Answer:
b
Step-by-step explanation:
The sum of the first ten terms of the sequence is -59,048. The correct option is C.-59,048
Here is the correct question:
What is the sum of the first ten terms of the sequence 4, -12, 36, -108...
From the question,
The given sequence is 4,-12, 36, -108...
This is a geometric progression since it has a common ratio.
The common ratio, r = -3
Recall that,
Given a geometric progression, the common ratio, r is given as
[tex]r = \frac{T_{2} }{T_{1}} = \frac{T_{3} }{T_{2}} =\frac{T_{4} }{T_{3}} = ...[/tex]
From the given sequence,
[tex]T_{1} = 4[/tex]
[tex]T_{2} = -12[/tex]
[tex]T_{3} = 36[/tex]
[tex]T_{4} = -108[/tex]
∴ [tex]r = \frac{-12 }{4} = \frac{36}{-12} =\frac{-108} {36} = -3[/tex]
Therefore, the sequence is a geometric progression with a common ratio of 3
Now, to determine the sum of the first ten terms of the sequence,
From the formula
[tex]S_{n} = \frac{a(1-r^{n}) }{1-r}[/tex]
Where [tex]S_{n}[/tex] is the sum of n terms
[tex]a[/tex] is the first term
[tex]r[/tex] is the common ratio
and [tex]n[/tex] is the number of terms in the series
From the question
[tex]a = 4[/tex]
[tex]r = -3[/tex]
and [tex]n = 10[/tex] (Since, we are to determine the sum of the first 10 terms)
Now, put the parameters into the formula
[tex]S_{n} = \frac{a(1-r^{n}) }{1-r}[/tex]
We get
[tex]S_{10} = \frac{4(1-(-3)^{10}) }{1-(-3)}[/tex]
[tex]S_{10} = \frac{4(1-59049) }{1+3}[/tex]
[tex]S_{10} = \frac{4(-59048) }{4}[/tex]
[tex]S_{10} = \frac{-236192 }{4}[/tex]
[tex]S_{10} = -59048[/tex]
Hence, the sum of the first ten terms of the sequence is -59,048. The correct option is C.-59,048
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which property of equality is if 4m + n = 7 and n = 3 then, 4m + 3 = 7
Answer:
m = 1
Step-by-step explanation:
4 x 1 + 3 = 7
Answer: Addition property
Step-by-step explanation:
In the equation 4m + n = 7 , it indicates that n is 3, which means 3 has been added to it to get 4m + 3 = 7 so 3 has been added on each side.
what is the value of X?
Step-by-step explanation:
The answer is 45
The total degree is 360 and opposite angles of two straight lines are equal so
3x+3x+x+x=8x
8x=360
X=45
Angle 1 and Angle 2 form a linear pair. If m41 = (5x + 9)® and m22 = (3x + 11)", find the measure of
each angle.
Answer:
2/23/140+50ismmm/50
148/'320"120+4640=%40=40
Simplify x + 2 + x + 2 + x + 2 + x + 2 + x + 2 + x + 2 + x + 2 + x + 2 + x + 2. Write in simplified form, giving reasons. Someone help please?
easiest thing to do is combine like terms. There are 9 2's, which means 9(2) which equals 18. Now for the X's. There are 9 X's meaning (9)x which is 9x. This all makes up
18+9x
hope this helps
Answer:
9x +18
Step-by-step explanation:
0.001429 in scientific notation
Answer:
1.429 × 10^-3
Step-by-step explanation:
since it's below 1, you're moving the decimal to the right, which makes the 3 negative.
[50pts] What is the volume of this Cone? (Rounded to the nearest hundredth)
Answer:
Step-by-step explanation:
where is the photo?
Answer:
536.17
Step-by-step explanation:
Giving 40 points to whoever can solve a through k I need it now
Answer:
a: -1
b: 3
c: DNE
d: -1
e: 1
f: 1
g: 1
h: 2
i: -infinity
j: 0
k: infinity
HELP PLZZZZZZZZ HELP PLZZZZZZZZZ
Sorry I know this is a lot
THANK U FOR YOUR EFFORT
1.Write 6,730,000 in scientific notation.
2. Write 13,300 in scientific notation.
3. An ordinary quarter contains roughly 97,700,000,000,000,000,000,000 atoms. Write this number using scientific notation.
4. The distance from the Earth to the Moon is roughly 384,000 kilometers. Write this number in scientific notation
5. Write `4\cdot10^{5}` in standard notation Hint: Move the decimal 5 place
6. Write `1.8499\cdot10^{9}` in standard notation Hint: Move the decimal 9 places
7. Write `1.8499\cdot10^{9}` in standard notation Hint: Move the decimal 9 places
8. Write `6.43\cdot10^{3}` in standard notation
9. Write `8.456\cdot10^{7}`
10. Write `8\cdot10^{5}` in standard notation
11. Write `9\cdot10^{10}` in standard notation
12. Describe how you would write 3,482,000,000 in scientific notation as if you were explaining it to someone who didn't know what scientific notation was.
Example: Write 58,927 in scientific notation Hint: move the decimal 4 places.
Answer for the example: 5.8927\ times\ 10\ ^{4}
Whta is 80 - (-9) = explain pls
Answer:
80 - (-9) = 89.
Explanation:
In math, two negatives next to each other will become a positive. Since a negative number is being subtracted, The negatives will cancel.
So this:
80 - (-9)
Is functionally the same as this:
80 + 9
Therefore, the answer is 89.
Which table represents a linear function?
Answer:Only the first table represents a linear function. In order to be in linear function, the graph of the function must be a straight line.
Step-by-step explanation:
D
1) Students in Jake's class were numbered in order from 1 to 24. Jake was asked to
choose classmates numbered with multiples of 5 to be in his group. Which
number could be the number of a classmate in his group?
>) 15
>) 16
() 21
>)7
Answer:
15
Step-by-step explanation:
15 is the only number with a multiple of 5.
The Number of classmates in his group is less than 21
What is an inequality?An inequality is an inequation separated by <,>≥,≤. the relationship between two values that are not equal is defined by inequalities. Inequality means not equal. Generally, if two values are not equal, we use “not equal symbol (≠)”. But to compare the values, whether it is less than or greater than, different inequalities are used.
Given here: Jake's class has 24 students and she is to choose a group which is a multiple of 5
Thus the possible multiples of 5 between 1 and 24 are
5,10,15,20
Therefore all these multiples are less than 21
Hence, The Number of classmates in his group is less than 21
Learn more about inequalities here:
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Tommy’s bedroom is in the shape of a square. If the area of Tommy’s bedroom is 225 square feet, what is the measurement of each side of the room? (I just wan't to mark someone as brainliest)
Answer:
15 feet
Step-by-step explanation:
PLEASE HELP I WILL MARK YOU BRAINLIEST
Answer:
[tex] \boxed{ \bold{ \huge{ \boxed{ \sf{32 \frac{6}{20} \: \: \: {ft}^{2} }}}}}[/tex]
Option D is correct.
Step-by-step explanation:
Length of the rectangle = [tex] \sf{6 \frac{4}{5} \: ft}[/tex]
Width of the rectangle = [tex] \sf{4 \frac{3}{4} } \: ft[/tex]
Finding the area of a rectangle having length of [tex] \sf{6 \frac{4}{5} \: ft}[/tex] and width of [tex] \sf{4 \frac{3}{4} } \: ft[/tex]
[tex] \boxed{ \sf{area \: of \: a \: rectangle = length \times width}}[/tex]
[tex] \dashrightarrow{ \sf{6 \frac{4}{5} \times 4 \frac{3}{4} }}[/tex]
Convert the mixed number into improper fraction
[tex] \dashrightarrow{ \sf{ \frac{6 \times 5 + 4}{5} \times \frac{4 \times 4 + 3}{4}}} [/tex]
[tex] \dashrightarrow{ \sf{ \frac{30 + 4}{5} \times \frac{16 + 3}{4} }}[/tex]
[tex] \dashrightarrow{ \sf{ \frac{34}{5} \times \frac{19}{4}}} [/tex]
To multiply one fraction by another, multiply the numerators for the numerator and multiply the denominators for its denominator
[tex] \dashrightarrow{ \sf{ \frac{34 \times 19}{5 \times 4}}} [/tex]
[tex] \dashrightarrow{ \sf{ \frac{646}{20} }}[/tex]
Convert the improper fraction into mixed number
[tex] \dashrightarrow{ \boxed{ \sf{32 \frac{6}{20} \: \: {ft}^{2} }}} [/tex]
Hope I helped!
Best regards! :D
PLZ ANSWER QUICKLY, I NEED THIS SOON, thx :) If m∠A = m∠B and m∠A + m∠C = ∠D, then m∠B + m∠C = ∠D. Which property is shown? reflexive property substitution property symmetric property transitive property
Answer:
Substitution Property
What is the question to b(x)=3x-1.
Answer:
x = 1/3
Step-by-step explanation:
Which of the following expressions match the translation “nineteen more than the product of 4 and a number”? 4n + 19 4(n + 19) 19(n + 4) 4 + 19n
Answer:
4n+19
Step-by-step explanation:
The product of 4 and a number=4n
nineteen more than=+19
therefore the equation is 4n+19
Hope this helps!
Answer:
4n+19
Step-by-step explanation:
4n+19
nineteen more than=+19
therefore the equation is 4n+19
Hope this helps!
2.9 x 10^5 + 8.7 x 10^5
Answer:
So this is scientific notation what you do is
2.9x10^5 so you put however many zeros the is powered to 10. See there is a 5 It has to be behind or in front of the decimal you might be saying how do you know if its behind or in front well negative is in front and positive is behind .
290,000 there was a number already behind the decimal so there you go 5 number behind the decimal.
Same for the second one
290,000 870,000 is your answers so now you add hem together
1,160,000 is your final answer
Step-by-step explanation:
One number is two-thirds of another number. The sum of the numbers is 55.
Answer:
bl
Step-by-step explanation:
what is the right answer
Answer:
{y≥1
,{y-x>0
Step-by-step explanation:
First of all you have to consider the shaded region. It is bound by two lines.
The first line is a solid line that cuts the y-axis at +1. it's equation is y = 1. since the shade region is on the upper side where y values increase, the unequivocally will be y≥1. notice that the sign ≥ is due to the solid line which indicates points on the solid line are part of the solution.
the second line is the broken line. it passes through the origin (0,0) and (1,1) any two points can be taken. the gradient is 1. m= (y1-y2)/(x1-x2) = (0-1)/(0-1)=(-1/-1)= 1. the equation of a straight line is
y=mx + c where m is gradient and c is the VA)ue of y as the line crosses the y axis ( y-intercept) which in this case is 0 at (0,0).so the equation will be y=1(x) + 0
y=x if we subtract x from both sides we have
y-x=0
since the shaded region is on the upper side as y-x increases the in equality will be
y-x>0 notice since the line is broken it shall be just > not≥ because points on a broken line are not included in the shaded region.
Determine whether each identity is true or false.
Answer:
TrueTrueFalseFalseTrueFalseStep-by-step explanation:
6n + 4 = -6 what does n equal
Answer:
-5/3 or -1.7
Step-by-step explanation:
Answer:
n= [tex]-1\frac{2}{3}[/tex] or [tex]-\frac{5}{3}[/tex]
What is the value oíz in the equation 3x - y = 13, when y=272
05
45
-(x+3) = 2x-6 what is x
Answer:
x=1
Step-by-step explanation:
So, first you make sure to multiply the parenthesis by the negative so then it would be,
-x-3=2x-6
Then you add the -3 from the right to the other side
so, -x=2x-3
Then you want all the X variables to one side so you subtract the 2x to both sides.
so, -3x=-3
divide both by -3
x=1
Lamar bought a 6-kilogram can of pistachios for $6.90. What is the unit price?
A $1.90
B) $1.30
C$1.10
D $1.15
Answer:
$1.15
Step-by-step explanation:
6.90/6=1.15
Miss bird can make 8 sculptures in 6 months. If she prepared 12 sculptures, how much time would she take
Answer:
9 months
Step-by-step explanation:
8 sculptures....... 6 months
12 sculptures...... X months
X=12 ×6 :8
X=72 :8
X=9 months
2. True or False: The point of intersection of the x-axis and the y-axis on a coordinate plane is the origin.
Answer:
true
Step-by-step explanation:
Answer: true
Step-by-step explanation:
A rectangular swimming pool measures 50 meters in length and 25 meters in width. Noah is make a scale drawing of the pool using the scale 1 centimeter represents 5 meters. What would the length and width of his scale drawing be in centimeters. ( scale is 1 cm =5 meters)
Answer;13
Step-by-step explanation:
13 bc she was adding
A car is traveling at 35 mph. If its tires have a diameter of 27 inches, how fast are the car's tires turning? Express the answer in revolutions per minute. If necessary, round to two decimal places. Group of answer choices
Answer:
435.73 revolutions per minute
Step-by-step explanation:
Find the circumferance of the wheel.
27 times π which is 84.823 inches
divide that by 12 to get it into feet, 7.061 feet
Divide by 5280 to get that to miles, 0.001 miles
Divide 35 by 60 to get how many miles per minute the car travels, 0.583
Divide your miles per minute by the diameter of wheel
Your answer will be 435.73 Revolutions per Minute
what coordinate expression represents the coordinates of any point after dilation by any scale factor, a?
Answer:
(x,y) → (ax,ay) .
Step-by-step explanation:
A dilation is a transformation that changes the size of the image. It either shrink or enlarge a shape by using a scale factor about a center of dilation.
If we transform point (x,y) by using dilation with scale factor k (assume center of dilation at (0,0) then the coordinate of the image will be (kx,ky).
So, the coordinate expression represents the coordinates of any point after dilation by a scale factor of a:
(x,y) → (ax,ay) .
Answer:
[tex]\huge\boxed{(ax, ay)}[/tex]
Step-by-step explanation:
In order to dilate the coordinates of a point, we want to make it [tex]a[/tex] times bigger. In order to do this, we can multiply the x and y values by our scale factor, a. This is called mapping. What it does is it basically multiplied our points by a specific number so that we end up with a figure that is [tex]a[/tex] (the scale factor) times bigger than the original.
So in order to make an expression for this, we multiply the x and y coordinates by a. So we have ax and ay.
Hope this helped!
Is 10x=10x equal infinitely many?