Write an explicit and a recursive formula for each arithmetic sequence. 17,8,-1, . . . . .

Answer:

1: P = -3

2: X = -60

3: N = 5

Step-by-step explanation:

Ok, for number one you are going to add 4 on the -4 canceling that out, and adding 4 on the -7 making that -3.

Number 2 you times 10 on the x/10 to cancel out the 10 (making it x) then you do -6 times 10, and then you get -60

Last one is a little tricky here's the equations I used to get the last one

-3 x 8n = -24x

New equation: 4-24x=-104

                        +4         +  4

___________________________

                        -24x = -100

                         ___     ___

                         -24      -24

                                                   _

so the answer would be x = 5

The toy rocket will take a time of 8.999 seconds to hit the ground.

The height of the rocket (h), in meters, in terms of time (t), in seconds, is defined by a quadratic equation. In this question we must determine the time needed for the rocket to hit the ground, that is, a time t greater than zero such that the height is zero. Now we proceed to solve the polynomial:

- 4.9 · t² + 43.4 · t + 6.3 = 0

- 4.9 · (t² - 8.857 · t - 1.286) = 0

- 4.9 · (t - 8.999) · (t + 0.143) = 0

Only the first root offers a realistic value as time is a whole number. Hence, the toy rocket will take a time of 8.999 seconds to hit the ground.

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Answer:

2.5t

Step-by-step explanation:

Let the man be

x

feet away from the street light, and his shadow length be

y

, Let the tip of the shadow be

l

feet away from the light such that

l

=

x

+

y

and we are given that

d

x

d

t

=

2

By similar triangles:

y

6

=

x

+

y

30

∴

30

y

=

6

(

x

+

y

)

∴

30

y

=

6

x

+

6

y

∴

30

y

−

6

y

=

6

x

∴

24

y

=

6

x

∴

y

=

1

4

x

Now,

l

=

x

+

y

⇒

l

=

x

+

1

4

x

∴

l

=

5

4

x

Differentiating wrt

x

gives;

d

l

d

x

=

5

4

And by the chain rule we have:

d

l

d

t

=

d

l

d

x

d

x

d

t

∴

d

l

d

t

=

5

4

×

2

∴

d

l

d

t

=

2.5

feet/sec

Answer:

what

Step-by-step explanation:

Answer:

Step-by-step explanation:

18. Supplementary angles add up to 180°therefore

∠W+∠V=180°

∠W+49°=180°

∠W=180°-49°

∠W=131°

19.Complementary angles are angles that add up to 360°

∠2+∠3=90°

∠2+56°=90°

∠2=90°-56°

∠2=34°

Vertical angles are equal therefore this tells us that ∠1 and ∠2 are equal

∠1=∠2

∴∠1=34°

20. Angles which are in a linear pair add up to 180°(supplementary)

Mathematically what the statement is sayin is :

∠1+∠2=180°

and ∠1=5(∠2)-18°

therefore we can plug in ∠1=5(∠2)-18° in ∠1+∠2=180°

(5(∠2)-18°)+∠2=180°

5(∠2)+∠2=180°+18°

6(∠2)=192°

[tex]\frac{6 < 2}{6} =\frac{198}{6} \\ < 2=33[/tex]

∠1=5(33°)-18°

∠1=165°-18°

∠1=147°

If Martina has 16 cars available to rent, and if c is the number of cars she would have left after renting r of them, then the equation relating c to r will be c = 16 - r, and the number of cars she would have been left with after renting 14 of them is calculated to be 2.

An algebraic expression is a type of expression consisting of both numerals and letters.

If Martina has a total of 16 cars available to rent, then the equation or algebraic expression relating c to r is,

c = total number of cars available to rent - r

c = 16 - r

After renting 14 of the total cars available, then the number of cars left can be calculated using this equation,

c = 16 - r

c = 16 - 14

c = 2

Thus, the number of cars she would have been left with is calculated to be 2.

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Answer:

Well 40% of 15 is 6

Step-by-step explanation:

It depends on how many shots it takes to win a prize

The distance between points F and G is 15 units.

The length of the line segment connecting two points on a plane is known as the distance between the points. The formula for distance between two points ([tex]x_{1}[/tex],[tex]x_{2}[/tex]) and ([tex]y_{1}[/tex],[tex]y_{2}[/tex]) is given by

distance between two points =[tex]\sqrt{(x_{1}-x_{2})^2+(y_{1}-y_{2})^2 } }[/tex]

The equation can be used to calculate the distance between any two locations on an x-y plane or coordinate plane.

The point F is (-9,14) and point G is (1,-19)

distance between F and G

=[tex]\sqrt{(x_{1}-x_{2})^2+(y_{1}-y_{2})^2 } }[/tex]

=[tex]\sqrt{(-9-1)^2+(-14-(-19))^2 } }[/tex]

=[tex]\sqrt{(-9-1)^2+(-14+19)^2 } }[/tex]

=[tex]\sqrt{(-10)^2+(5)^2 } }[/tex]

=[tex]\sqrt{100+25}[/tex]

=[tex]\sqrt{125}[/tex]

=15 units.

Distance between point F and G is 15 units.

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The factored form of the expression 16x² + 9y² over the complex numbers is; (4x + 3iy)(4x − 3iy)

We want to find the factored form of the expression 16x² + 9y² over the complex numbers.

We can rewrite the given expression 16x² + 9y² as perfect squares;

= (4x)² + (3y)²

Now, from using the difference of squares formula, we know that;

a² - b² = (a + b)(a - b)

Thus;

(4x)² + (3y)² = (4x)² - (√-9)²y²) can be expressed as;

(4x + 3iy)(4x − 3iy)

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Answer:

.002 or

2x10^-3

Step-by-step explanation:

make sure the exponents match

8 x 10^-3 =

.008 × 10^-3

(.008 × 10^-6) ÷ (4 x 10^-6)

10^-6 cancels out

.008 ÷ 4 = .002

or

2x10^-3

In linear equation, a = (n+p)/m is equation for the indicated variable.

What in mathematics is a linear equation?

In terms of algebra, writing "am" is the same as writing "a*m" or "a times m"

To undo the multiplication, we use division. We will divide both sides by m to get 'a' all by itself on the left side

So...

am = n+p

a*m = n+p

(a*m)/m = (n+p)/m .... divide both sides by m

a = (n+p)/m ... notice how the 'm's cancel out when we divide on the left side

a = (n+p)/m

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Using it's formula, the average rates of change are given as follows:

a) 30 meters per second.

b) -10 meters per second.

The average rate of change of a function is given by the change in the output divided by the change in the input. Hence, over an interval [a,b], the rate is given by the following equation:

[tex]r = \frac{f(b) - f(a)}{b - a}[/tex]

For item a, taking the data from the table, we have that:

Hence the rate is given as follows:

r = (138 - 0)/(4.6 - 0) = 30 meters per second.

For item b, taking the data from the table, we have that:

Hence the rate is given as follows:

r = (0 - 23)/(11.5 - 9.2) = -10 meters per second.

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How many terms are there in the surface area formula below?2(lw + wh + hl) 3 terms.

What are the three terms ?

The total surface area of a cuboid= 2(lw + wh + hl)

Here, w= width, h= height, l= length

Thus, there are 3 terms in the surface area formula.

What is a total surface area?

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According to the solving the slope of the ramp = 0.175.

shows the steepness of an inclination The slope is just the ratio of the rise over the run, or the change there in vertical out over change in the horizontal, as seen below:

find the coordinates of two points on the line. Calculate the difference in y-coordinates between these two places (rise). Determine the x-coordinate difference between these two places (run). Divide the y-coordinate difference by the x-coordinate difference (rise/run or slope).

The given values are indeed the heights of a two beams and indeed the distance between them, which are:

Y₁ = 3.5ft

Y₂ = 10.5 ft

ΔX = 40 ft

To get the slope of both the ramp, enter the following values into the slope formula:

m = (Y₂ - Y₁)/ΔX

  = (10.5 - 3.5)/40

  = 7/40

= 0.175

According to the solving the slope of the ramp = 0.175

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The seventh term of the given geometric progression is: 729.

A geometric progression, sometimes referred to as a geometric sequence in mathematics, is a series of non-zero numbers where each term following the first is obtained by multiplying the preceding one by a constant, non-zero value known as the common ratio.

Now,

Given GP: 1, -3, 9, .....

Here, a₁ = 1

a₂ = a₁ (r)

=> 3 = 1 (r)

=> r = 3

Thus, a₇ = a₁ (r⁷⁻¹) = 1 (3⁶) = 729.

Hence, The seventh term of the given geometric progression is: 729.

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Answer:

190

Step-by-step explanation:

Similar to the handshake problem, if every student must talk with another person, each student will talk to 19 other students. However, a conversation consists of two people, so we must divide the number of ways we can rearrange the two people. Therefore, our answer is 190

According to the centroid theorem, the triangle's centroid is located 2/3 of the way between the vertex and the midpoint of the sides.

The coordinates of the centroid (P) are (3 + 2, 6) or (5, 6).

The centroid method is an agglomerative clustering method in which the similarities (or dissimilarities) between clusters are defined in terms of the centroids (i.e., the multidimensional means) of the clusters on the clustering variables.

According to the centroid theorem, the triangle's centroid is located 2/3 of the way between the vertex and the midpoint of the sides.

The triangle has a balance point at the centroid.

Find the centroid of the triangular coffee table.

Use the centroid formula [tex](x_1+x_2+x_3/3, y_1+y_2+y_3/3)[/tex]

The centroid of the triangle is (3 + 5 + 7/3, 6 + 2 + 10/3) or(5, 6).

Let the points be A(3, 6), B(5, 2), and C(7, 10). The midpoint D of BC is  (5 + 7/2, 2 +10/2) OR (6, 6).

Note that AD is a line that connects the vertex A and D, the midpoint of BC. The distance from D(6, 6) to A(3, 6) is 6 – 3 or 3 units.

If P is the centroid of the triangle ABC, then So, the centroid is 2/3(3) or 2 units to the right of A.

The coordinates of the centroid (P) are (3 + 2, 6) or (5, 6).

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x = 73 is the value of x.

To find the value of x:

So,

Then rounding to the nearest tenths gives x = 73.

Therefore, x = 73 is the value of x.

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The three interior angles of a triangle have a sum of 180°. If two of the three angles are complementary, then the triangle is right. The correct option is B

A triangle is a polygon that has three angles and three sides. The sum of angles in a triangle is 180 degrees.

Types of triangles are isosceles, scalene and equilateral triangles. Two angles are said to be complementary if their sum is 90 degrees.

The three interior angles of a triangle have a sum of 180°. If two of the three angles are complementary, then the triangle is right.

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exact form:

decimal form:

mixed number form:

Answer:

-11/3

Step-by-step explanation:

Convert −4 5/9 to improper fraction -41/9 and do the math.

-41/9 + 8/9

-33/9

-11/3

The sequence partially defined by the recursive formula f(n+1) = f(n)+2.5, n≥1 is -10, -7.5, -5, -2.5, …

Given recursive formula is f(n+1) = f(n)+2.5, n ≥ 1.

So the first term of the sequence is f(1) since n ≥ 1.

Given options for the sequences are:

a. 2.5, 6.25, 15.625, 39.0625, …

b. 2.5, 5, 10, 20

c. -10, -7.5, -5, -2.5, …

d. -10, -25, 62.5, 156.25

We compare the first term of each sequence with the given recursive formula.

a.  2.5, 6.25, 15.625, 39.0625, …

In this sequence, the first term, f(1) = 2.5

Using recursive formula, f(2) = f(1) + 2.5 = 2.5 +2.5 = 5.

But the second term in the given sequence is 6.25. So the recursive formula does not match with this sequence.

b.2.5, 5, 10, 20

Here, f(1) = 2.5

By the recursive formula, f(2) = f(1) + 2.5 = 5

f(3) = f(2) + 2.5 = 5 +2.5 = 7.5, which does not match with the third term of the given sequence. So this sequence is not defined by the recursive formula.

c. -10, -7.5, -5, -2.5, …

Here, f(1) = -10

Using recursive formula, f(2) = f(1) + 2.5 = -10 + 2.5 = -7.5

f(3) = f(2) + 2.5 = -7.5 +2.5 = -5

f(4) = f(3) +2.5 = -5 +2.5 = -2.5

So far the recursive formula matches with the given sequence. So the sequence defined partially by the recursive formula, f(n+1) = f(n)+2.5, n ≥ 1 is -10, -7.5, -5, -2.5, …

d.  -10, -25, 62.5, 156.25

Here the first term is, f(1) = -10.

But the sequence which matches with the recursive formula and starting with -10 is option c. So this sequence does not need to be verified.

The question is incomplete. Find out the complete question below:

Which sequence could be partially defined by the recursive formula f(n+1) = f(n)+2.5, n≥1 ?

a. 2.5, 6.25, 15.625, 39.0625, …

b. 2.5, 5, 10, 20

c. -10, -7.5, -5, -2.5, …

d. -10, -25, 62.5, 156.25

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2 and 18 are the two pairs of whole numbers with a geometric mean that is also a whole number.

The geometric mean is defined as the nth root of the product of n numbers, which means for a set of numbers x1, x2, ..., xn. The Geometric Mean is a special type of average where we multiply the numbers together and then take a square root (for two numbers), cube root (for three numbers) etc.

For example, we multiply them: 2 × 18 = 36

Then (as there are two numbers) take the square root: √36 = 6

Conditions: The square roots of the product of the pair of numbers must be whole-number. These two conditions must be met to have an exact geometric mean

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Answer:

Choice 4

Step-by-step explanation:

A one to one function has every domain with only one range as their individual output. Choice 4 has the output 6 mentioned twice for both 2 and 4 so therefore it's not a one to one function because the range 6 has two outputs 2 and 4.

Answer:

Step-by-step explanation:

x=5

If Jim is running a race against his best friend Ryan and Jim runs at a rate of 18 miles in 3 hours while Ryan runs at a rate of 11 miles in 2 hours, then Jim can run 0.5 miles further compared to his friend Ryan.

If Jim runs at a speed of 18 miles in 3 hours, it can be represented as,

Speed = distance / time = 18 miles / 3 hours = 6 miles per hour

As Ryan runs at a rate of 11 miles in 2 hours, it can be given as,

Speed = distance / time = 11 miles / 2 hours = 5.5 miles per hour

To determine how much further Jim can run in an hour compared to his friend Ryan,

Distance ( Jim ) = speed x time = 6 x 1 = 6 miles

Distance ( Ryan) = speed x time = 5.5 x 1 = 5.5 miles

The distance that Jim can run further in an hour can be calculated by subtraction.

Distance ( Jim ) - Distance ( Ryan) = 6 - 5.5 = 0.5 miles

Thus, Jim can run 0.5 miles further in an hour compared to his friend Ryan.

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Answer: factor, in mathematics, a number or algebraic expression that divides another number or expression evenly—i.e., with no remainder. For example, 3 and 6 are factors of 12 because 12 ÷ 3 = 4 exactly and 12 ÷ 6 = 2 exactly. The other factors of 12 are 1, 2, 4, and 12.

Step-by-step explanation:

   The equation of the parabola that has vertex at (0,0 ) and focus (-1, 0) is

  A parabola is a quadratic function that can move on any axis, it is composed of:

   The equation that defines a parabola can be given by:

(x - h)² = 4p(y - k)

(y - k)² = 4p(x - h)

  This will depend on its aperture

  Since the vertex and the focal axis are on the same axis, we analyze that:

(y - 0)² = 4p(x - 0)

f = (0 + p, 0)

0 + p = -1

p = 0 - 1

p= -1

(y - 0)² = 4*-1(x - 0)

(Y)² = -1(X)

x = -y²

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13.5 cm²   is the surface area of the cube  .

What is surface area of cuboid?

If the edge of a cube have a length =  a unit

then, the surface area of the cube = 6a² unit

here, the edge of a cube have length  a = 1.5 cm

Therefore , the surface area of the cube 6a² = 6 × 1.5²

                                                                          = 13.5 cm²

The area of each face = ( the length of the edges)²

The surface area of whole cube = 6 × the area of one face

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