Answer:
14th term
Step-by-step explanation:
12÷10 = 1.2
14.4÷12 = 1.2
17.28÷14.4 = 1.2
Then it’s a geometric sequence of first term ‘V₀=10’ and common ration ‘q = 1.2’
We call it (Vn)
The general term of the sequence:
Vn = V₀×qⁿ⁻¹ = 10×(1.2)ⁿ⁻¹
To determine the term at which the sequence exceeds 100 we have to solve the equation:
Vn ≥ 100
⇔ 10×(1.2)ⁿ⁻¹ ≥ 100
⇔ (1.2)ⁿ⁻¹ ≥ 100/10
⇔ (1.2)ⁿ⁻¹ ≥ 10
⇔ ln(1.2)ⁿ⁻¹ ≥ ln(10)
⇔ (n-1)×ln(1.2) ≥ ln(10)
[tex]\Longleftrightarrow n-1\geq\frac{ln10}{ln1.2}[/tex]
[tex]\Longleftrightarrow n-1\geq12.6\\\Longleftrightarrow n\geq13.6\\\Longrightarrow n=14[/tex]
Verification:
[tex]V_{14}=10\times \left( 1.2\right)^{14-1} =106.993205379072[/tex]
A system of equations is graphed on the coordinate plane.
y = 1/2+2
y = x + 1
What is the solution to the system of equations?
Answer:
y=2.5, x=1.5
Step-by-step explanation:
y=1/2+2 ---(1)
y=x+1 ---(2)
y=1/2+2=2.5
Substitute y=2.5 into equation (2)
y=x+1
2.5=x+1
2.5-1=x
x=1.5
The speed of light in a vacuum is 29,980,000,000
centimeters per second. In scientific notation, this
number is written as
A. 2.998 x 10⁹.
B. 2.998 x10¹0.
C.
29.98 x 10⁹.
D. 29.98 x10¹0.
Answer:
[tex]\huge\boxed{\sf 2.998 \times 10^{10}}[/tex]
Step-by-step explanation:
Given number:
29,980,000,000
Rules:
Move the decimal point after the first non-zero digit. (after 2)Here, we will move the decimal point 10 places to the left to move it after the first non-zero digit.Since we move the decimal point 10 places, we will write the number as a multiple of 10¹⁰ (10 being the exponent).The number will become:
2.998 × 10¹⁰
[tex]\rule[225]{225}{2}[/tex]
Answer:
B. 2.998 x 10¹⁰
Step-by-step explanation:
Given :
29,980,000,000Steps in solving :
Take the zeros after the last non-zero digit as a power of 10.Take the non-zero part (in the part) and put a decimal point after between the thousands and hundreds place, and shift the remaining powers of 10 to the previously grouped part.Adjust further if needed to match an answer.Solving :
29,980,000,0002,998 x 10⁷2.998 x 10³ x 10⁷2.998 x 10¹⁰I need help with this equation. Please solve for k
Hey there!
18 = -k + 3
-k + 3 = 18
-1k + 3 = 18
SUBTRACT 3 to BOTH SIDES
-1k + 3 - 3 = 18 - 3
SIMPLIFY IT!
-1k = 18 - 3
-1k = 15
DIVIDE -1 to BOTH SIDES
-1k/-1 = 15/-1
SIMPLIFY IT!
k = 15/-1
k = -15
Therefore, the answer is: k = -15
Good luck on your assignment & enjoy your day!
~Amphitrite1040:)
two squares have a total area of 208cm square and sum of their perimeter is80cm what are the length of sides of square
The length of the sides of the square are 8 centimetres and 12 centimetres respectively
How to finds area of a square?area = l²
where
l = side lengthTherefore,
x² + y² = 208
How to finds perimeter of a square?perimeter = 4l
4x + 4y = 80 cm
x + y = 20
x = 20 - y
(20 - y)² + y² = 208
y² - 40y + 400 + y² = 208
2y² - 40y + 192
y² - 20y + 96
(y - 12)(y - 8)
Therefore, y = 12 and y = 8
when y = 8
x + 8 = 20
x = 12
when y = 12
x + 12 = 20
x = 8
Therefore, the length of the sides of the square are 12 cm and 8 cm.
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Factor 6x^2+14x.
Please, help
Factor 2x from 6x².
2x (3x)+14x
Factor 2x from 14x.
2x (3x) + 2x (7)
Factor 2x from 2x (3x) + 2x (7).
2x(3x+7) ====> Answers
Answer:
(2x)(3x + 7)
Step-by-step explanation:
Hello!
We can factor this expression by taking out the GCF of both the terms.
The GCF is 2x, because it is the largest factor that is in common between 6x² and 14x
Factor6x² + 14x2x(3x) + 2x(7)(2x)(3x + 7)The factored expression is (2x)(3x + 7)
In the figure below, what is the value of x?
Answer:
x = 31.
Step-by-step explanation:
93 = x + 62 (External Angle Theorem).
x = 93 - 62
= 31
what is the value of x
Answer:
x= 96
Step-by-step explanation:
I know this is might not be the best reasoning, but if 56+40=96, then the other consecutive angle should be 96 degrees by the Consecutive Interior Angles theorem.
Solve equation 2x+7=17
Answer: x =5
Step-by-step explanation:
subtract 7 on both sides than divide by 2
Answer:
x = 5
Step-by-step explanation:
Given: 2x + 7 = 17
1. Subtract 7 from both sides
2x + 7 - 7 = 17 - 7
2x = 10
2. Divide both sides by 2
2x ÷ 2 = 10 ÷ 2
x = 5
Final answer: x = 5
Learn more about solving equations here:
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look at the picture to solve it
Answer:
6^7
Step-by-step explanation:
To multiply powers of the same base, add their exponents. Add 4 and 2 to get 6.
To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 6 from 13 to get 7.
Answer:
6^7
Step-by-step explanation:
6^13/6^6 = 6^7
Solve for x: 2x² - 7x - 30 = 0
Answer:
x=-10
Step-by-step explanation:
2x²-7x=0+30
2x²-7x=30
4x-7x=30
-3x=30
x=-10
Answer:
Step-by-step explanation:
(2x + 5)(x - 6) = 0
2x + 5 = 0
x = -5/2
x - 6 = 0
x = 6
What is the slope of a line that goes through (2,-2) and (5,6)?
Step-by-step explanation:
The slope formula from 2 points is:
m=(y2-y1)/(x2-x1)
So input the numbers:
m = (6 - -2) / (5 - 2)
Solve within parenthesis:
m = (8) / (3)
Then divide!
8/3 = 2 2/3
the slope of the line is 2 and 2/3
A bag contains 3 red marbles, 4 blue marbles, and 2 yellow marbles. What is the probability of pulling out a blue marble?
Probability of pulling out the Blue Marbels = 4/9
Step-by-step explanation:
Red Marbels = 3
Blue Marbels = 4
Yellow Marbels = 2
Total Marbels = 9
P( Blue Marbels) = Number of favorable outcomes/Total number of possible outcomes = 4/9
I need some help answering this
Answer:
Θ = 50°
Step-by-step explanation:
Using the cofunction identity
tan(90 - x)° = cotx°
Given
cot40°, then
tan Θ = tan(90 - 40)° = tan50°
Thus Θ = 50°
Ashmita is 63 inches tall. How does her height compare with the other AP Stats students in her class?
Answer:
Using Logic...she is shorter than most children at that level.
Step-by-step explanation:
Ashmita is 63 inches tall which is 5 foot 3. or 5.25 feet
When AP stats starts you should be in Highschool.
Here are the averages of highschool students, in height.
14 years = 5ft 4.5in (163.8 cm) 5ft 2.5in (158.7 cm)
15 years = 5ft 7in (170.1 cm) 5ft 2.9in (159.7 cm)
16 years = 5ft 8.3in (173.4 cm) 5ft 4in (162.5 cm)
17 years = 5ft 9in (175.2 cm) 5ft 4in (162.5 cm)
Please answer c.) with working
Answer:
a: 44%
(11×100)÷25=44
b: 3
2×4=8
3×1=3
8+3=11
14-11=3
Write the ratios for sin A and cos A.
A
26
B
10
C
24
Not drawn to scale
The price of a train ticket costs of an initial fee of $5 plus a fee of $2.75 per stop. Julia has $21 and would like to travel 50 kilometers. She wants to know the largest number of stops she can afford to buy on a ticket
Let S represent the number of stops that Julia buys
Which inequality describes the scenario and What is the largest number of stops that Julia can afford?
Answer:
Julia can afford 5 stops including the initial fee
Step-by-step explanation:
Initial Fee = $5
Rate per stop = $2.75
Amount = $21
$21 - $5 ÷ $2.75 = 5 with remainder
[tex]\frac{x+3}{x-3} +\frac{36}{9-x^{2} } =\frac{x-3}{x+3}[/tex]
Answer:
Here is the ans ...hope it helps
Question Number 14 of 20 - Geometry The equation of line kis y = = 1 -X – 2. The equation of line m is -2x + 6y = 18. Lines k and m are - 3 F perpendicular G intersecting but not perpendicular H parallel I the same line
Based on the calculations, the two lines have the same slope but different intercepts and as such are parallel.
The condition for two parallel lines.In Geometry, two lines are considered to be parallel under the following conditions:
m₁ = m₂
Note: m is the slope.
For two perpendicular lines, we have:
m₁m₂ = -1.
From line k, we have this equation:
y = 1/3x - 2
From line m, we have this equation:
-2x + 6y = 18.
6y = 18 + 2x
y = 18/6 + 2/6x
y = 1/3x + 3.
Therefore, we can deduce that the two lines have the same slope (1/3) but different intercepts and as such are parallel.
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ТУ
Which quadratic function is represented by the graph?
6
5
4
O FUX) = - (x + 1)(x – 5)
O f(x) = - (x – 11x + 5)
3
2-
14
O f(x) = -5(x + 1)(x - 5)
2 3 4 5 x
3 -5 -5 -4 -3 -2 -21
-2
O f(x) = -5(x - 1)(x + 5)
+
-3
4
6
Answer:
the first one
Step-by-step explanation:
because I know the answer
The quadratic function represented in the graph is f(x) = -5 (x - 1) (x + 5).
What are Quadratic Functions?Quadratic functions are polynomial functions consisting of variables and exponents and the degree of the variable is 2.
The general form of a quadratic function is f(x) = ax² + b x + c.
Given a graph of a quadratic function.
The graph is directed downwards. So the leading coefficient is negative.
The function touches the X axis at two points, x = -5 and x = 1.
So -5 and 1 are the zeroes of the function.
So the function can be factored as,
f(x) = (x + 5)(x - 1)
So the quadratic equation is,
f(x) = -5 (x - 1) (x + 5)
Hence the equation of the given quadratic equation is f(x) = -5 (x - 1) (x + 5).
Learn more about Quadratic Equations here :
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8 is 80% OF WHAT NUMBER?
155 is 25% of WHAT NUMBER?
Answer:
8 is 80% of 10
155 is 25% of 465
Step-by-step explanation:
the first one is easy, and the second one, 25% is 1/4, so if you multiply 155 by 4, you get 465
Does anybody know this? I don't have much time and Also it is not the forth option. What is the approximate surface area of the cylinder shown?
Answer:
C) [tex]628\:\text{cm}^2[/tex]
Step-by-step explanation:
[tex]SA=2\pi rh+2\pi r^2\\\\SA=2\pi(\frac{10}{2})(15)+2\pi(\frac{10}{2})^2\\ \\SA=150\pi+50\pi\\\\SA=200\pi\:\text{cm}^2\approx628\:\text{cm}^2[/tex]
The side lengths of the rectangle are multiplied by 1/3 what is the new area
Answer:
New area is 1/9th the original area
Step-by-step explanation:
Original area = L x W
now reduce the side lengths
1/3 L x 1/3 W
1/3 * 1/3 * L x W
1/9 L x W <===== the new area is 1/9th the original area
Simplify this expression.
8(h-4)-h-(h+7)
Solve step-by-step
Answer:
6h - 39 or 3(2h - 13)
Step-by-step explanation:
Distribute the terms in the parentheses.
8(h - 4) - h - (h + 7)8h - 32 - h - h - 7Combine like terms
8h - h - h - 32 - 76h - 393(2h - 13) [by grouping]8 (h - 4) - h - (h + 7)
8h - 32 - h - h - 7
6h - 39
3 (2h - 13)
The value of “p” in 1
3
+ p = 2
5
is .............
Answer:
p = 12
Step-by-step explanation:
13 + p = 25 ( subtract 13 from both sides )
p = 12
Answer:
the value of P is 12
Step-by-step explanation:
if 13+P=25 then P must be 12
subtract 13 from both sides
you're left with P=12
how to make a histogram
[tex]x \6 - 1 = x \4 + 1 \2[/tex]
answer. the question pls pls pls pls
Answer:
-18
Step-by-step explanation:
Hope it helps....................................................
The coordinates of the vertices of quadrilateral HIJK are H (-2, -1), I (2, 1), J (5, 0), and K (-1, -3). Isabella states that quadrilateral HIJK is a parallelogram. Is Isabella correct? Support your answer and show all work.
Answer: No
Step-by-step explanation:
Find the measure of <1, <2 and <3 In P
Answer:
Step-by-step explanation:
If a positive is subtracted from a negative, will the answer be true or false. ans:true
Answer:
It depends. If the negative number is greater than the positive, the answer is true. Otherwise, false.
