The first five terms of a geometric sequence in which the second term is 6 and fourth term is 54 are 2, 6, 18, 54, 162. Thus, the correct option is option D.
A Geometric progression may be defined as a series of terms in which the ratio between each succeeding term and the preceding term of the series is constant.
It is given that the second term of the series is 6 and the fourth term is 54.
The first five terms of geometric sequence are given by a, ar, ar², ar³ and ar⁴.
Thus, ar = 6 ......(1)
ar³ = 54 ......(2)
Divide equation (2) by (1)
ar³/ar = 54/6
r² = 9
=> r = 3
Putting value of r in equation (1)
ar = 6
=> a×3 = 6
=>a = 2
Now, substituting the values of a and r the terms of Geometric progression are given by:
a = 2, ar = 6, ar² = 18, ar³ = 54 and ar⁴ = 162.
Thus, the first five terms of Geometric sequence are given by 2, 6, 18, 54, 162.
Learn more about Geometric sequence at:
brainly.com/question/10564422
#SPJ9
Solve two thirds times v plus 6 equals one third times v minus 2.
v equals negative eight thirds
v equals eight thirds
v = −24
v = 24
The value of v using the equation ( 2v/3 ) + 6 = ( v/3 ) - 2 is v = - 24.
Two-thirds of anything is an amount that is two out of three equal parts of it. Similarly, one-third of something is an amount that is one out of three equal parts of it.
Now, we have
Two-thirds times v plus 6 equals one-third times v minus 2.
Hence, when the above statement is expressed as an equation we get:
Two third of v + 6 = one third of v - 2
2/3 × v + 6 = 1/3 × v - 2
( 2v/3 ) + 6 = ( v/3 ) - 2
Adding 2 on both sides of the equation,
( 2v/3 ) + 6 + 2 = ( v/3 ) - 2 + 2
( 2v/3 ) + 8 = ( v/3 )
Subtracting 2v/3 from both sides of the equation,
2v/3 + 8 - 2v/3 = v/3 - 2v/3
8 = ( v - 2v )/3
- v/3 = 8/1
By cross multiplication,
- v × 1 = 8 × 3
- v = 24
Multiplying each side by - 1,
v = - 24
Learn more about equations here:
https://brainly.com/question/2972832
#SPJ1
4|2x + 5|-7≤9
How would you solve this?
Answer:
- [tex]\frac{9}{2}[/tex] ≤ x ≤ - [tex]\frac{1}{2}[/tex]
Step-by-step explanation:
inequalities of the type | x | ≤ a , have solutions of the form
- a ≤ x ≤ a , then
4 | 2x + 5 | - 7 ≤ 9 ( add 7 to both sides )
4 | 2x + 5 | ≤ 16 ( divide both sides by 4 )
| 2x + 5 | ≤ 4 , so
- 4 ≤ 2x + 5 ≤ 4 ( subtract 5 from each interval )
- 9 ≤ 2x ≤ - 1 ( divide each interval by 2 )
- [tex]\frac{9}{2}[/tex] ≤ x ≤ - [tex]\frac{1}{2}[/tex]
a line segment has (x1, y1) as one endpoint and (xm, ym) as its midpoint. find the other endpoint (x2, y2) of the line segment in terms of x1, y1, xm, and ym. use the result to find the coordinates of the endpoint (x2, y2) of each line segment with the given endpoint (x1, y1) and endpoint (xm, ym).
The coordinates are:
For the first line, coordinates are (3, 7).For the second line, the coordinates are (12, 0).What are coordinates?A coordinate system in geometry is a system that uses one or more numbers, or coordinates, to determine the position of points or other geometric elements on a manifold such as Euclidean space.To find the coordinates:
In Analytical Geometry, the midpoint of a line is calculated as the mean of two points, as follows:
[tex]$$x_m=\frac{x_1+x_2}{2}, y_m=\frac{y_1+y_2}{2}$$[/tex]
Each segment has two endpoints and two midpoints, which are as follows:
(1,-9), as well as its midpoint (2,-1)(-2,18), as well as its midpoint (5,9)We must be cautious not to add the wrong coordinates.
In the first line A:
[tex]$$\begin{aligned}&2=\frac{1+x_2}{2} \\&4=1+x_2 \\&4-1=-1+1+x_2 \\&x_2=3 \\&-1=\frac{y_2-9}{2} \\&-2=y_2-9 \\&+2-2=y_2-9+2 \\&y_2=-7\end{aligned}$$[/tex]
So (3,7) is the other endpoint where the segment begins (1,-9).
The endpoint of the second line b at (-2,18) and its midpoint (5,9).
[tex]$$\begin{aligned}&5=\frac{-2+x_2}{2} \\&10=-2+x_2 \\&+2+10=+2-2+x_2 \\&x_2=12 \\&9=\frac{18+y_2}{2} \\&18=18+y_2 \\&-18+18=-18+18+y_2 \\&y_2=0\end{aligned}$$[/tex]
So, (12,0) is the opposite endpoint.
Therefore, the coordinates are:
For the first line, coordinates are (3, 7).For the second line, the coordinates are (12, 0).Know more about coordinates here:
https://brainly.com/question/17206319
#SPJ4
The correct question is given below:
A line segment has (x1, y1) as one endpoint and (xm, ym) as its midpoint. Find the other endpoint (x2, y2) of the line segment in terms of x1, y1, xm, and ym. Use the result to find the coordinates of the endpoint of a line segment when the coordinates of the other endpoint and midpoint are, respectively, (1, −9), (2, −1) and (−2, 18), (5, 9).
does the ratio 2/5 to 1/3 has a unit rate of 2/15
The statement that the ratio 2/5 to 1/3 has a unit rate of 2/15 is; True
How to find the unit rate?
A unit rate is defined as a rate for one of something. This can be written as a ratio with a denominator of one.
For example, if you ran 50 meters in 10 seconds, you ran an average 5 meters in 1 second. Both of the ratios, 50 meters in 10 seconds and 5 meters in 1 second, are rates, but the 5 meters in 1 second is a unit rate.
We are given the ratio 2/5 to 1/3. Now, this can be expressed as;
(2/5)/(1/3) = 2/5 * 1/3 = 2/15
Thus, this corresponds with the given unit rate of 2/15.
Read more about Unit rate at; https://brainly.com/question/4895463
#SPJ1
a major disadvantage of correlations is that they cannot make a(n) blank statement. multiple choice question.
A major disadvantage of correlations is that they cannot make a cause-and-effect statement.
What are correlations?Correlations are statistical measures that describe the size and direction of a relationship between variables.
Correlations are expressed as numbers. Correlations establish that relationships exist but do not explain if the change in one variable is caused by the change in another variable's value.
The disadvantages of correlations include:
There are no causes and effects.Results can find no inference.The strength of the relationship is not explained.There is the possibility of a confounding factor.Thus, a major disadvantage of correlations is that they cannot make a cause-and-effect statement.
Learn more about correlations at https://brainly.com/question/5483638
#SPJ1
if asked to evaluate the following expression (5x+25) for x=3,5,-5,0 how many different substitutions will you make?
we did 4 different substitutions to evaluate the expression in 4 different values of x.
when x = 3 we get 40when x = 5 we get 50when x = -5 we get 0when x = 0 we get 25.How to evaluate an expression?
Here we have a linear expression that depends on the variable x, and can be written as:
(5x + 25)
And we want to evaluate this in some different values of x. This just means that we need to replace the value of x by different numbers.
First, let's use x = 3
This will give:
(5*3 + 25) = 15 + 25 = 40
Then we use x = 5
(5*5 + 25) = 25 + 25 = 50
Then we use x = -5
(5*-5 + 25) = -25 + 25 =0
Finally, we evaluate in x = 0.
(5*0 + 25) = 0 + 25 = 25
So we did 4 different substitutions to evaluate the expression in 4 different values of x.
Learn more about evaluating expressions:
https://brainly.com/question/4344214
#SPJ1
What is the percentage efficiency of a motor that does 60J of work from 240J of electrical energy?
Answer:
25% is the correct answer
.
Nickels: Someone offers to double the amount of money you have every
day for 1 month (30 days). You have 1 nickel. On the first day, you will
have 2 nickels worth $.10. On the second day, you will have 4 nickels
worth $.20. How much money will you have on the 30th day?
Answer: you will have $53,687,091.2 dollars once you reach the thirty-day milestone.
Step-by-step explanation:
Multiply 0.05 by 2 thirty times to get your answer.
0.05 * 2^30
0.05 * 1,073,741,824 = $53,687,091.2 or 10,737,418.24 nickels.
suppose you have an argument that has three premises, all of which are true, and a true conclusion. if so, then the argument must be
The conclusion might be accurate or inaccurate.
The conclusion could be true or false if an argument has some true premises and some false premises and is valid. You only know that the premises cannot both be true and the conclusion must be false because the argument is sound. But the incorrect premises already rule out the possibility of possessing this set of truth values (that is, you cannot have all true premises). As a result, the argument's validity is unaffected whether the conclusion is true or untrue. As a result, the conclusion of an argument that contains only false premises may or may not be true.
Can an argument have all true premises and a false conclusion?TRUE. A valid argument cannot, by definition, have a false conclusion and all true premises.
Therefore, a valid argument must have an erroneous premise if it has a false conclusion.
To learn more about true premises and a false conclusion visit:
https://brainly.com/question/15019295
#SPJ4
If a first integer is represented by the variable x, then which of the following would be the next four consecutive odd integers?
Choose the correct answer below.
A. x+1, x+2, x+3, x+4
B. x+2, x+4, x+6, x+8
Points: 0 of 1
C. x, x+2, x+4, x+6
OD. x+1, x+3, x+ 5, x+7
the next four consecutive odd integers will be given by the option (B) x + 2, x + 4, x + 6 and x + 8.
We are given that:
The first integer is represented by the variable x.
We need to find the next four consecutive odd integers.
We know that the difference between the two consecutive odd integers will always be 2.
So, this means, we can always get the next odd integers by adding 2 to the previous one.
So, we get that:
x + 2
x + 2 + 2 = x + 4
x + 4 + 2 = x + 6
x + 6 + 2 = x + 8
Therefore, we get that, the next four consecutive odd integers will be given by the option (B) x + 2, x + 4, x + 6 and x + 8.
Learn more about integers here:
https://brainly.com/question/17695139
#SPJ9
Sue's science class is competing to see who can build the tallest tower. Each group of students gets 10 newspapers and 2 meters of tape. Sue's group decides to roll up each of their newspapers. Then, they tape each roll with 125 millimeters of tape. How many meters of tape do they have left?
The amount of tape left in metres is 0.75 metres.
How to find the length of the tape left in metres?Each group of students gets 10 newspapers and 2 meters of tape.
This means the total length of tape for each group of student is as follows:
length of tape for each group = 2 metres
Sue's group decides to roll up each of their newspapers. Then, they tape each roll with 125 millimetres of tape.
Each roll of the 10 newspaper was taped with 125 mm tape.
Hence,
total taping = 125 × 10
total taping = 1250 mm
Let's convert from millimetres to metres.
Therefore,
1 mm = 0.001 m
1250 mm = ?
cross multiply
amount of taping done by Sue's group = 1.25 m
Therefore,
amount of meters of tape left = 2 - 1.25 = 0.75 metres
learn more on length in metres here:https://brainly.com/question/327206
#SPJ1
6. A triangle has a perimeter of exactly 24 units. Which of the following could be the vertices of the triangle
(-1,3), (2, -1),(-1,-1)
(6, 0), (6, 7), (0,7)
(-1,-1), (-6, -13), (-9,-9)
(-3,-4), (3,-4), (3,4)
Answer:
Question:
A triangle has a perimeter of exactly 24 units. Which of the following could be the vertices of the triangle?
A.) (-1,3),(2,-1),(-1,-1)
B.) (6,0),(6,7)(0,7)
C.) (-1,-1),(-6,-13),(-9,-9)
D.) (-3,-4),(3,-4),(3,4)
Triangle and Coordinate Geometry
As the name suggests 'tri-angle' means it has three angles that are formed only when three sides are joined together.
So the triangle is a planner geometry that has three sides and three interior angles. In a triangle, the sum of all three interior angles is always
180
∘
.
If a triangle
A
B
C
has the sides
a
,
b
,
and
c
, then
The perimeter of the triangle:
P
=
a
+
b
+
c
In coordinate geometry, the distance between two points:
D
=
√
(
x
2
−
x
1
)
2
+
(
y
2
−
y
1
)
2
Answer and Explanation:
Given:
The perimeter of the triangle is
24
units.
There are four options with different-different vertices and one of them is correct, so we choose one option randomly and check it for the given perimeter.
Firstly we chose the option
D
:
The vertices of the triangle are:
P
(
−
3
,
−
4
)
,
Q
(
3
,
−
4
)
,
and
R
(
3
,
4
)
Using the distance formula:
D
=
√
(
x
2
−
x
1
)
2
+
(
y
2
−
y
1
)
2
So
P
Q
=
√
(
3
+
3
)
2
+
(
−
4
+
4
)
2
=
√
6
2
+
0
=
6
u
n
i
t
And
Q
R
=
√
(
3
−
3
)
2
+
(
4
+
4
)
2
=
√
0
+
8
2
=
8
u
n
i
t
And
P
R
=
√
(
3
+
3
)
2
+
(
4
+
4
)
2
=
√
6
2
+
8
2
=
√
36
+
64
=
√
100
=
10
u
n
i
t
So
The perimeter of the triangle
P
Q
R
is:
Perimeter
=
P
Q
+
Q
R
+
P
R
=
6
+
8
+
10
=
24
u
n
i
t
s
Step-by-step explanation:
how many time does 13 go into 26
Answer:
2
Step-by-step explanation:
13+13=26
Answer:
Twice
Step-by-step explanation:
13+13=26
The slope for a wheelchair ramp for a home has to be 1/2.
If the vertical distance from the ground to the door bottom is 3 ft, find the distance the ramp has to extend from the home in order to comply with the needed slope.
In order to comply with the required slope, the ramp must extend 36 ft from the house.
What do we mean by Distance?Distance is a mathematical or qualitative measure of the distance between two objects or points. Distance can refer to a physical length or an estimate based on other criteria in physics or everyday usage (e.g. "two counties over").So, to find the distance:
The formula of slope:
m = change in vertical height/change in horizontal heightVertical distance is now given as 3 ft.
To conform to the given slope, this means that:
1/12 = 3/xCross multiply:
x = 3 × 12x = 36 ftTherefore, in order to comply with the required slope, the ramp must extend 36 ft from the house.
Know more about Distances here:
https://brainly.com/question/17273444
#SPJ9
Which liner function represents the line given by the point-slope equation y + 7 = -2/3(x + 6)?
the linear function that represents the given line is:
y = f(x) = (-2/3)*x - 11
Which linear function represents the given line?
Here we have a line given by a point-slope equation:
y + 7 = (-2/3)*(x + 6)
And we would want to get a function of the form y = f(x). So the first thing we need to do is isolate y in one side of the above equation. If we subtract 7 in both sides we will get:
y = (-2/3)*(x + 6) - 7
Expanding that:
y = (-2/3)*x + (-2/3)*6 - 7
y = -(2/3)*x - 4 - 7
y = (-2/3)*x - 11
Then the linear function that represents the given line is:
y = f(x) = (-2/3)*x - 11
If you want to learn more about linear functions:
https://brainly.com/question/4025726
#SPJ1
#11 i Solve -14>w+3 or 3w > -27 Solution: or
The values of the inequalities will be:
1. -14>w+3 = w < -17
2. 3w > -27 = w > -9
How to explain the inequality?It should be noted that an inequality simply means the expression that illustrates that the variables aren't equal. This can be used by uinng less than, greater than, etc.
The inequalities will be:
-14>w+3
Collect like terms
-14 - 3 > w
-17 > w
w < -17
3w > -27
Divide both side by 3
3w/ 3 > -27/3
w > -9
Learn more about inequalities on:
brainly.com/question/24372553
#SPJ1
If f(x)=-2x+3then f(3)-f(4)
The graph below shows the distance a helicopter traveled over time. Find the rate of change from 1 hour to 2 hours.
The rate of change from 1 hour to 2 hours will be 125 miles per hour. Option C is correct.
What is linear equation?
A relationship between two or more parameters that, shown on a graph, produces a linear model. The degree of the variable will be one.
Given that;
Two points on the graph are (1, 125) and (2, 250).
Now, The slope of the line is calculated as;
m = ( y₂ - y₁ ) / ( x₂ - x₁ )
Hence, Slope of the line passes through the points (1, 125) and (2, 250).
m = (250 - 125) / (2 - 1)
m = 125
So, The rate of change from 1 hour to 2 hours will be 125 miles per hour.
Learn more about the linear equation visit:
https://brainly.com/question/4074386
#SPJ1
Does 44,555 and 45,555 round to 50,000?
45,555 does, but the other one doesn't.
find the percentage if the denominators are not the factors of 100
Answer:
external factors that impact negatively on lifestyle choices namely.unsafe road use
Consider the arithmetic sequence (87, 83, 79,75...)
A. Find common difference, d
B. Find explicit formula
Answer:
see explanation
Step-by-step explanation:
A
the common difference d of the arithmetic sequence is
d = a₂ - a₁ = 79 - 83 = - 4
B
the explicit formula of an arithmetic sequence is
[tex]a_{n}[/tex] = a₁ + (n - 1)d
where a₁ is the first term and d the common difference
here a₁ = 83 and d = - 4 , then
[tex]a_{n}[/tex] = 83 - 4(n - 1) = 83 - 4n + 4 = 87 - 4n
How can you adjust both numbers and use compensation to find $7.99 + $19.99 mentally?
The adjustment of both numbers and using compensation to find $7.99 + $19.99 mentally is $27.98
How to calculate the value?It should be noted that compensation is the mental strategy in Mathematics used for addition by adjusting one of rte addends.
It should be noted that $7.99 is almost the same as $8. It should be noted that $19.99 is the same as $20. This is the compensation or the numbers.
Therefore, the addition of the numbers $7.99 + $19.99 will be:
= $7.99 + $19.99
= $27.98
In conclusion, the answer is $27.98.
Learn more about numbers on:
brainly.com/question/25734188
#SPJ1
Solve for x in the diagram below
The value of x will be 34°
Given that
(x+12)°+100°+x° are forming linear pair
Linear pair of angles are formed when two lines intersect each other at a single point. The angles are said to be linear if they are adjacent to each other after the intersection of the two lines. The sum of angles of a linear pair is always equal to 180°. Such angles are also known as supplementary angles.
As mentioned, adjacent angles are angles that are next to each other. If you are sitting next to someone in class or on the bus, you could say that you are adjacent to them. More specifically, adjacent angles share a vertex and have a common side.
(x+12)°+100°+x°= 180°
⇒ x+ 12+ 100+x = 180°
⇒ 2x+112 = 180°
⇒ 2x = 180- 112
⇒ 2x = 68
⇒ x= 68/2
⇒ x= 34
For verification we will put value of x
(34+12)°+100°+34°
⇒ 46°+100°+34°
⇒146°+34°
⇒ 180°
So here we can see that by putting value of x we are getting the sum of 180°
Therefore value of x is 34
To learn more about angles
visit-:https://brainly.com/question/28451077
#SPJ9
A city park measures 7/8 mile wide by 3/4 mile long. What is the area of the park?
94.
Scale: 1 in. = 3 ft
The diagram above shows a plan for a community garden. The plan is drawn on a grid made up of 1-inch squares. About how many square yards will be used to grow herbs?
Answer:
About 9 sq yd
Step-by-step explanation:
First, you know that 3ft. = 1 yd. That means each square is 1 sq yd. The length of the herb garden is 6 squares, while the width is about 1.5 squares. If you multiply those two to find the area, then you get about 9 square yards.
Bob fenced in his backyard. the perimeter of the yard is 22 feet, and the length of his yard is 5 feet. use the perimeter formula to find the width of the rectangular yard in inches: p = 2l 2w. (1 foot = 12 inches)
The width of yard in inches is 72 inches.
We are given the perimeter and length of yard. We are also given the perimeter of the rectangle, which is as follows -
P = 2l 2w
Rewriting this formula in simplified form, by taking 2 common from both the values -
P = 2×(l + w), where P refers to perimeter, l refers to length and w refers to width.
Now, keep the values in formula to find the width of rectangle -
22 = 2 × (5 + w)
Shifting 2 to other side of equation and performing division
5 + w = 22÷2
5 + w = 11
Shifting 5 to other side of equation and performing subtraction to find the value of width
w = 11 - 5
w = 6 feet
Now, we need the width in inches. We are given -
1 foot = 12 inches
So, 6 feet = 12 × 6
6 feet = 72 inches
Hence, the width of rectangular yard is 72 inches.
Learn more about calculations on rectangle -
https://brainly.com/question/19819849
#SPJ4
Answer:
72in
Step-by-step explanation:
Brian is throwing a party. He needs 3/4 of a pound of hamburger meat for each person at the party. If 12 people are coming to the party, how many pounds of hamburger meat will Brian need to buy?
9 pounds of hamburger meat will be needed by Brian.
We are given value for one unit. The calculation is required for more than one units, hence, multiplication will be performed.
As per the given information, amount of hamburger meat required for one person is = 3/4 pound
Amount of hamburger meat required for 12 people = (3/4) × 12
Performing division to find the amount of hamburger meat required for 12 people
Amount of hamburger meat required for 12 people = 3 × 3
Performing multiplication to find the amount of hamburger meat required for 12 people
Amount of hamburger meat required for 12 people = 9 pounds
Therefore, Brain needs to buy 9 pounds of hamburger meat.
Learn more about unitary method -
https://brainly.com/question/24587372
#SPJ9
This list gives information about a video collection.
Study the list carefully. Then, use the drop-down menu to complete the statement
below about the list.
It
make sense to add the items on the inventory because these quantities
have meaning for the inventory.
The number 299
Romance:
74
Comedy: 123
Action: 102
Total: 299
CLEAR
be expressed using the same unit.
CHECK
Answer:
oh no I lost the Answer is was 18369
Answer:
Step-by-step explanation:
9x10^4 + 9x10^2 ??
add
Answer:
90900
Step-by-step explanation:
Answer:
9.09 x 10*4.
Step-by-step explanation:
9x10^4 + 9x10^2
= 90000 + 900
= 90900
= 9.09 x 10*4.
Factor completely.
100-9x^2=
please help!!
Answer:
(10 + 3x) (10 - 3x)
Hope this helps!