The height of a ramp, y, is proportional to the
horizontal distance along the ramp, x. Both
lengths are measured in feet. The equation
that relates the two is:
y=1/4x
Produce a graph of this relationship on the grid
provided. Explain how you made your graph.

The coordinates of the circumcenter of the triangle will be (0, -1).

The circumscribed circular or circumcircle of polygons in geometry is a ring that goes through each of the polygon's corners. This circle's circumcenter and circumradius are its center and radius, respectively.

The coordinate of the triangle is given below.

W(-1, 4), X(1, 4), Y(1, -6)

The given triangle is a right-angle triangle. Then the vertices of the hypotenuse will be (-1, 4) and (1, -6). Then the circumcenter is given as,

(x, y) = [(-1 + 1) / 2, (4 - 6) / 2]

(x, y) = (0, -1)

The coordinates of the circumcenter of the triangle will be (0, -1).

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Answer:

11m + 4n ...............

Answer:

4

Step-by-step explanation:

3= a -1

+1 = a. you pass the negative 1 to the other side.

and it turns to a + 1 and then you add it which

gives you 4

4= a

Answer:

which solution are you looking for?

Step-by-step explanation:

Solving for X would be: x<0

Graph inequality would be the left side shaded i think

Answer:

B. 11 4 (11 with the exponent of 4) because 11 was multiplied 4 times.

Step-by-step explanation:

Answer:

Yes

Step-by-step explanation:

On my worksheet

Answer: Yes

Step-by-step explanation:

You asked if the line was linear not passing through the origin. The line is linear because it has a slope that is constant. Therefore, it will be drawn as a line, so it is linear.

Answer:

The length of a leg is 12.5 and its base is 15

Step-by-step explanation:

Using Heron's formula, the area of the triangle A = √[s(s - a)(s - b)(s - c)] where s = (a + b + c)/2. Now, for an isosceles, a = b and c = its base.

So,  A = √[s(s - a)(s - a)(s - c)] = √[s(s - a)²(s - c)] = (s - a)√[s(s - c)] and s = (a + a + c)/2 = a + c/2 ⇒ s = a + c/2 (1)

Given that the perimeter a + b + c = 2a + c = 40 = 2s ⇒ s = 40/2 = 20 and A = hc/2 where h = length of altitude to base = 10.

So, A = 10c/2 = 5c

So, 5c = (s - a)√[s(s - c)]

From (1) s - a = c/2.

So, 5c = (s - a)√[s(s - c)]

5c = (c/2)√[s(s - c)]

10 = √[s(s - c)]

squaring by sides, we have

100 = s(s - c) since s = 20,

s(s - c) = 100

20(20 - c) = 100

20 - c = 100/20

20 - c = 5

c = 20 - 5

c = 15

From (1),

s = a + c/2

a = s - c/2

= 20 - 15/2

= 20 - 7.5

= 12.5

Since a = b = 12.5

So, the length of a leg is 12.5 and its base is 15

Answer:

6.14 is Rational only

Answer:

5% of 117.50 is 5.875

117.50- 5.875= 111.625 => round it to two decimal places.

£111.63

Hope this helps :)

Answer:

18, 10

Step-by-step explanation:

because i said so

The third table shown in the diagram below can be modelled with the equation, y = x + 2, therefore, it represents a linear equation (see attachment).

A linear function is a function whose graph represents a straight line when the points are plotted, and also can be modelled by the equation, y = mx + b.

b is the value of y when x = 0 (y-intercept)

m is the slope or unit rate.

Thus, the third table shown in the diagram below can be modelled with the equation, y = x + 2, therefore, it represents a linear equation (see attachment).

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Answer:

Infinitely many solutions

Step-by-step explanation:

y = -1/6x + 5

x + 6y = 30

We can solve this system by using substitution or elimination. Since we are given an isolated y-value, I'll be using the substitution method.

Substitute y = -1/6x + 5 into the second equation for y.

Distribute 6 inside the parentheses.

Combine like terms.

Since this is a true statement, we can conclude that this system has a solution of all real numbers, or infinitely many solutions.

We can also see that these equations are indeed equivalent by multiplying the top equation by 6.

6 * (y = -1/6x + 5) → 6y = -x + 30

Adding x to both sides and rearranging terms gives us x + 6y = 30, which is the same as the second equation.

Answer:

.45

Step-by-step explanation:

Answer:

0.45

Step-by-step explanation:

Since 45 out of the 100 squares are shaded, it means the fraction would be 45/100 and 45/100 is equal to 0.45.

Answer:

The values of the multiplications are as follows:

1) 35/72

2) 7/16

3) 9/40

4)  10/3

5) 30/49

6) 1/5

Given,

Fractional multiplications.

Here,

In fractional multiplication the numerators are multiplied together and denominators are multiplied together.

The result can be further simplified .

So,

1)

7/9 × 5/8 = 35/72

2)

4/8 × 7/8 = 28/64

Further simplifying,

Divide numerator and denominator by 4,

= 7/16

3)

6/10 × 3/8

= 18 / 80

Divide numerator and denominator by 2,

= 9/40

4)

4 × 5/6

= 20/6

Divide numerator and denominator by 2,

= 10/3

5)

5/7 × 6/7

= 30/49

6)

2/5 × 4/8

= 1/5

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The homogeneous system of linear equations has a solution space with a basis of {(1, 2, -1)}. The dimension of the solution space is 1.

To find a basis for the solution space of the given homogeneous system of linear equations, we need to solve the system and express the solutions in terms of a linear combination of vectors.

The system of equations is as follows:

Equation 1: -x + y - z = 0

Equation 2: 2x - y = 0

Equation 3: 2x - 3y - 4z = 0

We can start by using the equations to eliminate variables. From Equation 2, we can express y in terms of x as y = 2x. Substituting this into Equation 1 gives us -x + 2x - z = 0, which simplifies to x - z = 0. Rearranging this equation, we have x = z.

Now, we can express the variables in terms of a single parameter. Let's choose z as the parameter. Thus, x = z and y = 2x = 2z.

Now, we can express the solutions in vector form as (x, y, z) = (z, 2z, z) = z(1, 2, 1). This means that the solution space is spanned by the vector (1, 2, 1).

To find the basis for the solution space, we need to check if the vector (1, 2, 1) is linearly independent. Since it is the only vector spanning the solution space, it is linearly independent. Therefore, the basis for the solution space is {(1, 2, 1)}.

The dimension of the solution space is equal to the number of vectors in the basis, which in this case is 1. Therefore, the dimension of the solution space is 1.

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Answer:

o.5,0.4

Step-by-step explanation:

4)20(0.5

-20

00

Answer:

Simplify the expression.

Exact Form:

5/2

Decimal Form:

2.5

Mixed Number Form:

2 1/2

Step-by-step explanation:

Answer:

The answer to this question is choice C.

Step-by-step explanation:

In order to solve this question, I first recognized which trigonometry function that I could use. I realized that I am given information about angle a which is 45 degrees and that the length of the side opposite to it is 7 units. Therefore, I used the sine function to create a mathematical equation which was sine(45) = 7/AB. I isolated AB, to get the equation AB = 7/sine(45) which I plugged into a calculator to get 9.899 which is closest to choice C.

Answer:

7\(\sqrt{2}\)

Step-by-step explanation:

In this question, we are going to either use the formula with tan, sin or cos.

We have the angle, which is θ, BC which is the opposite side, and we must find the length of AB which is the hypotenuse. So we are going to use the formula:

 sin θ = \(\frac{opposite}{hypotenuse}\)

 sin 45 = \(\frac{7}{hypotenuse}\)

 hypotenuse = \(\frac{7}{sin45}\)

hypotenuse = 9.899494937... which is also equal to 7\(\sqrt{2}\)

   If you check with the other options:

   \(\sqrt{2}\) = 1.414213562... which is wrong

   1 which is obviously not the answer

   7 which is also obvious.

∴ 7\(\sqrt{2}\), which is the 3rd option, is the answer.

Answer:

try 7

Step-by-step explanation:

Answer:

this is tricky b/c they are making the two triangles of different scales but of the same angles.... soooo  one is just a bigger copy of the other....

Step-by-step explanation:

Since this is a relation of the two side of each.. we can say the following...

\(\frac{6}{9}\) = \(\frac{4}{x}\)     where X = side  LA    soooo       solve for X  

 x *  \(\frac{6}{9}\) = 4   (move the X , to the other side of the '=' sign

x = 4 * \(\frac{9}{6}\)   ( yes.. we want to invert the fraction to move it to the other side )

x = \(\frac{36}{6}\)

x = 6

so side LA is 6    :)

Answer:

The water amount will be equal at 19.5 minutes

Step-by-step explanation:

Here, we want to find the value of t when the water level in both tanks will be equal

We simply proceed to equate both ;

That will be;

30t + 25 = -20t + 1000

30t + 20t = 1000-25

50t = 975

t = 975/50

t = 19.5 minutes

Carla's behavior of putting in extra practices to become faster can be seen as an example of (Option A.) compensation. This is because she is trying to make up for her perceived lack of speed by working harder to become as fast as her teammates.

Carla's behavior of putting in extra practices to become faster can be seen as an example of compensation. This is because she is trying to make up for her perceived lack of speed by working harder to become as fast as her teammates.

By engaging in extra practices, Carla is attempting to compensate for her lack of speed and improve her performance. This is different from rationalization, which is the act of making excuses for one's behavior, or from regression, which is the act of reverting to a younger age in response to a stressful situation.

Finally, displacement is the act of redirecting one's emotions or anger onto another person or object.

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a. The line represents the trend of decreasing pH over time.

b. The pH was around 5.8, and at the end, it was around 5.2.

c. The slope of the regression line represents the rate of change in pH, which is approximately -0.005 units per week.

Without the specific equation of the regression line, it is not possible to draw an accurate graph. However, based on the information provided, the graph of the line would show the trend of decreasing pH values over the 150 weeks of the study.

According to the regression line, the pH at the beginning of the study (week=1) would be higher than the pH at the end of the study (week=150). The slope of the regression line would give the rate of change in pH over time. A negative slope would indicate a decreasing pH value over time, while a positive slope would indicate an increasing pH value over time. The steeper the slope, the more rapid the rate of change in pH.

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Answer:

- 12

Step-by-step explanation:

the common ratio r of a geometric sequence is

r = \(\frac{a_{2} }{a_{1} }\) = \(\frac{-\frac{4}{3} }{\frac{4}{9} }\) = - \(\frac{4}{3}\) × \(\frac{9}{4}\) = - 3

to find the next term , multiply the previous term by r = - 3 , then

a₄ = 4 × - 3 = - 12

No, doubling the length of the sides of a triangle does not result in doubling the area. When the length of the sides of a triangle is doubled, the area of the triangle increases by a factor of four, not two.

The area of a triangle is determined by its base and height. When the sides of the triangle are doubled, both the base and height are doubled as well.

The formula for the area of a triangle is given by A = (1/2) * base * height. If we double both the base and the height, the new area becomes A' = (1/2) * (2 * base) * (2 * height), which simplifies to A' = 2 * 2 * (1/2) * base * height = 4 * A. Therefore, doubling the sides of a triangle results in quadrupling its area, not doubling it.

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Answer:

4) slope= 0

5) \(slope = - \frac{1}{7} \)

Step-by-step explanation:

\(\boxed{ slope = \frac{y _{2} - y_1 }{x_2 - x_1} }\)

4) Slope

\( = \frac{10 - 10}{ - 10 - 3} \)

\( = \frac{0}{ - 13} \)

= 0

The slope is zero as the line is a horizontal line (since both points have the same y-coordinate of 10).

5) Slope

\( = \frac{5 - 4}{2 - 9} \)

\( = \frac{1}{ - 7} \)

\( = - \frac{1}{7} \)

Since you have taken (x₁, y₁) to be (9, 4), the value of x₁ should be 9 instead of 2.

so, this is how I always do it as a little shortcut (it's the same as the formula, but it makes more sense lol):

4) 0/13 = 0 = slope

take your two points (-10, 10) and (3, 10) and just draw them relative to each other (it doesn't have to be to scale or anything)

. (-10, 10)           |     . (3,10)

                         |

                         |      

                         |    

------------------------------------------------

                         |

                         |

                         |

                         |

then, you just see how far up you go from (-10, 10) to get to (3, 10) --> look at the y-values, in this situation you do not go up or down, this means the "rise" for "rise/run" (slope) is 0

. (-10, 10)           |     . (3,10)

                         |

                         |      

                         |    

------------------------------------------------

                         |

then, you just see how far to the right you go from (-10, 10) to get to (3, 10) --> look at the x-values, in this situation you go over 13 units, this means the "run" for "rise/run" (slope) is 13

take your "rise" and your "run" and divide: 0/13 = 0**this is your slope because it is a horizontal line

5) 1/7 = slope

follow the same steps as above (just a quick little sketch on paper)

(9, 4) and (2, 5)

rise = 1

run =  7

rise/run = 1/7 = slope

Answer:

V=1/3πr^2h

π=1/3r^2hV

The coterminal angle to -ㅠ/2 in the range between 0 and 2ㅠ radians is 3ㅠ/2.

For any angle A, all the coterminal angles are of the form:

B = A + n*(2ㅠ).

Where n is an integer different than zero.

In this case, the angle is A = -ㅠ/2

So the coterminal angles are of the form:

B = -ㅠ/2 + n*(2ㅠ)

We want it to be between 0 and 2ㅠ, so we can define n = 1, then we get:

B = -ㅠ/2 + (2ㅠ) = -ㅠ/2 + ((4/2)ㅠ) = 3ㅠ/2

Then we can conclude that the correct option is b.

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To fully answer this question, I would need the information presented in Figure 3.14 that provides the computer solution. Unfortunately, I cannot access or view specific figures or external sources. However, I can explain the general approach to solving such a problem and provide a LaTeX code snippet to format the question.

To solve the given problem, it appears to be a linear programming problem where the goal is to optimize the total annual return subject to certain constraints. The decision variables are the number of shares of US Oil (U) and Huber Steel (H) to be purchased.

a. The optimal solution would provide the values of U and H that maximize the total annual return while satisfying the given constraints. The value of the total annual return would be the objective function value at the optimal solution.

b. The binding constraints are those that are active and determine the solution. These constraints limit the risk index, the total investment amount, and the maximum number of shares of US Oil. Interpretation of these constraints would depend on the specific problem and its context.

c. The dual values for the constraints represent the marginal values or shadow prices associated with each constraint. They indicate the rate of change in the objective function value for a small change in the right-hand side of the constraint. Interpretation of dual values would also depend on the specific problem and its context.

d. The impact of increasing the maximum amount invested in US Oil would depend on the objective function and the constraints. It could lead to a higher total annual return if US Oil has a higher return rate and the constraint on the risk index or total investment amount allows for it. However, if the maximum number of shares of US Oil is already binding, increasing the maximum investment amount would not be beneficial.

Please provide any additional information or specific values from Figure \(3.14\) if you have access to it, and I can assist further.

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The value of the additional data point is 36

To find the value of the additional data point, we can use the concept of the sample mean.

Given the data set: 23, 28, 20, 33, 42, 12, 19, 50, 36, 25, 19.

The sample mean of this data set is 26.5.

To find the value of the additional data point, we can use the formula for the sample mean:

(sample mean) = (sum of all data points) / (number of data points)

In this case, we have 11 data points in the original data set. Let's denote the value of the additional data point as x.

Therefore, we can set up the equation:

26.5 = (23 + 28 + 20 + 33 + 42 + 12 + 19 + 50 + 36 + 25 + 19 + x) / 12

Multiplying both sides of the equation by 12 to eliminate the fraction, we have:

318 = 282 + x

Subtracting 282 from both sides of the equation, we find:

x = 318 - 282

x = 36

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.

Answer:

50.

Step-by-step explanation:

12 x 45 = 540. 45 + 5 = 50.