The sum of the first 14 terms of the finite geometric series 0.5+ (-1) +2+... is -2730.5
How to determine the sum of the series?The series is given as:
0.5+ (-1) +2+...
The above series is a geometric series, with the following parameters:
First term, a = 0.5Common ratio, r = -2Number of terms, n = 14The sum of the first 14 terms is calculated using:
[tex]S_n= a *(1 - r^n) \div (1 - r)[/tex]
So, we have:
[tex]S_{14}= 0.5 *(1 - (-2)^{14}) \div (1 + 2)[/tex]
Evaluate
[tex]S_{14}= -2730.5[/tex]
Hence, the sum of the series is -2730.5
Read more about series at:
https://brainly.com/question/6561461
#SPJ1
[PRECALC] Verify the following trigonometric identity using sin2x + cos2x = 1
Answer:
See below ~
Step-by-step explanation:
Identities :
cot x = cos x / sin xsin²x + cos²x = 1Changing the Left Hand Side (LHS) :
1/cot x + cotx1/(cos x / sin x) + cos x / sin xsin x / cos x + cos x / sin xTake (sin x)(cos x) as the LCM (Least Common Multiple)sin x (sin x) + cos x (cos x) / (sin x) (cos x)sin²x + cos²x / cos x sin x1/cos x sin xEqual to the RHSI really need help on this one
Answer:
-3x+9y=-57
Substitute the x for 4
-3(4)+9y=-57
-12+9y=-57
Add +12
-12+9y=-57
+12 +12
9y=-45
Now divide the 9 to get y by itself
9y=-45
÷9 ÷9
y=-5
So the value of y is -5
☆anvipatel77☆
•Expert•
Brainly Community Contributor
Steven is puiting a design that contains two repeating patterns that start in the same place. One pattern repeats every 12 inches and the other repeats every 18 inches. How many inches will it take for the patterns to begin together again?
Answer:
36
Step-by-step explanation:
So, taking 12 inches and 18 inches, we can figure out where they both meet. To do this, you want to change these number into a fraction (12/18). Simplifying this gives you 2/3. So if you flip this fraction (3/2) and then use these number and multiply them with the first numbers (so we do 3*12 and 2*18, they both equal 36, so they would both meet at 36, our final answer. they would also meet at 72, 108, 144, etc. if you were to keep going.
which value make the inequality c+10<17
Answer:
c < 7
Step-by-step explanation:
Given inequality:
c + 10 < 17
Subtract 10 from both sides:
⇒ c + 10 - 10 < 17 - 10
⇒ c < 7
Let's solve
c+10<17c<17-10c<7The solution set is
(-oo,7)
In his first week at college, Anthony spent $17 on entertainment, $33 on food, and $23 on gas. If there are 11 weeks in the semester, estimate the total amount of money Anthony will spend on these things throughout the semester.
Answer:
$803
Step-by-step explanation:
17 + 33 + 23 = 73
73 * 11 = 803
If Sam invested $3,000 and he earned $300 over six months, the return is _____.
six months
$3,300
$300
$3,000
Answer:
ROI = 10.00%
Step-by-step explanation:
Investment Gain = $300.00
ROI = 10.00%
Annualized ROI = 21.00%
Investment Length = 0.50 years
A king decided to pay a knight one inch of gold for each day's protection on a 6-day trip. The king took a gold bar 6 inches long and paid the knight at the end of each day; however, he made only two cuts. How did he do this?
A king gives 1 inch per day to the knight as there are three pieces of length 1, 2, and 3 inches.
What is Algebra?Algebra is the study of mathematical symbols, and the rule is the manipulation of those symbols.
A king decided to pay a knight one inch of gold for each day's protection on a 6-day trip. The king took a gold bar 6 inches long and paid the knight at the end of each day.
The gold is divided into 2 parts.
First at the 1-inch mark, then the second mark will be
For the second mark, there are two conditions.
Condition 1 = mark can be made at 4 inches, then the next piece will be of 2 inches.
There will be a total of three pieces of 3 inches, 1 inch, and 2 inches.
Condition 2 = Mark can be made at 5 inches, then the next piece will be of 1 inch.
There will be a total of three pieces of 3 inches, 1 inch, and 2 inches.
The division is shown below.
The king will take 1 inch back from the knight and give him 2 inches.
According to the condition = A king gives 1 inch per day to the knight as there are three pieces of length 1, 2, and 3 inches.
So on the first day, 1 inch will be given. On the second day, he will give 2 inches and take 1 inch. On the third day, he will give 3 inches and take back 2 inches. On the fourth day, he will give 1 inch. On the fifth day, he will give 2 inches and take back 1 inch. On the sixth day, he will give 1 inch.
More about the Algebra link is given below.
https://brainly.com/question/953809
#SPJ1
Alexandra has a bag of stickers, 1/4 are red, 1/3 are black, 1/8 are green, and 1/12 are yellow. She picks a sticker without looking. What color is she MOST likely to choose?
Answer:
las negras, 1/3 es mayor
Step-by-step explanation:
Espero te sirva <3
What is the measurement at plot a?
Answer:
An Acre is a propduct of any rectangular plot of land giving a total of 4,046sqm OR 43,560sq ft. An Acre consist of 6 plots each measuring 6 x 120ft. In Lagos State, the standard size of a plot is 60 x 120ft (18m x 36m ie 648sqm), while in some other cities of the country, plots are measured in 50 x100ft.
Step-by-step explanation:
fractions were never my strong suit can anyone help?
Answer:
See below ~
Step-by-step explanation:
Find the decimal values of the fractions on each side :
Left side Right side
⇒ 4/10 = 0.4 ⇒ 2/5 = 0.4
⇒ 1/2 = 0.5 ⇒ 9/12 = 0.75
⇒ 1/4 = 0.25 ⇒ 2/8 = 0.25
⇒ 3/4 = 0.75 ⇒ 5/10 = 0.5
Hence, the matched fractions are :
4/10 ↔ 2/5
1/2 ↔ 5/10
1/4 ↔ 2/8
3/4 ↔ 9/12
Answer:
Step-by-step explanation:
100 POINTS!! NEED ANSWER ASAP!! A circle with center O is shown. Match each part of the circle to the term that describes it. Match the tiles.
Answer:
Step-by-step explanation: Parts of a circle.
Radius - the side of one slice of pizza
minor arc - The arc formed by the outer side of 3 or less slices of pizza
Diameter - the slice of pizza from side to side that passes through the center
Major arc - The arc formed by the outer side of 5 to 7 slices of pizza
semi circle - 4 slices of pizza or half of the whole pizza
Pairs:
angle BAC - Inscribed angle
Line IE - Secant
Segment AC - Chord
Arc FH - Minor arc
Angle HGF - Circumscribed angle
The complete sentences are:
angle BAC - Inscribed angleLine IE - SecantSegment AC - ChordArc FH - Minor arcAngle HGF - Circumscribed angleWhat is secant and chord?A secant line is a straight line that passes through two points on a circle. The section of the line that connects two separate circle points is known as a chord. Every secant line defines a distinct chord, and each chord is in its own unique secant line.
Given:
We have circle with center O.
Now, <BAC is inside the circle.
So, <BAC is an Inscribed angle.
then, IE is a secant as it is intersecting circle at two points
then, AC id a chord
then, Arc FH is a minor arc
and, <HGF is an Circumscribed angle as it is outside the circle.
Learn more about secant & chord here:
https://brainly.com/question/19008587
#SPJ5
Find dy/dx if y= (x²-3)³cos2x
Answer:
dy/dx = 6x(x²-3)cos2x - 2(x²-3)³sin2x
Step-by-step explanation:
We use the Product Rule:
y= (x²-3)³cos2x
dy/dx = (x²-3)³ d(cos2x)/dx + cos2x * d ((x²-3)³)/dx
= (x²-3)³ * -2sin2x + cos2x * 3(x²-3)*2x
= -2sin2x*(x²-3)³ + 6xcos2x*(x²-3)
= 6x(x²-3)cos2x - 2(x²-3)³sin2x
Find the volume of a cylinder 9in 9in
Answer:
2290.22
Step-by-step explanation:
Formula: V=pi*r^2*h
Plug in the values:
V=pi*81*9
81*pi=~254.469
~254.469 * 9 = 2290.22
Please help me I'll mark brainliest
Answer:
B
Step-by-step explanation:
Solve for -5v+6 = -12v+62 Simplify your answer as much as possible.
Hey there!
Answer :[tex] \displaystyle \blue{\boxed{\green{\bold{v = 8}}}} [/tex]
[tex] \\ [/tex]
Explanation:-5v + 6 = -12v + 62
[tex] \\ [/tex]
▪️Subtract 6 from both sides :
-5v + 6 - 6 = -12v + 62 - 6
-5v = -12v + 56
▪️Add 12v to each side :
-5v + 12v = -12v + 56 + 12v
7v = 56
▪️ Divide both sides by 7 :
7v / 7 = 56 / 7
v = 8
[tex] \\ [/tex]
Therefore, our answer is v = 8.
[tex] \\ [/tex]
▪️ Learn more about solving equations:
↣https://brainly.com/question/14700809
↣https://brainly.com/question/27597890
Answer:
v = 8
Step-by-step explanation:
Hello!
We can solve the equation by moving all terms of V to one side, and all integer values to the other.
Solve-5v + 6 = -12v + 62-5v + 6 + 12v = -12v + 62 + 12v7v + 6 = 627v + 6 - 6 = 62 - 67v = 56v = 56/7v = 8The value of v is 8.
We can plug back 8 into the original to check our answer:
-5(8) + 6 = -12(8) + 62-40 + 6 = -96 + 62-34 = -34Since both sides match, the solution of v = 8 is correct.
Please help. What is the area?
The area of the composite figure = area of rectangle 1 + area of rectangle 2 + area of triangle = 56 km²
What is the Area of a Composite Figure?Find the area of each shape that make up the figure, then add up to get the area of the composite figure.
The area of the composite figure = area of rectangle 1 + area of rectangle 2 + area of triangle
Area of rectangle 1 = (length)(width) = (6)(3) = 18 km²
Area of rectangle 2 = (length)(width) = (7 + 3)(2) = 20 km²
Area of triangle = 1/2(base)(height) = 1/2(10 - 4)(6) = 18 km²
The area of the composite figure = 18 + 20 + 18 = 56 km²
Learn more about area of composite figure on:
https://brainly.com/question/23781238
#SPJ1
what is 1+1? please provide a long sentence stating why it is correct
Answer:
[tex]1 + 1 = 2[/tex]
Step-by-step explanation:
1 + 1 is equal to 2 because it is- at least that's what we believe the answer to be. It doesn't have to, but it is just what we as humans have come to recognize because it is internationally accepted.
Heck, you don't need to be a genius to understand that when you inherently have exactly one more of a thing, you have more of it. Numbers are just a way to represent more (or less if we're talking negatives). Now, we'll probably never understand why mathematics is so beautifully synchronized with our world, but it is, and we as a sentient species have come to recognize that for the longest time.
Numbers are abstract, as long as you are consistent, anything can be a number if you give it value. [tex]1+1[/tex] doesn't have to equal [tex]2[/tex], if we wanted we could make it equal to [tex]:)[/tex]. [tex]1 + 1 =\ :)[/tex]
Whether we are solving basic algebra:
[tex]:)x + 4 = 10\\:)x = 6\\x = \frac{6}{:)} =3[/tex]
Or calculating integrals:
[tex]\int\limits^{0.5}_{0} {8xe^{:)x}} \, dx\\= \frac{xe^{:)x}}{:)}-\int\limits{\frac{e^{:)x}}{:)}} \, dx\\= 4xe^{:)x} - :)e^{:)x} + C = (4x-:))e^{:)x} + C\\=(4x-:))e^{:)x}|^{0.5}_{0}\\= (4(0.5)-:))e^{:)(0.5)} - (4(0)-:))e^{:)(0)}\\= :)[/tex]
[tex]1+1[/tex] will always be whatever [tex]1+1[/tex] is.
Hopefully, I didn't get too philosophical lol.
In ΔABC, AB = 16 in, BC = 9 in, AC = 10 in. AD is perpendicular to the extension of BC . Find CD.
Answer:
Your answer is 4.171) Draw the figure; make sure angle C is obtuse.
(2) There are two right triangles -- ADC and ADB.
(3) Let CD=x and AD=y; use the Pythagorean Theorem to form two equations in x and y.
4) Solve the pair of equations. The x^2 and y^2 terms cancel, leaving you with a linear equation in x which is easily solved to find the answer.
So, The length of CD will be 25/6 = 4.17
PLEASE HELP!!!
Which point is tangent to the circle?
A
D
M
Q
Mrs. Forsyth has 130 pieces of candy. She wants to split it into fifths for each of her classes. How
many pieces of candy will each class get?
Answer: The answer is 26
I just divided it by 5
Find the surface area and volume of the prism.
10 cm
6 cm
8 cm
The surface area of the prism is
The volume of the prism is
17 cm
cm².
cm³.
I’ll mark you as Brainly please help
help me wiht ixl pls
Answer:
it's either 42 If you add all the sides, or 1769472 if you multiple
A bag of snacks contains 3 flavors: cherry, lemon, and grape. Carol will take 1 snack from the bag without looking. The probability for each flavor is shown in the table.
Two quantities, Pand Q, are connected by
the relationship P= kQ+ c, where k and c
are constants. Q= 60 when P= 10 and
Q= 240 when P= 100.
Find the equation connecting P and Q.
Answer:
P = 0.5Q - 20
Step-by-step explanation:
P = kQ + c
substitute Q = 60 , P = 10 into the equation
10 = 60k + c → (1)
substitute Q = 240, P = 100 into the equation
100 = 240k + c → (2)
subtract (1) from (2) term by term to eliminate c
90 = 180k ( divide both sides by 180 )
[tex]\frac{90}{180}[/tex] = [tex]\frac{1}{2}[/tex] = 0.5 = k
substitute k = 0.5 into (1) and solve for c
10 = 60(0.5) + c
10 = 30 + c ( subtract 30 from both sides )
- 20 = c
then
P = 0.5Q - 20
The class was divided into 4 teams. Each team had 5 players. The
remaining class members- Ty, Keesha, and Sam- served as score keepers.
How many students were in the class?
EASY QUESTIONS EASY POINTS!!
Answer:
23 players.
Step-by-step explanation:
5 x 4 + 3 = 23
x + 14 = 28
Solve for ‘x’.
[tex] \Large{\boxed{\sf x = 14}} [/tex]
[tex] \\ [/tex]
Explanation :Given equation:
[tex] \sf x + 14 = 28 [/tex]
[tex] \\ [/tex]
Subtract 14 from both sides :
[tex] \sf x + 14 - 14 = 28 - 14 \\ \\ \\ \boxed{\boxed{\sf x = 14}} [/tex]
[tex] \\ \\ [/tex]
▪️Learn more about equations here:
↣https://brainly.com/question/19225782
Find the factor of each ff.
x²+27x+49
Answer:
There are no factors.
Step-by-step explanation:
x²+27x+49 is prime.
convert from decimal to fraction(
all steps) 0.36
[tex]0.36[/tex]
Answer:
this gives 36/100 that is the fraction for the decimal
Answer:
9/25
Step-by-step explanation:
Step 1. Multiply by 100 :
0.36 × 10036Step 2. Divide by 100 and leave in fractional form :
36/100Step 3. Simplify by dividing throughout 4 :
(36/4)/(100/4)9/25yr8 enlargements......
If the triangle ABC is enlarged using the point P as a center, then the point of the dilated triangle will be A'(-3, 2), B'(1, 2), and C'(-1, -2).
What is dilation?Dilation is the process of increasing the size of an item without affecting its form. Depending on the scale factor, the object's size can be raised or lowered.
The coordinate of point P will be (5, 4).
Let shift the origin at P, then the coordinate of ABC will be
A(-4, -1), B(-2, -1), and C(-3, -3)
If the scale factor is 2. Then the coordinate of the triangle A'B'C' will be
A'(-8, -2), B'(-4, -2), and C'(-6, -6)
Then shift the origin at (0, 0), then the coordinate of A'B'C' will be
A'(-3, 2), B'(1, 2), and C'(-1, -2)
The graph is shown below.
More about the dilation link is given below.
https://brainly.com/question/2856466
#SPJ1
A circle has a radius of 6/7 units and is centered at (-2.3,5). Write the equation of this circle.
Answer:
[tex](x + 2.3)^{2} + y^{2} = \frac{36}{49}[/tex]
Step-by-step explanation:
To get the equation of a circle, plug your information into this equation:
[tex](x - h)^2 + (y - k)^2 = r^2[/tex]
Therefore, the equation of this circle is:
[tex](x + 2.3)^{2} + y^{2} = \frac{36}{49}[/tex]
