A recursive definition of the given Geometric progression is: [tex]a_{n}=a_{n-1}r[/tex], with a₁ = 2 and n > 1.
What is a geometric progression?A geometric progression, sometimes referred to as a geometric sequence in mathematics, is a series of non-zero numbers where each term following the first is obtained by multiplying the preceding one by a constant, non-zero value known as the common ratio.
Now,
Given: 2, -4, 8, -16, ...
Here, [tex]r = \frac{-4}{2} = -2[/tex] and a₁ = 2.
Thus, a recursive formula for this geometric progression can be: [tex]a_{n}=a_{n-1}r[/tex], with a₁ = 2 and n > 1.
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What does f(5) =23 mean
Answer:
Step-by-step explanation:
when f is evaluated at 5 the output is 23
draw base ten blocks to show the number 200 in the place value chart below
Answer:
Step-by-step explanation:
The base ten blocks to show the number 200 in the place value chart is shown below.
What is an expression?
Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
The number 200 in the place value.
Now,
Since, the number 200 in the place value.
Hence, The figure for the base ten blocks to show the number 200 in the place value chart is shown in figure.
Thus, The base ten blocks to show the number 200 in the place value chart is shown below.
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Help Please
Solve for y : | y | = 16 .
y= ____ , ____
Give an example of a 2x2 matrix whose
determinant is 13.
Answer:
The method for appearing with numbers for the 2x2 matrix whose determinant is 13 is clarified.
Step-by-step explanation:
Determinant of 2×2 matrix
If we have a 2×2 matrix A of the form;
A =
\binom{a \: \: \: b}{c \: \: \: d}(
cd
ab
)
The determinant of the matrix is;
|A| = (a.d) - (b.c)
Therefore, to appear with numbers for a, b, c, and d, we must ensure; (a.d) - (b.cdeterminantse, if a = 3, d = 15, b = 2, and v = 1.
Ultimately, |A| = (3×5) - (2×1) = 13
#3 i
The endpoints of AB are A (-8, 5) and B (0,7). Find the coordinates of the midpoint M.
The coordinates of the midpoint M
The coordinates of the midpoint M of the segment AB is (-4,6).
What is the coordinates of the midpoint M of the segment AB?The midpoint formula is expressed as;
M = ( (x₁+x₂)/2, (y₁+y₂)/2 )
Given the data in the question;
Point A (-8, 5)
x₁ = -8y₁ = 5Point B (0,7)
x₂ = 0y₂ = 7To determine the midpoint, plug the given points into the formula above and simplify.
M = ( (x₁+x₂)/2, (y₁+y₂)/2 )
M = ( ((-8)+0)/2, (5+7)/2 )
M = ( ( -8+0 )/2, (5+7)/2 )
M = ( ( -8 )/2, (12)/2 )
M = (-4,6)
Therefore, the coordinates of the midpoint M of the segment AB is (-4,6).
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Find the expression for h(x)
Hello,
[tex]f(x) = - {x}^{2} + 8[/tex]
[tex]h(x) = - {x}^{2} + 8 - 3 = - { {x}^{2} } + 5[/tex]
Find the center and the radius of each circle. x²+y²-4 y-16=0
The center and radius of the circle given by the equation x^2 + y^2 - 4y - 16 = 0 is (0 , 2) and 2√5, respectively.
The standard form of the equation of circle is given by
(x - h)^2 + (y - k)^2 = r^2
where (h , k) is the location of the center and r is the radius of the circle.
On the other hand, the general form of the equation of circle is given by
x^2 + y^2 + Dx + Ey + F = 0
where D = -2h, E = -2k, and F = h^2 + k^2 -r^2.
If the equation of the circle in general form is x^2 + y^2 - 4y - 16 = 0, then the coefficients are:
D = 0
E = -4
F = -16
If D = -2h and D = 0, then
0 = -2h
h = 0
If E = -2k and E = -4, then
-4 = -2k
k = 2
If F = h^2 + k^2 -r^2 and F = -16, then
-16 = 0^2 + 2^2 - r^2
r^2 = 0 + 4 + 16
r^2 = 20
r = 2√5
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pls helppppppppppppp
Answer:
Option 2
Step-by-step explanation:
2.2 x 1.25 = 2.7510-2.75=7.25
there are 5 more of this same question get free pounts! Rex and Samir participated in a walkathon. Rex walked for 1 2/3 hours, and Samir walked for 3 1/3 hours. complete the comparison. Samir walked _____ times ad many hours as Rex walked.
Answer:
2 times as much
Step-by-step explanation:
1 hour 2/3 = 60 + (2/3) 40 mins = 100 minutes
3 hours 1/3 = (60 ×3 ) + 20 mins = 200 mins
200 is twice as much as 100
Urijah is starting a food cart business. The cost to start the business is $20,000 and the monthly costs are $8,000. He has been earning $8,800 every month in revenue. In how many months will Urijah's business break-even and earn a profit?
He will break even on the 25th month.
How to find the number of month his business will break even?The cost to start the business is $20,000 and the monthly costs are $8,000.
He has been earning $8,800 every month in revenue.
Profit = Selling Price - Cost Price
Therefore,
let
x = number of month
Hence,
selling price = 8800x
cost price = 20000 + 8000(x) = 20,000 + 8000x
Therefore,
profit = 8800x - (20,000 + 8000x)
profit = 8800x - 20000 - 8000x
profit = 8800x - 8000x - 20000
profit = 800x - 20000
Hence,
The month when they will break even is as follows:
8800x = 20,000 + 8000x
20000 = 8800x - 8000x
20000 = 800x
x = 20000 / 800
x = 25
Therefore, he will break even on the 25th month.
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FITNESS A fitness instructor is starting a new aerobics class using fitness hoops. She, wants to confirm that all of the hoops are the same size. What measure(s) can she use to prove that all of the hoops are congruent? Explain your reasoning.
The instructor can use Mathematical coincidence to prove that all of the hoops are congruent.
What do we mean by Mathematical coincidence?The term "coincide" refers to something happening at the same time. In mathematics, coincident lines are lines that lie on top of each other so that when we look at them, they appear to be a single line rather than double or multiple lines. Two lines as well as shapes that are exactly on top of one another.For instance, these two lines are coincidental, but they appear to be one line because they are on top of each other.So, the fitness instructor should use Mathematical coincidence and should keep the hoops on one another to check the congruency.
Therefore, the instructor can use Mathematical coincidence to prove that all of the hoops are congruent.
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A major fishing company does its fishing in a local lake. The first year of the company's operations it managed to catch 175,000 fish. Due to population decreases, the number of fish the company was able to catch decreased by 8% each year. How many total fish did the company catch over the first 10 years, to the nearest whole number?
The company catches 1,237,275.5 fishes over 10 years.
Given that, a company catches 175000 fishes in a year, the population decreases, the number of fish the company was able to catch decreased by 8% each year.
So, the population in 10 year =
The second year = 175000 × 0.92 = 161000
The third year = 161000 × 0.92 = 148120
The fourth year = 148120 × 0.92 = 136,270.4
The fifth year = 136270.4 × 0.92 = 125368.8
The sixth year = 125268.8 × 0.92 = 115339.3
The seventh year = 115339.3 × 0.92 = 106112.2
The eighth year = 106112.2 × 0.92 = 97623.2
The ninth year = 97623.2 × 0.92 = 89813.3
The tenth year = 89813.3 × 0.92 = 82628.3
The total = 175,000+161000+148120+136,270.4+125368.8+115339.3+106112.2+97623.2+89813.3+82628.3 = 1,237,275.5
Hence, the company catches 1,237,275.5 fishes over 10 years.
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Ms. Lopez is creating posters to decorate
her classroom. She uses 0.25 ounce of paint
per poster. If she has 4.05768 ounces of
paint, how many posters can she make?
A die is rolled. Find the probability of the outcome. P( less than 2 )
When a die is rolled, the probability of outcome less than 2 is 1/6.
As given in the question,
Let the possible outcomes of the given event is represented by S.
Formula used :
Probability of an event
= (Favorable outcomes) /(Total Number of possible outcomes)
When a dice is rolled, all possible outcomes are 1, 2, 3, 4, 5, 6.
Sample space, S =(1, 2, 3, 4, 5, 6)
Favorable outcomes = Only 1 is smaller than 2, remaining number is greater than 2
So, total number of favorable outcomes = 1
Probability of outcome less than 2
= (Favorable outcomes) /(Total Number of possible outcomes)
⇒ Probability = 1/6
Therefore, when a die is rolled, the probability of outcome less than 2 is 1/6.
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A b = 8x - 7 BC = 6X + 7 what is AC
Answer:
a
Step-by-step explanation: codigo binario
If p(a|b) =0.40, p(b) = 0.74, and p(a) = 0.42, are the events a and b independent?
The set of items that exist as part of both sets A and B exists at the intersection of the two sets.
If p(a|b) =0.40, p(b) = 0.74, and p(a) = 0.42, then P(A∩B) is 0.46.
What is Probability?The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true.
It exists given that the Probability of two independent event A and B exists given by P(A) and P(B).
The intersection of event A and B is given by P( A∩B).
The group of items that are part of both sets A and B is the intersection of the two sets. A ∩ B represent the intersection. The symbol "∩" can be used to represent the intersection of sets.
The collection of all outcomes that are components of both sets A and B is known as the intersection of events A and B (abbreviated AB).
Given: P(a|b) = 0.40
P(A) = 1 - 0.40 = 0.6
P(B) = 1 - 0.74 = 0.26
P(A∪B) = P(A) + P(B) − P(A∩B)
substitute the values in the above equation, we get
0.40 = 0.6 + 0.26 - P(A∩B)
- P(A∩B) = 0.40 - 0.6 - 0.26
P(A∩B) = 0.46
Therefore, the independent events of A and B exists 0.46.
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Find the values of x and y given that 182x + 247 y = gcd(182, 247)
Answer:
Hello,
x=-4, y=3
Step-by-step explanation:
14*x+19*y=1 since gcd(182,247)=13
Here is a automatic calculus (using Bezout 's method)
All you have to do is to put in B1 and B2 the right numbers
The values of x and y given that 182x + 247 y = gcd(182, 247) would be x=-4 and y=3.
What does it mean to solve an equation?An equation represents equality of two or more mathematical expression.
To solve an equation, then the values of the unknowns for which that equation would be true (the equality between expressions should hold true for those values).
And Solutions to an equation are values of the variables involved in that equation for which the equation is true.
We have given the equation as;
182x + 247 y = gcd(182, 247)
Then we get
14*x+19*y=1
Thus, x=-4 and y=3.
since we have given gcd(182,247)
=13
Hence, The values of x and y given that 182x + 247 y = gcd(182, 247) would be x=-4 and y=3.
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After robbing a bank in Dodge City, a robber gallops off at 14 mi/h. 30 minutes later, the marshall leaves to pursue the robber at 16 mi/h. How long (in minutes) after the marshall takes off does it take the marshall to catch up to the robber?
The number of minutes it will take the marshal to catch up to the robber in discuss is; 210.
How long will it take to catch up with the robber?Let 30minutes = 0.5 hours.
Let x represent the time for which the marshal has ran.
On this note, the robber must have galloped at; (x +0.5) hours.
Hence, it follows from the task content that if they are at the same distance from the bank; we have;
14(x+0.5) = 16(x)
14x + 7 = 16x
7 = 2x
x = 7/2 = 3.5 hours.
= 3.5 × 60minutes = 210minutes.
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help asap!! check screenshot
The sequence of the angles from lower to bigger will be ∠WXY < ∠YXZ < ∠WYX < ∠XZY < ∠XYZ.
What is the triangle?A triangle is a three-sided polygon with three angles. The angles of the triangle add up to 180 degrees.
In a triangle, if the angle is small then the opposite side will be short, and if the angle increases then the side also increases.
The sides of the triangle are in ascending order, then we have
WY < YZ < WX < XY < XZ
Then the sequence of the angles is given as,
∠WXY < ∠YXZ < ∠WYX < ∠XZY < ∠XYZ
The sequence of the angles from least to biggest is ∠WXY < ∠YXZ < ∠WYX < ∠XZY < ∠XYZ.
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What's 3/6 + 2/6? (Note: you will get 99 points if you solve this!)
================================================
the fractions have like denominators so we add numerators :
[tex]\sf{\frac{3}{6} +\frac{2}{6} =\frac{3+2}{6} =\frac{5}{6}[/tex]
5/6================================================
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[tex]\textcopyright ELIZA[/tex]
What is the 2 nd term of the geometric sequence 3, II, 12, . . . . . . . ?
The second term of the given geometric sequence is: 6.
What is a geometric progression?A geometric progression, sometimes referred to as a geometric sequence in mathematics, is a series of non-zero numbers where each term following the first is obtained by multiplying the preceding one by a constant, non-zero value known as the common ratio.Given:
First term of GP = 3 (a₁).Third term of the GP = 12 (a₃).To find: Second term of the GP (a₂).
Finding:
Since the given sequence is a GP, the nth term will be given by: [tex]a_n=a_1(r^{n-1})[/tex], where r = common ratio of the GP.
Now, for n = 3, [tex]a_3=3(r^{3-1})[/tex]
=> 12 = 3 (r²)
=> 4 = r²
=> r = ±2
Since the given sequence is increasing and positive, r = 2.
Thus, a₂ = a₁ (r¹)
=> a₂ = 3 (2) = 6
Hence, The second term of the given geometric sequence is: 6.
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What is the slope of a line perpendicular to the line whose equation is x+4y=16x+4y=16. Fully simplify your answer.
The slope of a line perpendicular to the line of x + 4y = 16 is 4.
What is the slope of a line perpendicular to the line of the given equation?Given the equation of line;
x + 4y = 16
First, rearrange in slope intercept form ( y = mx + b ) by solving for y
x + 4y = 16
Subtract x from both sides
x - x + 4y = 16 - x
4y = -x + 16
Divide each term by 4 and simplify
4y/4 = -x/4 + 16/4
y = -(1/4)x + 4
Using the slope intercept form ( y = mx + b ) to compare.
y = -(1/4)x + 4
Slope m = -(1/4)
Now, the equation of a perpendicular line to y = -(1/4)x + 4 must have a slope that is the negative reciprocal of the original slope.
Hence, m_perpendicular will be;
m_perpendicular = -( 1 / original slope )
m_perpendicular = -( 1 / -(1/4) )
m_perpendicular = -( -4 )
m_perpendicular = 4
Therefore, the slope of a line perpendicular to the line of x + 4y = 16 is 4.
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Write a two-column proof. (Lesson 4-4)
Given: Δ L M N is isos. with LM ≅ NM , and MO bisects ∠L M N .
Prove: Δ M L O ≅ ΔM N O
It is proved that ΔLMN is an isosceles triangle.
What exactly do we mean by a triangle's congruency?Two triangles are said to be congruent if all three corresponding sides are equal and all three corresponding angles are equal in measure.These triangles can be moved, rotated, flipped, and turned to appear identical.If they are repositioned, they will coincide.If two triangles satisfy the five congruence conditions, they are congruent.They are side-side-side (SSS), side-angle-side (SAS), angle-side-angle (ASA), angle-angle-side (AAS), and right angle-hypotenuse-side (RHS).So,
Given:
LM ≅ NMMO bisects ∠L M NTo prove congruency:
MO = MO (Common line)LM = NM = Given∠LM0 = ∠NMO = equal angles (As MO bisects ∠LMN)Therefore, ΔM LO ≅ ΔMNO under SSA congruency.
Since the 2 sides are similar so the angles in front of them will also be similar.So we can say that ΔLMN is an isosceles triangle.Therefore, it is proved that ΔLMN is an isosceles triangle.
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-8(-10/7)=4(-10/7+5)+2(-10/7)
help pls
just like show solution
Answer:
Step-by-step explanation:
[tex]\displaystyle\\-8(-\frac{10}{7})= 4(-\frac{10}{7} +5)+2(-\frac{10}{7} )\\[/tex]
[tex]\displaystyle\\Let \ -\frac{10}{7} =t\\Hence,\\(-8)(t)=(4)(t+5)+(2)(t)\\-8t=(4)(t)+(4)(5)+2t\\-8t=4t+20+2t\\-8t=6t+20\\-8t+8t=6t+20+8t\\0=14t+20\\0-20=14t+20-20\\-20=14t\\-20=(14)(-\frac{10}{7} )\\-20=-\frac{(14)(10)}{7} \\\\-20=-\frac{(7)(2)(10)}{7} \\-20=-(2)(10)\\-20\equiv-20[/tex]
The temperature is 10 degrees below zero. The sun come out and the temperature went
up 15 degrees. What is the temperature now since the sun came out?
Answer:
5 degres
Step-by-step explanation:
0-10 is -10
-10+15 is 5
The monthly cost of using a cell phone is $29.95 plus $0.035 per minute of talk time. An equation to
represent this monthly cost would be:
C = 29.95 + 0.035x, where C represents the monthly cost and x represents the number of minutes used.
How many minutes were used during a month if the cost amounted to $43.53 ?
O 506 minutes
O 426 minutes
O 388 minutes
438 minutes
Answer:
c) 388 minutes
Step-by-step explanation:
Given equation,
→ C = 29.95 + 0.035x
Then the call duration will be,
→ C = 29.95 + 0.035x
→ 43.53 = 29.95 + 0.035x
→ 0.035x = 43.53 - 29.95
→ x = 13.58/0.035
→ [ x = 388 ]
Hence, option (c) is correct.
Thomas took a 140-mile bus trip to visit his grandparents.
His trip is outlined on the graph
Explain what might have happened in the interval
between D and E.
a. Show work (50 points). Mark the graph
Answer:
they stopped at 110 for a restroom break?
I don't think I fully understand lol srry
Thomas and his grandparents are on a trip of 140-mile. From Points D and E, there is no movement of the bus, which means they halt at the point.
What is a graph?An orderly schematic illustration or diagram of facts or quantities is known as a graph in mathematics.
Usually, the graph's examples indicate how two or more items are related to one another.
As per the graph provided in the question,
As we can see in the graph there are covering 140 miles in a bus and the graph shows distance (in miles) and time (in hours).
From the graph we can see that between point D and E only time is increasing but the distance is constant which means they stopped at some place to halt.
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The scatter plot shows the number of stamps Katie collected in different months:
plot ordered pairs 1, 30 and 2, 70 and 3, 110 and 4, 150 and 5, 190
What is the approximate predicted number of stamps she collected in the 25th month? (1 point)
980
990
1,000
1,010
Hello!
The approximate predicted number of stamps she collected in the 25th month is 990.
Step-by-step explanation:
The ordered pairs are as follows:
( 1, 30), ( 2, 70), ( 3, 110), ( 4, 150), and ( 5, 190).
The pattern visible is that each month the value increases by 40 from each previous month.
The equation you would have to do in order to see how many stamps she collected is:
[tex]30[/tex] + [tex]40[/tex] × [tex]24=30[/tex] + [tex]960=990[/tex]
Hope this helps!
help me with this question
Find the values of x and y. State which theorem(s) you used.
The required simplified value of x and y is 32 and 84 respectively.
Given that,
To find the values of x and y. State which theorem(s) you used.
The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
Vertical opposite angles
3x = 5x - 64
2x = 64
x = 32
Now,
5x - 64 = 5*32 - 64
= 160 - 64
= 96°
Now complementary angle y
y = 180 - 96°
y = 84°
Thus, the required simplified value of x and y is 32 and 84 respectively.
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