Question 6
For each equation, determine whether x and y are directly proportional (that is, if the equation shows direct variation).
If so, then find the constant of proportionality (the constant of variation).

(a) =yx
Proportional
Constant of proportionality: =k
Not proportional
(b) =y−52x
Proportional
Constant of proportionality: =k
Not proportional



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they are all absolute value, so the negatives are removed

thus the values are 10, 3, 6, 9 (biggest would be 10)

Answer:

the volume of the prism at the right is 56.7 cm³

Step-by-step explanation:

To find the volume of the prism at the right, we need to first find the area of the base, which is a triangle. The area of a triangle is given by A=21​bh

where A

is the area, b

is the base, and h

is the height of the triangle.

The base of the triangle is 4.2 cm and the height of the triangle is 3 cm. So, we can plug these values into the formula and get:

A=21​(4.2)(3)

A=6.3 cm2

Now that we have the area of the base, we can multiply it by the height of the prism, which is 9 cm. This will give us the volume of the prism:

V=B×h

V=6.3×9

V=56.7 cm3

The expression (-3)0 has a value of 0 when evaluated because a number multiplied by 0 gives 0

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

(-3)0

The above statement is a product expression that multiplies the values of -3 and 0

Also, there is no need to check if there are like terms in the expression or not

This is  because we are multiplying the factors

So, we have

(-3)0 = 0

This means that the value of the expression is 0 i.e a number multiplied by 0 gives 0

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Answer:

(a) Christine will have to pay $400 in total interest.

(b) Christine will have to repay a total of $4400, including interest.

Step-by-step explanation:

(a) The interest charged on the loan is calculated as simple interest, which means that it is calculated as a percentage of the principal amount for each year. The interest rate is 5%, and the principal amount is $4000.

The total interest charged on the loan is:

Interest = Principal x Rate x Time

Interest = $4000 x 0.05 x 2

Interest = $400

Therefore, Christine will have to pay $400 in total interest.

(b) The total repayment amount is the sum of the principal and the interest charged on the loan.

Total repayment amount = Principal + Interest

Total repayment amount = $4000 + $400

Total repayment amount = $4400

Therefore, Christine will have to repay a total of $4400, including interest.

The graph represents the quadratic equation y = 2 · x² - 12 · x + 9. The values of the coefficients are b = - 12 and c = 9.

In this problem we find the graph of a quadratic equation and the expression in standard form with two missing coefficients, whose values can be found by considering two points of the graph. If we know that (x₁, y₁) = (3, - 9) and (x₂, y₂) = (5, - 1), then the coefficients are, respectively:

2 · 3² + b · 3 + c = - 9

2 · 5² + b · 5 + c = - 1

3 · b + c = - 27

5 · b + c = - 51

The solution to the system of linear equations is (b, c) = (- 12, 9).

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Answer: D. y=1/2x+1

Step-by-step explanation:

For every 2 x values on the table, y increases only by 1. To find the slope of the table you can also use the slope formula with two points. y2-y1/x2-x1=m

For example,

(4, 3) & (6, 4)

The first point has the ordered pair of x1 and y1. The second point is the ordered pair of x2 and y2. Plug the numbers into the equation and you'll find the slope.

So, 4-3 / 6-4 = 1/2.

Now that we have the slope we can use the point-slope formula to find the y-intercept. y-y1=m(x-x1)

This formula only requires 1 point from the table and the slope so you can use any point, I'll use (4,3). After that, you plug in your numbers into the equation and solve for y.

y-3=1/2(x-4)

y-3=1/2x-2

Add 3 to both sides

y=1/2x+1

And you're done :)

The value of x in the similar triangle is 2 units.

Two triangles are said to be similar if their corresponding angles are congruent and the corresponding sides are in proportion .

Therefore, let's use the ratio to find the side length of x in the triangle.

Hence, the right angle triangle FHJ is similar to the right angle triangle GFJ. Using the similarity ratios,

GH / GF = GF / GJ

Hence,

GH = 9

GF = 3√11

GJ =  x + 9

9 / 3√11 = 3√11 / x + 9

cross multiply

9(x + 9) = (3√11)(3√11)

9x + 81 = 9(11)

9x + 81 = 99

9x = 99 - 81

9x = 18

divide both sides by 9

x = 18 / 9

x = 2

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The walkway is 11 feet 6 inches long.

To find the length of the walkway, we need to add the lengths of the two boards.

The first board is 6 feet 11 inches long, which can be written as 6 + 11/12 feet using the fact that there are 12 inches in a foot.

The second board is 5 feet 7 inches long, which can be written as 5 + 7/12 feet.

Now we can add the lengths of the two boards:

6 + 11/12 feet + 5 + 7/12 feet

= 11 + 6/12 feet

=11 + 1/2 feet

Therefore, the walkway is 11 feet 6 inches long.

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The LSA of prism is  157  square feet.

The TSA of prism is  169.738  square feet

We have,

Height = 10 feet

Area of base = 20 square feet

So, area of pentagonal base = 1/4 √5 (5 + 2√5) a²

20 = 1/4 √5 (5 + 2√5) a²

a = 3.14

Now, LSA of prism

= 5bh

= 5(3.14)(10)

= 157  square feet

and, TSA of prism

= 5 x 2(20)/ 15.7  + 157

= 169.738 square feet

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[tex]\begin{array}{llll} \textit{Logarithm of exponentials} \\\\ \log_a\left( x^b \right)\implies b\cdot \log_a(x) \end{array} ~\hspace{7em} \begin{array}{llll} \textit{Logarithm of rationals} \\\\ \log_a\left( \frac{x}{y}\right)\implies \log_a(x)-\log_a(y) \end{array} \\\\[-0.35em] ~\dotfill\\\\ 2\log(6)-\log(9)\implies \log(6^2)-\log(9)\implies \log\left( \cfrac{6^2}{9} \right)\implies \log(4)[/tex]

Inductive reasoning is the process of making generalizations based on specific observations or examples. Deductive reasoning, on the other hand, is the process of reasoning from general principles to specific examples.

To determine whether the type of reasoning used is inductive or deductive reasoning, we need to look at the nature of the argument being made. If the argument is moving from specific examples to a general conclusion, it is using inductive reasoning. If the argument is moving from general principles to specific examples, it is using deductive reasoning.

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The part of a financial aid letter that shows what you will have to pay after deducting all gift aid is the D. net cost.

The net cost can be described as the amount that is usually meant for paying out of pocket or through loans after all gift aid.

The net cost can be calculated usually by subtracting all gift aid from the total cost of attendance.

The net cost is an important figure to consider when you want evaluate your financial aid package and also decide how to pay for college.

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Originality is the quality of being unique, new, and innovative. It requires creativity, imagination, inspiration, and nonobviousness. Special or interesting aspects may be present, but they are not sufficient to define originality.

Originality refers to the quality of being unique, new, and innovative. It involves creating something that has not been seen or experienced before. The best description of originality is that it is having a low probability and being unique.

An original idea, product, or work of art is something that has not been copied or imitated from others. It represents a new perspective or approach that can offer a fresh insight into a problem or challenge. Originality requires a high level of creativity, imagination, and inspiration, as well as a willingness to take risks and explore new possibilities.

Nonobviousness is also an important factor in originality. It means that the idea or invention is not something that would be obvious to someone skilled in the same field or industry. In other words, an original idea should not be something that could be easily predicted or anticipated.

Special or interesting are also characteristics of originality, but they are not sufficient to define it. An idea or product can be special or interesting without being truly original. For example, a new flavor of ice cream may be interesting, but it may not be original if it has already been created by someone else.

Convergent thinking, on the other hand, involves finding a single solution to a problem. It is the opposite of divergent thinking, which involves generating multiple ideas and possibilities. Convergent thinking is important for finding effective solutions to problems, but it is not the same as originality.

In conclusion, originality is the quality of being unique, new, and innovative. It requires creativity, imagination, inspiration, and nonobviousness. Special or interesting aspects may be present, but they are not sufficient to define originality.

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The result of carrying out the addition operation on the given fractions, 9/-8 + -2/5, is -61/40.

From the question, we are to determine the sum of the given fractions

From the given information,

The fraction are 9/-8 and -2/5

We are to carry out the addition operation on the fractions

The addition operation can be carried out on the fractions as follows:

9/-8 + -2/5

First, find the LCM of 8 and 5

The LCM of 8 and 5 is 40

Then,

We can write that

(-45 + -16)/40

= (-45 - 16)/40

= (-61)/40

= -61/40

Hence, the result of adding the fractions is -61/40

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The volume of the prism is 14.67 units³

A prism is a solid shape that is bound on all its sides by plane faces.

The general formula for the volume of a prism is ;

V = base area × height

here the base area has already been calculated and the value is 7 1/3 unit²

The height of the prism is 2 units

Therefore ;

The volume of the prism = 7 1/3 × 2

= 22/3 × 2

= 44/3

= 14.67 units³

therefore the volume of the cuboid is 14.67 units³

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Answer:

-3/7

Step-by-step explanation:

-7/3 × ? = 1

-7/3 × -3/7 = 1

you see how both the three's and Steven's canceled out resulting in one as the answer. also it has to be a negative 3/7 since two negative signs in multiplication result in a positive sign.

The exact values of x for x² - 8x - 5 = 0 are x = 4 + √21 or x = 4 - √21

To solve for x in the equation x² - 8x - 5 = 0, we can use the quadratic formula, which is:

x = (-b ± √(b² - 4ac)) / 2a

where a, b, and c are the coefficients of the quadratic equation ax² + bx + c = 0.

Using this formula, we can identify the values of a, b, and c in the equation x² - 8x - 5 = 0.

Here, a = 1, b = -8, and c = -5.

Substituting these values into the formula, we get:

x = (-(-8) ± √((-8)² - 4(1)(-5))) / 2(1)

Simplifying this expression, we get:

x = (8 ± √(64 + 20)) / 2

x = (8 ± √84) / 2

Now, we can simplify the square root of 84 as 2√21:

x = (8 ± 2√21) / 2

We can further simplify this expression by factoring out 2 from the numerator:

x = 2(4 ± √21) / 2

Canceling out the 2s, we get:

x = 4 ± √21

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17.5, if both were the same difficulty homework for "Monie".

Answer:

Since the figures are similar, their corresponding side lengths are proportional.

Let x be the scale factor between the larger and smaller figures. Then, the volume of the larger figure is x^3 times the volume of the smaller figure.

We can set up an equation to solve for x:

2500 = x^3 * 160

Divide both sides by 160:

x^3 = 2500/160

x^3 = 15.625

Take the cube root of both sides:

x = 2.5

So, the scale factor between the larger and smaller figures is 2.5.

Since surface area is proportional to the square of the scale factor, we can set up another equation to solve for the surface area of the smaller figure:

S.A. of smaller figure / S.A. of larger figure = (scale factor of smaller figure)^2 / (scale factor of larger figure)^2

Solving for the surface area of the smaller figure:

S.A. of smaller figure / 1400 = 2.5^2 / 1^2

S.A. of smaller figure / 1400 = 6.25

S.A. of smaller figure = 6.25 * 1400

S.A. of smaller figure = 8750

Therefore, the surface area of the smaller figure is 8750 meters squared.

Step-by-step explanation:

If v = 4i and w = 2i + 5i, the angle between the vectors v and w is approximately 47.32 degrees.

To find the angle between two vectors, we can use the dot product formula, which relates the cosine of the angle between the vectors to their dot product and magnitudes. The dot product of two vectors v and w is given by:

v · w = |v| |w| cos(θ)

where |v| and |w| are the magnitudes of the vectors, and theta is the angle between them.

In this case, we are given the vectors v = 4i and w = 2i + 5j. We can compute their dot product as:

v · w = (4i) · (2i + 5j) = 8 + 0 = 8

We can also compute the magnitudes of the vectors as:

|v| = √((4² + 0²)) = 4

|w| = √((2² + 5²)) = √(29)

Substituting these values into the dot product formula, we get:

8 = 4 √(29) cos(θ)

Solving for cos(θ), we get:

cos(θ) = 2 / √(29)

Taking the inverse cosine of both sides, we get:

θ = cos⁻¹(2 / √(29)) = 47.32 degrees

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The expression -2/5 . 12 is equivalent to the expression (a) 2 . (-12/5)

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

-2/5 . 12

The above statement is a product expression that multiplies the values of -2/5 and 12

So, we have

-2/5 . 12 = -24/5

This is  because we are multiplying the factors

Next, we ave

(a) 2 . (-12/5) = -24/5

(a) -2/12 . (1/5) = -2/60

This means that the value of the expression is equivalent to (a) 2 . (-12/5)

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The monthly income of the first person is $600.

Given that, the average monthly income of three persons is RS 3,600.

The income of the first is 1/5 of the combined income of the other two.

Here, Let income of the first be A, let income of the second be B and let Income of the third be C.

A+B+C=3600 -----(i)

Income for the first person = 1/5(B+C) -----(ii)

Substitute equation (ii) in equation (i), we get

(B+C)/5 +B+C =3600

B+C+5B+5C=3600×5

6B+6C=18000

6(B+C)=18000

B+C=3000 ------(iii)

Substitute (iii) in equation (i), we get

A=$600

Therefore, the monthly income of the first person is $600.

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The test Statistic and the critical value is 20.692 and 15.308 respectively.

Given that,

Null and Alternative hypothesis,

Null hypothesis: H₀ = 5.7

and Alternative hypothesis: H₁ < 5.7

∴

Test Statistic =

x² = (n-1)s²/σ², where s is the standard deviation = 4.9 and n sample size = 29,

= 28 × 4.9² / 5.7²

= 20.692

The critical value of the left tailed test at significance level 0.025 and df = 28,

x²(critical) = x²(1-α), (n-1) = x²(0.975, 28)

= 15.308

Hence, the test Statistic and the critical value is 20.692 and 15.308 respectively.

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The pattern is empty the second pail, leaving the first and third pail full and the fourth and sixth pails empty.

Given that, there are 6 pails in a row. The first 3 pails are filled with water.

The easiest way to solve this problem is to empty the second pail, leaving the first and third pail full and the fourth and sixth pails empty. This will create the desired pattern of full, empty, full, empty, full, empty.

Therefore, empty the second pail, leaving the first and third pail full and the fourth and sixth pails empty.

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The requreid match of each conic section has been shown below.

For a general quadratic polynomial of the form Az² +By+Cz+Dy+E=0

Ellipse: A and B have different signs.

Parabola: A = 0 or B = 0, but not both.

Circle: A and B have the same value, and this value is not zero.

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The number is given as follows:

x = -3.

The variable representing the number is given as follows:

x.

The product of 3 and the number is given as follows:

3x.

Twenty less than the product of 3 and the number is:

3x - 20.

The entire expression is equivalent to -29, hence the value of x, representing the number, is obtained as follows:

3x - 20 = -29

3x = -9

x = -3.

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Answer: 49.2 feet

Step-by-step explanation:

The given equation h = -16t^2 + 56t represents the height of a football kicked by Lauren as a function of time t in seconds.

In the context of the problem, the vertex of the parabolic function (-16t^2 + 56t) represents the point at which the football reaches its maximum height. The vertex of a parabola is the point where the function reaches its highest or lowest value, and it is given by the coordinates (h, t) in this case.

Interpreting the coordinates of the vertex in context, the h-coordinate represents the maximum height of the football, while the t-coordinate represents the time at which the football reaches that maximum height. So, if we determine the vertex of the given function, we can interpret the maximum height and the time it occurs.

The formula for the x-coordinate (t) of the vertex of a quadratic function in the form y = ax^2 + bx + c is given by t = -b/2a. Comparing this with the given equation, we can identify that a = -16 and b = 56.

Plugging in the values of a and b into the formula, we get:

t = -56 / (2 * -16)

t = -56 / -32

t = 1.75

So, the t-coordinate of the vertex is 1.75 seconds, which represents the time at which the football reaches its maximum height.

To find the h-coordinate of the vertex, we can substitute the value of t we found (1.75) into the given equation:

h = -16(1.75)^2 + 56(1.75)

h = -16(3.0625) + 98

h = -48.8 + 98

h = 49.2

So, the h-coordinate of the vertex is 49.2, which represents the maximum height of the football in feet.

In conclusion, the coordinates of the vertex (49.2, 1.75) in the given context represent the maximum height (49.2 feet) of the football and the time (1.75 seconds) at which the football reaches its maximum height after being kicked by Lauren.