The graph models the value of a machine over a 10 -year period. Which equation best represents the relationship between x , the age of the machine in years, and y , the value of the machine in dollars over this 10-year period? A.​​​​​​y=500x+8,000 B.y=−500x+8,000 C.​​​​​​y=−0.002x+2,500 D.y=0.002x+2,500

The function equation for the graph above include the following: B. f(x) = -[x] + 3.

In Mathematics and Geometry, a greatest integer function can be defined as a type of function which returns the greatest integer that is less than or equal (≤) to the number.

Mathematically, the greatest integer that is less than or equal (≤) to a number (x) is represented as follows:

y = [x].

By critically observing the given graph, we can logically deduce that the parent function was reflected over the y-axis (negative slope) and it was vertically translated from the origin by 3 units up;

y = [x]

f(x) = -[x] + 3.

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Answer:

6 cm³

Step-by-step explanation:

The figure is a triangular prism with a triangular base with side lengths 3 cm, 4 cm, 5 cm. The height of the prism is 1 cm.

The sides measuring 3 cm and 4 cm form a right angle.

V = BH

where B = area of the base, and

H = height of the prism.

The base is a triangle, so B = (1/2)bh,

where b = base of the triangle, and

h = height of the triangle

V = (1/2)bhH

V = (1/2)(3 cm)(4 cm)(1 cm)

V = 6 cm³

Answer:131

Step-by-step explanation:

Use BEDMAS

9x(7+7)+5

=9 x 14 + 5

= 126 + 5

= 131

The required, -x is also 13 units from 0, but to the right of 0 instead of to the left.

The statement about -x is that it is 13 units to the right of 0. This is because the original number, which is 13 units to the left of 0, is represented by a point on the number line to the left of 0. If we negate this number to get -x, then we are reflecting it across the origin (0) to the right side of the number line. This means that the distance of -x from 0 is the same as the distance of the original number from 0, which is 13 units.

Therefore, -x is also 13 units from 0, but to the right of 0 instead of to the left.

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Answer:

m = [tex]\frac{3}{2}[/tex]

Step-by-step explanation:

calculate the slope m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (- 3, - 1 ) and (x₂, y₂ ) = (3, 8 )

m = [tex]\frac{8-(-1)}{3-(-3)}[/tex] = [tex]\frac{8+1}{3+3}[/tex] = [tex]\frac{9}{6}[/tex] = [tex]\frac{3}{2}[/tex]

Answer:

3/2

Step-by-step explanation:

To find the slope, we use the slope formula

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

    = (8- -1)/( 3 - -3)

    = (8+1)/(3+3)

     = 9/6

    = 3/2

The hotel charge in the first city before tax was $6000 and the hotel charge in the second city before tax was $7500.

Let x be the hotel charge before tax in the first city, and y be the hotel charge before tax in the second city. Then we have:
y = x + 1500   (the hotel charge before tax in the second city was $1500 higher than in the first)
0.075x + 0.05y = 825   (the total hotel tax paid for the two cities was $825)
We can use the first equation to solve for y in terms of x:
y = x + 1500
Then we can substitute this expression for y into the second equation:
0.075x + 0.05(x + 1500) = 825
Simplifying this equation, we get:
0.075x + 0.05x + 75 = 825
0.125x = 750
x = 6000
So the hotel charge before tax in the first city was $6000. Using the first equation, we can find the hotel charge before tax in the second city:
y = x + 1500
y = 6000 + 1500
y = 7500
So the hotel charge before tax in the second city was $7500.
Therefore, the answer is: The hotel charge in the first city before tax was $6000 and the hotel charge in the second city before tax was $7500.

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The solution to a system of two linear equations is x = 3; y = 9. the following response is form the solution

1. From the origin, move 3 units right and 9 units up

2. The point of intersection of the two lines

3.Yes, if both lines are the same exact line

4. Can you have exactly two solutions to a Linear system of equations?

5. No, because lines are straight

6. Yes, if the lines are parallel

Parallel lines refers to lines that has equal slopes, such lines do no intersect each other at any point.

Hence we say that no solution is obtained in when linear equations turns out to be parallel lines.

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The solution to the system of linear inequalities is the shaded region that satisfies both inequalities.

We have,

To find the solution to the system of linear inequalities:

2x - 3y < 12

y ≤ 2

We first graph the line 2x - 3y = 12:

To graph the line, we can find the x and y intercepts:

When x = 0, we have -3y = 12, then y = -4, so (0, -4) is a point on the line.

When y = 0, we have 2x = 12, then x = 6, so (6, 0) is a point on the line.

Plot these two points and draw the line passing through them:

Next, we shade the region that satisfies the inequality 2x - 3y < 12:

We can choose a test point not on the line, such as (0,0).

Substitute the coordinates into the inequality:

2(0) - 3(0) < 12, which is true.

Now,

We shade the region that satisfies the inequality y ≤ 2:

We shade the region below the horizontal line y = 2:

Therefore,

The solution to the system of linear inequalities is the shaded region that satisfies both inequalities.

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The value of x that satisfies the equation -1.5x - 2.7 = 20.1 + 4.5x is -3.8.

To solve this equation, we need to isolate the variable x on one side of the equation. We can do this by using basic algebraic operations, such as adding, subtracting, multiplying or dividing both sides of the equation by the same value.

The first step in solving this equation is to get rid of the constant terms on one side of the equation. We can do this by adding 2.7 to both sides of the equation:

-1.5x - 2.7 + 2.7 = 20.1 + 4.5x + 2.7

Simplifying the left-hand side of the equation, we get:

-1.5x = 20.1 + 4.5x + 2.7

Next, we can move the variable terms to the left side of the equation and the constant terms to the right side of the equation by subtracting 4.5x from both sides:

-1.5x - 4.5x = 20.1 + 2.7

Simplifying the left-hand side, we get:

-6x = 22.8

Finally, we can solve for x by dividing both sides of the equation by -6:

x = -3.8

Therefore, the value of x that satisfies the equation -1.5x - 2.7 = 20.1 + 4.5x is -3.8.

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Answer: 40 cups per min = 2.5 gallons per hour

Step-by-step explanation:

Answer:

Step-by-step explanation:

A:  V = πr²h

B:  V = 1/3π(2r)²(2h) = 1/3π(4r²)(2h) = 1/3π8r²h = 8/3πr²h

C:  V = π(2r)²(2h) = π(4r²)(2h) = π8r²h = 8πr²h

D:  V = 1/3πr²(2h) = 2/3πr²h

The distance from point B to point A is given as follows:

15,893 ft

The three trigonometric ratios are the sine, the cosine and the tangent, and they are defined as follows:

For each angle, we have that:

Hence the position A is obtained as follows:

tan(16º) = 7200/a

a = 7200/tangent of 16 degrees

a = 25109 ft.

The position B is obtained as follows:

tan(38º) = 7200/b

b = 7200/tangent of 38 degrees

b = 9216 ft.

Hence the distance is of:

25109 - 9216 = 15,893 ft.

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The required dimensions are

22. x = 9.45

23. perimeter = 198.2

24. angle NSR = 110

25. x = 10

22. The value of x is solved using Pythagoras theorem

x² = (7.4 + 4.6)² - 7.4²

x² = 144 - 54.76

x = √89.24 = 9.45

23. perimeter of tringle GHI

solving for x

7x + 4 = 12x - 20

x = 4.8

perimeter = 52 + (52 - 15 + 7x + 4) + 15 + 12x - 20

perimeter = 52 + (52 - 15 + 7(4.8) + 4) + 15 + 12(4.8) - 20

perimeter = 198.2

24. angle NSR = 1/2 (170 + 50 )

angle NSR = 1/2 (220) = 110

25.

angle V = 1/2 * 290 = 145

4x - 5 + 145 = 180

4x - 5 + 145 = 180

4x + 140 = 180

4x = 40

x = 10

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Miles is the number of miles Martin has run, and Total Time is the total time in minutes that he has been running, which is 11Miles + 5.

To create a linear model, we need to find the equation of the line that best fits the data.

We can do this by finding the slope and y-intercept of the line.
First, we need to find the slope, which is the change in y divided by the change in x.

We can choose any two points on the line to calculate the slope.

Let's use the first and second data points:
Slope = (y2 - y1) / (x2 - x1)
Slope = (104 - 60) / (9 - 5)
Slope = 44 / 4
Slope = 11
Now we can use the point-slope form of the equation of a line to find the y-intercept.

We can use the first data point:
The linear model has the form y = mx + b, where y represents the total time (in minutes), x represents the miles run, m is the slope, and b is the y-intercept.

We can use the data points to find the slope (m) as follows: m = (change in total time) / (change in miles)

Using the first two data points, (5, 60) and (9, 104):

m = (104 - 60) / (9 - 5) = 44 / 4 = 11

Now that we have the slope, we can find the y-intercept (b) using one of the data points.

Let's use (5, 60): 60 = 11 * 5 + b 60 = 55 + b b = 5

So the linear model representing Martin's pace is: y = 11x + 5 In this model, x is the miles run, and y is the total time in minutes.
y - y1 = m(x - x1)
y - 60 = 11(x - 5)
y - 60 = 11x - 55
y = 11x + 5
So the linear model that shows the miles Martin has run as the input, and the total time, in minutes, he has been running as the output is
Total Time = 11Miles + 5

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The next time trains to Aybrin and Bleechtree leave the station together is 280 minutes (or 4 hours and 40 minutes) after 7 am.

To find the next time trains to Aybrin and Bleechtree leave the station together, we need to determine the least common multiple (LCM) of 35 and 40, which represents the time interval at which both train schedules align.

The prime factorization of

35 = 5 x 7,

and 40 = 2 x 2 x 2 x 5

Now, the highest power of each prime factor that appears in either factorization.

So the LCM of 35 and 40 = 2 x 2 x 2 x  5 x  7 = 280.

Therefore, the next time trains to Aybrin and Bleechtree leave the station together is 280 minutes (or 4 hours and 40 minutes) after 7 am.

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17.55% is the probability for any day, the number of special orders sent out will be exactly 5

The given situation describes a Poisson distribution with a mean of 5 special orders per day. The probability of getting exactly 5 special orders in a day can be calculated using the Poisson probability formula, which is:

P(X = k) = (e^(-λ) * λ^k) / k!

where X is the random variable representing the number of special orders, λ is the mean number of special orders per day, and k is the number of special orders we want to find the probability for.

Plugging in the given values, we get:

P(X = 5) = (e^(-5) * 5^5) / 5!

Simplifying this expression, we get:

P(X = 5) = 0.1755

Therefore, the probability of getting exactly 5 special orders in a day is 0.1755 or 17.55%, rounded to four decimal places.

Intuitively, this means that out of many days, we can expect around 17.55% of them to have exactly 5 special orders sent out. The Poisson distribution is commonly used to model the number of events occurring in a fixed period of time, given a known average rate of occurrence. In this case, the Poisson distribution can be used to estimate the likelihood of a particular number of special orders being sent out in a day.

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The entries of the first row is 3,6. Option B

To add the entries of the first row in the two matrices, we need to first identify the first row of each matrix and then add the corresponding entries together.

Matrix A:

[1  4]

[7  1]

Matrix B:

[2  2]

[4  3]

To add the first rows of these matrices, we simply add the corresponding entries:

1+2      4+2

2          6

Hence, the entries of the first of the two matrices is 2,6

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Answer:

side AC

Step-by-step explanation:

is the opposite angle B because it is the furthest you can get on the triangle to be away from point B.

It should be noted that the ratio between the lengths of the two legs is B. 1: ✓3.

It should be noted that the ratio between the lengths of the two legs will be equal to the tangent.

In this case, tan (30°) = ✓3/3

Tan (60°) = ✓3

Therefore, the ratio between the lengths of the two legs of a 30-60-90 triangle will be 1 : ✓3.

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Answer:

Tickets Sold: 146

Step-by-step explanation:

Let's assume that the number of adult tickets sold is "x".

According to the problem, the number of student tickets sold is three times the number of adult tickets sold. Therefore, the number of student tickets sold is 3x.

The total number of tickets sold is 584, so we can set up an equation:

x + 3x = 584

Simplifying the equation, we get:

4x = 584

Dividing both sides by 4, we get:

x = 146

Therefore, the number of adult tickets sold is 146.

Answer: 146

Step-by-step explanation:

let x = # of adult tickets sold

let y = # of student tickets sold

x + y = 584

this is because the sum of adult tickets and student tickets is 584.

3x = y

this equation is written because there is 3 times more students there than adults

using substitution, we can find the equation :

x + (3x) = 584

4x = 584

x = 146

since x is equal to the number of adult tickets sold, your answer is 146.

Answer:

Step-by-step explanation: 78 +3x+x=180 deg.

                                                 4x=180-78

                                                 4x=102/:4

                                                    x=25.5 deg

Step-by-step explanation:

180 = 78° + 3x°

78° + 3x° = 180°

3x°= 180° - 78°

3x = 102°

x = 102°/3

The weight before the party could be any positive number

The weight of the bag of ice after the party was 7/8 pounds. So we can set up an equation:

x - weight used at the party = 7/8

We know that the weight used at the party is the weight before the party minus the weight after the party.

So we can substitute 3x for the weight before the party:

3x - (7/8) = weight used at the party

We don't know the exact weight used at the party, but we do know that it was less than or equal to the weight before the party.

So we can set up another inequality:

weight used at the party ≤ 3x

Putting it all together:

3x - (7/8) ≤ 3x

Simplifying:

-(7/8) ≤ 0

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The 6 drawings are grouped to one another

Given data ,

Let the 6 drawings into be divided into two groups of 3 drawings each

And , drawings of each group is similar to one another in some way

where Group 1: ABD

On simplifying the equation , we get

Their curves and the points are in a same order

Group 2: CEF

On simplifying the equation , we get

Their curves and points are oppositely drawn

Hence , the drawings are solved

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The complete question is attached below :

Group the 6 drawings into two groups of 3 drawings each. The drawings of each group must be similar to one another in some way - they must belong together.

Little's prediction for the second tests median score  is 84

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

The dot plot

The median is the middle number on the dot plot

From the dot plot, the middle number is

Middle = 70

This means that

Median = 70

For the new prediction, we have

New median = 70 * (1 + 20%)

Evaluate

New median = 84

Hence, Little's prediction for the second tests median score  is 84

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The baker would need 47. 25 cups of floor

We need to know that proportion is a form of mathematical comparison with two equations made equal to each other.

From the information given, we have that;

baker used 33 3/4 cups of flour to make 15 batches of cookies

This is represented as;

Convert to improper fractions

135/4 cups = 15 batches of cookies

Then, x cups = 21 batches of cookies

cross multiply the values

15x = 708. 75

Divide both sides by the coefficient of x, we have ;

x = 708. 75/15

x = 47. 25 cups of floor

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The height of the skyscraper is D. 156.26 ft

To determine the height of the skyscraper,  we need to consider the following trigonometric identities listed thus;

From the information given, we have that;

Angle, θ = 38 degrees

The shadow casted is the adjacent side of the angle and is 200 ft

The height off the skyscraper is the opposite side

Now, using the tangent identity, we have that;

tan θ = opposite/adjacent

tan 38 = h/200

cross multiply the values, we get;

h = 200(0.7812)

Multiply the values

h = 156. 26 ft

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The value of x is 3 and angle Q is 39°

A circle is a special kind of ellipse in which the eccentricity is zero and the two foci are coincident.

A circle theorem states that : angles in thesame segment are equal.

With this theorem is means that angle 13x is equal to angle x +36 .

Therefore;

13x = x +36

collecting like terms

13x -x = 36

12x = 36

divide both sides by 12

x = 36/12

x = 3

therefore the value of angle Q = 13 × 3

= 39°

Therefore the value of angle Q is 39°

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Answer:

Solving the system of equations.

Point form: (3+√25,−3+√2),(3−√25,−3−√2)

Equation form:

x=3+√25,y=−3+√2x=3−√25,y=−3−√2

Step-by-step explanation: