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2 years ago

Find the 11th term of the following geometric sequence. 10, 50, 250, 1250

Mathematics

2 answers:

Natasha2012 [34]2 years ago

8 0

Answer:

97656250

Step-by-step explanation:

keep multiplying each term by 5 until you get to the 11th one. the 11th term is 97656250

Kazeer [188]2 years ago

3 0

To find the nth term do you know the equation

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Drag each expression to show whether it is equivalent to 6(4x−1), 24x+6, or (4⋅6x)+(4⋅2) somebody please help me i need to get t

faltersainse [42]

Answer:

6(4x-1) is equivalent to 24x-6 and (2*12x)-(2*3)

24x+6 is equivalent to 6(4x+1) and (6*4x)+(6*1)

(4*6x)+(4*2) is equivalent to 24x+8 and 4(6x+2)

Step-by-step explanation:

An equivalent expression is an expression which either simplified or factored is equal to it.

6(4x-1) is equivalent to 24x-6 and (2*12x)-(2*3)

24x+6 is equivalent to 6(4x+1) and (6*4x)+(6*1)

(4*6x)+(4*2) is equivalent to 24x+8 and 4(6x+2)

5 0

2 years ago

Roberta invested $600 into a mutual fund that paid 4% interest each year compounded annually. Write an exponential function of t

Oksanka [162]

Answer:

The exponential equation is A = 600(1.04)^15

The value of the mutual fund after 15 years is $1,081

Step-by-step explanation:

The value of the mutual fund after the number of years can be represented using the compound interest equation below;

A = P(1 + r/n)^nt

Where A is the value of the mutual fund after 15 years, P is the initial amount invested which is $600, r is the interest rate which is 4% or 0.04(4% = 4/100 = 0.04), n is the number of times we are compounding per year(which is 1 since it is a one time payment per year) and t is the number of years which is 15

Let's plug these values, we have;

A = 600(1 + 0.04/1)^15

A = 600(1.04)^15

A = $1,081 approximately

8 0

2 years ago

Read 2 more answers

The length of the shadow of a pole on level ground increases by 90m when the angle of elevation of the sun changes from 58° to 3

viva [34]

Answer:

119.45 m

Step-by-step explanation:

Given:

When angle of elevation of the sun changes from 58° to 36° the length of shadow of a pole increases by 90 m.

To find:

Length of pole = ?

Solution:

Kindly refer to the attached image.

$\triangle ABC$ represents the 1st angle of elevation of sun i.e. 58°

$\triangle ABD$ represents the 2nd angle of elevation of sun i.e. 36°

Change in shadow is represented by CD = 90 m

Let height of pole, AB = $h$ m

Let side BC = $x$ m

Now, let us apply tangent rules in $\triangle ABC, \triangle ABD$ one by one:

$tan\theta = \dfrac{Perpendicular}{Base}\\\Rightarrow tan58^\circ=\dfrac{AB}{BC}\\\Rightarrow tan58^\circ=\dfrac{h}{x}\\\Rightarrow x = 0.624h ..... (1)$

$tan36^\circ = \dfrac{h}{x+90}$

Putting value of $x$ using equation (1):

$tan36^\circ = \dfrac{h}{0.624h+90}\\\Rightarrow 0.726\times 0.624h+0.726\times 90 = h\\\Rightarrow h-0.453h =65.34\\\Rightarrow \bold{h = 119.45\ m}$

119.45 m is the height of pole.

7 0

2 years ago

Which composition of transformations maps figure RSTUV to figure R"S"T"U"V"?

Sergeu [11.5K]

Answer:

option: B is correct

A reflection across line n followed by a 270° rotation about point P.

Step-by-step explanation:

Clearly from the figure we could see that the graph is first reflected across the given line n such that we obtain the figure R'S'T'V'U' and then it is rotated 270° across the point P so that we obtain the figure R"S"T"U"V".

Hence, option B is correct.

( A reflection across line n followed by a 270° rotation about point P )

5 0

2 years ago

Read 2 more answers

The coordinates of the vertices of quadrilateral ABCD are A(−6, 3) , B(−1, 5) , C(3, 1) , and D(−2, −2) . Which statement correc

Pavlova-9 [17]

Answer:

C.Quadrilateral ABCD is not a rhombus because there are no pairs of parallel sides.

Complete question:

A. Quadrilateral ABCD is not a rhombus because opposite sides are parallel but the four sides do not all have the same length.

B. Quadrilateral ABCD is a rhombus because opposite sides are parallel and all four sides have the same length.

C. Quadrilateral ABCD is not a rhombus because there are no pairs of parallel sides.

D. Quadrilateral ABCD is not a rhombus because there is only one pair of opposite sides that are parallel.

Step-by-step explanation:

Rhombus states that a parallelogram with four equal sides and sometimes one with no right angle.

Given: The coordinate of the vertices of quadrilateral ABCD are A(−6, 3) , B(−1, 5) , C(3, 1) , and D(−2, −2) .

The condition for the segment $(x_{1},y_{1}), (x_{2},y_{2})$ to be parallel to $(x_{3},y_{3}), (x_{4},y_{4})$ is matching slopes;

$\frac{y_{2}-y_{1}}{x_{2}-x_{1}}= \frac{y_{4}-y_{3}}{x_{4}-x_{3}} \\(y_{2}-y_{1}) \cdot (x_{4}-x_{3}) =(y_{4}-y_{3}) \cdot (x_{2}-x_{1})$ ---->1

So, we have to check that AB || CD and AD || BC

First check AB || CD

A(−6, 3) , B(−1, 5) , C(3, 1) , and D(−2, −2)

substitute in [1],

$(5-3) \cdot (-2-3) = (-2-1) \cdot (-1-(-6))2 \cdot -5 = -3 \cdot 5$

-10 ≠ -15

Similarly,

check AD || BC

A(−6, 3) , D(−2, −2) , B(−1, 5) and C(3, 1)

Substitute in [1], we have

$(-2-3) \cdot (3-(-1)) = (1-5) \cdot (-2-(-6))-5 \cdot 4 = -4 \cdot 4$

-20 ≠ -16.

Both pairs of sides are not parallel,

therefore, Quadrilateral ABCD is not a rhombus because there are no pairs of parallel sides.

8 0

2 years ago