The formula for the nth term of an arithmetic sequence can be found using the formula a Subscript n Baseline = a Subscript 1 Baseline + (n minus 1) d. Which of the following is equivalent to this equation?

[tex]~~~~~~~~y = 1- \sqrt{ 1- \dfrac 2x}\\\\\\\implies \sqrt{ 1- \dfrac 2x} = 1 - y\\\\\\\implies 1 - \dfrac 2x = (1 -y)^2~~~~~~~~~~~~~;[\text{Square on both sides}]\\\\\\\implies \dfrac 2x = 1-(1-y)^2\\\\\\\implies \dfrac{1}{x} = \dfrac{1-(1-2y+y^2)}{2}\\\\\\\implies x = \dfrac{2}{1-1+2y-y^2}\\\\\\\implies x = \dfrac{2}{2y-y^2}\\\\\\\implies x = -\dfrac{2}{y(y-2)}~~~~~~~~~~~~~~~~~;[y\neq 0,~ y \neq 2]\\[/tex]

Step-by-step explanation:

it is just a line covering all values smaller than -8 (that means left of -8).

so, it is a line starting at -8 and going all the way to the left (to the arrow on the left). and you make an empty (hollow) dot at -8, because the value -8 is not included (otherwise it would be p <= -8, and it would be a filled dot at -8).

Answer: -329 sorry if i'm not right

Answer:

  6 h

Step-by-step explanation:

The relation between time, speed, and distance is ...

  time = distance / speed

The total time for the two segments of her ride will be the sum of the times for each of the segments.

__

  t1 = (9 miles)/(3 mi/h) = 3 h

After riding 9 miles of the 15-mile distance, Dana had 15 -9 = 6 miles to go.

  t2 = (6 miles)/(2 mi/h) = 3 h

The total time required for the distance of 15 miles is ...

  t1 +t2 = (3 h) +(3 h) = 6 h

It took 6 hours for Dana to cover the distance.

Answer:

c.

Step-by-step explanation:

because on you have to add 4 to the number above. so 3+4 equals 7 so you move 4 spaces to the right on the number line to get you 7. so C is the correct answer

Answer:

Area: 1,200 square centimeters. Perimeter: 140 centimeters.

Step-by-step explanation:

Since you have to multiply the length and width in order to find the area, multiply 30 and 40 together and you can find 1,200. Next, to find the perimeter you have to add all the lengths of the rectangular swimming pool, which will result in 140 centimeters.

Answer:

.66 cu. meters

Step-by-step explanation:

volume for cone is V=1/3 x TT x r^2 x height

TT (pi) is 3.14

radius is 1/2 of diameter (1/2 x 1.5 =  .75 )

height is 1.5 x radius (1.5 x .75 = 1.125)

V= 1/3 x 3.14 x .75^2 x 1.125

V= .66  cu. meters

The total change in the amount of water in the pool is 288 gallons.

Volume is a scalar quantity expressing the amount of three-dimensional space enclosed by a closed surface.

Here, Rate of water pumped into her pool = 6 gallons / minute.

          Total Duration = 48 minutes

Total amount of water = Rate X Time

                                     = 6 X 48

                                     = 288 gallons

Thus, the total change in the amount of water in the pool is 288 gallons.

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Reason:

Start at the y intercept (0,4) which is where the red line crosses the y axis.

Then move up 2 units, and to the right 1 unit to arrive at (1, 6) which is another point on this red line.

The motion of "up 2, right 1" means:

Feel free to use any other two points you prefer and you should get the same result. For instance, you could have started at the x intercept (-2,0) and did the "up 2, right 1" motion to arrive at (-1, 2).

The water consumption based on the information for three months will be 22267m³.

The total water consumption for the three months will be:

= 7219 + 7390 + 7658

= 22267m³

In conclusion, the information simply wants you to add the values of the water given.

Therefore, the water consumption based on the information for three months will be 22267m³.

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Answer:

The horizontal cross-sections of the prisms at the same height must have the same area.

Step-by-step explanation:

A pyramid and a cone are both 12 centimeters tall and have the same volume.... What is the volume?

Volume is the quantification of the three-dimensional space a substance occupies.

We have to determine the true statement, and it is

The horizontal cross-sections of the prisms at the same height must have the same area cone and given pyramid are looks like same in two-dimensional.

The horizontal cross-sections of the prisms at the same height must have the same area thus the correct option is A.

A pyramid and a cone are both 12 centimeters tall and have the same volume, we know that Volume is the quantification of the three-dimensional space a substance occupies.

We have to determine the true statement, and it is the horizontal cross-sections of the prisms at the same height must have the same area cone and given pyramid are looks like same in two-dimensional.

If we cross-section the figures at the same height, it won't get the same shape but we should get the same area, as the area of the cross-section will be proportional to the base area, and the base area of both figures are the same.

Thus, the correct option is A.

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Answer:

Hi,

Step-by-step explanation:

x>=0

y>=0

x+y-5<=0 line passing through (0,5)  and (5,0) with (0,0) in minus region

2x-y-8<=0 line passing trough (0,-8) and (4,0) with (0,0) in minus region

Answer C

Answer:

C: The average of the data is a closer to the least value than it is to the greatest value

Answer:

Step-by-step explanation:

mean is found by adding the numbers and dividing the sum by the number while the median is the middle value of the list ordered in an ascending order

[tex]\text{Let,}\\\\~~~~~~~a^x =b^y = c^z = k\\\\\text{So,}\\ \\a = k^{\dfrac 1x}\\\\b=k^{\tfrac 1y}\\\\\ c = k^{\tfrac1z}\\\\\text{Now, given that,}\\\\~~~~~~~~~b^2 = ac\\\\\implies \left( k^\tfrac 1y \right)^2 = k^{\tfrac 1x} \cdot k^{\tfrac 1z}\\\\\implies k^{\tfrac 2y} = k^{\tfrac 1x + \tfrac 1z} ~~~~~~~~~~;[a^m \cdot a^n = a^{m+n}]\\\\\implies \dfrac 2y = \dfrac 1x + \dfrac 1z\\\\\implies \dfrac 1x + \dfrac 1z = \dfrac 2y \\\\\text{Proved.}[/tex]

(2x−3)(x+3)

HAVE A NICE DAY!

Answer:

x=3/2 or x=-3

Step-by-step explanation:

first off equate the equation to zero

2x²+3x-9=0

then using factorisation method multiply 2 and -9 to get -18.

factors of -18 include +6 and -3

2x²+6x-3x-9=0

then factorise it

2x(x+3)-3(x+3)

(2x-3)(x+3)=0

2x=3 x+3=0

x=3/2 or -3

If we reflect across the y-axis and then reflect again across the y-axis , it will give result an image that maps onto itself , Option B is the right answer.

The reflection of the point (x,y) across the x-axis is the point (x,-y), across the y-axis is the point (-x,y). , across the line is the point (y, x)

The 90 degree counterclockwise rotation of a point (x, y) is the point (-y, x)

The 180 degree counterclockwise rotation of a point (x, y) is the point (-x, -y)

The 270 degree clockwise rotation of a point (x, y) is the point (-y, x)

Therefore on application of these rules

For Case A

The point will be (-y , x)

For Case B

The point will be (x,y)

Therefore Option B is the answer.

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Answer:

8n is the same as 8 times a number.

That means...

Continuation:

[tex]8 * n = 128[/tex]

[tex]128 \div 8 = n[/tex]

[tex]128 \div 8 = 16[/tex]

Therefore, n is 16.

Answer:

42

Step-by-step explanation:

6 times 7 is 42

The true statement about the angles in the figure is m∠1 + m∠8 = 90°. The correct option is the last option m∠1 + m∠8 = 90°

From the question, we are to determine the statement that is true about the angles in the given figure

In the given diagram, we can observe that

m∠3 + m∠8 + m∠9 + m∠10 = 180° (Sum of angles in a triangle)

Also,

m∠3 = m∠1 (Vertically opposite angles)

m∠9 + m∠10 = 90° (Vertically opposite angles)

∴ m∠1 + m∠8 + 90° = 180°

m∠1 + m∠8 = 90°

Hence, the true statement about the angles in the figure is m∠1 + m∠8 = 90°. The correct option is the last option m∠1 + m∠8 = 90°

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Part A: The amount of ice cream increases as the temperature increases. Part B: the slope is 2 and the y-intercept will be 5.

Its slope would be:

[tex]m = \dfrac{y-q}{x-p}[/tex]

Part A: The relationship between the temperature of the city and the number of ice cream cones sold.

From the graph, the dots on the graph increase in the up-right direction.

Thus, The amount of ice cream increases as the temperature increases.

Part B: The line of best fit

First, if we draw a line through the points

we select any 2 points on the line:

( p,q) and (x,y) as (15, 35) and (0, 5).

The slope (m) is:

[tex]m = \dfrac{y-q}{x-p}[/tex]

[tex]m = \dfrac{5 - 35}{0-15}\\\\m = 2[/tex]

So, the line of best fit is:

y = mx + c

y = 2(x - 0) + 5

y = 2x + 5

The y-intercept will be when x = 0

y = 2x + 5

y = 0 + 5

y = 5

Thus, the slope is 2 and the y-intercept will be 5.

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The equation of direct variation given that y varies directly with x.

y is 15 when x is 11 will be [tex]y = \dfrac{15}{11} x[/tex].

The proportional relationship between x and y can be written symbolically as

[tex]x \propto y[/tex]

That middle sign is called the sign of proportionality.

Variation: Direct from y to x:

[tex]x \propto y[/tex]

y = 15, x= 11

Write the equation

[tex]x \propto y[/tex]

Express as an equation

[tex]y = kx[/tex]

Where k is the constant of variation

Substitute

y = kx

15 = 11k

Solve for k

k = 15/11

Substitute  in [tex]y = kx[/tex]

[tex]y = \dfrac{15}{11} x[/tex]

Thus, the equation of direct variation given that y varies directly with x.

y is 15 when x is 11 will be [tex]y = \dfrac{15}{11} x[/tex].

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To solve this question, let's find the surface area of the entire pie and then divide it by 6 for each slice.

The area of a circle is pi*r^2. We are given the diameter, so divide that by 2 to get the radius.



Now that you have the area, divide by 6. That is the area of each slice. The problem asks for the area of 2 slices though, so multiply that by 2.

There are enough oysters to filter the whole Chesapeake Bay in one day.

The numbers can be affected by the water temperature and the cleanliness of the water.

The total number of water that can be filtered by the oysters is a function of the total amount of oysters in the bay and the quantity of water they can filter.

Total amount of water they can filter = oysters per acre x total acre x total gallons they can filter each day

(2.9 x[tex]10^{6}[/tex]) x (7.5 x [tex]10^{5}[/tex]) x (5 x 10) = 1.0875 x [tex]10^{14}[/tex]

The gallons of water in the bay in standard form = 1.8 x [tex]10^{13}[/tex]

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Answer:

R'(2,4)

Step-by-step explanation:

When doing translations you subtract or add within the coordinates like a normal problem.

If it helps you, write it as seperate equations like:

1-1 and 5-1

Hope that helps ✓

A correct sequence of similarity transformations that shows AABC~ ADEF is that D. a counterclockwise rotation of 90 degrees about point E followed by dilation with a scale factor of 2 centered at point E.

A similarity transformation refers to a geometric similarity, or to a matrix transformation that results in a similarity.

In this case, the correct sequence of similarity transformations that shows AABC~ ADEF is that a counterclockwise rotation of 90 degrees about point E followed by dilation with a scale factor of 2 centered at point E.

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Both circle C and circle E are similar to each other but the radii are different.

It is the center of an equidistant point drawn from the center. The radius of a circle is the distance between the center and the circumference.

Circle C is shown with a center at (negative 3, 1) and a radius of 4.

Circle E is shown with a center of (4, 9) and a radius of 3.

There is only one parameter in the circle which is radius or diameter.

Then both circle C and circle E are similar to each other but the radii are different.

As shown in the graph.

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Answer:

Answer

4.9/5

345

author link

audreyburkett12

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Assuming the time changes at a constant rate, the equation for this is linear (so has the equation y=mx +c)

8am = -2

9am = -0.5

10am = 1.0

11am = 2.5

12pm = 4

m = change in each value or the slope , for this it is m=1.5

c = the y intercept, we find this by: when x=8 y must = 1.5 , which it isn't , y has to = -2 . So c = -3.5

The equation then is: y= 1.5*x - 3.5

The gradient/slope/m value is 1.5. The answer is 1.5

Answer:

C) 56

Step-by-step explanation:

. What is the length of BC¯¯?

2. What is the length of AC¯¯?

3. What is the length of AD