Answer:
Step-
Honey it c !!!!………!l║.by-step explanation:
The explicit formula for the given "geometric-sequence" is aₙ = 4 × 2ⁿ⁻¹, and the eight term is 512, Option(c) is correct.
To find the explicit formula for a geometric-sequence, we need to find the common ratio between any two consecutive terms.
In this sequence, we can see that each term is obtained by multiplying the previous term by 2. So, the "common-ratio" is 2.
We also know the "first-term" is 4, so we use the formula for the nth term of a geometric sequence which is : aₙ = a₁ × rⁿ⁻¹,
Substituting the values,
We get,
⇒ a₈ = 4 × 2⁽⁸⁻¹⁾
⇒ a₈ = 4 × 2⁷
⇒ a₈ = 512,
Therefore, the correct answer is (c) aₙ = 4 × 2ⁿ⁻¹; 512.
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The given question is incomplete, the complete question is
Find the explicit formula for the geometric sequence. Then find a₈.
4, 8, 16, 32, 64,....
Which Answer is Correct:
(a) aₙ = 4 × rₙ - 1; 1024
(b) aₙ = a₁ × 2ⁿ⁻¹; 256
(c) aₙ = 4 × 2ⁿ⁻¹; 512
(d) aₙ = 2 × 4ⁿ⁻¹; 512
Factor the expression given below. Write each factor as a polynomial in
descending order. Enter exponents using the caret (^). For example, you
would enter x2 as x^2.
343x3 + 216y3
Answer:
(7x +6y)(49x^2 -42xy +36y^2)
Step-by-step explanation:
The factoring of the sum of cubes is a special form:
a³ +b³ = (a +b)(a² -ab +b²)
We recognize the given expression as a sum of cubes, so we can use this pattern to factor it.
Identifying the cubesFrom our memory of the cubes of small numbers (or from the cube root function of our calculator), we can identify the terms as ...
343x³ +216y³ = (7x)³ +(6y)³
ApplicationOur factoring pattern above can be used with ...
a = 7xb = 6ySubstituting these values, we have ...
343x³ +216y³ = (7x)³ +(6y)³ = (7x +6y)((7x)² -(7x)(6y) +(6y)²)
343x³ +216y³ = (7x +6y)(49x² -42xy +36y²)
1) A microbiologist measures the length of a bacterium of 0.000163 m and the
length of yeast as 0.0087 mm.
a) Which is longest? (Hint: Both must be the same units)
b) How much longer is the longer specimen than the shorter specimen?
Answer:
a) The bacterium is longer;
b) The bacterium is 0.1543 mm longer than the yeast.
Step-by-step explanation:
In order to compare the length of the two beings we need to convert them to the same unit. We can do it either way, but we'll choose to convert from meters to milimetres, since we're dealing with small numbers. To do that we need to multiply the length that is in "m" by 1000.
[tex]length_{bac} = 0.000163*1000 = 0.163 \text{ mm}[/tex]
a) The bacteria is longer than the yeast.
b) We need to subtract their length in order to find this answer:
[tex]\text{dif} = length_{bac} - length_{yeast}\\\text{dif} = 0.163 - 0.0087 = 0.1543 \text{ mm}[/tex]
In a plane, line b is parallel to line f, line f Is parallel to line g, and line h is perpendicular to line b. Which of the following cannot be true?
hif
bih
bllg
GIlh
One leg of a right triangle is 21 inches longer than the other leg, and the hypotenuse is 39 inches.
Find the lengths of the legs of the triangle
Answer:
One leg - 15 inches
Second leg - 36 inches.
Step-by-step explanation:
One leg - x inches.
Second leg - (x + 21) inches.
Hypotenuse - 39 inches.
Using Pythagorean theorem
x² + (x + 21)² = 39²
x² + x² + 2*21x + 21² = 39²
2x² + 42x - 39² + 21² = 0
2x² + 42x - 1080 = 0
x² + 21x - 540 = 0
(x - 15)(x + 36) = 0
x = 15, x = - 36
We can use only positive value.
One leg - x inches = 15 inches
Second leg - (x + 21) inches = 15+21=36 inches.
Select the correct answer.
Shareese has a credit line of $3,000 on her credit card. Review the summary of her latest credit card statement.
Previous
Balance
Payments/Credits
Summary
New
Finance New
Purchases Charge Balance
$1,299.00 $18.00 $1,567.25
$1,250.25
$1,000.00
What is the available credit on Shareese's card?
O A $1,432.75
B. $1,299.00
$317.00
Reset
Net
reserved.
Answer:
the answer is A)1,432.75.
Santana went for a hike on the 21 mile South Boundary Trail. If she can hike2 miles
in 60 minutes, how long will it take her to hike the entire trail?
Draw a diagram to support your thinking and demonstrate your understanding. Be sure
to show all of your work.
Answer:
It will take santana 630 minutes or 10.5 hours to complete the 21 miles.
Step-by-step explanation:
[tex]\frac{2}{60\\}[/tex] [tex]\frac{21}{y}[/tex] y is what you are trying to find multiple her miles by the number of minutes and then divided by how many miles in 60 min.Kassy is traveling to Peru for her summer vacation. She looks at a map of the path of her flight. Her plane leaves from Texas, located at(5, 16) on the map’s coordinate grid, makes a stop at the halfway point, Panama, and then heads to its destination, Peru, located at(7, 8) on the map’s coordinate grid. Find the location of Panama on Kassy’s map. Enter as a coordinate with no spaces.
Answer:
(6,12)
Step-by-step explanation:
Use the mid point formula to find the answer. Add the first x value to the second and divide by two for your x midpoint, then add the first y value to the second y value and divide by two for your y midpoint.
A school determined that there is about a 33% chance that a student will choose a salad over a grilled chicken sandwich for lunch. Which simulation could you use to answer questions about the type of lunch students will choose?
Answer:
Picking and replacing
Step-by-step explanation:
theres only a 33% chance to get blue
Answer:
LOOk at the PicTure !!
Step-by-step explanation:
If the line segment AB is on a number line, and point A is at 4 and Point B is at 19, then the length of AB is ____. Select one: a. 15 b. - 15 c. 23 d. 12
Answer: 15
Step-by-step explanation:
If two points are together, then you subtract the numbers to get the distance
19 - 4 = 15
PLEASE ANSWER THIS, ITS DUE TODAY!! *100 POINTS*
Answer:
B. Spread
Step-by-step explanation:
Find the sum of the measures of the exterior angles of a convex 65-gon.
Answer:
Answer is below
Step-by-step explanation:
The sum of the measures of exterior angles on any shape is always 360 degrees.
If you meant to say the sum of the measures of the interior angles of a convex 65-gon, then it would be 11340 degrees.
(n-2)(180) Substitute
(65-2)(180) Subtract
(63)(180) Multiply
11340
Sum of the measures of the exterior angles of a convex [tex]\boldsymbol{65-}[/tex]gon is equal to [tex]360^{\circ}[/tex]
An exterior angle is an angle between a side of a polygon and an extended side adjacent to it.
A polygon refers to any closed curve comprised of a set of connected sides such that no two sides cross.
Convex [tex]\boldsymbol{65-}[/tex]gon means a convex polygon with [tex]\boldsymbol{n}[/tex] sides.
The sum of measures of any polygon is equal to [tex]\boldsymbol{360^{\circ}}[/tex]
So, the sum of the measures of the exterior angles of a convex [tex]\boldsymbol{65-}[/tex]gon is equal to [tex]360^{\circ}[/tex]
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If two coins are flipped, what is the probability that both coins will not land on heads?
0%
25%
50%
75%
Will mark as brainliest!
Answer:
50%
is the probability of this question
Answer:
25%
Step-by-step explanation:
We have 4 choices when flipping two coins, HH, HT, TH and TT where H and T are heads and tails respectively. The only option where both coins will not land on heads is TT so the probability is 1/4 = 25%.
PLEASE HELP ME THIS IS URGENT I AM BEING TIMED!!
A game has 150 cards, and five of them are bonus cards. If all the cards are on the table, what is the probability of getting a bonus card when choosing a card at random? Write your answer as a fraction.
Answer:
1/30
Step-by-step explanation:
well if there are 150 cards on the table and 5 are bonus, this can be turned into a simple fraction 5/150. just simplify and you are good to go!
((x - 4) + (x + 2)) *
2x – 2
x2 – 8
x2 – 2x – 8
x2 + 2x – 8
Answer:
the 3 one is 4+5=9876
Step-by-step explanation:
Evaluate the following expression.
6
Step-by-step explanation:
first change it to fraction
1/6
use long division method to simplify
you will get
0.66666666666
leave your answer in 2 place decimal
0.167
Colleen is knitting a scarf. For every 45 pieces of blue yarn she uses, she uses 18 pieces of red yard. What equation can be used to represent the proportional relationship between the amount of blue yarn, b, and red yard, r, that Colleen uses when knitting a scarf?
Answer:
The equation that can be used to represent the proportional relationship between the amount of blue yarn, b, and red yarn, r, that Colleen uses when knitting a scarf is:
b = 2.5 ror
b = 5r/2Step-by-step explanation:
In the exercise are given the variables that we must use in the equation: b and r, where b is the amount of blue yarn and r is the amount of the red yarn, now it's just missing the proportion that must be used in the equation, to identify this you only must divide the biggest amount (45) by the smallest amount (18), how I show below:
Proportion = 45/18 = 2.5 or 5/2Having this, you can make the equation taking into account the proportion:
b = 2.5 rThis equation marks that by each piece of blue yarn, are needed 2.5 pieces of red yarn, we can prove the equation replacing the r-value by 18:
b = 2.5 r b = 2.5 (18) b = 45How you can see, replacing the r-value by 18, the value given for red yarn, we obtain the value given for the blue yarn: 45.
Answer:
b = 2.5 r
or
b = 5r/2
match the words that have the same roots. Every word listed has a matching word.
Answer:
Biology- Biography, Mortal-Mortify, Percent-Century, Revise-Adviser, dialogue-monologue.
Step-by-step explanation:
Bio
Mor or Mort
Cent
Vise
Logue
Are all the different latin roots present here.
Answer:
1) biology- biography
2) revise-adviser
3) mortal-mortify
4) percent- century
5) dialogue-monologue.
Step-by-step explanation:
1) Bio-Bio
2) vise-viser
3) mor-mor
4) cen-cen
5) logue-logue
are all matching words.
the numerator of a fraction is 1 more than twice its denominator if 4 is added to both the numerator and the denominator the fraction reduces to 5/3 find the denominator
Answer:
11
Step-by-step explanation:
Given Fraction
Let the denominator = x
The numerator is 2x + 1
2x + 1
=====
x
The new fraction
2x + 1 + 4
=========
x + 4
Equation
2x + 5 5
====== = ====
x + 4 3
Solution
Cross Multiply
3(2x + 5) = 5(x + 4)
Remove the brackets
6x + 15 = 5x + 20
Subtract 5x from both sides
6x - 5x + 15 = 20
Subtract 15 from both sides
x = 20 - 15
x = 5
============
Answer
2(5) + 1 = 11
The original numerator is 11
What is the slope of the line represented by the equation y-6 = 5(x - 2)?
Answer & Step-by-step explanation:
The equation for slope-intercept form is y=mx+b
In order to solve this problem, we can just solve the equation to find y.
y - 6 = 5(x - 2)
Distribute 5 to (x - 2)
y - 6 = 5x - 10
Add 6 to both sides of the equation.
y = 5x - 4
So, the slope of the line is 5.
The required slope of the line m = 5
What is the slope of the line represented by the equation y-6 = 5(x - 2)
What is line?
line, is curve showing the shortest distance between 2 points.
Given line y-6 = 5(x - 2)
standard equation of line = [tex]y-y_1=m(x-x_1)[/tex]
compare the standard equation of line with standard equation
m=5
Thus, The required slope of the line m = 5
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Pleasee help I am being timed
Answer:
A: 33.5
B: 24.5
Step-by-step explanation:
Answer:add the cost for all the books for answer one and for number 2 subtract 9 from the total of answer 1.
Step-by-step explanation:
If the circumference of a circle is 484 cm, what is the area and diameter
Answer:
[tex]18641.50 \: cm^2\\154.06 \: cm[/tex]
Step-by-step explanation:
[tex]C=\pi d[/tex]
[tex]484=\pi d[/tex]
[tex]\frac{484}{\pi } =d[/tex]
[tex]d=154.06198[/tex]
[tex]A=\pi r^2[/tex]
[tex]\pi (\frac{d}{2}) ^2[/tex]
[tex]\pi (\frac{154.06198}{2}) ^2[/tex]
[tex]A=18641.49898[/tex]
Answer:
The area of the circle is approximately 18641.5 because you need to round to the nearest place value. The diameter of the circle is approximately 154.06.
Step-by-step explanation:
Area=πr2
Circumference=2πr
Solving for Area
Area= C²/4 π = 484²/4·π ≈ 18641.50017
———————————————————————————
Circumference =2πr
Diameter= πr
Solving for Diameter
Diameter= C/π = 484/π≈ 154.06198
what do you think that ADA has explicit regulations on slopes and ramps?
Answer:
I think that the ADA (Americans with Disabilities Act) has explicit regulations on slopes and ramps so that people with disabilities can go about their daily life easier, and to guarantee the safety and wellbeing of the disabled. If, for instance, a wheelchair ramp were too steep, there would be a danger of the wheelchair rolling down too quickly, or the person falling backward on their way up.
Find f(2) and f(a + h) when f(x) = 3x^2 + 2x + 4
Answer:
[tex]f(2)=20\\f(a+h)=3a^2+6ah+3h^2+2a+2h+4[/tex]
Step-by-step explanation:
[tex]f(x)=3x^2 + 2x + 4[/tex]
[tex]f(2)=3(2)^2 + 2(2) + 4\\f(2)=3(4)+ 2(2) + 4\\f(2)=12+ 4+ 4\\f(2)=20[/tex]
[tex]f(a+h)=3(a+h)^2 + 2(a+h) + 4\\f(a+h)=3(a+h)(a+h) + 2(a+h) + 4\\f(a+h)=3a^2+3ah+3ah+3h^2+2a+2h+4\\f(a+h)=3a^2+6ah+3h^2+2a+2h+4[/tex]
Answer:
f(2) = 20
f(a+h) = 3a²+6ah+3h²+2a+2h+4
Step-by-step explanation:
f(x) = [tex]3x^2+2x+4[/tex]
A) Putting x =2
=> f(2) = 3(2)²+2(2)+4
=> f(2) = 12+4+4
=> f(2) = 20
B) Putting x = a+h
=> f(a+h) = 3(a+h)²+2(a+h)+4
=> f(a+h) = 3a²+6ah+3h²+2a+2h+4
A box of 120 crayons contains variations of three
colors: blue, red, and purple. The ratio of blue
crayons to red crayons is 11:2, and the ratio of the
number of red crayons to purple crayons is 2:7. If
all of the purple crayons were removed, how many
crayons would be left in the box?
E. 16
F. 42
G. 78
H. 113
Answer:
G. 78
Step-by-step explanation:
Blue to red=11:2
Red to purple=2:7
Total crayons =120
Total ratio
=11+2+7
=20
Blue=11
Red=2
Purple=7
Purple crayons
=Ratio of purple /Total ratio× Total crayons
=7/20×120
=42
If all the purple crayons were removed
=Total crayons - purple crayons
=120-42
=78
Solve this equation: -7x + 12 – 2x = 23 + 13.0
Step 1: Simplify by combining like terms that are on the
same side of the equation. Which terms can be
combined?
Answer:
Step-by-step explanation:
We can combine the -7x and the -2x and the left side to get -9x and the 23 and 13 on the right side to get 36.
This gives us
-9x + 12 = 36
Subtacting 12 from both sides gives us
-9x = 24
dividing by -9 gives us
x = - 8/3
Answer:
see below
Step-by-step explanation:
-7x + 12 – 2x = 23 + 13.0
Combine like terms
(-7x-2x) +12 = (23+13)
-9x +12 = 36
Subtract 12 from each side
-9x +12 -12 = 36 -12
-9x = 24
Divide each side by -9
-9x/-9 = 24/-9
x = -8/3
You need 3 sticks of butter for every 24 cookies you bake.
Complete the table using equivalent ratios.
Answer: 8
Step-by-step explanation:
there is no table
I need to do this assignment
Answer:
c
Step-by-step explanation:
(3x+1)(x+6)
3x^2+18x+1x+6
Graph the inequality.
3x + 4y <4
In the box below, describe the graph.
Answer:
y < 1 - (3x)/4
Step-by-step explanation:
Graph the inequality by finding the boundary line, then shading the appropriate area.
y < 1 − 3 x /4
the graph is partially shaded. the shade crosses through (0,1) and (1,0). I hope you can figure that out :)
what is the inverse of the function y=4x+5
Answer:
the answer for this question is (y-5)/4=x
Use the fact that the length of an arc intercepted by an angle is proportional to the radius to find the arc length given the circle area A = 25π cm2 and Θ = straight pi over 4 Your answer: 20straight pi fraction numerator 5 pi over denominator 4 end fraction fraction numerator 4 pi over denominator 5 end fraction fraction numerator 10 pi over denominator 4 end fraction
Answer:
s = 5/4 pi
Step-by-step explanation:
A = 25π cm2
Theta = pi/4
A = pi r^2 = 25 pi
Divide each side by pi
r^2 = 25
Taking the square root of each side
sqrt(r^2) = sqrt(25)
r = 5
The arc length is
s = r * theta where theta is in radians
s = 5 * pi/4
s = 5/4 pi
