Two different infinite geometric series that each have a sum of 8 are 32 + 32(3) +32(3)² + 32(3)³ + ................. and 24 + 24(2) + 24(2)²+ 24(3)³+ .............
What is an infinite geometric series?An Infinite geometric series is the sum of the infinite terms and these terms have constant ratio between successive terms.
Let us take first term of the infinite series be a and r be the constant ratio between successive terms. Then formula for such geometric series be a+ar+ar²+ar³+.............
And sum of such series is ,S =a/(1+r)
We have to find two infinite geometric series with sum S = 8
Let us take a=24 and r=2
Then sum, S = [tex]\frac{24}{2+1} =\frac{24}{3}=8[/tex]
Therefore such series will be:
24 + 24(2) + 24(2)²+ 24(3)³+ .............
Another possibility for sum 8 will be with a =32 and r=3
Then the sum, S = [tex]\frac{32}{3+1} =\frac{32}{4}=8[/tex]
Therefore another such infinite geometric series will be
32 + 32(3) +32(3)² + 32(3)³ + .................
Thus, two different infinite geometric series that each have a sum of 8 are 24 + 24(2) + 24(2)²+ 24(3)³+ ............. and
32 + 32(3) +32(3)² + 32(3)³ + .................
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Write a flow proof.
Given: ZX bisects ∠ W Z Y ; XZ bisects ∠Y X W.
Prove: Δ W X Z ≅Δ X Z Y
We can conclude that ΔWXZ ≅ ΔXZY under ASA condition.
What do we mean by the congruency of a triangle?Two triangles are said to be congruent if all three corresponding sides and angles are equal in size.To appear identical, these triangles can be moved, rotated, flipped, and turned.They will coincide if they are moved.Congruence exists when two triangles satisfy the five congruence conditions.They are the side-side-side (SSS), the side-angle-side (SAS), the angle-side-angle (ASA), the angle-angle-side (AAS), and the right angle-hypotenuse-side (RHS).So,
To Prove: ΔWXZ ≅ ΔXZY
ZX = ZX = (Common)∠WZX = ∠YZX = (Equal as ZX bisects ∠WZY)∠ZXW = ∠ZXY = (Equal as XZ bisects ∠WXY)So, ΔWXZ ≅ ΔXZY under ASA consition.
Therefore, ΔWXZ ≅ ΔXZY.
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Assume you make $10 an hour and work 20 hours a week. In addition, you receive $1,200 a year in income from a trust fund. What is your total annual income
By adding wages and incomes, we conclude that the worker has a total annual income of $ 11,600.
What is the total annual income?
A year comprises a total of 52 weeks and the worker works 20 hours a week at a wage of $ 10 an hour and receive a total of $ 1,200 in income from a trust fund. The total annual income is the sum of wages of the entire year and the income from the trust fund:
x = (52 weeks) · (20 hours / week) · (10 USD / hour) + 1,200 USD
x = 11,600 USD
The worker has a total annual income of $ 11,600.
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Help pls I really need if help then thank you you really help
Answer - put the dot on -1
(-2)-(-1) = -1
Compare the two numbers. Use > or < .
√63, 7.5
Compare the two numbers √63, 7.5
[tex]\sqrt{63} =7.93[/tex]
So, √63 > 7.5
What is a square root?
A square root is a factor of a number in mathematics that, when multiplied by itself, equals the original value.Square roots can be taken into account more broadly in any situation where the concept of an object's square is specified.Among other mathematical structures, these include function spaces and square matrices.The term square root is sometimes used to refer to the major square root of a positive number, even though it is merely one of the two square roots of that number.To learn more about square roots, refer:
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Assume that x is an int variable. what value is assigned to x after the following assignment statement is executed? x = -3 4 / 5;
The value of x as an int variable is 0
What is a int variable?An int(integer) variable is a variable containing only whole numbers.
Given the expression;
x = - 3 + 4 % 6/ 5
Let's make into proper fraction, we have
x = - 3 + {}4/ 100 × 6/ 5
Multiply through
x = -3 + 6/ 5/ 4/ 100
x = -3 + {6/ 5 ÷ 0. 4}
x = -3 + {3}
expand the bracket
x = -3 + 3
Add like terms
x = 0
Thus, the value of x as an int variable is 0
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Complete question;
Assume that x is an int variable. what value is assigned to x after the following assignment statement is executed? x = -3 + 4 % 6/ 5;
A rental car company charges $71.87 per day to rent a car and $0.09 for every mile driven. Aaliyah wants to rent a car, knowing that: she plans to drive 475 miles. She has at most $320 to spend. Which Inequality can be used to determine d, the maximum number of days Aaliyah can afford to rent for while staying within her budget?
Answer: Yes, she can affort to rent the car.
Step-by-step explanation:
You multiply 0.09 times 475 which equals $42.75. Next you use the remaining amounts that Aaliyah has and divide it by $71.87.
Evaluate the function.
f(x) = x² + 3x - 7
2
Find f(-5)
Mars has volume 1.31 × 1021
m3
whereas
Pluto has volume 4.93 x 1019
m3
How many times bigger is Mars than Pluto?
Main Answer:
Mars is bigger than Pluto by 27 times.
Explanation:
Volume is defined as the space occupied within the boundaries of an object in three-dimensional space.It is also termed as the capacity of the object.Given: Volume of Mars = [tex]1.31[/tex] × [tex]10^{21} m^{3}[/tex]
Volume of Pluto = [tex]4.93[/tex] × [tex]10^{19} m^{3}[/tex]
To find: Determine how many times bigger is Mars than Pluto.
No. of times bigger = [tex]\frac{Volume of Mars}{Volume of Pluto}[/tex]
= [tex]\frac{1.31 * 10^{21} m^{3} }{4.93 * 10^{19}m^{3} }[/tex]
= [tex]\frac{131}{493} * 10^{2}[/tex]
=0.2657 × 100
= 26.57
=27
Final Answer:
Therefore, 27 times bigger is Mars than Pluto.
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# SPJ 9
what is the correct answer to the following solution 5−3y≤−y−15.
Suppose x and y vary together such that y = 2 x 8 . suppose x varies from x = 3 to x = 9.5 . over this interval, how much does x change by?
A function assigns the values. The value of x changes by 6.5, and the value of y changes by 13.
What is a Function?A function assigns the value of each element of one set to the other specific element of another set.
Given that x and y vary together such that y = 2x+8. Also, the of x varies from x = 3 to x = 9.5. Therefore, we can write,
x change by = Maximum value of x - Minimum value of x
= 9.5 - 3
= 6.5
Further, the minimum and the maximum value of y will be when the value of x is minimum and maximum, this is because the function is linear. Therefore, we can write,
Minimum value of y, y = 2(3) - 8 = -2
Maximum value of y, y = 2(9.5) - 8 = 11
y change by = Maximum value of y - Minimum value of y
= 11 - (-2)
= 11 + 2
= 13
Hence, the value of x changes by 6.5, and the value of y changes by 13.
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Find the equation of the axis of symmetry of the following parabola algebraically.
y=-x^2+12x-38
the independent variable is the one that's squared, namely the "x", that means that the parabola is a vertically opening parabola, so its axis of symmetry will simply be the equation of the vertical line that passes through the vertex, hmmm what's its vertex anyway?
[tex]\textit{vertex of a vertical parabola, using coefficients} \\\\ y=\stackrel{\stackrel{a}{\downarrow }}{-1}x^2\stackrel{\stackrel{b}{\downarrow }}{+12}x\stackrel{\stackrel{c}{\downarrow }}{-38} \qquad \qquad \left(-\cfrac{ b}{2 a}~~~~ ,~~~~ c-\cfrac{ b^2}{4 a}\right)[/tex]
[tex]\left(-\cfrac{ 12}{2(-1)}~~~~ ,~~~~ -38-\cfrac{ (12)^2}{4(-1)}\right) \implies \left( - \cfrac{ 12 }{ -2 }~~,~~-38 - \cfrac{ 144 }{ -4 } \right) \\\\\\ (6~~,~~-38+36)\implies (\stackrel{x}{6}~~,~~-2)~\hfill \stackrel{\textit{axis of symmetry}}{x=6}[/tex]
Check the picture below.
(5x^4)^2 solve this equation
what is 49/200 equal to explain
Answer: It can not be simplified
Step-by-step explanation:
49 is divisible by 1 and 7
200 is not divisible by 7
m jkm = 77 m nkm = 22 and kn bisects lkm find jkl
The measure of the angle JL is 33 degrees
Bisection of anglesA bisection is a line that divides an angle into two equal portion. Using the addition postulate below:
<JKM = <JKL + <LKN + <NKM
If the line KN bisects <LKM then <LKN = <NKM = 22 degrees
Substitute the given parameters
<JKM = <JKL + <LKN + <NKM
77 = <JKL + 22 + 22
77 = <JKL + 44
<JKL = 77 - 44
<JKL = 33 degrees
Hence the measure of the angle JL is 33 degrees
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Which statements have an inverse that is false?
1.If two angles are congruent, then they are vertical angles.
2.If two angles are a linear pair, then they are supplementary.
3.If two angles are acute, then their sum is less than 90.
4.If two angles are complementary, then both angles are acute.
Statement 1 is a false statement.
What are supplementary angle?
Supplementary angles are two angles whose measures add up to 180° . ex 150° and 30°
What are complementary angles?
When the sum of two angles is equal to 90° degrees, they are called complementary angles. For example, 30° and 60° are complementary angles.
What are vertical angles?
Vertical angles are formed when two lines meet each other at a point. A vertical angle and its adjacent angle are supplementary angles, i.e., they add up to 180°What are congruent angles?
Two or more angles that are identical to each other.
False - All vertical angles are considered congruent but not all congruent angles are considered vertical angles. Any acute or obtuse angle may also be considered congruent. True - If 2 angles whose measures add to 180°, it means they are supplementary. They form a linear pair.True - Let one angle be 30° and the other angle is 40° , both of which are acute angles, then their sum is 70°, which is less than 90° True - Both angles in a complementary pair will always be acute. For ex: 30° and 60° are complementary angles , but are less than 90°, so they both are acuteThus we can conclude that all vertical angles are congruent but not all congruent angles are considered vertical angles
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Evaluate 81^2/3 then find the square root
Answer:
Below in bold.
Step-by-step explanation:
81^2/3
= 81^2 = 6561
6561^1/3
= ∛(6561)
= 18.72
√18.72
= 4.33 to nearest hundredth.
The approximate weights of two animals are 5.36 x 104 lbs. and 6.2 x 104 lbs. Find the total weight of the two animals. Write the final answer in scientific notation with the correct number of significant digits.
12 x 104 lbs.
5.9 x 104 lbs.
1.22 x 105 lbs.
1.2 x 105 lbs.
Help plssss answer fast
The total weight of the two animals is 1.2 x 10^5 lbs
How to determine the total weight of the two animals?The given parameters are
Animal 1 = 5.36 x 104 lbs.
Animal 2 = 6.2 x 104 lbs
Rewrite the parameters properly
Animal 1 = 5.36 x 10^4 lbs.
Animal 2 = 6.2 x 10^4 lbs
The total weight of the two animals is calculated as
Total weight = Animal 1 + Animal 2
This gives
Total weight = 5.36 x 10^4 lbs + 6.2 x 10^4 lbs.
Factor out 10^4 lbs
Total weight = (5.36 + 6.2) x 10^4 lbs.
Evaluate the sum
Total weight = 11.56 x 10^4 lbs.
Rewrite as
Total weight = 1.156 x 10^5 lbs.
Approximate
Total weight = 1.2 x 10^5 lbs.
Hence, the total weight of the two animals is 1.2 x 10^5 lbs
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How to do 0.86 \ 0.004
Since 0.004 is 4/1000, muiltiply the numerator and denominator by 1000.
That is: (0.86×1000)= 860
(0.004×1000) = 4
860/4= 215
Answer:
215
Step-by-step explanation:
0.86 ÷ 0.004 = 215
Write these numbers in order of size.
Start with the smallest number.
0.6
2
3
65%
0.606
Given LM- MP and L, M, and P are collinear, which of the following is false about the relationship of L, M. and P?
(1) LM = MP (2) M is the midpoint of LP (3) LM +MP=180 (4) M bisects LP
The statement that is false about the relationship of L, M, and P that are collinear is: 3. LM + MP = 180.
What are Collinear Points?When two or more points are on a straight line, they are classified as collinear points.
What is the Midpoint of a Segment?The point on a line segment that bisects the segment into two equal parts is referred to as the midpoint of the line segment.
We are given that:
LM = MP, since, points L, M. and P are collinear points, therefore, it implies that point M is the midpoint of segment LP.
It also means that M bisects segment LP since LM = MP, where M is the midpoint of segment LP.
Thus, the statement that is false about the relationship of L, M, and P that are collinear is: 3. LM + MP = 180.
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Divide. State any restrictions on the variables.
7 x / 4 y³ ÷ 21 x³ / 8 y
The restrictions on the variables x and y be
x = 0 ⇒ 2/0 = ∞
y = 0 ⇒ 2/0 = ∞
What is meant by expression?
Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation. An expression's structure exists as pursues: Expression: (Math Operator, Number/Variable, Math Operator)
How to divide the given expression (7x/4y³) ÷ (21x³/8y)?(7x/4y³) × (8y/21x³) = (2/3x² y³)
What are the restrictions on the variables?
Here, x = 0 ⇒ 2/0 = ∞
Similarly, y = 0 ⇒ 2/0 = ∞
So , x, y ≠ 0
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Hello I will AWArd Brainlist !!!! Please Help me Its a geometry Math Problem!! Find the value of Sin(A)
Solution -:
By Using Pythagoras theorem-:
We know that,,
(Hypotenuse)²= ( Base )² + ( Perpendicular)²
than,,,, AC²= BC² + AB²
so,,,
[tex]( h) {}^{2} = ({15}^{2} ) + (\ {8}^{2} )[/tex]
[tex]AB = \sqrt{225 + 64} [/tex]
[tex]AB = \sqrt{289} [/tex]
then,,
[tex]AB \: = 17[/tex]
then,,, the value of sin a
[tex] \bold{= \frac{8}{17} }[/tex]
Thus option ( B ) is correct
The population of Georgia is growing at a yearly rate of about 1.3%. The current population is
about 9,815,210 people. The population of North Carolina is growing at a yearly rate of about
1.25%. North Carolina's current population is about 9,656,401 people.
a. What is the equation that models Georgia's population growth?
b. What is the equation that models North Carolina's population growth?
c. What do the graphs of the equations look like? Graph the equations on the provided grid.
The equation for population growth in Georgia is P = 8,815,210 ( 1.013 )ⁿ ( red line on the graph) and the equation for population growth in North Carolina is P = 9,656,401 ( 1.0125)ⁿ ( blue line on the graph).
We are given that:
For Georgia:
Growth rate of population = 1.3 %
Population = 8,815,210
For North Carolina:
Growth rate of population = 1.25 %
Population = 9,656,401
a) The equation that models Georgia's population growth can be found out by using the concept of compound interest as the population will increase in a compounded way.
So, the equation will be:
P = 8,815,210 ( 1 + 1.3 % )ⁿ
P = 8,815,210 ( 1.013 )ⁿ
where P is the population after n years.
b) the equation that models North Carolina's population growth:
P = 9,656,401 ( 1.0125)ⁿ
where P is the population after n years
Therefore, we get that, the equation for population growth in Georgia is P = 8,815,210 ( 1.013 )ⁿ ( red line on the graph) and the equation for population growth in North Carolina is P = 9,656,401 ( 1.0125)ⁿ ( blue line on the graph)
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determine whether the conclusion follows from the given statements by the law of detachment or the law of syllogism. given: if you go camping, then you will need a flashlight. given:if you need a flashlight, then you will need extra batteries. conclusion: if you go camping you will need extra batteries
The statement can be proved by the law of syllogism.
A formal logical framework used to infer a conclusion from a series of premises is referred to as a syllogism, also known as a rule of inference.
The law of syllogism in conditional statement is given as:
if p then r and if r then q , then we can state that if p then q , where p , q, and r are statements.
Now in the given conditional statements we can write it as:
let p = You go camping
r = you will need a flashlight
q = you will need extra batteries.
Now it is given the if p then r and again if r then q , so by using the law of syllogism we can state that if p then q , that is
If you camping you will need extra batteries.
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The conclusion follows from the law of syllogism .
Law of Syllogism : The Law of Syllogism allows to squeeze together the conditional statements and draw a conclusion .
In general ,
If
p → q
q → r
Then , p → r .
In the given case ,
p = if you go camping
q = then you will need a flashlight
r = then you will need extra batteries
Hence , since p → r
if you go camping → then you will need extra batteries .
Therefore , the conclusion follows from the law of syllogism .
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If you were to graph the inequality below on a number line
42≤−7x
Would you use an open circle, or a closed circle?
Would your arrow go to the left or the right?
what is the exact distance from (-5, 1) to (3, 0)
Answer:
[tex]\sqrt{17} }[/tex]
Step-by-step explanation:
To find the distance between these points in the Cartesian Plane, apply the distance formula (aka pythagorean theorem).
(x1-x2)^2+(y1-y2)^2= d^2 , where d is distance.
(-5-3)^2+(1-0)^2 -> (-8)^2+(1)^2 ->
16+1 -> 17
Find square root of d^2 to find d, which gives you the exact answer of [tex]\sqrt{17}[/tex].
write each expression in factored form
1. 3m + 9n
Answer: 3(m+3n)
Step-by-step explanation:
3m + 9n=
3*m + 3*3n=3(m+3n)
Solve for x.
A. 8
B. 4.8
C. 4
D. 7.2
Humpback whales are known to weigh as much as 80,000 pounds. The tiny krill they eat weigh only
2
.
1875
×
10
−
3
pound. About how many times greater is the weight of a humpback whale?
Select Choice
The weight of the Humpback whale is 3.6571 x [tex]10^{7}[/tex] times greater than the weight of the tiny krill.
What are factors of a number?A factor is a number that divides the given number without any remainder.
We have,
Weight of a Humpback whale = 80,000 pounds
Weight of tiny krill = 2.1875 x [tex]10^{-3}[/tex] pounds
We need to find what value multiplied with 2.1875 x [tex]10^{-3}[/tex] would give 80,000.
Let the value be M.
M x 2.1875 x [tex]10^{-3}[/tex] = 80,000
M = 80,000 / 2.1875 x [tex]10^{-3}[/tex]
M = 80,000 x / 2.1875 x [tex]10^{-3}[/tex]
M = 3.6571 x [tex]10^{7}[/tex]
Thus the weight of the Humpback whale is 3.6571 x [tex]10^{7}[/tex] times greater than the weight of the tiny krill.
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Maria has a square brick patio. She wants to reduce the width by 3 feet and
increase the length by 3 feet.
T
3 ft
3 ft
3 ft
O A. Iw= x(x-3); 40 square feet
3 ft
Let x represent the length of one side of the square patio. Write expressions
for the length and width of the new patio. Then find the area of the new patio
if the original patio measures 8 feet by 8 feet.
Answer:
Length = x + 3 ft
Width = x - 3 ft
Area of new patio = x² - 9 sq ft
If original side length = 8, new area = 55 sq ft
Step-by-step explanation:
The original patio has side length of x
If one side is reduced by 3 we get (x - 3) as the new side
If the side is increased by 3' we get (x + 3) as the new side
Area of new Patio = (x - 3)(x+3) = x² - 9
Original patio is 8 x 8
New patio width = 8 - 3 = 5
New patio length = 8 + 3 = 11
Area = 5 x 11 =55 sq ft
