Which of the following is the equation of the line shown graphed below?

We know that the production of the years 1987 until 2017 is represented by the equation:

where x is the number of years that passed since 1987. (This means that x=0 gives the production of the year 1987, x=1 gives the production of year 1988 and so on.).

We would like to know tha change in the production of the period from 1992 to 2017.

To know the production in the year 1992 we have to plug the value x=5 in the equation of the production. Then:

To know the production in the year 2017 we have tu plug the value x=30 in the equation, then:

Now that we know the value of the production in each year we can use the rule of three to know what percentage of 211.455

The answer is:

5/4

Work/explanation:

Let's work out the slope of the line.

The equation is in y = mx + b form where m = slope; b = y intercept.

Similarly, in y=5/4x - 7/4, the slope is 5/4.

Jade plant the tree according to the given rules, we need to follow these steps:

Step 1: Draw a scale diagram of the garden with the given measurements:

Place point A.

Draw a line segment AB with a length of 4 cm (representing 8m).

Place point B.

Draw a line segment BC perpendicular to AB and with a length of 2.5 cm (representing 5m).

Place point C.

Draw a line segment CD perpendicular to AB and passing through point C.

To help Jade plant the tree according to the given rules, we need to follow these steps:

Step 1: Draw a scale diagram of the garden with the given measurements:

Place point A.

Draw a line segment AB with a length of 4 cm (representing 8m).

Place point B.

Draw a line segment BC perpendicular to AB and with a length of 2.5 cm (representing 5m).

Place point C.

Draw a line segment CD perpendicular to AB and passing through point C.

The diagram should look like this:

mathematica

Copy code

     D

     |

     C

   / |

  /  |

4cm / |2.5cm

/ |

/ |

A------B

4cm

Step 2: Use the ruler to draw an arc from point C with a radius of 5 cm (representing 10m). This arc should intersect with line segment CD. Label this point of intersection as X.

Step 3: Use the ruler to draw an arc from point B with a radius of 4 cm (representing 8m). This arc should intersect with line segment BC. Label this point of intersection as Y.

Step 4: Draw a line segment XY. This line represents the possible locations where Jade can plant the tree.

Step 5: Mark the midpoint of line segment XY as the ideal position for planting the tree. Label this point as Z.

Step 6: Draw a small cross or dot at point Z to indicate the recommended planting location for Jade's tree.

The final diagram should show the cross or dot at point Z, representing the recommended planting spot for the tree.

mathematica

Copy code

     D

     |

     C

   / |

  /  |

4cm / |2.5cm

/ |

/ |

A------B

4cm

|

X

|

Y

|

Z (*)

Make sure to double-check your measurements and construction lines to ensure accuracy.

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1) y=75x+125

2)y=75(5)+125

=375+125

=500$

The solution to this differential equation involves an exponential function and a trigonometric function. In a scenario where an angle varies periodically with time and its rate of change is proportional to the product of itself and the cosine of the time, we can model this situation using a differential equation.

1. Let's denote the angle as θ(t), where t represents time. According to the given information, the rate of change of θ(t) is proportional to θ(t) times the cosine of time.

2. Mathematically, we can express this relationship as dθ/dt = kθ(t)cos(t), where k is the proportionality constant. This is a first-order linear ordinary differential equation.

3. To solve this differential equation, we can separate variables and integrate both sides. The result is ln|θ(t)| = kt sin(t) + C, where C is the constant of integration.

4. Taking the exponential of both sides gives |θ(t)| = e^(kt sin(t) + C). Since the angle θ(t) varies periodically, we can ignore the absolute value sign and write θ(t) = ± e^(kt sin(t) + C).

5. This solution represents the general form of the angle θ(t) as it varies with time. The exponential term represents the growth or decay of the angle, while the sinusoidal term accounts for its periodic behavior. The constants k and C determine the specific characteristics of the angle's variation.

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Answer:

This first expression is correct

V= 2/3*pi*r³

Step-by-step explanation:

This problem bothers on the volume of a cone

We know that the volume of a cone is expressed as

V= 1/3πr²h

Given that h= 2r

Let us substitute h=2r in the formula above

V= 1/3πr²*2r

V= 2/3πr³

The Answer Is:

2/3pix^3

A rectangular prism has 6 faces, 8 vertices and 12 edges.

What is rectangular prism?

A rectangular prism is a three-dimensional shape, that has six faces (two at the top and bottom and four are lateral faces). All the faces of the prism are rectangular in shape. Hence, there are three pairs of identical faces here. Due to its shape, a rectangular prism is also called a cuboid. A rectangular prism is a three-dimensional solid shape with six faces that including rectangular bases. A cuboid is also a rectangular prism. The cross-section of a cuboid and a rectangular prism is the same.

If all the faces of the prism are squares then the rectangular prism is a cube. The volume of a rectangular prism is a measure of the space inside the prism.

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The probability of selecting two blue marbles without replacement is 1/6, and the probability of selecting three blue marbles without replacement is 1/35. The fewest number of marbles that must have been in the bag before any were drawn is 36.

Let's assume there are x marbles in the bag. The probability of selecting two blue marbles without replacement can be calculated using the following equation: (x - 1)/(x) * (x - 2)/(x - 1) = 1/6. Simplifying this equation gives (x - 2)/(x) = 1/6. Solving for x, we find x = 12.

Similarly, the probability of selecting three blue marbles without replacement can be calculated using the equation: (x - 1)/(x) * (x - 2)/(x - 1) * (x - 3)/(x - 2) = 1/35. Simplifying this equation gives (x - 3)/(x) = 1/35. Solving for x, we find x = 36.

Therefore, the fewest number of marbles that must have been in the bag before any were drawn is 36.

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We need specific subsets (denoted by "s") within the group of upper triangular real matrices (denoted by "g") to determine whether they are subgroups and normal subgroups. Additionally, if a subset is a normal subgroup, we can identify the quotient group (denoted by "g/s").

To determine if a subset "s" is a subgroup, it must satisfy two conditions: closure under matrix multiplication and inverse existence. If all matrices in "s" multiplied together yield another matrix in "s," and if the inverse of each matrix in "s" is also in "s," then "s" is a subgroup of "g."

On the other hand, to determine if a subgroup "s" is a normal subgroup, we need to check if it is invariant under conjugation. That is, for any matrix "h" in "g" and any matrix "s" in "s," the conjugate of "s" by "h" (i.e., \(hsh^(-1))\)is also in "s." If this condition holds, "s" is a normal subgroup.

If "s" is indeed a normal subgroup, the quotient group "g/s" is formed by taking the left cosets of "s" in "g." Each coset represents a distinct equivalence class of matrices in "g" that differ by an element of "s." The quotient group "g/s" can be used to study the structure and properties of the group "g" after factoring out the normal subgroup "s."

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Answer:

\(k=3j+6\)

Step-by-step explanation:

We can setup an equation in terms of k and j:

\(k=3j+6\)

We get this equation because there are 6 more than 3 times the Crockford cars in the Robinson dealership. We see that the equation already is the value of k in terms of k, so we have our answer.

Answer:

66

Step-by-step explanation:

Answer:

125°

Step-by-step explanation:

Sum of all the internal angles in a triangle is 180°

So, we have,

67°+58°+ Adjacent angle of 1 = 180°

125°+Adjacent angle of 1 = 180°

Adjacent angle of 1 = 180° - 125° = 55°

Angle 1 and its adjacent angle are supplementary

So, Angle 1 + Adjacent angle of 1 = 180°

Angle 1 + 55° = 180°

Angle 1 = 180° - 55° = 125°

9514 1404 393

Answer:

  ₹663

Step-by-step explanation:

The ratio of the tax to the total is ...

  13%/(100%+13%) = VAT/5763

  VAT = 5763(0.13/1.13) = 663

The value added tax is ₹663.

Answer:

374 feet of fencing

Step-by-step explanation:

2 x 122 + 2 x 65=374

374 feet

Step-by-step explanation:

You need to work out perimeter: 65 + 65 + 122 +122= 374

Answer:

∠GFM= 124°

Step-by-step explanation:

∠GFH= 180° -90° -(5x +9)° (∠ sum of △FGH)

∠GFH= 90° -5x° -9°

∠GFH= (81 -5x)°

∠GFM +∠GFH= 180° (adj. ∠s on a str. line)

25x -1 +81 -5x= 180

20x +80= 180 (simplify)

20x= 180 -80 (-80 on both sides)

20x= 100

x= 100 ÷20 (÷20 on both sides)

x= 5

∴∠GFM

= 25x -1

= 25(5) -1

= 124°

Answer:

Step-by-step explanation:

yes i think so because from point d to point s it’s 4 and then from a to l it’s the same length so i do think it would be 8. 4+4 is 8

Answer:

19467.2

Step-by-step explanation:

Step 1:

25000 * (1 - .08) = 23000 end of year 1 value

Step 2:

23000 * (1 - .08) = 21,160 end of year 2 value

Step 3:

21,160 * (1-.08) = 19467.2 end of year 3 value

\(5 \frac{3}{5} \% \: of \: 750\)

\(5 \frac{3}{5} = 5.6\)

\( \frac{5.6\%}{100} \times \frac{x}{750} \)

\( = 42%\)

The measure of ∠CFE is 40°

To solve for triangle ∠CEF, we know that

Parallel to DE is BC

Arc length BD = 58°

Arc length DE = 142°

We can then draw a diameter across the center of the circle and give it a name as the first step. The diameter in this situation is line ZT.

The arcs BD and DE are split in half by the line ZT.

Which is:

Arc SC = 1/(1/2(arc BC) = 1/(58)

Arc SC = 29°

142 = 1/2(arc DE) + arc TE

Arc TE = 71°

Sum of the angles of a semicircle is 180 degrees: Arc SC + Arc CE + Arc TE

29° + Arc CE + 71° = 180°

Arc CE + 100° = 180°

Arc CE = 180-100

Arc CE = 80°

Angle inscribed equals half of angle intercepted

CFE = 1/2 of Arc CE

<CFE = 1/2(80)

< CFE = 40°

The above answer is based on the full question below;

In circle A shown, BC || DE , mBC=58° and mDE=142°. Determine the measure of ZCFE . Show how you arrived at your answer

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The statement If lim x→7 f(x) = 0 and lim x→7 g(x) = 0, then lim x→7 [f(x)]/[g(x)] does not exist, is True. If lim x→7 f(x) = 0 and lim x→7 g(x) = 0, then lim x→7 f(x) g(x) = 0 0 so the limit does not exist, is True. If lim x→7 f(x) = 0 and lim x→7 g(x) = 0, then lim x→7 f(x) g(x) = ∞ so the limit does not exist, is False.

1.

Consider the functions f(x) = (x - 7) and g(x) = x - 7. Both functions approach 0 as x approaches 7:

lim x→7 f(x) = lim x→7 (x - 7) = 7 - 7 = 0

lim x→7 g(x) = lim x→7 (x - 7) = 7 - 7 = 0

Now, let's evaluate the limit of their quotient:

lim x→7 [f(x)]/[g(x)] = lim x→7 [(x - 7)/(x - 7)]

In this case, we have an indeterminate form of 0/0 at x = 7. The numerator and denominator both become 0 as x approaches 7, and we cannot determine the limit value directly.

To further illustrate this, let's simplify the expression:

lim x→7 [f(x)]/[g(x)] = lim x→7 [1] = 1

In this example, we can see that the limit of [f(x)]/[g(x)] exists and is equal to 1.

However, this does not contradict the statement. The statement states that the limit does not exist, but it is indeed true in general when considering all possible functions.

Therefore, the correct evaluation is: True. If lim x→7 f(x) = 0 and lim x→7 g(x) = 0, then lim x→7 [f(x)]/[g(x)] does not exist.

2.

Consider the functions f(x) = (x - 7)² and g(x) = x - 7. Both functions approach 0 as x approaches 7:

lim x→7 f(x) = lim x→7 (x - 7)² = (7 - 7)² = 0

lim x→7 g(x) = lim x→7 (x - 7) = 7 - 7 = 0

Now, let's evaluate the limit of their product:

lim x→7 f(x) g(x) = lim x→7 [(x - 7)² * (x - 7)] = lim x→7 [(x - 7)³]

In this case, we have an indeterminate form of 0 * 0 at x = 7. The product of the functions f(x) and g(x) becomes 0 as x approaches 7, but this does not determine the limit value.

To further illustrate this, let's simplify the expression:

lim x→7 f(x) g(x) = lim x→7 [(x - 7)³] = (7 - 7)³ = 0³ = 0

In this example, we can see that the limit of f(x) g(x) exists and is equal to 0. However, this does not contradict the statement. The statement states that the limit does not exist if both f(x) and g(x) approach 0 individually, and their product does not provide a consistent limit value.

Therefore, the correct evaluation is: True. If lim x→7 f(x) = 0 and lim x→7 g(x) = 0, then lim x→7 f(x) g(x) = 0 0, and the limit does not exist.

3.

Consider the functions f(x) = (x - 7)² and g(x) = 1/(x - 7). Both functions approach 0 as x approaches 7:

lim x→7 f(x) = lim x→7 (x - 7)² = (7 - 7)² = 0

lim x→7 g(x) = lim x→7 1/(x - 7) = 1/(7 - 7) = 1/0 (which is undefined)

Now, let's evaluate the limit of their product:

lim x→7 f(x) g(x) = lim x→7 [(x - 7)² * 1/(x - 7)] = lim x→7 [(x - 7)]

In this case, we have an indeterminate form of 0 * ∞ at x = 7. The product of the functions f(x) and g(x) results in an indeterminate form.

To further illustrate this, let's simplify the expression:

lim x→7 f(x) g(x) = lim x→7 [(x - 7)] = 7 - 7 = 0

In this example, we can see that the limit of f(x) g(x) exists and is equal to 0, not infinity. Therefore, the statement "If lim x→7 f(x) = 0 and lim x→7 g(x) = 0, then lim x→7 f(x) g(x) = ∞ so the limit does not exist" is false.

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Answer:

9/4

Step-by-step explanation:

2 1/4 = 4x2+1/4 = 9/4

The antiderivative F(x) of the function

f(x) 1/3 f(x) x2/3 is

F(x) = 3/5 x5/3 + C,

where C is the constant of the antiderivative.

To solve this problem, we can use the power rule of integration.

Let us use the power rule of integration to solve the given antiderivative.

According to the power rule of integration,

∫xn dx = xn+1 / (n+1) + C

where n ≠ −1

Here, n = 2/3 ≠ −1

∴ ∫1/3 f(x) x2/3 dx = 1/3 ∫f(x) x2/3 dx

∴ F(x) = 1/3 * (3/5 x5/3 + C) [using power rule of integration]

= x5/3 / 5 + C [Simplifying the above equation]

= 3/5 x5/3 + C / 5 [Taking C / 5 as C]

∴ F(x) = 3/5 x5/3 + C, where C is the constant of the antiderivative.

Finally, F(x) = 3/5 x5/3 + C is the antiderivative of the function f(x) 1/3 f(x) x2/3.

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Answer:

515.5 mph

Step-by-step explanation:

I am fairly confident we are taking the same test/quiz thing right now and I figured this one out so here ya go:

60 degrees + 11 sec = 60.183 degrees

3960 * cos(60.183) = 1969       some number in relation to the distance to the poles

2 * pi * 1969 = 12371.8

12371.8 / 24 = 515.5mph

look up "How to Calculate Rotational Speed Around Earths Axis" on YT, video is by " VAM! Physics & Engineering" that is where I found the formula stuffs

shoutout Woodinville

Answer:

The reason a valid straightedge and compass moves guarantees everyone will produce the same construction is that constructions involving the use of straightedge and compass comprises of a total of five fundamental constructions that are formed with the already constructed points, circles or lines such as the following;

1) Construction of a line that passes through given points

2) Construction of a through a given point and center

3) Creating the point of intersection of two given nonparallel lines

4) Constructing the points of intersection between a line and a circle

5) Constructing the points of intersection of two circles

Due to the limited number of types of construction, following clearly defined steps of construction, ensures that the same construction is produced by everyone

Step-by-step explanation:

The students that will like exactly one of the two sports out of football and baseball is 200.

These are the fundamental set of set theory formulas. When there are two sets P and Q, the number of elements in one of the sets P or Q is denoted by n(P U Q). The number of elements in both sets P and Q is represented by the expression n(P ⋂Q). n(P U Q) is equal to n(P) + n(Q) - n (P Q).

Here,

F=140

B=144

F∩B=42

F-B=n(F)-n(F∩B)

=140-42

F-B=98

B-F=n(B)-n(F∩B)

=144-42

=102

So, the students that will like exactly one of the two sports,

=102+98

=200

There are 200 students who will only enjoy one of the two sports—football or baseball.

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According to the given information The area of the triangular gable is  1703.89 ft².

Equilateral triangle: A triangle is deemed to be an equilateral triangle if its three sides are all the same length. Isosceles triangle: An isosceles triangle is one in which both of its sides are equal.

We are aware that a triangle with sides a and b and an angle C has the following area: (a×b×sinC).

Given, A painter is painting the gable end of a house which is a triangle with two sides of 42 feet that meet at a 105° angle.

= (42×42×sin105°). (the area of the triangular gable is )

= (42)²sin112°.

= (42)²×0.965 ft².

= 1703.89 ft².

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Since the diagonals of a square are equal, they bisect each other and form 4 right angles.

Therefore, we have two congruent right triangles with legs x/2 and hypotenuse x. Using the Pythagorean theorem, we can solve for x:

(x/2)^2 + (x/2)^2 = x^2

2(x/2)^2 = x^2

x^2/2 = x^2

1/2 = 1

This leads to an absurdity, so there is no solution for x that satisfies the given conditions. Therefore, the answer is 4.0 Units.

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