Write a rule for the nth term of the sequence. Then find a..
3. 4, 20, 100, 500, ...
Answers
Answer:
Rule is 4(5)^(n-1).
a7 = 62500.
Step-by-step explanation:
This is a geometric sequence with a1 = 4 and r = 20/4 = 5.
a7 is 4(5)^(7-1)
= 4 * 5^6
= 62500.
the general form of the given sequence is a(n) = 4 * 5ⁿ⁻¹ and a(7) is 62500.
What is the geometric sequence?A geometric sequence is a sequence of numbers that follows a pattern where the next term is found by multiplying by a constant called the common ratio, r.
Given a sequence 4, 20, 100, 500, ...
From the general formula of the nth term of the geometric sequence:
a(n) = arⁿ⁻¹
where,
a is the first term
r = ratio of two subsequent terms
in our case
a = 4
r = 20/4 = 5
thus, the general form of the given sequence
a(n) = 4 * 5ⁿ⁻¹
To find: a(7)
a(7) = 4 * 5⁶
a(7) = 62500
therefore, the general form of the given sequence is a(n) = 4 * 5ⁿ⁻¹ and a(7) is 62500.
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Related Questions
Help solve pls fast
it's a maths question
Answers
Answer:
Step-by-step explanation:
[tex][(\sqrt[4]{x^{\dfrac{3}{4}}})^{\dfrac{-4}{3}} ]^{4}[/tex]
[tex]= [(x^{\frac{3}{4}*\frac{1}{4}})^{\frac{-4}{3}}]^{4}\\\\\\= [(x^{\frac{3}{16} ) ^{\frac{-4}{3}}}]^{4}\\\\=[ x^{\frac{3}{16}*\frac{-4}{3}}]^{4}\\\\=[x^{\frac{-1}{4}}]^{4}\\\\=x^{\frac{-1}{4}*4}\\\\=x^{-1}\\\\=\dfrac{1}{x}[/tex]
Hint:
[tex](a^{m})^{n}=a^{m*n}[/tex]
Answer:
[tex]1/x[/tex]
Step-by-step explanation:
To simplify, work from the inside out.
We start with
[tex]\sqrt[4]{x^{3/4}}[/tex]
on the inside. And we can change the fourth root into a fractional exponent -- 1/4:
[tex](x^{\frac{3}{4})^{1/4}[/tex]
A power of a power means multiply the exponents, giving
[tex]x^{\frac{3}{4} * \frac{1}{4}} = x^{3/16}[/tex]
So now we have
[tex][(x^{3/16})^{-4/3}]^4[/tex]
From here, apply the "power of a power rule" again, working from the inside out.
[tex](x^{-12/48})^4[/tex]
[tex]x^{-48/48}[/tex]
[tex]x^{-1}[/tex]
or
[tex]1/x[/tex]
If there is food enough for 200 army for 30 days. How many army should be transferred from there to last food for 40 days?
Answers
The presence of a midpoint will result in what type of segments?
Answers
Step-by-step explanation:
The presence of a midpoint will result in congruent segment.
The type of segment that the presence of a midpoint will result in is called; Congruent Segments
Types of Segments
Now, when we are talking about congruency, we are simply referring to the concept of equality.
Thus, when we say that two angles are congruent, it simply means they are equal.
Now, when we introduce a mid point to a line segment, what this does is to divide the line into two equal parts.
Equal segments are congruent and as such we can say that congruent segments are formed.
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HEEEEELLLLLLPPPPPPP!!!!!!!!!!!!!!
Find the area and perimeter.
20x2 − 12x; 10x − 5
12x2 − 20x; 7x − 5
7x2 − 5; 11x − 10
12x2 − 20x; 14x − 10
Answers
Area
(3x - 5) · 4x = 3x · 4x - 5 · 4x =
= 12x² - 20x
Perimeter
2 · (3x - 5) + 2 · 4x =
= 6x - 10 + 8x = 14x - 10
What was the original price of an MP3 player that is advertised as on sale for 25%
off and the sale price is $60?
can i get an explanation, please :)
Answers
Answer:
$80
Step-by-step explanation:
the original price (in percent) = 100%
the discount (25% off) = - 25%
_________________
the sale price (in percent) = 75% =>
equal to $60
so, the original price =
100/75 × $60 = $80
Now
Cost price be x.[tex]\\ \rm\longmapsto 100-25=75\%[/tex]
75% of x=60[tex]\\ \rm\longmapsto \dfrac{75}{100}x=60[/tex]
[tex]\\ \rm\longmapsto x=60\times \dfrac{100}{75}[/tex]
[tex]\\ \rm\longmapsto x=80[/tex]
If x=1/8 what is the value of y when 2/x = y/4
Answers
Answer:
y = 64
Step-by-step explanation:
x = 1/8
Substituting x in the equation,
=> 2/(1/8) = y/4
=> 2 x 8 = y/4
=> 16 = y/4
=> y/4 = 16
=> y = 16 x 4
=> y = 64
The value of y will be;
⇒ y = 64
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
The expression is,
⇒ 2/x = y/4
Now,
Since, The expression is,
⇒ 2/x = y/4
Substitute x = 1/8, we get;
⇒ 2/(1/8) = y /4
⇒ 2 × 8 = y / 4
⇒ 16 × 4 = y
⇒ y = 64
Thus, The value of y = 64
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Trena's jump rope is 3.5 feet
long. Jackie's is 3.8 feet long.
How much longer is Jackie's
jump rope than Trena's?
Answers
Answer:
0.3 feet
Step-by-step explanation:
3.8 - 3.5 = 0.3 feet
Find the image of (-1, 3) obtained by translating
2 units down, followed by a rotation of 180°
counterclockwise about the origin.
HELP QUICK
Answers
Answer:
(1, - 1 )
Step-by-step explanation:
A translation of 2 down means subtract 2 from the y- coordinate
(- 1, 3 ) → (- 1, 3 - 2 ) → (- 1, 1 )
Under a counterclockwise rotation about the origin of 180°
a point (x, y ) → (- x, - y ) , then
(- 1, 1 ) → (1, - 1 )
Overall
(- 1, 3 ) → (- 1, 1 ) → (1, - 1 )
The image of (-1, 3) was obtained by translating 2 units down, followed by a rotation of 180° counterclockwise about the origin is (1,-1).
What is coordinate?A coordinate system in geometry is a system that employs one or more integers, or coordinates, to define the position of points or other geometric components on a manifold such as Euclidean space.
The given point with coordinates of (-1,3), when translated downwards will have the coordinated equal,
(-1,3) ⇒ (-1, 3-2) ⇒ (-1, 1)
Now, since the translation is about 180° in the counter-clockwise direction, the coordinates of the new point will be equal to,
(-1,1) ⇒ (1, -1)
Hence, the image of (-1, 3) obtained by translating 2 units down, followed by a rotation of 180° counterclockwise about the origin is (1,-1).
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find the radius of a circle that has an area of 803.84 cm squared
Answers
Answer:
Radius = 16
Step-by-step explanation:
Area = πr²
803.84 = 3.14(r²)
256 = r²
√256 = 16
If my answer is incorrect, pls correct me!
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-Chetan K
There is a plant whose growth can be represented by a linear function. At 1 week it is
2 inches tall and at 2 weeks it is 4 inches tall. Write a linear equation to represent the
growth of the plant.
O y = 2x + 2
O y = 2x
O y = 4x + 2
Answers
Answer:
y=2x
Step-by-step explanation:
we can set x=number of week, and y=inches
as you can see, 1 week-> x=1 :y=2(1) = 2 inches
2 week-> x=2 :y=2(2)=4 inches
**if we substitute x to y = 2x + 2 and y = 4x + 2, it will not works.
d. 3h =
h = 3.66 hours
2. Jane can run 2 miles per hour around the Belmont Track. He
needs to run a total of 10 miles and has already done 3
miles. Which equation and answer shows the number of
hours (h) it will take for him to run the rest of the miles?
e. 2h + 3 = 10; h = 3.5 hours
f. 3h + 2 = 10; h = 2.66 hours
g. 2h = 10 ; h = 5 hours
h. 3h = 10 ; h = 3.33 hours
(hp
Answers
Explanation:
Jane can run 2 miles per hour. (2h)
He need to run 10 miles in total and has done 3 so far. (+ 3 = 10)
The equation can be written:
2h + 3 = 10
2h = 7
h = 7/2 = 3.5
32. DINING OUT The Ross family recently diped at an Italian restaurant/ Each of the four family members ordered a
pasta dish that cost $11.30. a drink that cos($1.50, and dessert that cost $2.75,
a. Write an expression that could be used to calculate the cost of the Ross' dinner before adding tax and a tip.
Answers
Two students created a list of steps for the following construction. Which student has steps in the correct order, and which does not? Explain.
You are given line AB and point C. Construct a line parallel to line AB that passes through point C.
Student A Steps:
1. Draw a line that intersects points B and C.
2. Draw a line through point C and point G.
3. Keep the compass at the same width, and place it on point C.
4. Keeping the compass at the same width, place it on point F.
5. Mark the intersection of the two arcs as point G.
6. Open the compass to the width between points D and E.
7. Place the compass on point B, and swing an arc that crosses line AB and line BC.
8. Label the points D and E.
9. Swing an arc that crosses line BC, and label the point F.
10. Swing an arc that intersects the arc created from line BC at point C.
Student B Steps:
1. Draw a line that intersects points B and C.
2. Place the compass on point B, and swing an arc that crosses line AB and line BC.
3. Label the points D and E.
4. Keep the compass at the same width, and place it on point C.
5. Swing an arc that crosses line BC, and label the point F.
6. Open the compass to the width between points D and E.
7. Keeping the compass at the same width, place it on point F.
8. Swing an arc that intersects the arc created from line BC at point C.
9. Mark the intersection of the two arcs as point G.
10. Draw a line through point C and point G.
Answers
Answer:
This was not done by me! Credit to another expert on Brainly named caylus.
As it is impossible to understand who have done what ,
the correct construction should be :
You are given point A, point B and point C.
Construct a line parallel to that line AB passing through point C.
1) Place the compass on point B, and swing an arc that crosses line AB and line BC.
Label the points D and E.
2) Keep the compass at the same width, and place it on point C.
3) Swing an arc that crosses line BC, and label the point F outside the segment [BC] .
4) Open the compass to the width between points D and E.
Keeping the compass at the same width, place it on point F.
5) Swing an arc that intersects the arc created from line BC at point C.
6) Mark the intersection of the two arcs as point G.
7) Draw a line through point C and point G.
You just have to discover who has done that.
9. El radio de una pelota de básquetbol es aproximadamente 3.6 veces mayor
que el radio de una pelota de tenis. ¿Cuántas veces mayor es el volumen
de una pelota de básquetbol que el volumen de una pelota de tenis?
4
Nota: El volumen de una esfera es V = -tr
Answers
Answer:
so the volume of the basketball is 46.656 times greater than the volume of the tennis ball.
Step-by-step explanation:
midpoint (10,5), endpoint (4, - 1)
Answers
Answer:
M=(7,2)
Step-by-step explanation:
M=(10+4/2,5+-1/2)
M=(7,2)
Aaron has a collection of American coins. He has 3 times as many 10 cent coins as 25 cent coins, and he has some 5 cent coins as well. If he has 8 coins with total value $11.40. how many of each type does he have?
Answers
Step-by-step explanation:
SEE THE IMAGE FOR SOLUTION
HOPE IT HELPS
HAVE A GREAT DAY
Acellus
Complete the data table for the function
f(x) = (x + 2 - 6.
X
-2
-1
2
Y
[?]
Enter
Answers
[tex]\\ \sf\Rrightarrow f(x)=\sqrt{x+2}-6[/tex]
[tex]\\ \sf\Rrightarrow f(-2)[/tex]
[tex]\\ \sf\Rrightarrow \sqrt{-2+2}-6[/tex]
[tex]\\ \sf\Rrightarrow 0-6[/tex]
[tex]\\ \sf\Rrightarrow -6[/tex]
And
[tex]\\ \sf\Rrightarrow f(-1)[/tex]
[tex]\\ \sf\Rrightarrow \sqrt{-1+2}-6[/tex]
[tex]\\ \sf\Rrightarrow \sqrt{1}-6[/tex]
[tex]\\ \sf\Rrightarrow 1-6[/tex]
[tex]\\ \sf\Rrightarrow -5[/tex]
And
[tex]\\ \sf\Rrightarrow f(2)[/tex]
[tex]\\ \sf\Rrightarrow \sqrt{2+2}-6[/tex]
[tex]\\ \sf\Rrightarrow \sqrt{4}-6[/tex]
[tex]\\ \sf\Rrightarrow 2-6[/tex]
[tex]\\ \sf\Rrightarrow -4[/tex]
And
[tex]\\ \sf\Rrightarrow f(7)[/tex]
[tex]\\ \sf\Rrightarrow \sqrt{7+2}-6[/tex]
[tex]\\ \sf\Rrightarrow \sqrt{9}-6[/tex]
[tex]\\ \sf\Rrightarrow 3-6[/tex]
[tex]\\ \sf\Rrightarrow -3[/tex]
will mark brainliest pls help !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answers
Answer:
Simplify the expression
5 +10/3
=
7
PEMDAS. Do division first.
Step-by-step explanation:
Simplify the expression
18/2*3
/ 3(3)
=3
I know this for a fact both are correct took test got a 100 also its easy PEMDAS
Answer:
[tex]{ \tt{first \: image}} \\ [/tex]
[tex] = \frac{18 \div (2 \times 3)}{3(3)} \\ \\ = \frac{18 \div 6}{9} \\ \\ = \frac{3}{9} \\ \\ = \frac{1}{3} [/tex]
[tex]{ \tt{second \: image}}[/tex]
[tex]5 + 10 \div 5 [/tex]
introduce a bracket:
[tex] = 5 +( 10\div 5) \\ = 5 + 2 \\ = 7[/tex]
help me please I need help to my question
[tex] \sqrt{50} + \sqrt[]{18} - 8 \sqrt[]{2} [/tex]
Answers
Answer:
[tex] \sqrt{50} + \sqrt{18} - 8 \sqrt{2} \\ \\ 5 \sqrt{2} + 3 \sqrt{2} - 8 \sqrt{2} \\ \\ 8 \sqrt{2} - 8 \sqrt{2 } \\ \\ = 0[/tex]
Given the expression:
[tex] \displaystyle \large{ \sqrt{50} + \sqrt{18} - 8 \sqrt{2} }[/tex]
Since we have 2 in the square root from 8√2. We will be converting terms in √2 form so we can. evaluate.
As we know, 50 comes from 5×10 = 5×5×2
and 18 comes from 9×2 = 3×3×2.
[tex] \displaystyle \large{ \sqrt{5 \times 5 \times 2} + \sqrt{3 \times 3 \times 2} - 8 \sqrt{2} }[/tex]
In the square root, if there are two same numbers, we can pull it out as one.
Ex. √5×5 would be 5. Refer to below:
[tex] \displaystyle \large{ \sqrt{a \times a} = \sqrt{ {a}^{2} } = |a| }[/tex]
Since there are two fives and two threes in the square root, we pull these numbers out only one.
[tex] \displaystyle \large{ 5\sqrt{2} + 3 \sqrt{2} - 8 \sqrt{2} }[/tex]
Because these terms have the same square root of 2, we can evaluate 5+3-8.
[tex] \displaystyle \large{ 8 \sqrt{2} - 8 \sqrt{2} } = 0[/tex]
Of course, like term - like term = 0
Hence, the answer is 0.
Markus has 4 white hats and 5 black hats in his closet. If he
randomly takes 1 of these 9 hats from his closet, what is the
probability that the hat that Markus takes is black?
Answers
Answer:
black hat
Step-by-step explanation:
as you know that there are 5 black hats so any of one black hat will be on his hand
PSSSSS HELPPPP MEEEE
Answers
Answer:
x≥ 21 2/3
Step-by-step explanation:
81 - 1 1/5x ≤ 55
Subtract 81 from each side
81 -81- 1 1/5x ≤ 55-18
- 1 1/5x ≤ -26
Change the mixed number to an improper fraction
-(5*1+1)/5 x ≤ -26
-6/5 x ≤ -26
Multiply each side by -5/6, remembering to flip the inequality
-5/6 *-6/5x≥ -26 * -5/6
x≥130/6
Changing back to a mixed number
x≥ 21 2/3
Answer:
Answer: A
Step-by-step explanation:
[tex]81 - 1 \frac{1}{5} x \leqslant 55[/tex]
subtract 81 from both sides:
[tex](81 - 1 \frac{1}{5} x) - 81 \leqslant 55 - 81 \\ \\ - 1 \frac{1}{5} x \leqslant - 26[/tex]
express the mixed fraction into a proper fraction:
[tex] - \frac{6}{5}x \leqslant - 26[/tex]
multiply -5 on both sides:
[tex] ( - \frac{6}{5} x) \times 5 \leqslant ( - 26 \times - 5) \\ \\ 6x \leqslant 130[/tex]
divide all sides by 6:
[tex] \frac{6x}{6} \leqslant \frac{130}{6} \\ \\ x \leqslant 21 \frac{2}{3} [/tex]
Which function is graphed below?
Answers
Answer:
f(x) = sin(x)
Step-by-step explanation:
If you want to remember how sine graph looks like it's always an s-like shape.
The Sierpinski triangle (pictured below) is a fractal image. The original figure is an equilateral triangle. In each step, the computer splits every triangle in the design into 444 congruent equilateral triangles, and removes the center one from the design. The area remaining in a particular design after nnn steps can be shown using the following expression:
\qquad\dfrac{25\sqrt{3}}{2}\cdot\left(\dfrac{3}{4}\right)^n
2
25
3
⋅(
4
3
)
n
start fraction, 25, square root of, 3, end square root, divided by, 2, end fraction, dot, left parenthesis, start fraction, 3, divided by, 4, end fraction, right parenthesis, start superscript, n, end superscript
The image shows 4 triangular figures, which represent the Sierpinski triangle fractal at 0, 1, 2, and 3 iterations.
The original triangular figure is an equilateral triangle which is entirely shaded. The triangular figure labeled n = 1 is formed by subdividing the original triangle into 4 congruent triangles and removing the middle triangle. The triangular figure for n = 2 is formed by subdividing each of the congruent triangles from the figure labeled n = 1 into 4 congruent triangles and removing the middle triangles.
The triangular figure for n = 3 is formed by subdividing each of the congruent triangle from the figure labeled n = 2 into 4 congruent triangles and removing the middle triangles.
The image shows 4 triangular figures, which represent the Sierpinski triangle fractal at 0, 1, 2, and 3 iterations. The original triangular figure is an equilateral triangle which is entirely shaded. The triangular figure labeled n = 1 is formed by subdividing the original triangle into 4 congruent triangles and removing the middle triangle. The triangular figure for n = 2 is formed by subdividing each of the congruent triangles from the figure labeled n = 1 into 4 congruent triangles and removing the middle triangles.
The triangular figure for n = 3 is formed by subdividing each of the congruent triangle from the figure labeled n = 2 into 4 congruent triangles and removing the middle triangles.
What does \dfrac{25\sqrt{3}}{2}
2
25
3
start fraction, 25, square root of, 3, end square root, divided by, 2, end fraction signify in the expression?
Answers
Answer:
B
Step-by-step explanation:
thats what it is in khan i think
help me on questions 27-35 and no linkss
Have a good day!!
Answers
Answer:
-8vhvcdzssaghjkgddsaaasdggbhA polynomial function h(x) has a zero of x = 2 + 7i with a multiplicity of one. Certain values of h(x) are given in the following table. x h(x) –5 0 –2 3 –1 –1 1 2 4 0 7 6 10 0 If every real x-intercept of h(x) is shown in the table and each has a multiplicity of one, what is the degree of h(x)? 3
Answers
Degree of h(x) is 5 because there are 5 x intercepts
Given :
The function h(x) has a zero of x = 2 + 7i with a multiplicity of one.
Every x intercept has multiplicity 1
Explanation
x intercept x=2+7i has multiplicity one
For complex intercepts occurs in pairs
So another x intercept is x=2-7i
From the given table , when h(x) is 0 then x is the x intercepts
other x intercepts from the given table are -5, 4,10
There are 5 x intercepts with multiplicity one
h(x) has 5 x intercepts . so , the degree of h(x) is 5
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Answer:
5
Step-by-step explanation:
mark most brainiest
what is ordered pair
Answers
Answer:
see explanation
Step-by-step explanation:
An ordered pair is a set of coordinates (x, y )
This can be o point on a graph or the solution to a system of equations or values from a table
Answer: It's a point on a graph (y,x)
Step-by-step explanation:
The angless of a quadrilateral are in the ratio 3:5:9:13. Find all the angles of the quadrilateral
Answers
Answer: 156°
Step-by-step explanation:
As you know angle sum of a quadrilateral = 360°
So, 3x + 5x + 9x + 13x = 360°
Or, 30x = 360°
Or, x = 12°
Hence: 3x = 36°, 5x = 60°, 9x = 108° and 13x = 156°
plz answer this question for me
Answers
Answer:
Top left one
Step-by-step explanation:
A receptionist named Tanner spends 3 minutes routing each incoming phone call. In all,
how many phone calls does Tanner have to route to spend a total of 21 minutes on the
phone?
Answers
Answer:
7
Step-by-step explanation:
21/3 = 7
Hope this helps!
The midpoint of AB is M(3,-2). If the coordinates of A are (1, -3),
what are the coordinates of B?
Answers
Answer:
23 just took the test
Step-by-step explanation:
Answer:
B(5,-1)
Step-by-step explanation:
The formula for finding the midpoint of any line is: [ (x1+x2) / 2 ] , [ (y1+y2) / 2 ] .So, x1=1 and x2=x. And y1=-3 and y2=y.
So,
(1+x)/2=3, then manipulating it gives x=5.
And,
(-3+y)/2=-2, then manipulating the equation gives y=-1.
Hence B(5,-1)