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3 years ago

Which of the sequences is an arithmetic sequence?

Mathematics

2 answers:

Lady bird [3.3K]3 years ago

6 0

Answer:

The sequence -2, -8, -14, -20, -26 is an A.P

Option A is correct

Step-by-step explanation:

Given the sequence we have to choose the option which is an arithmetic sequence.

In A.P, the common difference i.e d remains the same

$d=x_2-x_1=x_3-x_2$

Option A: -2, -8, -14, -20, -26, ...

$x_2-x_1=-14-(-8)=-14+8=-6$

$x_3-x_2=-20-(-14)=-20+14=-6$

which is same hence A.P

Option B: -48, -24, -12, -6, -3,...

$x_2-x_1=-24-(-48)=-24+48=24$

$x_3-x_2=-12-(-24)=-12+24=-12$

which is not same hence not an A.P

Option C: -2, 6, -10, 14, -18,...

$x_2-x_1=6-(-2)=6+2=8$

$x_3-x_2=-10-6=-16$

which is NOT same hence not an A.P

Option D: 1, 6, 12, 18, 24,..

$x_2-x_1=6-1=5$

$x_3-x_2=12-6=6$

which is not same hence not an A.P

Rina8888 [55]3 years ago

3 0

Sequence A is the only one with a common difference (-6).

_____

Sequence D comes close, but its first difference is 5 while the others are 6. Hence there is no common difference.

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A stunt driver wants to make his car jump over 8 cars parked side by side below a horizontal ramp. The vertical height of the ra

mr Goodwill [35]

Answer:

v=26.41 m/s

Step-by-step explanation:

From the Newtons laws of motions, we sew that x= (2v₁²sin∅os∅)/g where x is the horizontal distance v is the initial speed and ∅ is the launch angle.

From trigonometry we see that 2 sin∅cos∅=sin 2∅

Therefore, x=(v²sin2∅)/g

x=22m

∅=9°

g=9.8m/s²

22m=v²×sin(2×9)/(9.8m/s²)

v²=(22×9.8)/(sin 18)

v²=697.696

v=√697.696

v=26.41 m/s

3 0

4 years ago

2 - 3d = 4d - 19 Answer and show steps

defon

2 - 3d = 4d - 19

Add the opposite to both sides to get the variable on the left side only.

2 - 3d = 4d - 19

-4d -4d

2 - 7d = - 19

Then get the terms w/o variables on the right,

2 - 7d = - 19

-2 -2

-7d = -21

Then divide by the number paired with the variable.

--7d = -21

----- ----- ; d = 3

-7 -7

Final answer = 3

Hope I helped :)

3 0

3 years ago

Which expression is equivalent to 24? O 2√3 23√/3 O 2√6 O 23√√6

vredina [299]

$24^{1/3}=\sqrt[3]{24}=\sqrt[3]{8 \cdot 3}=\sqrt[3]{8}\sqrt[3]{3}=\boxed{2\sqrt[3]{3}}$

5 0

2 years ago

In the following figure, the square ABCD is inscribed in the circle centered at point P. What is the area of the circle?

Ainat [17]

Answer:

$A_{Circle} \approx 39.24\: units^2$

Step-by-step explanation:

Square ABCD is inscribed in a circle with center P such that BC = 5 units.

BD will be diagonal of the square as well as diameter of the circle.

$BD = BC\times\sqrt 2$

$\implies BD = 5\sqrt 2$

-> Diameter of the circle $(d) = 5\sqrt 2$

-> Radius of the circle $(r) = 2.5\sqrt 2=3.535\: units$

$A_{Circle} =\pi(r)^2$

$\implies A_{Circle} =3.14(3.535)^2$

$\implies A_{Circle} =39.2381465$

$\implies A_{Circle} \approx 39.24\: units^2$

8 0

3 years ago

Kari's paper cup holds 6 fluid ounces. If one ounce is equivalent to 29.6 milliliters, how many milliliters does her paper cup h

Degger [83]

Answer:

Equivalent measurements: teaspoon, ounce, pint, pound

You will find a table of equivalent measurements in the back of many cookbooks:

1 tablespoon = 3 teaspoons

1 cup = 16 tablespoon = 8 ounces

1/4 cup = 4 tablespoons

1/3 cup = 5 tablespoons plus 1 teaspoon

1 pint = 2 cups = 16 ounces

1 quart = 4 cups (2 pints) = 32 ounces

1 gallon = 4 quarts

1 pound = 16 ounces

1/2 pound = 8 ounces

1/4 pound = 4 ounces

Note that a pint is 16 ounces of volume, while a pound is 16 ounces of weight. The popular rhyme "A pint's a pound, the world around" can help you remember this, but keep in mind that they're not really equivalent.

Doubling a recipe can be easy (just put in two of each measurement), but what if you need to divide a recipe in half? Here are some measurements that may help:

Measurement 1/2 Measurement

1/8 teaspoon just a dash

1 tablespoon 1 1/2 teaspoons

1/4 cup 2 tablespoons

1/3 cup 2 tablespoons + 2 teaspoons

3/4 cup 6 tablespoons

Step-by-step explanation:

7 0

3 years ago