Consider the arithmetic sequence with a first term of 11 and sixth term of 21. What is the
sum of these first six terms?

A: 192
B: 52
C: 142
D: 96

The equation represents the value of the car after 3 years is  V = 28900 (1 - 0.05)³

Price of the car = 28,900

Depreciation rate = 5%

Time period = 3 years

Calculating the amount of depreciation -

V = 28900 x (1 - 0.05)³

= 28900 x  (0.95)³

= 28900 x (0.857375)

= 24,827.75

Thus, the equation will be - V = 28900 (1 - 0.05)³ ( Depreciation means loss in value, thus the negative sign)

This equation accounts for the 5% yearly depreciation rate, which indicates that car value declines by 5% annually. The original cost of car must be multiplied by the depreciation factor (1 - 0.05) raised to the total time period (3 years) to get the car worth after three years.

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Complete Question:

A new car is purchased for 28,900 dollars. The value of the car depreciates at a rate of 5% per year. Which equation represents the value of the car after 3 years?

a. V = 28900 (1 + 0.05)^3

b. V = 28900 (1 - 0.05)^3

c. V = 28900 (0.05)^3

Answer:

area of triangles = 1/2 base*height.

=1/2*12*10

=60 answer

The rate (in km/h) at which the distance from the plane to the radar station is increasing a minute later is 0 km/h (rounded to the nearest whole number).

To solve this problem, we can use the concepts of trigonometry and related rates.

Let's denote the distance from the plane to the radar station as D(t), where t represents time. We want to find the rate at which D is changing with respect to time (dD/dt) one minute later.

Given:

The plane is flying with a constant speed of 360 km/h.

The plane passes over the radar station at an altitude of 1 km.

The plane is climbing at an angle of 30°.

We can visualize the situation as a right triangle, with the ground radar station at one vertex, the plane at another vertex, and the distance between them (D) as the hypotenuse. The altitude of the plane forms a vertical side, and the horizontal distance between the plane and the radar station forms the other side.

We can use the trigonometric relationship of sine to relate the altitude, angle, and hypotenuse:

sin(30°) = 1/D.

To find dD/dt, we can differentiate both sides of this equation with respect to time:

cos(30°) * d(30°)/dt = -1/D^2 * dD/dt.

Since the plane is flying with a constant speed, the rate of change of the angle (d(30°)/dt) is zero. Thus, the equation simplifies to:

cos(30°) * 0 = -1/D^2 * dD/dt.

We can substitute the known values:

cos(30°) = √3/2,

D = 1 km.

Therefore, we have:

√3/2 * 0 = -1/(1^2) * dD/dt.

Simplifying further:

0 = -1 * dD/dt.

This implies that the rate at which the distance from the plane to the radar station is changing is zero. In other words, the distance remains constant.

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Answer:

Well, I think that the answer is l-2l + l9l

Step-by-step explanation:

I think that it is l-2l + l9l. First off, an absolute value is the distance between a number and zero.

An absolute value is always positive. For example, l4l = 4 because it is always positive.

Opposites are numbers that are the same distance from zero in opposite directions. For example, -4 = 4.

On this case, the absolute value of (-2,3) is l-2l because in the coordinate graph, it is on Quadrant 2. What you need from the graph is the x-axis which is -2.  So you get, I-2I

And, the absolute value of (9,3) is I9I because in the coordinate graph, it is on Quadrant 1. Again, What you need from the graph is the x-axis, which is 9. So you get, I9I.

And if you are finding the distance between the two points, you need to add. So, there you have it, I-2I + I9I. Hopefully, it's right. :)

The average rate of change of the function graphed is -4.

What is average rate of change?

The average rate at which one item is changing in relation to another is known as the average rate of change.

The function y = f(x) is graphed.

We have to find the average rate of change of the function on the interval

2 ≤ x ≤ 4.

The average rate of change is defined as,

Average rate of change = \(\frac{f(b)-f(a)}{b-a} = \frac{f(4)-f(2)}{4-2}\)

From graph,

f(4) = -4, f(2) = 4

So,

Average rate of change = \(\frac{-4-4}{4-2} = \frac{-8}{2} = -4\).

Therefore, for the given graphed function, the average rate of change is, -4.

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Answer:

Step-by-step explanation:

Just like any shape and/or geometry in general they are very important. Regardless of what you will ultimately study they can be used in many normal life scenarios. Since everything in our world is a shape you may need to calculate if something may fit somewhere, or if a certain fence can be made a certain way. This also applies to parallelograms, maybe you are trying to build a cabinet that will go in the corner, but the corner is not a 90 degree angle, knowing parallelograms and geometry can help you design and build the best cabinet.

Note that the parameters of the graph a and graph b are given below.

Graph A - y=2(x-1)²

See graph attached.

Graph B - y = 1/2x² + 3

Vertex: The vertex of the function is (0, 3).

Axis of symmetry: The axis of symmetry is the vertical line passing through the vertex, which is x = 0.

Y-intercept: The y-intercept is the point where the graph intersects the y-axis. It is (0, 3).

Minimum or maximum: The coefficient of x² is positive, which means the parabola opens upwards, and therefore the function has a minimum value. The minimum value is 3.

Solutions: To find the solutions or roots of the quadratic equation, we need to set y or f(x) equal to zero and solve for x.

0 = 1/2 x² + 3

Subtracting 3 from both sides, we get:

-3 = 1/2 x²

Multiplying both sides by -2, we get:

6 = -x²

Taking the square root of both sides, we get:

x = ±√(-6)

Since the square root of a negative number is not a real number, the function has no real roots.

Minimum or maximum value: The minimum value of the function is 3.

Range: The range of the function is y ≥ 3, because the function has a minimum value of 3.

Domain: The domain of the function is all real numbers, because there are no restrictions on the values of x for which the function is defined.

Stretch/Shrink/Standard: The coefficient of x^2 is positive and less than 1, which means that the graph of the function is narrower than the graph of y = x². This is an example of a standard quadratic function that has been vertically compressed by a factor of 1/2.

See graph attached.


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The constant of proportionality is equal to 3/10.

In Mathematics and Geometry, a proportional relationship refers to a type of relationship that produces equivalent ratios and it can be modeled or represented by the following mathematical equation:

y = kx

Where:

Next, we would determine the constant of proportionality (k) by using various data points as follows:

Constant of proportionality, k = y/x

Constant of proportionality, k = 3/10 = 6/20 = 9/30

Constant of proportionality, k = 3/10.

Therefore, the required linear equation is given by;

y = kx

y = 3/10(x)

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The reasonable domain of the growth function is [0, 8], the y-intercept is 3 cm and the average rate of change of the function is 0.40 cm per month.

The growth function, also called the shatter coefficient or the shattering number, measures the richness of a set family. It is especially used in the context of statistical learning theory, where it measures the complexity of a hypothesis class.

A marine biologist is studying the growth of a particular species of fish, given by the exponential equation,

f(m) = \(3(1.09)^{m}\)

We need to find, reasonable domain to plot the growth function, the y-intercept of the graph of the function f(m) to represent and average rate of change of the function f(m) from m = 1 to m = 9,

f(m) = \(3(1.09)^{m}\)

m = 0

f(0) = 3(1.09)⁰  = 3 cm

The length of the fish was approximately 5.98 cm.

5.98 = \(3(1.09)^{m}\)

1.99 = \((1.09)^m\)

m = 8

Domain = [0, 8]

Reasonable domain to plot the growth function = [0, 8]

The y-intercept of the graph of the function f(m) represent initial length of fish = 3 cm

The average rate of change of the function f(m) from m = 2 to m = 8

m = 2, f(2) = 3(1.09)² = 3.56  cm

m = 8, f(8) = 3(1.09)⁸ = 5.97 cm

Change in 8-2 = 6 months = 5.97-3.56 = 2.41 cm

The rate of change of the function f(m) from m = 2 to 8

= (2.41/6)

= 0.40 cm per month

Hence, the reasonable domain of the growth function is [0, 8], the y-intercept is 3 cm and the average rate of change of the function is 0.40 cm per month.

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Answer: I(s,t) = {(6s, 5s+6t, 5t)| sER, tER }

Step-by-step explanation:

Given the data in the question;

A vector is in the span of V1 and V2 only if it is a linear combination.

of V1 and V2.

so 'V' is in the span if;

V = SV1 + tV2 [ S and t are real numbers ]

V =    [ 6si + 5sj ] + [ 6tj + 5tz]

V = 6s, 5s+6t, 5t

so

I(s,t) = {(6s, 5s+6t, 5t)| sER, tER }

Vector notation is indeed a commonly utilized notation in maths and physics for expressing vectors, which can be either Euclidean carriers or, more generally, members of a vector space, and the calculated value "\(\bold{I(s,t) = {(2s,7s+2t,7t)| sER, tER}}\)".

\(v = s v_1 + t v_2\) [ s and t are real numbers ]

\(v = [2si + 7sj ] + [ 2tj + 7tz]\\\\v = 2s,7s+2t,7t\\\\I(s,t) = {(2s,7s+2t,7t)| sER, tER}\)

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Answer:

That is a rectangle.

Step-by-step explanation:

We cannot say a circle because it is the shape that is being cross sectioned.

Answer:

The chance of 18.18 percent.

Step-by-step explanation:

9 red marbles

6 blue marbles

7 green marbles

11 yellow marbles

9+6+7+11=33

33 total marbles.

The chance of getting red marbles of the 33 is 27.27

The chance of getting blue marbles of the 33 is 18.18

The chance of getting green marbles of the 33 is 21.21

The chance of getting yellow marbles of the 33 is 33.33

Answer:

She need to divide 24 by 2 to get 12. She can fill 12 tortillas

Step-by-step explanation:

We can claim that after answering the above question, the So, logarithm \(log4 (0.5^(1/2)) =-0.0752\)

The logarithm is a power's reciprocal in mathematics. Accordingly, the exponent by which b must be raised to obtain a number x equals the logarithm of that number in base b. For instance, since 1000 = 103, its base-10 logarithm is 3, or log10 = 3. As an illustration, the base 10 logarithm of 10 is 2, while the square of 10 is 100. Log 100 = 2. To answer a question like, For example, how many times must a base of 10 be multiplied by itself to achieve 1,000, a logarithm (or log) is the mathematical term utilized. The solution is 3 (1,000 = 10 10 10).

Using the following property of logarithms:

\(log_a (b^c) = c * log_a (b)\\log4 (0.5^(1/2))\\(1/2) * log4 (0.5)\\log4 (0.5) = log (0.5) / log (4)\\log (0.5) ≈ -0.3010\\log (4) = 2\)

Therefore,

\(log4 (0.5) ≈ -0.3010 / 2 ≈ -0.1505\\(1/2) * log4 (0.5) ≈ (1/2) * (-0.1505) ≈ -0.0752\\\)

So, \(log4 (0.5^(1/2)) =-0.0752\)

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Answer:

4/15

Step-by-step explanation:

2/5 drive

1/3 bus

and rest walk

fraction of those who walk is 1-(2/5+1/3)

2/5+1/3=(6+5)/15=11/15

15/15-11/15=4/15

Answer:

WHat is it :(

Step-by-step explanation:

Answer:

Easy Question: I/pt=r

Step-by-step explanation:

You take the equation i=prt and you solve it out.

You divide the half "prt" by pt like this: prt/pt

You also do that to the other side "I"

You are left with I/pt=r and there it is!!

Answer:

x=3.4 and x=2.5

Step-by-step explanation:

i took an exam and got it right

Step-by-step explanation:

19. Kim's Path = √240² + 100²

= √57600 + 10000

= √67600

= 260 ft.

Answer:

17 question: we are going to use Pythagorean Theorem :

33^2 + 56^2 = x^2

1089+3165 = x^2

4225=x^2

x=-65

x=65

the answer is c)65

18 question i dont know :((

19 question : we are going to use same method as the first question : the answer is 260 ft

that's all that i can do for you

Step-by-step explanation:

hope this helps you :)

Answer:

625

Step-by-step explanation:

Step-by-step explanation:

√z is defined only when z >= 0

Therefore √x - 1 is defined only when (x - 1) >= 0, x >= 1.

The only graph that shows the domain x >= 1 is graph Y.

Answer:

73.72 units²

Step-by-step explanation:

Area of the shaded region = Area if the rectangle - area of the semicircle

Area of the rectangle = length*width

Length = 10 units

Width = 8 units

Area of rectangle = 10*8 = 80 units²

Area of semicircle = ½(πr²)

radius (r) = 8/2 = 4 units

π = 3.14

Area of semicircle = ½(3.14*4) = 3.14*2 = 6.28 units²

Area of the shaded region = 80 - 6.28 = 73.72 units²

Answer: 54.88

Step-by-step explanation:​

The shape shown is a circle that overlaps a rectangle. The shaded region is a rectangle with half a circle cut out. To find the area of the shaded region, we can find the area of the rectangle and the area of the overlapping semi-circle and subtract them. The rectangle has a height of 10. The width of the rectangle is the diameter of the circle, 8. First, find the area of the rectangle:

AAA=length×width=10⋅8=80

To find the area of the circle, we need to find the radius. The radius is one half the diameter, therefore r=4. Use the value of r to solve for the area:

AAA=πr2=3.14⋅(42)=50.24

Now we can subtract half the area of the circle from the area of the rectangle:

Area of rectangle−Area of half circle=Area shaded region

80−50.242

A=54.88

So the area of the shaded region is 54.88.

Answer:

The exponent of y is 1

Step-by-step explanation:

Given

\(6xy^2 - 5x^{[]}y^{[]} + 9x^{[]}\)

\(degree = 3\)

Required

The exponent of y (second term)

Since the polynomial has a degree of 3, the exponents of y will decrease from left to right (i.e. 2,1,0) while x will increase from left to right (i.e. 1,2,3)

So, we have:

\(6xy^2 - 5x^{[]}y^{[]} + 9x^{[]} = 6xy^2 - 5x^{[2]}y^{[1]} + 9x^{[3]}\)

Remove square brackets

\(6xy^2 - 5x^{[]}y^{[]} + 9x^{[]} = 6xy^2 - 5x^2y + 9x^3\)

The second term is:

\(T_2 =5x^2y\)

The exponent of y is 1

The graph which represents the polar curve r = -4 sin ( 3θ ) is plotted

Polar coordinates describe the position of a point P in the plane by its separation from the origin, r, and the angle formed between the positive x-axis and the line segment leading to P.

To graph the polar curve, we make use of the following representations:

r represents the y-axis

θ represents the x-axis

Polar coordinates can also be extended into three dimensions using the coordinates (ρ, φ, θ), where ρ is the distance from the pole, φ is the angle from the z-axis ( called the co-latitude or zenith and measured from 0 to 180° ) and θ is the angle from the x-axis ( as in the polar coordinates ).

Given data ,

Let the polar curve be represented as A

Now , the polar coordinates is given as

r = -4 sin ( 3θ )

And , To graph the polar curve, we make use of the following representations:

r represents the y-axis

θ represents the x-axis

So , on simplifying , we get

The graph which represents the polar curve r = -4 sin ( 3θ ) is plotted

Hence , the polar curve is r = -4 sin ( 3θ )

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Answer:

D

Step-by-step explanation:

The solution to the system of equations is x = 1 and y = -3.

To solve the system of equations using the substitution or elimination method, let's start with the substitution method.

Given equations:

y = 4x - 7

4x + 2y = -2

We'll solve equation 1) for y and substitute it into equation 2):

Substituting y from equation 1) into equation 2):

4x + 2(4x - 7) = -2

4x + 8x - 14 = -2

12x - 14 = -2

Now, we'll solve this equation for x:

12x = -2 + 14

12x = 12

x = 12/12

x = 1

Now that we have the value of x, we can substitute it back into equation 1) to find y:

y = 4(1) - 7

y = 4 - 7

y = -3

Therefore, the solution to the system of equations is x = 1 and y = -3.

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Answer:

f=1               e=2          d=3

Step-by-step explanation:

Answer:

1. ..................

2. ,,,,,,,,,,,,,,,,,,

3. _______

Step-by-step explanation:

I don't know