Graph the linear system and tell how many solutions it has. If there is exactly one solution, estimate the solution and check it algebraically.

The system of equations can be written as:-

10x + 4y = 42

6x + 8y = 14

A system of equations, also known as a set of simultaneous equations or an equation system, is a finite set of equations for which we sought common solutions in mathematics. A system of equations can be classified in the same way that a single equation can.

Given that in an online quiz, positive points are awarded for a correct answer, and negative points are awarded for an incorrect answer. Elena answers 10 questions correctly and 4 incorrectly and scores 42 points. Kiran answers 6 questions correctly and 8 incorrectly and scores 14 points.

The system of equations can be written as:-

10x + 4y = 42

6x + 8y = 14

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The system of linear inequalities that represents the graph is:

y ≥ x - 2

y ≥ -3x + 2

The system of linear inequalities for the given graph can be written as explained below.

Inequality 1:

Slope (m) = rise/run = 3/3 = 1

The y-intercept (b) = -2

Since the line is a solid line and the shaded region is above the line, the inequality sign to use is, ≥. Therefore, substitute m = 1 and b = -2 into y ≥ mx + b:

y ≥ x - 2

Inequality 2:

Slope (m) = rise/run = -3/1 = -3

The y-intercept (b) = 2

Since the line is a solid line and the shaded region is above the line, the inequality sign to use is, ≥. Therefore, substitute m = -3 and b = 2 into y ≥ mx + b:

y ≥ -3x + 2

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The equation for g(x) by the given data is g(x) = (-1/4)(x^2).

An equation is an expression that shows the relationship between two or more numbers and variables.

A mathematical equation is a statement with two equal sides and an equal sign in between. An equation is, for instance, 4 + 6 = 10. Both 4 + 6 and 10 can be seen on the left and right sides of the equal sign, respectively.

We are given that;

The function f(x)=x^2

Now,

Since the function g is a scaled version of f(x) = x^2, we can write:

g(x) = a(x^2)

where 'a' is the scaling factor.

To find the value of 'a', we can use the given point on the graph of g:

g(2) = -1

Substituting x = 2 and g(x) = -1 in the above equation, we get:

-1 = a(2^2)

-1 = 4a

a = -1/4

Therefore, the equation for g(x) will be g(x) = (-1/4)(x^2).

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To maximize the number of interviews, 12 undergraduate students, 4 graduate students, and 4 faculty members should be hired. The maximum number of interviews that can be conducted is 684.

Let x, y, and z be the number of undergraduate students, graduate students, and faculty members hired, respectively. The objective is to maximize the number of interviews, which is given by the function

N = 18x + 25y + 30z.

The total cost of hiring interviewers is given by the function

C = 100x + 150y + 200z.

The constraints are x + y + z ≤ 20 (due to transportation limitations), and C ≤ 3200 (the budget constraint). Using linear programming techniques, we can solve for the optimal values of x, y, and z, which are 12, 4, and 4, respectively.

The maximum number of interviews is 18(12) + 25(4) + 30(4) = 684.

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Answer: The graph of y = 3/4 is a horizontal line with y-intercept at 3/4. When this graph is translated, its y-intercept changes, while its slope remains the same.

Since the new graph has asymptotes at x = -5 and y = 14, the new equation must be of the form y = m(x + 5) + 14, where m is the slope of the original line, which is 3/4. Substituting the values, we get:

y = (3/4)(x + 5) + 14

So the equation of the translated graph is y = (3/4)(x + 5) + 14.

Step-by-step explanation:

The value of the variable x as required to be determined from the given image is; 11.

As evident in the task content; it can be inferred that there are similar triangles from the image.

Since the ratio of corresponding sides of similar triangles are equal; we have that;

x / 22 = (9+3) / (9+3+12)

x / 22 = 12 / 24

x = (22 × 12) / 24

x = 11.

Ultimately, the value of x from the given image is; 11.

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The limit of (3x - 3)^(5/2) as x approaches 4, [tex]\lim_{x \to } _4[/tex] (3x - 3)^(5/2) is 243.

The limit of a function as x approaches a certain value can be thought of as the value that the function approaches as x gets arbitrarily close to that value.

To find the limit of (3x - 3)^(5/2) as x approaches 4, we need to evaluate the expression for values of x that are close to 4 and see what the result approaches.

First, let's substitute 4 for x in the expression:

[tex]\lim_{x \to } _4[/tex] (3x - 3)^(5/2) = (3*4 - 3)^(5/2)

                                = (9)^(5/2)

                                = (√9)⁵

                                = 3⁵

                               = 243

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Algorithm is a set of instructions for solving a problem or performing a task, typically designed for a computer to follow.

An algorithm is essentially a step-by-step procedure for solving a problem or accomplishing a specific task. It is used in various fields, including mathematics, computer science, engineering, and many others. In computer science, algorithms are essential for software development and programming, as they provide a systematic approach to designing and implementing complex programs. The process of developing an algorithm typically involves breaking down a problem into smaller sub-problems, identifying the key steps required to solve each sub-problem, and then putting the steps together in the correct order to form a complete solution.

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Answer:

Second one

20/50=v/100

Step by step explanation:

Cross multiplying;

(20×100)÷50 = v

v = 40

Answer:

417.6 in sq

Step-by-step explanation:

9 x 4 x 11.6 = 417.6

Answers:

(12, 7)

(20, 11)

(32, 17)

There are infinitely many possible answers.

=======================================================

Explanation:

The equation given to us is the same as y = 0.5x+1 because 1/2 = 0.5

If we replace x with even numbers, then we'll get whole number outputs for y.

Example: if x = 12, then y = 0.5x+1 = 0.5*12+1 = 7

This leads to (12,7) as one solution to this equation. A solution is a point that is on the line. Use graphing software like Desmos or GeoGebra to confirm.

Another example: if x = 20, then y  = 0.5x+1 = 0.5*20+1 = 11. Therefore, another solution point is (20, 11)

Final example: If x = 32, then y = 0.5x+1 = 0.5*32+1 = 17. This gives the point (32,17)

There are infinitely many possible answers since we can replace x with infinitely many real numbers.

The correct option is A, equilibrium price increases from $6 to $8.

In economics, equilibrium is a state in which the supply and demand for a product or service are balanced, resulting in a stable price. This can occur in a free market, where the price of a good or service is determined by the interaction of buyers and sellers.

Overall, equilibrium is a fundamental concept in many different fields, representing a state of balance or stability in a system or situation.

If the demand schedule changes from D2 to D1, then the demand curve shifts to the left. As a result, the new equilibrium point will be where the new demand curve (D1) intersects with the supply curve (S1).

From the table, we can see that the new equilibrium point is at a price of $8 and a quantity of 15. Therefore, the equilibrium price increases from $6 to $8, but the equilibrium quantity decreases from 15 to 13.

So the correct answer is: equilibrium price increases from $6 to $8.

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IQR =  16.5

The range = 31

Mean absolute deviation = 9.5

The median is the value that splits the mathematical numbers or expressions in the half. The median value is the middle number of data points. to find the median first arrange the data points in ascending order.

Given:

A data set:

15, 22, 16, 13, 14, 20, 40, 44.

The lower half of median Q1 = (14 + 15)/2 = 14.5

The upper half of median Q3 = (40 + 22)/2 = 31

So IQR = Q3 - Q1 = 31 - 14.5 = 16.5

The range = 44 - 13 = 31

Mean absolute deviation = 9.5

Therefore, MAD = 9.5.

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The solution is, The population would reach 111 million in next 7 years

An exponent refers to the number of times a number is multiplied by itself. For example, 2 to the 3rd (written like this: 23) means: 2 x 2 x 2 = 8. 23 is not the same as 2 x 3 = 6. Remember that a number raised to the power of 1 is itself.

here, we have,

given that,

The initial population of Mexico was 100 million

The growth rate of the population is 1.53 %per year

Then the future population of Mexico is given by

P = P_0(1+r)^t

Where P = future population after t years

P_0= initial population

t = time period in years

Substituting the given vales in above equation we get

(1+ 0.0153)^t = 1.11

Taking log on both sides we get

t* log (1.0153) = log(1.11)

solving we get,

t = 6.87

≈ 7 years

The population would reach 111 million in next 7 years.

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Melanie's account balance after t years is, A = 500 x [tex](1 + 0.00425)^{4t[/tex].

Compound interest is when you receive interest on both your interest income and your savings.

Given:

Initial deposit = $ 500

Interest rate = 1.7 % = 0.017/4 = annual compounded quarterly

Now, Account balance = Initial deposit x [tex](1 + r)^{4t[/tex]

                                   A = 500 x [tex](1 + 0.00425)^{4t[/tex]

Where:

A = Account balance

4t = Number of quarters (4 x Number of t years)

Suppose we want to calculate the account balance after 4.5 years, then we substitute this way:

A = 500 x [tex](1 + 0.00425)^{4(4.5)[/tex]

A = 500 x (1 + 0.00425)¹⁸

A = 539.66

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Answer:

$65.394

Step-by-step explanation:

The bill is $60.55, and you have to pay 8% tax.

8% = 0.08

60.55 times 0.08 = $4.844

So, the

8% tax = $4.844

What is the new total?

We take

60.55 + 4.844 = $65.394

So, the new total is $65.394

Answer:

$65.39

Step-by-step explanation:

multiply 60.55 by .08. then add 4.84 to 60.55

The inequality is solved using graphical method to give a solution of

The system of equation are y ≥ 1/3 x + 4 and y ≤ -5/3 x - 2

Using x values of -5, 0, 5

y ≥ 1/3 x + 4

x = -5, y ≥ 1/3 (-5) + 4, y ≥ 7/3

x = 0, y ≥ 1/3 (0) + 4, y ≥ 4

x = 5, y ≥ 1/3 (5) + 4, y ≥ 17/3

table of values

x    y

-5  7/3

0   4

5   17/3

y ≤ -5/3 x - 2

x = -5, y ≥ -5/3 (-5) - 2,  y ≤  19/3

x = 0, y ≥ -5/3 (0) - 2,  y ≤  -2

x = 5, y ≥ -5/3 (5) - 2,  y ≤  -31/3

table of values

x    y

-5  19/3

0   -2

5   -31/3

The graph is attached and the solution is (-3, 3)

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The percentage error made by the person is 25%.

To get the percentage error, multiply the relative error by 100%. In other words, first, calculate the difference between the true value and the measured value. Then, divide the obtained difference by the true value. Then take the absolute value of the obtained result and multiply it by 100%.

The measured value is 4 feet.

The true value is 3.2 feet.

So, the difference between the true value and the measured value is (4 feet - 3.2 feet), that is, 0.8 feet.

Now, divide the obtained difference by the true value.

(0.8 feet)/(3.2 feet) = 1/4

= 0.25

To get the percentage error, take the absolute value of the obtained result and multiply it by 100%.

|0.25|×100% = 0.25×100%

= 25%

Therefore, the obtained answer is 25%.

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To write 9 in Roman Numerals, you would use the symbols "IX".

The symbol "I" represents the number 1 and the symbol "X" represents the number 10. When a smaller symbol is placed before a larger symbol, it means that the smaller symbol is subtracted from the larger symbol.

In this case, "I" is placed before "X", so it is subtracted from 10, giving us the value of 9.

Here is a step-by-step explanation:

1. Identify the symbols for 1 and 10: "I" and "X"
2. Place the smaller symbol before the larger symbol: "IX"
3. Subtract the smaller symbol from the larger symbol: 10 - 1 = 9
4. The result is the value of the Roman Numeral: "IX" = 9

Therefore, the Roman Numeral for 9 is "IX".

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Answer:

yes

Step-by-step explanation:

if i did the math right marcy should have enough

A) An algebraic expression that could be used to model the situation where a horse's weight decreases by ¹/₂ pounds weekly is w/r, where w is the total weight lost and r is the constant rate of weight loss.

B) Using division operation and decreasing rate, if a horse's weight decreases by ¹/₂ pounds weekly, it will take the horse 11 weeks to lose a total of 5¹/₂ pounds.

An algebraic expression combines constants, variables, and mathematical operations (+, -, ×, ÷) without the equal sign (=) found in equations.

While equations show the equality of expressions, algebraic expressions merely state values.

Division operation is one of the four basic mathematical expressions, including addition, subtraction, and multiplication.

Division operations involve the dividend, the divisor, the equal sign (=), the division operand (÷), and the result called the quotient.

The total weight loss over time = 5¹/₂ pounds

The constant rate of weight loss = ¹/₂ pounds per week

The number of weeks for the horse to lose 5¹/₂ pounds = 11 weeks (5¹/₂ ÷ ¹/₂).

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Properties of determinants are Reflection Property, Reliable scales Property, Scalar Multiple Property, Switching Property and All-zero Property.

1. Reflection Property: The determinant remains unchanged when its columns turn into rows and vice versa. The reflection property is what is used to describe this.

2. If every element in a row (or column) is zero, the determinant is zero, according to the all-zero property.

3. Reliable scales (Repetition) Property: If every element in a row or column is proportional to or identical to every element in another row, the determinant is zero (or column).

4. When any two of the determinant's rows (or columns) are exchanged, the sign of the determinant changes.

5. Scalar Multiple Property: If all of a determinant's components in a row (or column) are multiplied by a non-zero constant, the determinant is multiplied by that constant.

6. Factor Property: If a determinant Δ becomes zero when we put x = α, then (x – α) is a factor of Δ.

Hence this is all about determinants problems.

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Answer:

= - 7x - 25.

Step-by-step explanation:

[tex] \frac{ - 1}{2} (14x \ + 50) \\ \\ = - 0.5(14x + 50) \\ \\ = - 7x + - 25 \\ = - 7x - 25[/tex]

Parameters are a set of values or characteristics that help to define or limit a system or process.

In computer programming, parameters are values or arguments that are passed to a function or method to specify how it should operate. Parameters can also be used in mathematical equations, scientific experiments, and other fields to specify conditions or constraints.

For example, in the equation y = mx + b, m and b are parameters that determine the slope and intercept of the line.

In a scientific experiment, parameters might include the temperature, pressure, or other conditions under which the experiment is conducted. In computer programming, parameters can be used to specify the input data, options, or other information that a function or method needs to operate correctly.

Overall, parameters are an important tool for defining and controlling systems, processes, and functions in a wide range of fields. By specifying parameters, we can ensure that a system operates in a predictable and consistent manner, and that we can accurately measure and compare results.

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The distance is decreasing at a rate of 1028.30 miles/hour.

An indicator of how one quantity changes in proportion to another is called a rate of change. If x and y are the independent and dependent variables, respectively, then rate of change is equal to y-to-x conversions. Positive or negative change rates are possible.

Plane X: The first plane is due west of you, or at x = -280

traveling towards you at 560 mph

Plane Y: The second plane is due south of you, or at y = -450

traveling towards you at 900 mph.

D = Distance between the two planes.

D = √( x² + y² )

d/dt [ D ] = d/dt [ √( x² + y² ) ]

dD/dt = 1 / 2√( x² + y² ) (2XX' + 2YY')

dD/ dt = 1/2 √(-280)² + (-450)² (2 (-280)(560) + 2(-450)(900)

dD/ dt = 1/2 √(-280)² + (-450)² (2 (-280)(560) + 2(-450)(900))

dD/ dt = 1/ 530 (-140,000 - 405, 000)

dD/ dt = -1028.30

Thus, The distance is decreasing at a rate of 500 miles/hour  

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Answer: smaller

Step-by-step explanation:

hope this helpsss

Answer:

The answer to this question depends on the values of the numbers involved. In general, when you multiply a number by a fraction, the product will be smaller than the largest factor if the fraction is less than 1. For example, if you multiply 5 by 1/2, the product is 2.5, which is smaller than 5. On the other hand, if you multiply a number by a fraction that is greater than 1, the product will be larger than the largest factor. For example, if you multiply 5 by 2/1, the product is 10, which is larger than 5.

In conclusion, the size of the product obtained from multiplying a number by a fraction depends on the values of the numbers involved and can be either smaller or larger than the largest factor.

Answer:

17^1 . ......................

The two rectangles are joined to get the shape. And the area of the shape is 258 square feet.

The amount region shows how much an area is on a planar or hemispherical cup. Surface region alludes to the region of an open surface or the boundary of a multi-object, while the region of a plane locale or plane field alludes to the region of a structure or planar material.

The shape is a mix of the two rectangular shapes. Then the region is likewise the amount of these two square shapes. Then we have

A = (18 - 8) x (21 - 12) + 21 x 8

A = 10 x 9 + 21 x 8

A = 90 + 168

A = 258 square feet

The two rectangles are joined to get the shape. And the area of the shape is 258 square feet.

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The required paper over a total of 6 mini muffins of cylindrical shape is (A) 103 5/7 in².

One of the most fundamental curvilinear geometric shapes, a cylinder has historically been a three-dimensional solid.

It is regarded as a prism with a circle as its base in basic geometry.

In several contemporary fields of geometry and topology, a cylinder can alternatively be characterized as an infinitely curved surface.

So, the cylinder formula:

= 2πrh+2πr²

Now, insert values as follows:

= 2πrh+2πr²

= 2π1*1.75+2π1²

= 17.27 inches

Paper to wrap 6 muffins:

= 17.27*6

= 103.62

Which is close to option (A)

Therefore, the required paper over a total of 6 mini muffins of cylindrical shape is (A) 103 5/7 in².

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Complete question:

A bakery makes cylindrical mini muffins that measure 2 inches in diameter and 1 and three-fourths inches in height. If each mini muffin is completely wrapped in paper, then at least how much paper is needed to wrap 6 mini muffins? Approximate using pi equals 22 over 7.

A. 103 and 5 over 7 in2

B. 84 and 6 over 7 in2

C. 66 and 1 over 7 in2

D. 17 and 2 over 7 in2

Answer:

(A) 103 5/7 in².

Step-by-step explanation:

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