Find an expression which represents the difference when (5x + 6y) is subtracted
from (2x + 7y) in simplest terms.

Answer:

Step-by-step explanation:

Draw a line out in the 3rd quadrant.  Hyponuse would be 3; y=-2 find x using pythagorean theorem

so 3²=2²+x²

x=[tex]\sqrt{5}[/tex]

so cos Θ = [tex]\frac{\sqrt{5} }{3}[/tex]

The value of the expression, which serves as the basis for the response, is 265 for the provided question. answer is option (c).

An expression is a group of numbers, variables, and mathematical operations used to represent a quantity or value in mathematics. Expressions can be straightforward or intricate, and they can contain exponents, coefficients, variables, and constants. Several methods, including factoring, the order of operations, and algebraic manipulation, can be used to evaluate or simplify expressions. The values of an expression's variables and constants determine its value.

The expression −204 − 64 − (−3) can be streamlined by applying the following arithmetic rules:

−204 − 64 − (−3) = −204 − 64 + 3

[the double negative turns positive because]

= −265

Consequently, the expression's value is -265. The correct answer is option (c).

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Sequence 1: 13, 16, 19, 22, 25, Sequence 2: 15, 13, 11, 9, 7 and Ordered Pair: (13, 15), (16, 13), (19, 11), (22, 9), (25, 7).

what is sequence?

An ordered list of numbers is a sequence. The three dots indicate that the established pattern should move forward.

A. Sequence 1: 13, 16, 19, 22, 25

Sequence 2: 15, 13, 11, 9, 7

Ordered Pair: (13, 15), (16, 13), (19, 11), (22, 9), (25, 7)

B. Sequence 1: 1, 5, 17, 53, 161

Sequence 2: 6, 15, 33, 69, 141

Ordered Pair: (1, 6), (5, 15), (17, 33), (53, 69), (161, 141)

C. Input (x) | Output

1 | 17,  2 | 19, 3 | 21, 4 | 23

D. Input (x) | Output

1 | 30, 2 | 15, 3 | 7.5

To find the outputs, we use the formula: output = 60 ÷ 2x.

For x = 1, output = 60 ÷ 2(1) = 30

For x = 2, output = 60 ÷ 2(2) = 15

For x = 3, output = 60 ÷ 2(3) = 7.5

E. Input (x) | Output

1 | 23, 2 | 30, 3 | 37, 14 | 102, 15 | 109, 16 | 116, 27 | 205, 70 | 498

To find the outputs, we use the formula: output = 16 + 7x.

For x = 1, output = 16 + 7(1) = 23

For x = 2, output = 16 + 7(2) = 30

For x = 3, output = 16 + 7(3) = 37

For x = 14, output = 16 + 7(14) = 102

For x = 15, output = 16 + 7(15) = 109

For x = 16, output = 16 + 7(16) = 116

For x = 27, output = 16 + 7(27) = 205

For x = 70, output = 16 + 7(70) = 498

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The solutions to the equation [tex]x^{2} + x[/tex]  = 11/4 are x = -1/2 + [tex]\sqrt{3}[/tex] and x = -1/2 - [tex]\sqrt{3}[/tex]

What is the equation?

An equation is a mathematical statement that indicates that two expressions are equivalent. It has two sides, one on each side, divided by an equals sign (=). An equation's left and right sides can contain numbers, variables, and mathematical operations, including addition, subtraction, multiplication, and division.

The left side of the equation should be rewritten in the form (x + a)2, where an is a constant, in order to complete the square and find the solution to the equation [tex]x^{2}+x[/tex] = 11/4.

To accomplish this, add and remove [tex](1/2)^{2}[/tex](which is equivalent to 1/4) inside of the brackets, as seen in the example below:

[tex]x^{2} +x[/tex]= 11/4

[tex]x^{2} +x[/tex]+ 1/4 - 1/4 = 11/4

[tex](x+1/2)^{2}[/tex] - 1/4 = 11/4

[tex](x+1/2)^{2}[/tex] = 3

Next, we take the square root of both sides:

x + 1/2 = ±[tex]\sqrt{3}[/tex]

Finally, we solve for x by subtracting 1/2 from both sides:

x = -1/2 ± [tex]\sqrt{3}[/tex]

So the solutions to the equation [tex]x^{2} +x[/tex]  = 11/4 are x = -1/2 + [tex]\sqrt{3}[/tex] and x = -1/2 - [tex]\sqrt{3}[/tex].

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The graph will bounce like a polynomial of degree equal to the multiplicity minus 1.

What is polynomial?

A polynomial is a mathematical expression that consists of variables and coefficients, which are combined using arithmetic operations such as addition, subtraction, multiplication, and non-negative integer exponents.

The power of the factor that causes the graph to bounce at the corresponding zero depends on the multiplicity of the zero.

If the zero has odd multiplicity, the graph will cross the x-axis at the zero, meaning there will be no bounce.

If the zero has even multiplicity, the graph will bounce at the zero. Specifically, if the multiplicity is 2, the graph will bounce like a parabola; if the multiplicity is 4, the graph will bounce like a quartic; and so on. In general, the graph will bounce like a polynomial of degree equal to the multiplicity minus 1.

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The exponential growth equation that passes through the given points is [tex]y = 6 \times 1.5^x[/tex]

How to find an exponential growth equation ?

An exponential growth equation that passes through the given points. We aretaking the equation takes the form [tex]y = a×b^x [/tex] where a is the initial value and b is the growth factor. We can use the three given points to form a system of equations.

It is clear that the equation passes through points ( -1,4), (0,6), (1,9)

So,

[tex]4 = ab^{-1} \\ 6 = ab^0 \\ 9 = a \times b^1[/tex]

We are dividing the second equation by the first equation,

[tex] \frac{6}{4} = \frac{(ab^0)}{(ab^{-1})}[/tex]

1.5 = b

Next, we can use this value of b in the third equation to find a,

9 = a×1.5¹

a = 6

Therefore, the exponential growth equation that passes through the given points is [tex]y = 6 \times 1.5^x[/tex]

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It seems that the given data consists of two sets of numbers separated by an equals sign. The first set of numbers appears to be a list of math test scores, while the second set of numbers is unclear.

Assuming that the question is asking about the number of students represented by the first set of numbers (the math test scores), then the answer would be 31. This is because there are 31 numbers in the list, which could represent the scores of 31 individual students.

Answer: 31

Step-by-step explanation:

The correct answer is: B. They have the same y-intercept, but the graph of g(x) gets faster over time.

Exponents and powers are ways of representing very large  or very small numbers in a simplified way. For example, if we need to represent 3 x 3 x 3 x 3 in a simple way,  we can write it as 34, where 4 is the exponent and 3 is the base. The whole expression 34 is said to be a force.

The  functions provided are:

[tex]f(x) = 500(1.015)^x[/tex]

[tex]g(x) = 500(1.021)^x[/tex]

Both functions have an initial value of $500 (when x = 0). Therefore, they share the same y-intercept, which is (0, 500).  

To compare the graphs of f(x) and g(x), we can look at their growth rates. Note that the exponent of f(x) has a base of  1.015, while the exponent of g(x) has a base of  1.021. Since both bases are greater than 1, both functions grow exponentially with time.  

However, since 1.021 is greater than 1.015, the function g(x) increases with time faster than f(x). This means that the graph of g(x) is steeper than the graph of f(x).  

Therefore, the correct answer is:

B. They have the same y-intercept, but the graph of g(x) gets faster over time.

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Answer:

x = 7

Step-by-step explanation:

the sum of the 3 angles in a triangle = 180°

sum the 3 angles and equate to 180

9x - 3 + 30 + 90 = 180

9x + 117 = 180 ( subtract 117 from both sides )

9x = 63 ( divide both sides by 9 )

x = 7

Answer:

Yo, the equation of the circle that's chillin' and just grazin' against the line y = -4, with its center chillaxin' at (5, 4), is:

(x - 5)^2 + (y - 4)^2 = r^2

where r is the radius of the circle. Keep it cool, bro!

Answer: 12

                                                      ........................................

Answer:

it (8,0) or (0,8)

Step-by-step explanation:

im not sure but hope this helps.

Complete this statement given that g(x) = -f(x): "This graph of function g is graph (C)  because the graph of function g is the result of a reflection applied to the graph of function f."

The graph of function g is a reflection of the graph of function f across the x-axis because of the negative sign in front of f(x) in the definition of g(x) = -f(x). This reflection results in a vertical flip of the graph. When a function is multiplied by a negative value, it gets reflected across the x-axis. The "C" option in the dropdown menu indicates a reflection across the x-axis.

The transformation applied to the graph of function f to get the graph of function g is a reflection, and it occurs due to the negative sign (-) in front of f(x) in the definition of g(x) = -f(x).

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Answer:

We are given that 50% of the ELTs are made by Company A, 45% are made by Company B, and 5% are made by Company C. We also know the rate of defects for each company's ELTs: 4% for Company A, 6% for Company B, and 9% for Company C.

Let D be the event that an ELT is defective, and let Bi be the event that an ELT was made by Company i, where i = A, B, or C. We want to find the probability that an ELT is made by Company B given that it is defective, i.e., we want to find P(B|D).

Using Bayes' theorem, we can write:

P(B|D) = P(D|B) * P(B) / P(D)

where P(D|B) is the probability that an ELT made by Company B is defective, P(B) is the prior probability that an ELT is made by Company B, and P(D) is the overall probability of an ELT being defective.

We can calculate each of these probabilities as follows:

P(D|B) = 0.06 (given)

P(B) = 0.45 (given)

P(D) = P(D|A) * P(A) + P(D|B) * P(B) + P(D|C) * P(C)

= 0.04 * 0.5 + 0.06 * 0.45 + 0.09 * 0.05

= 0.0355

Substituting these values into Bayes' theorem, we get:

P(B|D) = P(D|B) * P(B) / P(D)

= 0.06 * 0.45 / 0.0355

≈ 0.762

Therefore, the probability that an ELT made by Company B is defective given that it is found to be defective is approximately 0.762, or 76.2%.

The solution to the equation ln {A} = .552 is A = e[tex]^{0.552}[/tex] = 2.7. In order to calculate eˣ for both sides of the equation ln {A}=.552, one must first understand what the equation signifies.

A logarithmic equation is an equation involving logarithms of different variables. Logarithmic equations are used to solve various types of problems. It uses the logarithmic properties of multiplication and division to simplify the equation.

This equation is a logarithmic equation, in which ln (natural logarithm) is used to represent a number's exponential value.

This means that the equation is actually stating that A is equal to e raised to the power of 0.552 (e[tex]^{0.552}[/tex] ).

In order to solve for A, one must use the basic rule of logarithms: for any logarithmic equation of the form ln {A} = B, A = e^B.

Therefore, the solution to the equation ln {A} = .552 is

A = e[tex]^{0.552}[/tex] .

This equation can be solved using basic algebra, as e[tex]^{0.552}[/tex]  can be replaced with an equivalent expression.

The equation can be rewritten as A = (e[tex]^{0.5}[/tex])(e[tex]^{0.052}[/tex]).

The value of e[tex]^{0.5}[/tex] can be calculated using a calculator, and can be rounded to the nearest tenth.

The value of e[tex]^{0.052}[/tex] can then be calculated, which can also be rounded to the nearest tenth.

Adding the two values together will give the solution to the equation, which is A = 2.7.

Therefore, the solution to the equation ln {A} = .552 is

A = e[tex]^{0.552}[/tex]

= 2.7.

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Answer:

33.444

Step-by-step explanation:

Answer:

71%

Step-by-step explanation:

To calculate the percent decrease in the stock, we can use the following formula:

Percent decrease = ((Original value - New value) / Original value) * 100

Given:

Original value (purchase price) = $2.99 per share

New value (selling price) = $0.88 per share

Plugging in the values into the formula:

Percent decrease = ((2.99 - 0.88) / 2.99) * 100

Percent decrease = (2.11 / 2.99) * 100

Percent decrease = 70.57%

Rounding to the nearest whole percent, the correct answer is 71%.

Answer:

$2.4675

Step-by-step explanation:

you could have just used a calculator for this one tbh

Carlos needs to earn at least 16 points on the final quiz to earn at least a 90% average.

We have,

Let's start by finding the total number of points that Carlos can earn in the class:

Total points

= 5 quizzes x 20 points per quiz

= 100 points

If Carlos needs an average of 90% or greater, that means he needs to earn at least 90 points out of 100.

Total points earned.

= 18 + 19 + 17 + 20

= 74 points

To find the minimum score Carlos needs on the final quiz, we can set up an inequality:

(74 + x) / 5 ≥ 0.9

where x is the score on the final quiz.

Simplifying this inequality.

74 + x ≥ 90

x ≥ 16

Therefore,

Carlos needs to earn at least 16 points on the final quiz to earn at least a 90% average.

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$8.11 was the percent increase in the median monthly rent prices from 2000 to 2003.

What is a linear equation in mathematics?

A linear equation in algebra is one that only contains a constant and a first-order (direct) element, such as y = mx b, where m is the pitch and b is the y-intercept.

                         Sometimes the following is referred to as a "direct equation of two variables," where y and x are the variables. Direct equations are those in which all of the variables are powers of one. In one example with just one variable, layoff b = 0, where a and b are real numbers and x is the variable, is used.

2000 = $602

2003  = $651

               = 651 - 602/602  * 100

                = $8.11

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Answer:

normal distribution curve

Step-by-step explanation:

It is given that the bars decrease evenly from the middle to the left and from the middle to the right.

The price for an adult ticket is $3 and the price for a student ticket is $14

Given that

So, we have

10x + 7y = 128

7x + 14y = 217

Where

x = adults and y = students

When solved graphically, we have

x = 3 and y = 14

Hence, the price of the student ticket is $14

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The probability that the point land in square S will be 5/6.

What is probability?

Probability is a branch of mathematics in which the chances of experiments occurring are calculated. It is by means of a probability, for example, that we can know from the chance of getting heads or tails in the launch of a coin to the chance of error in research.

The probability that the point does not land in triangle T is equal to subtract the area of triangle T from the area of rectangle and divided the result by the  the area of rectangle

so, Find out the area of rectangle

A = (6)(4)

= 24 unit²

Find out the area of triangle T

A = 1/2(2)(4)

= 4 unit²

The probability is equal to

P = (24-4) / 24

= 20/24

= 5/6

Hence, the probability that the point land in square S will be 5/6.

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Based on the calculations given below, the value of the marginal product is option A: $37.50.

The value of marginal product (VMP) is one that can be calculated as the additional revenue generated by hiring an additional worker.

So to o calculate the VMP of the first worker, it will be:

Hence:

VMP of the first worker = (output with one worker - output with zero workers) x price per unit

VMP of the first worker = (25 - 0) x $2

                                            = $50

Note that the ingredients needed to make each cup of coffee cost 50 cents, so the total cost of making 25 cups of coffee with one worker will be:

Total cost = ingredients cost x output

                = $0.50 x 25

                   = $12.50

So, the value of the marginal product of the first worker can be obtained by:

VMP of the first worker = additional revenue - additional cost

                                  = $50 - $12.50

                                    = $37.50

So the value of the marginal product is: $37.50.

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According to the given data the maximum profit is $780,000 when 6,500 bikes are sold.

The marginal profit function represents the rate at which the profit changes as the number of units sold changes. It is the derivative of the profit function with respect to the number of units sold. The marginal profit function is important in business because it helps companies to determine the optimal level of production that maximizes profit. The critical value of the marginal profit function (when it equals zero) indicates the point where the profit function changes from increasing to decreasing, or vice versa, which can help companies to identify the optimal production level that maximizes profit.

a) To find the marginal profit function, we need to take the derivative of the profit function with respect to x:

P'(x) = -4x + 260

b) To find the critical value, we need to set the marginal profit function equal to zero and solve for x:

-4x + 260 = 0

x = 65

Therefore, the critical value is x = 65.

c) To find the maximum profit, we need to evaluate the profit function at the endpoints of the given interval (3 and 80) as well as at the critical value (65), and then compare the values to see which one is the largest. We can use a table to organize the values:

x P(x)

3 190

65 7800

80 2600

Therefore, the maximum profit is $780,000, which occurs when 6,500 bikes are sold (since each x represents 100 bikes).

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the amount closest to the difference between the interest Victoria would earn in Account B and the interest she would earn in Account A at the end of 4 years is $22.32.

What is compound interest?

The interest on savings that is computed on both the initial principal and the interest accrued over time is known as compound interest. Compound interest is computed by multiplying the starting principal amount by one and the annual interest rate is raised to the number of compound periods minus one. The final step is to deduct the initial loan principal from the calculated value.

Using the formula for compound interest, we can find the amount at the end of 4 years in Account B:

[tex]A = P * (1 + r/n)^{(nt) = $1500 * (1 + 0.035/1)^{(14) = $1732.32[/tex]

The interest earned in Account B over 4 years is the difference between the amount at the end of the period and the principal:

I = A - P = $1732.32 - $1500 = $232.32

Therefore, the difference between the interest Victoria would earn in Account B and the interest she would earn in Account A at the end of 4 years is approximate:

$232.32 - $210 = $22.32

Therefore, the amount closest to the difference between the interest Victoria would earn in Account B and the interest she would earn in Account A at the end of 4 years is $22.32.

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The temperature at 8:00 A.M. was 15°C.

Using the given information:
1. At 7:00 P.M., the temperature was 16°C.
2. This temperature was 9°C less than the temperature at 2:00 P.M.

We can use this information to find the temperature at 2:00 P.M.:
Temperature at 2:00 P.M. = 16°C (temperature at 7:00 P.M.) + 9°C
Temperature at 2:00 P.M. = 25°C

3. The temperature at 2:00 P.M. was 10°C higher than the temperature at 8:00 A.M.

Now, we can find the temperature at 8:00 A.M.:
Temperature at 8:00 A.M. = 25°C (temperature at 2:00 P.M.) - 10°C
Temperature at 8:00 A.M. = 15°C

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