in part (a). Therefore, there is only one solution to this equation, and this solution is Y = 4114/5114.

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The actual distance between City C and City D is 4,224,000 feet.

What is total distance?

Whole distance refers to the actual travel distance between the origin and destination locations of the item.

We can use the given scale to convert the distance between City A and City B to feet:

500 miles = 500 * 5280 feet = 2,640,000 feet

Since 1.6 feet represents this distance on the wall map, we have:

1.6 feet = 2,640,000 feet / x

where x is the actual distance represented by 1.6 feet on the map. Solving for x, we get:

x = 2,640,000 feet / 1.6 feet = 1,650,000 feet per foot

Therefore, the  total distance between City C and City D, which is 2.56 feet on the map, corresponds to:

2.56 feet * 1,650,000 feet per foot = 4,224,000 feet

So the actual distance between City C and City D is 4,224,000 feet.

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Answer:

C: x+8= 6

Step-by-step explanation:

So if you were to work each of these out x + 6 = 8 that problem gives us positive 2, when we are looking for a -2 so that answer is ruled out. Then you go to x-6=8 you move the -6 and add it to the 8 and you get x = 14 still not our answer so thats also ruled out. Then x-8=6 is the same thing as the last one but with a -8 instead of a 6 but you get the same answer which is x=14 so not that one either. Then you work on the choice x+8=6 and you subtract 8 from both sides and you end up with a -2. So our final answer is C: X+8=6

Assuming the number of people who listen to the video increases by 45% each day, there would be approximately 24 new people who listen to the video on the 7th day after the initial 8 people.

According to the problem, the number of people listening to the video increases by 45% each day. Therefore, we can use the formula for compound interest to calculate the number of new people who listen to the video on the 7th day.

Let P be the initial number of people who listened to the video, which is 8.

Let r be the daily increase rate, which is 45% or 0.45 as a decimal.

Let n be the number of days, which is 7.

Then, the formula for compound interest is:

A = P(1 + r)^n

where A is the final number of people who listen to the video.

Plugging in the values, we get:

A = 8(1 + 0.45)^7

A ≈ 32

Therefore, the number of new people who listen to the video on the 7th day is approximately 32 - 8 = 24 people.

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Step-by-step explanation:

10^-3 is equivalent to 1/1000 or 0.001.

Both numbers are divisible by 2, 2 and 7.

What is Greatest Common Factor?

The greatest common factor (GCF) is the largest number that divides two or more numbers evenly. It is also known as the greatest common divisor (GCD) or highest common factor (HCF).

If 28 is the greatest common factor of two numbers, it means that both numbers have 28 as a factor. Thus, both numbers are divisible by 2, 2 and 7.

Additionally, the prime factorization of each number must contain all of the prime factors that are factors of 28, which are 2 and 7. However, there may be other prime factors as well. Without additional information, it is not possible to determine the complete prime factorization of each number.

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If the stove's output is greater than or equal to the estimated BTUs, then it should be large enough to heat her basement.

Cary can determine if a stove is large enough to heat her basement by checking the stove's specifications for its heating capacity or output. Typically, a stove's output is measured in British Thermal Units (BTUs) per hour. She can use the following formula to estimate the BTUs required to heat her basement:

BTUs = (Length x Width x Height of basement) x 5

Once Cary has an estimated BTU requirement, she can compare it to the output of the stove she's considering.

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The positive solution for x in the equation log_x(1)/256 = -4/3 is x = 4.57

To solve the logarithm problem for the positive solution for x, we can use the following steps:

1. First, we can rewrite the equation in exponential form:
x^(-(4)/(3)) = 1/256

2. Next, we can raise both sides of the equation to the power of -(3)/(4) to isolate x:
(x^(-(4)/(3)))^(-(3)/(4)) = (1/256)^(-(3)/(4))

3. Simplify the left side of the equation:
x = (1/256)^(-(3)/(4))

4. Simplify the right side of the equation:
x = 256^((3)/(4))

5. Take the fourth root of both sides of the equation:
x = (256^((3)/(4)))^(1/4)

6. Simplify the right side of the equation:
x = 256^((3)/(16))

7. Simplify the exponent:
x = 256^(3/16)

8. Calculate the value of x:
x ≈ 4.57

Therefore, the positive solution for x is approximately 4.57.

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Answer:

Part A: To create an expression to represent the amount of canned food collected so far by the three friends, we need to add up their individual contributions. Therefore, the expression would be:

Amount collected = (3x² - 2) + (x²) + (2xy + 5)

Amount collected = 4x² + 2xy + 3

Part B: To find the expression that represents the number of cans the friends still need to collect to meet their goal, we need to subtract the amount collected from their goal expression. Therefore, the expression would be:

Cans still needed = 6x² - 2xy + 8 - (4x² + 2xy + 3)

Cans still needed = 2x² + 5

Answer: We do not have enough information to provide an answer for Part C as we need to know the value of x to evaluate the expression 6.02.

The number of toppings where the cost of the pizza is the same at both Pizza Palace and Pizza Ranch is 10. The equation that represents the situation is $5 + $0.20T = $4 + $0.30T

A variable is a quantity that may change within the context of a mathematical problem or experiment.

Let's start by defining the variables we will use in the problem:

Cc: Cost of a pizza at Pizza Palace

Cr: Cost of a pizza at Pizza Ranch

T: Number of toppings

According to the problem, we have:

Cc = $5 + $0.20T

Cr = $4 + $0.30T

We want to find the number of toppings, T, where the cost of the pizza is the same at both Pizza Palace and Pizza Ranch. That is:

Cc = Cr

Substituting the expressions for Cc and Cr, we get:

$5 + $0.20T = $4 + $0.30T

Simplifying and solving for T, we get:

$1 = $0.10T

T = 10

Therefore, the number of toppings where the cost of the pizza is the same at both Pizza Palace and Pizza Ranch is 10.

The equation that represents the situation is $5 + $0.20T = $4 + $0.30T

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Answer: x-14

Step-by-step explanation:

A valid inference is a conclusion that is true about the subject based on the evidence or premises provided.

Mathematically, we can represent a valid inference using logical notation. In the example above, we can use the following notation:

Premise 1: All humans are mortal.

Premise 2: Samantha is a human.

Conclusion: Samantha is mortal.

We can use the logical connective "if-then" to represent a valid inference. In this case, we can say, "If all humans are mortal, and Samantha is a human, then Samantha is mortal." This statement is true based on the premises provided.

To determine the validity of an inference mathematically, we can use rules of logic such as the law of detachment or the law of syllogism. The law of detachment states that if we have a conditional statement, "If p, then q," and we know that p is true, then we can validly infer that q is also true.

The law of syllogism is another rule of logic that helps us determine the validity of an inference. This rule states that if we have two conditional statements, "If p, then q," and "If q, then r," we can infer that "If p, then r" is true.

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p(t) = {

P35.00 if t ≤ 2

P35.00 + P15.00 × (t - 2) if 2 < t ≤ 12

P250.00 if t > 12

} is the required function to represent given information.

Expressions are commonly used in programming to perform calculations, manipulate data, and make decisions based on the results of evaluations.

To represent the parking fee using the function p(t), we need to consider the different rates depending on the number of hours parked. Here are the different cases we need to consider:

If t ≤ 2, the parking fee is P35.00

If 2 < t ≤ 12, the parking fee is P35.00 plus P15.00 for each hour (or fraction of it) after the first two hours. This can be represented by the equation:

p(t) = P35.00 + P15.00 × (t - 2)

If t > 12, the parking fee is a flat rate of P250.00.

We can combine these cases into a single function using a piecewise function. Here is the function p(t):

p(t) = {

P35.00 if t ≤ 2

P35.00 + P15.00 × (t - 2) if 2 < t ≤ 12

P250.00 if t > 12

}

This function represents the parking fee in terms of the number of hours parked (t). To use it, simply substitute the number of hours parked into the function and calculate the resulting fee. For example, if you parked for 4 hours, the fee would be:

p(4) = P35.00 + P15.00 × (4 - 2) = P65.00

Therefore, p(t) = {

P35.00 if t ≤ 2

P35.00 + P15.00 × (t - 2) if 2 < t ≤ 12

P250.00 if t > 12

} is the required function to represent given information.

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The graph of the inequality y ≥ (1/2)x - 1 and x - y > 1 is attached. Shannon's graph is correct.

An equation is an expression that shows the relationship between two or more numbers and variables. Equations can either be linear, quadratic, cubic and so on depending on the degree.

Inequalities are used for the non equal comparison of numbers and variables.

Given the inequalities:

y ≥ (1/2)x - 1     (1)

and

x - y > 1     (2)

The graph of the inequality is attached. Shannon's graph is correct.

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Domain of function is 0 ≤ x < ∞ , range of function is 0 ≤ y < ∞

A function's domain  is the set of values ​​that can be put into the function. This set is the x-values ​​of a function like f(x). A function's range is the set of values ​​that the function takes on. This set is the value that the function outputs after inserting the x value.

Given,

graph of the function is drawn as a ray,

ray is starting from origin and extends to infinity on first quadrant

domain of the function

0 ≤ x < ∞

interval notation

Domain = [0, ∞)

range of the function

0 ≤ y < ∞

interval notation

Range = [0, ∞)

Hence, Domain and range of the function are 0 ≤ x < ∞ and 0 ≤ y < ∞ respectively.

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The sum of two rational expressions with unlike denominators is 1/(x+1) + 1/(x+2).

To split the given rational expression into a sum of two rational expressions with unlike denominators, we will use the partial fraction decomposition method. Here are the steps:

1. Factor the denominator of the given rational expression: (x^(2)+3x+2) = (x+1)(x+2)
2. Set up the partial fraction decomposition: (2x+3)/(x+1)(x+2) = A/(x+1) + B/(x+2)
3. Multiply both sides of the equation by the common denominator to get rid of the denominators: 2x+3 = A(x+2) + B(x+1)
4. Set up a system of equations by equating the coefficients of the like terms: 2x+3 = (A+B)x + (2A+B)
5. Solve the system of equations to find the values of A and B: A=1, B=1
6. Substitute the values of A and B back into the partial fraction decomposition: (2x+3)/(x+1)(x+2) = 1/(x+1) + 1/(x+2)

Therefore, the sum of two rational expressions with unlike denominators is 1/(x+1) + 1/(x+2).

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The decimal multiplier to increase by 6.1% is 1.061.

What is multiplication ?

Multiplication is a mathematical operation used for finding the result of adding a number to itself a certain number of times. It involves multiplying two or more numbers to find their product. For example, 2 times 3 is equal to 6, written as 2 x 3 = 6. In multiplication, the numbers being multiplied are called factors, and the result is called the product. Multiplication is often denoted by the symbol "x" or a dot ".".

A decimal multiplier is a factor that is used to increase or decrease a number by a certain percentage. It is commonly used in financial calculations such as interest rates, discounts, and taxes.

To find the decimal multiplier to increase by a certain percentage, you can use the following formula:

Decimal multiplier = 1 + (percentage increase/100)

For example, if you want to increase a number by 6.1%, the decimal multiplier would be:

Decimal multiplier = 1 + (6.1/100)

Decimal multiplier = 1.061

This means that to increase a number by 6.1%, you would multiply it by 1.061. For example, if you had a number of 100, to increase it by 6.1%, you would multiply it by 1.061 to get 106.1.

On the other hand, if you wanted to decrease a number by a certain percentage, you would use a decimal multiplier that is less than 1. For example, to decrease a number by 10%, the decimal multiplier would be 0.9, which means you would multiply the number by 0.9 to get the new decreased value.

Therefore, decimal multiplier to increase by 6.1% is 1.061.

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The height of a right cone is 42 units.

The area or volume occupied by a right circular cone is referred to as the right circular cone's volume. A three-dimensional solid object called a right circular cone has a pointed end on one side and a circle on the other. The vertex of the cone is another name for the sharp end. A cone with a right circular shape is one whose axis is parallel to the base plane.

Here, we have

Given: The volume of a right cone is 2016\piπ units^3. If its diameter measures 24 units

Height of the cone = Volume of a cone ÷ 1/3(πr²)

Where:

π = 22/7

r = radius = diameter / 2 = 24 / 2 = 12 units

h = height

2016π÷ (1/3 x π x 12²) = 42 units

Hence, the height of a right cone is 42 units.

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The total miles that all eight vehicles drove is 375 miles, and the correct answer is A. 375.

To calculate the total miles that all eight vehicles drove, we need to add up the miles driven by the seven vehicles that completed the trip and the miles driven by the eighth vehicle that only completed 50% of the journey.

The seven vehicles that completed the trip each drove 50 miles, so their total mileage is 7 x 50 = 350 miles.

The eighth vehicle only completed 50% of the journey, so it drove 50 x 0.50 = 25 miles.

To find the total miles driven by all eight vehicles, we add the miles driven by the seven vehicles and the miles driven by the eighth vehicle:
350 + 25 = 375 miles

Therefore, the total miles that all eight vehicles drove is 375 miles, and the correct answer is A. 375.

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Answer: ∠ABC = 29.745°

Step-by-step explanation:

I believe this is the answer , you should be golden.

Answer:

no se     y ademas me aparece en ingles :(

Step-by-step explanation:

The time taken to read 3 books is 8 weeks.

The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.

Given that, Christian read 1/4 book every 2/3 week.

Time taken to read 1 complete book is

1 × 2/3 ÷ 1/4

= 2/3 ÷ 1/4

= 2/3 × 4/1 (To divide two fractions, keep the first fraction same and change division to multiplication and inverse the second fraction)

= 8/3

Now, time taken to read 3 complete is

= 8/3 ×3

= 8

Therefore, time taken to read 3 books is 8 weeks.

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Answer:

2

Step-by-step explanation:

The margin of error of a study showed that 387 out of 900 people eat fast food regularly. We want to construct a 90% confidence interval for the population proportion of people who east fast food is   0.0234.The correct answer is option b. 0.0234.

To find the margin of error for a 90% confidence interval, we can use the formula:

Margin of error = z*√(p*(1-p)/n)

Where z is the z-score for a 90% confidence level, p is the sample proportion, and n is the sample size.

In this case, the z-score for a 90% confidence level is 1.645, the sample proportion is 387/900 = 0.43, and the sample size is 900.

Plugging these values into the formula, we get:

Margin of error = 1.645*√(0.43*(1-0.43)/900)

Margin of error = 0.0234

Therefore, the margin of error for the 90% confidence interval is 0.0234. Answer is b. 0.0234

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One euro is equivalent to $1.2 in dollars thanks to the $1.2/euro conversion rate. The EUR/USD exchange rate is another name for this rate.

A currency's relative value expressed in terms of another currency is called an exchange rate (or group of currencies). The exchange rate is a significant economic variable for nations with active international trade, like Australia. We can multiply the quantity of euros by the conversion rate to convert 160 euros to dollars:

1 euro Equals $1.22; 160 euros = $192.

Hence, 160 euros are equal to $192.

We can divide the amount in dollars by the conversion rate to convert $76.80 to euros:

64 euros are equal to $76,80 at the exchange rate of $1 to the euro.

Hence, 64 euros are equal to $76.80.

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The probability that a randomly selected school or district uses digital content and uses it as part of its curriculum is 48.6%.

Probability refers to the odds, chance, or likelihood that an expected outcome is obtained out of many possible outcomes.

Probability is a fractional value lying between zero and one based on the degree of certainty.

The percentage of K-12 schools or districts using digital content = 81%

The fractional value of those who use digital content as part of their curriculum = 12/20 = 0.6 or 60%.

Thus, the probability of randomly selecting a school or district using digital content as part of curriculum = 48.6% (81% x 60%).

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The requried measure of the angle x in at the point of intersection of tangent and secant of the circle is 30°.

The circle is the locus of a point whose distance from a fixed point is constant i.e center (h, k). The equation of the circle is given by

(x - h)² + (y - k)² = r²

Where h, k is the coordinate of the center of the circle on a coordinate plane and r is the radius of the circle.

Here,
From the figure the,
From a point, a tangent and a secant are drawn to the circle.
Since an equilateral triangle is formed with the help of a cord intersects the tangent and secant on the circumference of triangle.

Again from the figure, the sum of the angle in the triangle is equal to 180°.
90 - 60 + 180 - 60 + x = 180
30 + 120 + x = 180
x = 30°

Thus, the requried measure of the angle x at the point of intersection of tangent and secant of the circle is 30°.

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The domain of y = x + 6 - 7 is the set of all real numbers

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

y = x + 6 - 7

The domain of a function is the set of all possible input values (usually denoted by x) for which the function is defined

There is no restriction on the input values, x

So, the domain of y = x + 6 - 7 is all real numbers, since there is no restriction on the input (x).

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The diameter of the circle is 28 inches.

The formula for the area of a circle is:

[tex]A = \pi r^2[/tex]

Where A is the area and r is the radius.

Any straight line segment that travels through the centre of a circle and has endpoints that are on the circle is said to have a diameter.

To find the diameter of the circle, we first need to find the radius. We can rearrange the formula for the area to solve for the radius:

[tex]r = \sqrt{ (A/\pi )}[/tex]

Plugging in the given values:

[tex]r = \sqrt{(615.44/3.14)} = 14[/tex]

So the radius of the circle is 14 inches. The diameter is twice the radius, so:

d = 2r = 2(14) = 28

Therefore, the diameter of the circle is 28 inches.

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Answer: The mean increases by 1.6°.

Step-by-step explanation:

The mean is the average or the sum of all the data divided by the amount of data.

58 + 61 + 71 + 77 + 91 + 100 + 105 + 102 + 95 + 82 + 66 + 57 = 965

There are 12 data points so...

965 / 12 ≈ 80.4

To find the new mean add 101 to 965, then divide by 13.

965 + 101 = 1066

1066 / 13 = 82

The mean increases by 1.6°.

Hope this helps!

We are being informed that the sum of the two numbers is 12 and their difference is 6.

Thus, the two numbers whose sum is equal to 12 and their difference is equal to 6 are 9 and 3 respectively.

Let those two unknown numbers be (a) and (b)

a + b = 12

Their difference;

i.e.

a - b = 6

So, we can equate the two equations together:

i.e.

a + b = 12     --- (1)

a - b = 6        --- (2)

From equation (1); Let a be:

a = 12 - b

Now, Let's replace the value of (a) into equation (2)

12 - b - b = 6

12 - 2b = 6

-2b = 6 - 12

-2b = -6

2b = 6

b = 6/2

b = 3

If b = 3;

Then from equation, we have:

a + b = 12

replace b with 3 from the above equation, we have:

a + 3 = 12

a = 12 - 3

a = 9

Therefore, we can conclude that the sum of the two numbers are 9 and 3. respectively

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