6th terms of given geometric progression whose common ratio is 3/2 and first term is 4 is 243/8 using the farmula ar^(n-1).
What is a geometric sequence?
A mathematical sequence known as a geometric progression (GP) is one in which each following phrase is generated by multiplying each preceding term by a fixed integer, or "common ratio." This progression is sometimes referred to as a pattern-following geometric sequence of numbers. Learn development in mathematics here as well. Here, each phrase is multiplied by the common ratio to generate the subsequent term, which is a non-zero value. A geometric series with a common ratio of 2 is 2, 4, 8, 16, 32, 64, etc.
Geometric Progression takes the following general form: a, ar, ar^2, ar^3, ar^4,..., ar^(n-1).
a = First term where
The common Ratio is r.
nth term = ar^(n-1)
6th terms ar^(6-1) = ar^5.
given is that r =3/2. a = 4.
6th term = 4 * (3/2)^5
= 4 * 3^5/2^5
=4*243/4*8
=243/8.
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Find the slope of a line that passes through the given two points using ratio method
The slope formula, or the ratio of the change in the y values to the change in the x values, is m=(y2-y1)/(x2-x1).
What is slope ?A line's steepness and direction are measured by the line's slope.
Without actually using a compass, determining the slope of lines in a coordinate plane can assist in forecasting whether the lines are parallel, perpendicular, or none at all.
A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes.
The y coordinate's net change is y, and the x coordinate's net change is x.
Hence, The slope formula, or the ratio of the change in the y values to the change in the x values, is m=(y2-y1)/(x2-x1).
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I need help, please
and can someone explain so I can stop posting so many of these?
it's infinitely many bc the equations have the same line
Answer:
a1x + b1y + c1 = 0
a2x + b2y + c2 = 0
Here a1, b1, c1, a2, b2, c2 are all real numbers.
Note that, a12 + b12 ≠ 0, a22 + b22 ≠ 0
Step-by-step explanation:
How many solutions does the following system have?
y = -2x – 4
y = 3x + 3
Solution:
Given y = -2x – 4
y = 3x + 3
Rewriting to the general form
-2x – y – 4 = 0
3x – y + 3 = 0
Comparing the coefficients,
(a1/a2) = -⅔
(b1/b2) = -1/-1 = 1
(a1/a2) ≠ (b1/b2)
Hence, this system of equations will have only one
Can canvas track tabs?
Canvas cannot track tabs.
While Canvas cannot track whether students switch to new tabs in their web browsers during a quiz or test, it can track when a student completes a quiz and navigates to a different page on the website rather than the one they were previously on. However, the general public cannot access this data.
In a perfect world, Canvas wouldn't be able to tell if a student opened new tabs in a browser or a new program or online browser while taking a quiz or test. However, Canvas will watch over and restrict student internet activity if the exam is proctored.
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Is y 4 a vertical line?
y = 4 is a horizontal line.
The graph of the equation y=4 is a horizontal line. It is function since each x is mapped to one y or each element of the domain is mapped to only one element of the range. It also passes the vertical line test.
Now, According to the question:
Let's know:
What is Horizontal lines?
If we are given the equation of y equal to a number, our graph will be a horizontal line. Is this equation a function? The answer would be yes since it passes the vertical line test. The vertical line test tells us if we draw a vertical line through any point of the graph and it goes through only one point at each line, then it is a function. If it passes through more than one point, it does not. The slope of a horizontal line is zero.
The equation is y = 4.
The graph of the equation y=4 is a horizontal line. It is function since each x is mapped to one y or each element of the domain is mapped to only one element of the range. It also passes the vertical line test.
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The complete question is this :
Is y = 4 a vertical line?
The rectangular floor of a classroom is 24 feet in length and 40 feet in width. A scale drawing of the floor has a length of 6 inches. What is the area, in square inches, of the floor in the scale drawing?
HURRY! :D
The area of the floor in the scale drawing is 60 inches².
What is a rectangle?A rectangle is a two-dimensional shape where the length and width are different.
The area of a rectangle is given as:
Area = Length x width
We have,
Actual rectangle:
Length = 24 feet
Width = 40 feet
Scale rectangle:
Length = 6 inches
Width = 40/4 = 10 inches
The area of the scaled rectangle.
= Length x Width
= 6 x 10
= 60 inches²
Thus,
The area of the scaled rectangle is 60 inches².
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What are the properties of a 3 4 5 triangle?
The right angle with in 3-4-5 triangle is naturally 90 degrees. Always opposite the fourth side, at 53.13 degrees, are the other two angles: 36.87 degrees (just opposite the 3rd side).
Explain the 3 4 5 triangle and its properties?Specialized triangles, such as 3-4-5 triangles, can be solved using the Pythagorean theorem.
Any triangle with a single right (90°) angle is referred to as a right triangle. Typically, a tiny square marker is placed within the right triangle to denote this. In every right triangle, these two sides closest to the right angle are shorter than the hypotenuse, the side directly across from the right angle. A right triangle with integers on each side is known as a Pythagorean triple.Thus, this 3-4-5 right triangle is one of the most well-known Pythagorean triples. The hypotenuse, its longest side opposite its right angle, is measured at 5, while the shorter sides measure at 3 and 4.
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Use the parabola tool to graph the quadratic function f(x)=-5x2-2
Answer:
To graph the quadratic function f(x) = -5x^2 - 2, we can use the parabola tool.
First, let's plot the vertex of the parabola. The vertex is the highest or lowest point on the graph of a parabola, and it is located at the point (h, k), where h is the value of the x-coordinate and k is the value of the y-coordinate.
For the quadratic function f(x) = -5x^2 - 2, the vertex is located at the point (0, -2).
Next, we can use the parabola tool to draw the graph of the quadratic function. To do this, we need to set the value of a, b, and c in the equation y = a(x - h)^2 + k. For the quadratic function f(x) = -5x^2 - 2, the values of a, b, and c are -5, 0, and -2, respectively.
Therefore, the equation of the graph of the quadratic function f(x) = -5x^2 - 2 is y = -5(x - 0)^2 - 2.
Using the parabola tool, we can draw the graph of the quadratic function by plotting several points on the graph and connecting them with a smooth curve.
The graph of the quadratic function f(x) = -5x^2 - 2 is a downward-facing parabola with its vertex at the point (0, -2). The graph opens downward because the value of a is negative. The parabola is symmetrical about the y-axis because the value of h is 0. The graph passes through the y-intercept (0, -2) because the value of k is -2.
Step-by-step explanation:
A rectangle has the dimensions 2. 4 x 2. 2. If I want a rectangle that has the area
16 times the size of the original rectangle, what will be my new dimensions?
New dimensions:
The new dimensions of the rectangle will be 4.8 x 4.4.
To find the new dimensions, we need to find the area of the original rectangle (2.4 x 2.2 = 5.28), and then multiply it by 16 to find the desired new area (5.28 x 16 = 84.48).
Since the area of a rectangle is determined by the product of its length and width, we can find the new dimensions by taking the square root of the new area and dividing it by the original length.
So, √84.48/2.4 = 4.4 and √84.48/2.2 = 4.8.These are the new dimensions of the rectangle.
We have to make sure that the new dimensions are in the same proportion as the original one, we can use the same factor of multiplying to get the new length and width.
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Santos walks 222 kilometers south and then a certain number of kilometers east. He ends 555 kilometers away from his starting position. How many kilometers east did Santos walk
Answer:
4.6 km
Step-by-step explanation:
You want to know how many kilometers east Santos walked to end up 5 km from his starting position after walking 2 km south.
DistanceThe distance Santos is from his starting position will be the hypotenuse of a right triangle with one leg 2 km. Using the Pythagorean theorem, we can find the length of the other leg.
c² = a² + b²
5² = 2² + b²
21 = b²
b = √21 ≈ 4.583
Santos walked about 4.6 km east.
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Layla leans a 26-foot ladder against a wall so that it forms an angle of 61° with the
ground. How high up the wall does the ladder reach? Round your answer to the
nearest tenth of a foot if necessary.
Step-by-step explanation:
Calculate the approximate value: 26 x 0.87462
Calculate: 22.74012
Round 22.74012 to the required place
Answer:22.7
Hope this helps
A cubical box has each edge 10 cm and another cuboidal box is 12.5 cm long, 10 cm wide and 8 cm high. Which box has the greater lateral surface area and by how much
On solving the provided question, we can say that So, the total surface area of cuboid is larger by (610 — 600 = IO) cm2
what is cuboid?A cuboid is a solid or three-dimensional form in geometry. A cuboid is a convex polyhedron having 8 vertices, 12 sides, and 6 rectangular faces. Another name for a cuboid is a cuboid. A cube is a cuboid with six square faces. Boxes include things like books and bricks. The following are the key variations between cubic and cubic: In contrast to a cube, which has rectangular faces, a cube has six equally sized square faces. Even though the cube and cuboid structures have a similar appearance, they differ in some ways in terms of side length, diagonal, and area.
(Lateral surface area of cube = 4edge2
lateral surface area of cuboid =2h (l + b)
[tex]2 x 8(12.5+ 10)\\= 16 x 22.5\\= 360\\[/tex]
lateral surface area of the cube is larger by (400
- 360
= 40)cm2
Total surface area of cube = 6edge2
= 600
lateral surface area of cuboid
[tex]=2 (lb + bh + hl)\\2(12.5 x 10+ x 8+8 x 12.5)\\= 2 (125 + 80 + 100)\\= 610[/tex]
So, the total surface area of cuboid is larger by (610 — 600 = IO) cm2
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What is the value of log2 log32?
the value of log2 log32 is 0.5899 and the base of the logarithm is raised to the value that was equated earlier and this expression is equal to the logarithm.
logarithm, the exponent or power to which a base must be raised to yield a given number. Expressed mathematically, x is the logarithm of n to the base b if bx = n, in which case one writes x = logb n. For example, 23 = 8; therefore, 3 is the logarithm of 8 to base 2, or 3 = log2 8.J
The logarithmic equation that has the same solution as x-4=2^3 is log2(x-4)=3.
Logarithm
The logarithm of a number can be calculated from the following relationship:
Thus, the base of the logarithm is raised to the value that was equated earlier and this expression is equal to the logarithm.
So, we have that the third expression
Therefore, this expression is the one corresponding to x-4=2^3.
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How many cubic centimetres of iron are there in an open box whose external dimensions are 36 cm, 25 cm and 16 cm, the iron being 2 cm thick throughout? If 1 cubic cm of iron weighs 15 g. find the weight of the open box in kg
$7,400 at 10.5% for ¼ years
How do you graph log functions with transformations?
required transformed function will be y = parent function+5⇒y=logx+5.
Since, given function y= logx
According to the graph, the transformed function is getting after shifting the function by 5 unit upward.
Thus, transformed function must be equals to parent function+5.
Therefore, required transformed function will be y = parent function+5⇒y=logx+5.
How to do logarithmic transformations?
Image result for How do you graph log functions with transformations?
Recall the general form of a logarithmic function is: f ( x ) = k + a log b where a, b, k, and h are real numbers such that b is a positive number ≠ 1, and x - h > 0. A logarithmic function is transformed into the equation: f ( x ) = 4 + 3 log
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What is the smallest number with the factors 1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24
The smallest number with the factors 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, and 24 is 232792560.
With the elements 1, 2, 3, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, what is the smallest number?The smallest number that has all of the factors 1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24 is 27720. This number is a product of the prime factors 2, 3, 5, 7, 11, 13, 17, 19. All of the factors can be written as a product of these prime factors, and multiplying them all together gives 27720. This is the smallest number that can be created with all of the given factors.The smallest number with the given factors is 2520. This number is the product of all the prime numbers from 1 to 10 (2 x 3 x 5 x 7 x 11 x 13 x 17 x 19 = 2520). It is also the smallest number that can be divided evenly by all the numbers from 1 to 10. This number can also be evenly divided by 11, 12, 13, 14, 15, 16, 17, 18, 19 and 20, so it is the smallest number with the factors 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, and 24.The smallest number with the factors 1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24 is 2520. It is the smallest number that is evenly divisible by all of these numbers. To find it, the prime factorization of each of the numbers must be used. The prime factorization of each number is the product of the prime factors raised to the highest power.To learn more about the smallest number with the factors refer to:
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Maddie received a new iPhone for Christmas. There is no activation fee to use Apple Music but there is a $4.99 per month charge. How many months would Maddie have been a member it she spent $34.93%
Answer:
7 months
Step-by-step explanation:
Spotify is better
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Let g be a twice-differentiable function with g'(x) > 0 and g"(x) > 0 for all real numbers x, such that
g(3) 12 and g(5) = 18. Which of 20, 21, and 22 are possible values for g(6) ?
(A) 21 only
(B) 22 only
(C) 20 and 21 only
(D) 21 and 22 only
g(6) must be greater than 21 which is 22 only.
What is function?In mathematics, a function is an expression, rule, or law that establishes the relationship between an independent variable and a dependent variable.
Since g'(x) > 0 for all x and we know that g(x) is an increasing function.
Additionally, since g"(x) > 0 for all x, we know that g(x) is a concave-up function.
Since g(x) is increasing, we know that g(6) > g(5) = 18.
Now, we can use the fact that g(x) is concave-up to find a lower bound on g(6).
By the definition of concave-up, we know that the slope of the tangent line to g(x) is increasing.
This means that the slope of the line connecting (3,g(3)) to (5,g(5)) is less than the slope of the line connecting (5,g(5)) to (6,g(6)).
Using this information, we can find a lower bound on g(6):
g(5)- g(3) / (5-3) < g(6)- g(5)/ (6-5)
18- 12/2 < g(6)- 18
3 < g(6) - 18
g(6) > 21
Therefore, g(6) must be greater than 21.
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Write an explicit formula for a_na
n
, the n^{\text{th}}n
th
term of the sequence 27, 9, 3, ...27,9,3,....
The equation which correctly represents the explicit formula for the nth term of the given sequence is; a (n) = a (n - 1) × ( 1 / 3 ) and a (1) = 27.
Which equation represents the nth term of the given sequence?As evident in the task content; the given sequence is a geometric sequence and the common ratio of the sequence can be determined as;
r = 3 / 9 = 9 / 27 = 1 / 3.
On this note, since the common ratio of the consecutive terms of the sequence is; 1/3 it follows that the required explicit formula which represents the nth term , a (n) is;
a (n) = a (n - 1) × ( 1 / 3 ) and a (1) = 27.
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Hanna is recovering
hundreds of treasure chests from an ancient
shipwreck. She is able to
récover 8 chests every 4 hours.
Complete the table using equivalent ratios.
Treasure chests
Hours
8
10
Answer:
12
5
Step-by-step explanation:
if 8 chests = 4hrs
then X chests= 6hrs
cross multiply
48=4x
divide by 4
X= 12
repeat the same for the second using any and you'd get 5
What evidence from Gilgamesh a new English version best supports the conclusion that Gilgamesh is an epic hero?
In "Gilgamesh: A New English Version," several pieces of evidence support the conclusion that Gilgamesh is an epic hero.
Gilgamesh is the king of Uruk: He is the main character of the story, and his actions and deeds are the focus of the epic. As a king, he holds a position of power and authority and is responsible for the well-being of his people.
Gilgamesh undertakes a quest: He embarks on a journey to find immortality after the death of his dear friend Enkidu. His quest takes him to the ends of the earth and shows his determination and courage.
Gilgamesh faces challenges and monsters: During his journey, Gilgamesh faces several challenges and monsters, such as the giant Humbaba and the Bull of Heaven. His bravery in overcoming these obstacles demonstrates his heroic qualities.
Gilgamesh has supernatural strength and abilities: He is two-thirds god and one-third man, which means he is gifted with supernatural strength, speed and endurance. He is able to perform deeds that would be impossible for a mortal.
Gilgamesh demonstrates wisdom and self-awareness: Throughout his journey, Gilgamesh comes to understand the limitations of human life and the importance of living a meaningful existence. He demonstrates wisdom and self-awareness which are the hallmark of a true epic hero.
These examples of Gilgamesh's character and actions support the conclusion that he is an epic hero and his story is an epic.
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Please help I have a learning disabilty and need help with this.
Find the value of x that makes a true statement.
17 + x = 3 + 17
x = _______
Answer:
17 + x + 3 + 17
X is 3
What graph is best for comparing two variables?
A scatter plot is the best graph for comparing two variables.
A scatter plot is a graph that uses dots to represent individual observations of two variables. It is a powerful tool for comparing two variables because it allows us to see the relationship between the two variables and how they are distributed. It also helps to identify any patterns or trends in the data, such as a positive correlation, a negative correlation, or no correlation at all.
Additionally, scatter plots allow us to see outliers, which are data points that are far away from the majority of the data points. This makes it easy to identify any extreme values that may be skewing the data and affecting the overall pattern of the graph. Overall, scatter plots are useful for identifying patterns, trends, and outliers in data sets, making it the best choice for comparing two variables.
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Blair bought 3 1/6 pounds of nuts and 1 5/6 pounds of milk, what is total weight of the nuts and milk that Blair bought
Answer:
Step-by-step explanation:
3 [tex]\frac{1}{6}[/tex]
+ 1 [tex]\frac{5}{6}[/tex]
_______
4 [tex]\frac{6}{6}[/tex] = 5 pounds
[tex]\frac{6 }{6}[/tex] = 1 add this to the 4 and you have 5 pounds total
Find the measure of MN
Answer:
60 degrees
Step-by-step explanation:
The total measure of a circle is 360 degrees.
360-140-100 = 120
Angles MON and NOP are equivalent which makes MN and NP equivalent.
120/2 = 60 degrees = MN
Given
A
B
‾
∥
D
C
‾
AB
∥
DC
and
B
C
‾
∥
A
D
‾
BC
∥
AD
, prove
△
A
B
C
≅
△
C
D
A
△ABC≅△CDA by filling out the flowchart below.
The second row's third box AC = AC ( common side ) ( common side ) box last. Therefore, by applying the ABCD ASA congruence axiom.
What is triangle ?Three sides, three angles, and three vertices make up the closed, two-dimensional shape of a triangle. Polygons include triangles. Triangle ABC is depicted in the above figure. Triangular polygons in geometry are those with three sides and three vertices. There are three straight sides to this two-dimensional figure. Three-sided polygons include triangles. A triangle's three angles add up to a full 180 degrees. A single plane contains the triangle. Triangulus, which means "three-cornered" or "having three angles," is a Latin word with roots in tri-, "three," and angulus, "angle or corner."
given
AB||DC , BC||AD
To show that
ΔABC≅ ΔCDA
First box
AB || DC (given )
below box to the first box
∠BAC = ∠DCA ( parallel lies cut by the transverse form congruent alternate interior angles )
Second box
BC||AD ( given )
Below box to the second box
∠DAC = ∠BCA ( parallel lies cut by the transversal form congruent alternate interior angles )
Third box in the second row
AC = AC ( common side )
Last box
So by using ASA congruence axiom
ΔABC ≅ΔCDA
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May someone please help me.
Answer: x=9
Step-by-step explanation:
Here the given angles are,
50,80,6x-4
The sum of the angles of a triangle is 180 degrees and hence
50+80+6x-4=180
130+6x-4=180
126+6x=180
6x=180-126
6x=54
x=54/6
x=9
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Which is closest to the quotient 4,367 -- 0. 004?
1,000
10,000
100,000
1,000,000
Answer: 1000
Step-by-step explanation:
i took this quiz before ! !
Please help!!!! I'LL GIVE 5 STAR RATING AND A THANKS
Answer:
9.1
Step-by-step explanation:
For the first one, I just multiplied 4.55 and 0.5 by 2 somthey are proportional. Or divide distance by time!
What is the simplest form of 2√3 / √6
√2
√√3
3√2
2√3
O
The simplest form [tex]\frac{2\sqrt{3} }{\sqrt{6} }[/tex] is [tex]\sqrt{2}[/tex]
Step-by-step solution:
[tex]=\frac{2\sqrt{3} }{\sqrt{6} }[/tex]
[tex]=\frac{2\sqrt{3} }{\sqrt{2*3} }[/tex] (write factors of [tex]\sqrt{6}[/tex] i.e. [tex]\sqrt{2*3}[/tex])
[tex]=\frac{2\sqrt{3} }{\sqrt{2}\sqrt{3} }[/tex]
[tex]=\frac{2\ }{\sqrt{2}\ }[/tex]
[tex]=\frac{2\ }{\sqrt{2}\ } * \frac{\sqrt{2} }{\sqrt{2} }[/tex] (Rationalize it by [tex]\sqrt{2}[/tex])
[tex]=\frac{2\sqrt{2} }{2}[/tex]
[tex]=\sqrt{2}[/tex]
Therefore, the correct solution to this question is [tex]\sqrt{2}[/tex]
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