17. Name the polyhedron that can be constructed using the given net. Assume squares and equilateral triangles were used to form each net. a. b.

The length of the top of the workbench is 13m and the width is 7m.

To find the length and the width, we can use the formula for the area of a rectangle, which is A = L x W, where A is the area, L is the length, and W is the width. We can plug in the given values and solve for the unknowns.

Let's start by assigning variables to the length and the width. Let's call the width x and the length x + 6 (since the length is 6m greater than the width).

Now we can plug these values into the formula:

A = L x W

91 = (x + 6) x x

91 = x2 + 6x

Now we can rearrange the equation to solve for x:

x2 + 6x - 91 = 0

We can use the quadratic formula to solve for x:

x = (-6 ± √(62 - 4(1)(-91))) / (2(1))

x = (-6 ± √(36 + 364)) / 2

x = (-6 ± √400) / 2

x = (-6 ± 20) / 2

The two possible solutions are:

x = (-6 + 20) / 2 = 7

x = (-6 - 20) / 2 = -13

Since the width cannot be negative, the only valid solution is x = 7. This means that the width is 7m and the length is x + 6 = 7 + 6 = 13m.

So the length of the top of the workbench is 13m and the width is 7m.

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Answer:

the quotient of 100 and the sum of B and 24

Step-by-step explanation:

The word expression is: "the quotient of 100 and the sum of B and 24"

The algebraic expression is: 100 / (B + 24)

To evaluate this expression for the values 1, 6, and 13.5, we substitute each value in turn for B and simplify:

When B = 1:

100 / (1 + 24) = 100 / 25 = 4

When B = 6:

100 / (6 + 24) = 100 / 30 = 3.33...

When B = 13.5:

100 / (13.5 + 24) = 100 / 37.5 = 2.666...

Therefore, the values of the expression for B = 1, 6, and 13.5 are approximately 4, 3.33, and 2.67, respectively.

Answer:

33%

Step-by-step explanation:

Take the original amount and subtract to new amount.

330 -231

99

Divide this by the original amount.

99/300

.33

Change to a percent.

33%

This is the percent decrease.

Answer:

Option d: Side OP is congruent to side RS.

To prove that ΔNOP ≅ ΔQRS by ASA, we need to show that:

1. ∠N ≅ ∠Q (given)

2. Side NP ≅ Side QS (given)

3. Side OP ≅ Side RS (additional information needed)

Hence, option d is the correct answer.

Answer:

1/9

Step-by-step explanation:

I plugged it into a calculator.

The exact values of the trigonometric functions are

To find the exact value of the trigonometric functions, we will use the reference angle and the quadrant in which the terminal side of each angle is located.

For cos 17π/6, the reference angle is π/6 and the terminal side is in the fourth quadrant. The point on the unit circle in this quadrant with a reference angle of π/6 is (√3/2, -1/2). Therefore, the exact value of cos 17π/6 is √3/2.

For sin 20π/3, the reference angle is π/3 and the terminal side is in the first quadrant. The point on the unit circle in this quadrant with a reference angle of π/3 is (1/2, √3/2). Therefore, the exact value of sin 20π/3 is √3/2.

For tan 15π/4, the reference angle is π/4 and the terminal side is in the third quadrant. The point on the unit circle in this quadrant with a reference angle of π/4 is (-√2/2, -√2/2). Therefore, the exact value of tan 15π/4 is 1.

In summary, the exact values of the trigonometric functions are:
cos 17π/6 = √3/2
sin 20π/3 = √3/2
tan 15π/4 = 1

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The linear functions of the scenario are y = 12x and y = 24/2x

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

(1, 12) and (2,24)

From the question, we understand that the function is a linear function

A linear function is represented as

y = mx + c

Using the above as a guide, we have the following equations

m + c = 12

2m + c = 24

Subtract the equations

m = 12

Substitute 12 for m in m + c = 12

12 + c = 12

Evaluate

c =0

So, the equation is y = 12x

An equivalent equation is y = 24x/2

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Yes, the fraction 4/9 will make each equation true.

Fraction is an element of a whole is a fraction. The number is represented mathematically as a quotient, where the numerator and denominator are split. Both are integers in a simple fraction. A fraction appears in the numerator or denominator of a complex fraction. The numerator of a proper fraction is less than the denominator.

To see why, we can simplify the fraction 4/9 as follows:

4/9 = (4 x 7)/(9 x 7) = 28/63

Now, we can substitute 4/9 with 28/63 in each equation to see that they are all true:

63 x 28/63 = 28

18 x 28/63 = 8

96 x 28/63 = 42

36 x 28/63 = 16

We can also write it as:

63 × (4/9) = 28

18 × (4/9) = 8

96 × (4/9) = 42

36 × (4/9) = 16

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a. The expected number of applications rejected is 3  

b. The probability that among the next 15 applications, none will be rejected is 0.042

c. The probability that among the next ten applications, seven will be rejected is 0.48

d. The probability that among the next ten applications, between 1 and 8 applications is 0.95

The binomial distribution formula is used to calculate the probability of getting a certain number of successes (x) in a fixed number of independent trials (n) with a known probability of success (p) for each trial. The formula is:

Here we have

30% of the applications received for a position in a graduate school are rejected.

a) The number of rejected applications among the next 10 applications follows a binomial distribution with parameters n = 10 and p = 0.3.

The expected number of rejected applications is:

E(X) = np = 10 * 0.3 = 3

Hence, the expected number of applications rejected is 3

b) The probability of being rejected is 0.3

The probability that none of the next 15 applications will be rejected is:

P(X = 0) = (1 - p)ⁿ = (1 - 0.3)¹⁵= 0.042

Therefore, the probability that none of the next 15 applications will be rejected is 0.042 or approximately 4.2%.

c) The probability that 7 of the next ten applications will be rejected is:

By using the binomial distribution formula

P(X = 7) = (10, 7) × 0.3⁷ × 0.7³ =  

=  6435 × 0.0002187 × 0.343 = 0.48

Therefore, the probability that 7 of the next 10 applications will be rejected is 0.48 or approximately 48%.

d) The probability that between 1 and 8 (inclusive) of the next ten applications will be rejected is:

P(1 ≤ X ≤ 8) = P(X ≤ 8) - P(X ≤ 0) = Σ P(X = i) for i = 1 to 8

We can use the complement rule and calculate the probability of having 0 or 9 rejected applications, and subtract that from 1:

=> P(1 ≤ X ≤ 8) = 1 - [P(X = 0) + P(X = 9) + P(X = 10)]

= 1 - [(1 - p)ⁿ + (n, 1) × p¹ × (1 - p)⁽ⁿ⁻¹⁾ + (n, 0) × p⁰ × (1 - p)ⁿ]

= 1 - [(0.7)¹⁰ + ((10,1) × 0.3 × 0.7⁹) + (10, 0) (0.3)¹⁰]

= 1 - [ 0.02824 + 0.01210 + 0.000006]

= 1 - [ 0.040346]

= 0.95

Hence, The probability that between 1 and 8 (inclusive) of the next ten applications will be rejected is 0.95 or approximately 95%  

Therefore,

a. The expected number of applications rejected is 3  

b. The probability that among the next 15 applications, none will be rejected is 0.042

c. The probability that among the next ten applications, seven will be rejected is 0.48

d. The probability that among the next ten applications, between 1 and 8 applications is 0.95

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The solution to the given proportion is 7 / 8. The solution has been obtained by using the cross multiplication method.

The cross multiplication approach involves multiplying the denominator of the first phrase by the numerator of the second fraction, and vice versa.

We are given a proportion as

2 / (3b - 3) = 4 / (1 - 2b)

Now, by using cross multiplication method, we get

⇒2 (1 - 2b) = 4 (3b - 3)

⇒2 - 4b = 12b - 12

⇒-16b = -14

⇒16b = 14

⇒b = 14 / 16

⇒b = 7 / 8

Hence, the solution to the given proportion is 7 / 8.

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This means that there exists an element a of the ideal I, such that all other elements in the ideal can be written as a multiple of a. In other words, the ideal I can be written as I = (a) = {ar : r ∈ I}, where r is any element of the ideal I.

A principle ideal is an ideal that is generated by a single element. This means that there exists an element a of the ideal I, such that all other elements in the ideal can be written as a multiple of a. In other words, the ideal I can be written as I = (a) = {ar : r ∈ I}, where r is any element of the ideal I. This is an important concept in the study of rings and algebraic structures, as it allows us to understand how ideals are generated and how they relate to other ideals in the same ring.

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The value of (x-y)² is m^2-4n.

To find the value of (x-y)², we can use the formula for the difference of squares:
(x-y)² = (x+y)² - 4xy

We are given that x+y = m and xy = n, so we can substitute these values into the formula:
(x-y)² = m² - 4n

Therefore, the value of (x-y)² is m²-4n.

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Answer:

fraction 3/9

percentage is 90%

Answer:

80%

Step-by-step explanation:

96.3 - 53.5 = 42.8

42.8 / 53.5 = 0.8

0.8 × 100 = 80%

f(a) is concave down on the interval -∞ to -4 and on the interval 0 to ∞, f(x) is concave up on the interval -4 to 0, inflection point for this function is at x = -2 and x = 2, the minimum for this function occurs at x = -4, the maximum for this function occurs at x = 0.

In mathematics, an expression is a combination of numbers, symbols, and operators (such as +, -, *, /, ^) that represents a value or a quantity. Expressions can contain variables, which are symbols that can take on different values. An expression can also be a combination of other expressions. Expressions are used to represent mathematical relationships, make calculations, and solve problems.

To answer these questions, we need to find the first and second derivatives of the function:

f(x) = x√(x²+16)

f'(x) = √(x²+16) + x(x²+16)[tex]^{(-1/2)}[/tex](2x)

f''(x) = (2x)/(x²+16)[tex]^{(3/2)}[/tex]+ (x²+16)[tex]^{(-1/2)}[/tex] + 2(x²+16)[tex]^{(-1/2)}[/tex]

A. f(a) is concave down on the interval -∞ to -4 and on the interval 0 to ∞.

To determine where the function is concave down, we need to find where the second derivative is negative. The second derivative is negative on the intervals (-∞, -4) and (0, ∞), so the function is concave down on those intervals.

B. f(x) is concave up on the interval -4 to 0.

To determine where the function is concave up, we need to find where the second derivative is positive. The second derivative is positive on the interval (-4, 0), so the function is concave up on that interval.

C. The inflection point for this function is at x = -2 and x = 2.

The inflection points occur where the concavity of the function changes. We found that the function is concave down on (-∞, -4) and (0, ∞), and concave up on (-4, 0). Therefore, the inflection points occur at x = -2 and x = 2.

D. The minimum for this function occurs at x = -4.

To find the minimum, we can either use the first derivative test or the second derivative test. Using the first derivative test, we look for where the first derivative changes sign from negative to positive, which indicates a local minimum. Using the second derivative test, we look for where the second derivative is positive, which indicates a local minimum. Either way, we find that the minimum occurs at x = -4.

E. The maximum for this function occurs at x = 0.

To find the maximum, we can either use the first derivative test or the second derivative test. Using the first derivative test, we look for where the first derivative changes sign from positive to negative, which indicates a local maximum. Using the second derivative test, we look for where the second derivative is negative, which indicates a local maximum. Either way, we find that the maximum occurs at x = 0.

Therefore, f(a) is concave down on the interval -∞ to -4 and on the interval 0 to ∞, f(x) is concave up on the interval -4 to 0, inflection point for this function is at x = -2 and x = 2, the minimum for this function occurs at x = -4, the maximum for this function occurs at x = 0.

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In the parallel line measure of angle [tex]m\angle 7[/tex] is 32°.

In a plane, two lines are said to be parallel if they never cross at any point. A pair of lines that never cross paths and do not have a common junction point are said to be parallel. Parallel lines are represented by the symbol "||".

Here we know that If two lines which are parallel are intersected by a transversal then the pair of corresponding angles are equal.

Then,

=> [tex]m\angle3= m\angle10[/tex]

Here the given [tex]m\angle3=58\textdegree[/tex] the [tex]m\angle10=58\textdegree[/tex].

Now we know that sum of all angles in straight line is 180°.Then,

=> [tex]m\angle6+m\angle7+m\angle10=180\textdegree[/tex]

=> [tex]90\textdegree+m\angle7+58\textdegree=180\textdegree[/tex]

=> [tex]m\angle7=180\textdegree-90\textdegree-58\textdegree=32\textdegree[/tex]

Hence the measure of [tex]m\angle 7[/tex] is 32°.

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Answer:

A: 24, B: 12, C: 28, D: 24. Hope this helps

Step-by-step explanation:

Part A:

168/3 = 56

Therefore, Chad is driving the car in 56 mph.

672/56 = 12

Therefore, Chad drives 672 miles in 12 hours.

308/11 = 28

Therefore, Chad drives 28 miles per gallon of gas.

672/28 = 24

Therefore, Chad uses 24 gallons of gas to drive 672 miles.

Part B:

12 hours, you can use proportions, miles/hours.

[tex]\frac{56}{1}[/tex]= [tex]\frac{672}{x}[/tex]

x = 12

Part C:

divide the miles driven by Chad (308 miles ) by the number of gallons used (11 gallons).

308 miles / 11 gallons =28 miles per gallon

Chad's car gets 28 miles per gallon.

Part D:

[tex]\frac{28}{1} = \frac{672}{x} \\[/tex]

28x = 672

x = 672/28 = 24

24 gallons

Answer: A=56 B=12 C=28 and D=24

Step-by-step explanation:

A. Chad drove 168 miles in 3 hours

    In 1 hour he drove          168÷3

                                          = 56 Miles

B. We know,

    Covering 56 miles takes 1 hour

    So, It will take to cover 672 miles
                                           = 672÷56

                                           = 12 Hours

C. We know,

    Chad drove 308 miles with 11 gallons of gas

    So, miles per gallon chads car gave him 308÷11

                                                                       = 28 Miles Per Gallon.

D. We know,

   Chad car gives him 28 miles per gallon

   So, To cover 672 miles

   Chad needs                                            = 672÷28

                                                                    = 24 Gallons.

NOTE: Its simple math kiddo, do better in school

The equation is true for n = k+1, so the statement is true for all n>=1 by mathematical induction.

Proof by mathematical induction:

Base case: n = 1
1^(3) = ((1(1+1))/(2))^(2)
1 = ((2)/(2))^(2)
1 = 1^(2)
1 = 1
The base case is true.

Inductive step:
Assume that the statement is true for n = k, that is:
1^(3)+2^(3)+3^(3)+...+k^(3) = ((k(k+1))/(2))^(2)

Now we need to prove that the statement is also true for n = k+1:
1^(3)+2^(3)+3^(3)+...+k^(3)+(k+1)^(3) = (((k+1)((k+1)+1))/(2))^(2)

Substituting the assumption into the left-hand side of the equation:
((k(k+1))/(2))^(2) + (k+1)^(3) = (((k+1)((k+1)+1))/(2))^(2)

Expanding the right-hand side of the equation:
((k(k+1))/(2))^(2) + (k+1)^(3) = (((k+1)(k+2))/(2))^(2)

Simplifying the equation:
(k^(2)(k+1)^(2))/(2^(2)) + (k+1)^(3) = ((k+1)^(2)(k+2)^(2))/(2^(2))

Multiplying both sides of the equation by 2^(2):
(k^(2)(k+1)^(2)) + 2^(2)(k+1)^(3) = (k+1)^(2)(k+2)^(2)

Expanding the equation:
k^(2)(k+1)^(2) + 2^(2)(k+1)^(3) = (k+1)^(2)(k^(2)+4k+4)

Simplifying the equation:
k^(2)(k+1)^(2) + 2^(2)(k+1)^(3) = k^(2)(k+1)^(2) + 4k(k+1)^(2) + 4(k+1)^(2)

Subtracting k^(2)(k+1)^(2) from both sides of the equation:
2^(2)(k+1)^(3) = 4k(k+1)^(2) + 4(k+1)^(2)

Factoring out (k+1)^(2) from the right-hand side of the equation:
2^(2)(k+1)^(3) = (k+1)^(2)(4k+4)

Simplifying the equation:
2^(2)(k+1)^(3) = 4(k+1)^(2)(k+1)

Dividing both sides of the equation by (k+1)^(2):
2^(2)(k+1) = 4(k+1)

Simplifying the equation:
2^(2)(k+1) = 2^(2)(k+1)

The equation is true for n = k+1, so the statement is true for all n>=1 by mathematical induction.

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The answer of -x+3y=20; 7y=x will be x = -[tex]\frac{7}{2\\}[/tex] and y = - [tex]\frac{1}{2}[/tex].

Given,

-x+3y=20 .... (1)

7y=x .... (2)

By using the method of substitution.

We will use equation (2) as

7y=x

=>y= [tex]\frac{x}{7}[/tex] ....(3)

Putting equation (3) in (1)

We have, -x+3([tex]\frac{x}{7}[/tex])=20

Taking L.CM.

[tex]\frac{-7x+3x}{7}[/tex] = 20

-7x +3x = 140

-4x = 140

0r, x = - [tex]\frac{140}{4}[/tex]

x = - [tex]\frac{7}{2}[/tex]

Now by putting value of x in equation (2),  we get

7y = x

7y = -[tex]\frac{7}{2}[/tex]

0r, y = -[tex]\frac{1}{2}[/tex]

Thus, x = -[tex]\frac{7}{2\\}[/tex] and y = - [tex]\frac{1}{2}[/tex]

The three equations that have the same value of x as the original equation are:

18x - 15 = 72

3(6x - 3) = 72

x = 4.5

What is an equation?

An equation is a statement that two expressions are equal. It typically contains one or more variables (represented by letters) and mathematical operations such as addition, subtraction, multiplication, and division. Equations can be used to represent relationships between quantities or to solve for unknown values.

The correct options are:

18x - 15 = 72

18x - 9 = 72

x = 4.5

To see why, we can start by simplifying the original equation:

Three-fifths (30x - 15) = 72

(3/5)(30x - 15) = 72

18x - 9 = 72

18x - 15 = 72 + 15

18x = 87

x = 87/18

So we see that x = 87/18 is the solution to the original equation.

Now let's check each of the answer choices:

18x - 15 = 72

Solving for x, we get x = 87/18, which is the same as the solution to the original equation. This equation is equivalent to the original equation.

50x - 25 = 72

Solving for x, we get x = 97/50, which is not the same as the solution to the original equation. This equation is not equivalent to the original equation.

18x - 9 = 72

Solving for x, we get x = 81/18 = 9/2, which is not the same as the solution to the original equation. This equation is not equivalent to the original equation.

3(6x - 3) = 72

Simplifying, we get 18x - 9 = 72, which is equivalent to the second equation listed above. So this equation is also equivalent to the original equation.

x = 4.5

This is the same solution as the original equation, so this equation is also equivalent to the original equation.

Therefore, the three equations that have the same value of x as the original equation are:

18x - 15 = 72

3(6x - 3) = 72

x = 4.5

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Both products finish at the same time, which is D) 42 hours later.

The factory produces Product A every 6 hours and Product B every 21 hours.

If they started at the same time, they will finish at the same time after the lowest common multiple of the two intervals, which is 42 hours.

Therefore, the answer is D. 42 hours.

LCM is the short form for “Least Common Multiple.” The least common multiple is defined as the smallest multiple that two or more numbers have in common.

For example: Take two integers, 2 and 3.

Multiples of 2: 2, 4, 6, 8, 10, 12, 14, 16, 18, 20….

Multiples of 3: 3, 6, 9, 12, 15, 18, 21, 24, 27, 30 ….

6, 12, and 18 are common multiples of 2 and 3. The number 6 is the smallest. Therefore, 6 is the least common multiple of 2 and 3.

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Answer:

he walks 300 meters

Step-by-step explanation:

nbsjdjsj d f f f f f f f. f f f f f f f f f f

Answer:

The two points given are (-2, -8) and (8, -8), which lie on a horizontal line. Since the line is horizontal, the slope is zero.

To see this, we can use the formula for the slope of a line between two points:

slope = (y2 - y1)/(x2 - x1)

Substituting the coordinates of the two given points, we get:

slope = (-8 - (-8))/(8 - (-2)) = 0

Therefore, the slope of the line through the points (-2, -8) and (8, -8) is 0.

Step-by-step explanation:

Answer:  d = √(Δy2 + Δx2) = √(02 + 102) = √100 = 10

Step-by-step explanation:

The standard form of the equation of a quadratic function with roots of 4 and −1 that passes through (1, −9) is [tex]y = 1.5x^{2} - 4.5x - 6[/tex]

What is the quadratic function?

A quadratic function is a type of function that can be written in the form:

[tex]f(x) = ax^2 + bx + c[/tex]

where a, b, and c are constants, and x is the variable. This function is a second-degree polynomial function, which means that the highest power of the variable x is 2.

Quadratic functions can be graphed as a U-shaped curve called a parabola. The sign of the coefficient a determines whether the parabola opens up or down. If a > 0, the parabola opens up, and if a < 0, the parabola opens down. The vertex of the parabola is the minimum or maximum point of the function, depending on whether the parabola opens up or down.

Quadratic functions are used in many areas of mathematics, science, and engineering to model various phenomena such as projectile motion, population growth, and optimization problems.

To write the standard form of the equation of a quadratic function, we need to use the roots of the function and another point on the curve. The standard form of the quadratic function is:

y = a(x - r1)(x - r2)

where r1 and r2 are the roots of the quadratic function, and a is a constant.

Given that the roots of the quadratic function are 4 and -1, we can write:

y = a(x - 4)(x + 1)

To find the value of a, we can use the point (1, -9) that the function passes through:

-9 = a(1 - 4)(1 + 1)

-9 = -6a

a = 3/2

Substituting this value of a in the equation, we get:

[tex]y = 1.5(x - 4)(x + 1)[/tex]

Expanding this equation, we get:

[tex]y = 1.5x^{2} - 4.5x - 6[/tex]

Therefore, the standard form of the equation of the quadratic function with roots of 4 and −1 that passes through (1, −9) is [tex]y = 1.5x^{2} - 4.5x - 6[/tex]

So, the correct answer is: [tex]y = 1.5x^{2} - 4.5x - 6[/tex]

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Answer: ur mom anyways jk

Step-by-step explanation:

6hrs and 7mins pls dont trust me on this answer and if u get it wrong im  sorry

The zeros of P(x)=x^(4)+2x^(3)-7x-14 are 1, -2, and 2.

To find the rational zeros, we need to use the rational zero theorem. This theorem states that any rational zeros of a polynomial must be a factor of the constant term (in this case, -14) divided by a factor of the leading coefficient (in this case, 1).

So, the possible rational zeros of this polynomial are ±1, ±2, ±7, and ±14.

To confirm if these are indeed the zeros of the polynomial, we can plug each of these numbers into the polynomial and determine if the result is 0.

For example, when x=7, P(7) = 7^(4)+2(7^(3))-7(7)-14 = 2401+882-49-14 = 1720. Since the result is not 0, 7 is not a zero of the polynomial.

So when x=2,

P(2) = 2^(4)+2(2^(3))-7(2)-14

       = 16+16-14-14 = 0.

Therefore, 2 is a zero of the polynomial.

By repeating this process for all possible rational zeros, we can determine that the zeros of this polynomial are 1, -2, and 2.

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When a=6, the value of b is equals to -43.

What is Algebraic expression ?

Algebraic expression can be defined as combination of variables and constants.

An algebraic expression is a combination of variables, constants, and mathematical operations such as addition, subtraction, multiplication, and division, which can be simplified and evaluated.

In other words, an algebraic expression is a collection of terms and coefficients that are connected by mathematical operators.

Substitute the value of a=6 into the expression for b:

b = -1 - 7a

b = -1 - 7(6)

b = -1 - 42

b = -43

Therefore, when a=6, the value of b is -43.

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We fοund the inequality tο be  14 -0.6x ≤ 1.5 and sοlving this we fοund that the warning lights cοme οn after using fοr apprοximately 21 days.

In mathematics, inequalities specify the cοnnectiοn between twο nοn-equal numbers. Equal dοes nοt imply inequality. Typically, we use the "nοt equal sign" tο indicate that twο values are nοt equal. Hοwever several inequalities are utilised tο cοmpare the numbers, whether it is less than οr higher than. An inequality symbοl has nοn-equal expressiοns οn bοth sides. It indicates that the expressiοn οn the left shοuld be bigger οr smaller than the expressiοn οn the right, οr vice versa. Literal inequalities are relatiοnships between twο algebraic expressiοns that are expressed using inequality symbοls.

Given,

 The gallοns οf fuel that the car hοlds = 14 gallοns

Amοunt οf fuel used each day = 0.6 gallοns

When the remaining fuel is 1.5 gallοns οr less, warning lights cοme οn.

We can write an inequality fοr this situatiοn.

If x is the number οf days the car is used, then the warning lights cοme οn when,

 14 - 0.6x ≤ 1.5

This is the inequality expressiοn.

Sοlving,

12.5 ≤ 0.6x

x ≥ 12.5/0.6

x ≥ 20.8

Therefοre we fοund the inequality tο be 14 -0.6x ≤ 1.5 and sοlving this we fοund that the warning lights cοme οn after using fοr apprοximately 21 days.

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A solution to the given system of linear equations is (2, 6).

In order to to graph the solution to the given system of equations on a coordinate plane, we would use an online graphing calculator to plot the given system of equations and then take note of the point of intersection;

y = 4x - 2      ......equation 1.

y = 1/2(x) + 5  ......equation 2.

Next, we would use an online graphing calculator to plot the given system of equations as shown in the graph attached below.

Based on the graph (see attachment), we can logically deduce that the solution to the given system of equations is the point of intersection of the lines on the graph representing each of them, which lies in Quadrant I and it is given by the ordered pair (2, 6).

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