Given conditions:
6th term (T6) = -2
first term (a) = 18
n = 6, r = ?
Formula for finding the nth term of a GP:
[tex]tn = a {r}^{n - 1} [/tex]
Where:
T = the given value for the number of term(s)
n = the given number of term
a = The first term
r = The common ratio
Replacing for the values:
[tex] - 2 = 18 {r}^{6 - 1} \\ - 2 = 18 {r}^{5} [/tex]
Dividing both sides by 18, we have:
[tex] {r}^{5} = \frac{ - 2}{18} [/tex]
Now, we have to fifth root both sides to find the value of r.
[tex] \sqrt[5]{ {r}^{5} } = \sqrt[5]{ \frac{ - 2}{18} } [/tex]
Therefore:
Common ratio, [tex]r = -0.0638165752[/tex] [tex]≈ -0.064[/tex] to 3 decimal places.
I hope this helpsWhat is the correct classification for each given angle? Drag and drop the answer into the box to match each angle. Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse. ∠RQU ∠SQU ∠RQT Ray R Q and Ray Q T are connected at point Q 90 degrees apart from each other. Line VQS extends diagonally down to the up right at point Q and forms an interior angle labeled as 19 degrees and 71 degrees. Ray QU extends down to the right of the QT and forms an interior angle labeled as 18 degrees.
∠RQU is an obtuse angle.
∠SQU is an acute angle.
∠RQT is an right angle.
How to Classify Angles?A right angle equals 90 degrees.An acute angle is less than 90 degrees.An obtuse angle is less than 180 degrees but greater than 90 degrees.A straight angle equals 180 degrees.m∠RQU = 19 + 71 + 18 = 108°.
Therefore, ∠RQU is an obtuse angle.
m∠SQU = 71 + 18 = 89°
Therefore, ∠SQU is an acute angle.
m∠RQT = 71 + 19 = 90°
Therefore, ∠RQT is an right angle.
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Please help me with this question.
Answer:14m
Step-by-step explanation:
3 1/2 x 4= 14
If the temperature on the ground is 63F, then the air temperature x miles high is given by T=63−29x. Determine the altitudes at which the air temperature is less than 4.4F.
The temperature is less that 4.4 °F for altitudes greater than 2.021 miles high.
In which altitudes do we get a certain range of temperatures?
Herein we find that the temperature, in grades Fahrenheit, decreases linearly inasmuch as the altitude, in miles, increases. In accordance with the statement, we solve for T in the following inequality:
63 - 29 · x < 4.4
63 - 4.4 < 29 · x
58.6 < 29 · x
29 · x > 58.6
x > 2.021 mi
The temperature is less that 4.4 °F for altitudes greater than 2.021 miles high.
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The following table shows the average total cost, measured as dollars expended per pupil, of operating a high school with the given enrollment. This table is based on a study of economies of scale in high school operations from the 1960s.
Enrollment 170 250 450 650
Average total cost 539 482 421 415
What would you estimate for the average cost per student at an enrollment of 750 students? $
Using linear regression, the estimate for the average cost per student at an enrollment of 750 students is of $373.
How to find the equation of linear regression using a calculator?To find the equation, we need to insert the points (x,y) in the calculator.
For this problem, the points are given as follows:
(170, 539), (250, 482), (450, 421), (650, 415).
Inserting these points into the calculator, the function is:
y = -0.24733x + 558.23703.
When x = 750:
y = -0.24733(750) + 558.23703 = 373.
The estimate for the average cost per student at an enrollment of 750 students is of $373.
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On a sunny day, you and your friend were taking a long walk. You got tired and stopped near a telephone pole for a little rest, but your nervous
friend couldn't stand still. He paced out your shadow and discovered it was 5 meters long even though you are really only 1.5 meters tall. He
paced the long shadow of the telephone pole and found that it was 35 meters long. How high is the telephone pole in meters? Enter your answer
with one digit to the right of the decimal point.
The telephone pole will stands 10.5 meters tall.
Given shadow of you = 5 meters
The true height is 1.5 meters.
We must determine the telephone pole's height because its lengthy shadow is 35 meters long.
Assume that x is the height of the telephone pole..
Now we can write this as
height of shadow/ actual height
5 / 1.5 = 35 / x
By cross multiplication we get
5 * x = 35 * 1.5
We get it by dividing '5' by both sides
x = 35 * 1.5 / 5
x = 10.5 meters
Therefore ,The telephone pole is 10.5 meters tall.
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100 points!
what is/are the function(s) graphed in the photo provided?
The interval(s) over which the function is decreasing is (-∞, -2) U (-2, -1) U (-1, 1) U (5, +∞)
What is graph?According to the given graph
the increasing points:
[1, 5]
and the decreasing are:
(-∞, -2) U (-2, -1) U (-1, 1) U (5, +∞)
The correct and complete question is:
Use the graph to answer the question. 1. Find the interval(s) over which the function is decreasing. (1 point)
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What is the value of x? URGENT
Step-by-step explanation:
If you check by inspection there are two sides which are equal. The triangle is considered an Isosceles Triangles where two sides amd angles are equal.
The two base angles are equal=x°
38°+x°+x°=180°
2(x°)=180°-38°
2x°=142°
x=71°
10) 2−(n+2) >-(7 + n) + 7
Answer:
This is a false statement so there is no solution.
Step-by-step explanation:
2-(n+2) > -(7 +n) + 7
2 -n -2 > -7 -n + 7
-n > -n This cannot be true, so there is not solution.
Answer:
No solutions
Step-by-step explanation:
2-(n+2) > -(7+n)+7 Distribute the -1 to both parentheses
2 - n - 2 > -7 - n + 7 Simplify values (2 - 2; -7 + 7)
-n > -n Add n to both sides
No solutions (There are no solutions because when the equation simplifies, there are no variables and values left)
Hope this Helps! :)
Have any questions? Ask below in the comments and I will try my best to answer.
-SGO
A taxi service charges you $1.25 plus $0.75 per mile
driven to the airport. The total cost of the trip to the
airport was $12.50. How many miles was the trip to the
airport?
19 miles
17 miles
13 miles
15 miles
11 miles
Jane is a cleaner the table shows information about the time it will take to clean each four rooms in the house. Jane wants to clean all four rooms in one day she will have breaks for a total time of 45 minutes. Jane is going to start at 7am what time will she finish?
Answer:
Dat is
45/7
6.43
6.43+4+4
14.43
Answer:
b c
Step-by-step explanation:
have a great day
PERSEVERE The sum of 4 consecutive odd integers is equal to zero.
a. Write an equation to model the sentence. Let n = the first odd integer.
b. Solve the equation to find the numbers. Write the numbers from least to greatest. Check your solution.
n =
The numbers are _________ ,__________, and __________
1. The equation that models the sentence is 4n + 12 = 0.
2. The numbers from least to greatest are -3, -1, 1, 3.
What are integers?Integers are whole numbers. An integer a number without a fraction or decimal component. Integers can either be positive, negative or zero. An odd number is a number that cannot be divided perfectly into two halves. An example of odd numbers are -11, 21.
Consecutive odd numbers are whole numbers that follow each other on the number line. Consecutive odd numbers increase by 2. Examples of consecutive odd numbers are 7, 9, 11.
If 4 consecutive odd integers are: n, (n +2) (n + 4) , (n + 6)
n + n + 2 n + 4 + n + 6 = 0
4n + 12 = 0
4n = -12
n = -12 / 4
n = -3
The numbers are -3, -1, 1 , 3
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Determine the mass in (g) of 2.6x10-3 mol Na2So4
Answer:
0.36933g or 0.3693g in 2.6 x 10^-3 moles of Na2SO4
Step-by-step explanation:
Molar mass
Na = 22.99
S = 32.07
O = 16
Na(2) + S + O(4) =
22.99(2) + 32.07 + 16(4) =
45.98 + 32.07 + 64 = 142.05g
Na2SO4 = 142.05g
2.6 x 10^-3 moles = 0.0026 moles
0.0026 x 142.05 = 0.36933
Delilah is making a garden that she wants to be 5 feet longer than it is wide. Write
the equation that Delilah should use to determine the width of a garden that has an
area of 50 square feet.
How wide and how long does Delilah need to make her garden to achieve the desired speciation?
Width =
The equation is 50 = (5 + w)w and the width is 5 and the length is 10
Write the equation that Delilah should use to determine the width of a garden that has an area of 50 square feet.The given parameters are
Area = 50
Length = 5 + Width
This means that
l = 5 + w
The area is calculated as
A = lw
Substitute l = 5 + w in A = lw
A = (5 + w)w
Substitute A = 50 in A = (5 + w)w
50 = (5 + w)w
Hence, the equation is 50 = (5 + w)w
How wide and how long does Delilah need to make her garden to achieve the desired speciation?We have
50 = (5 + w)w
Express 50 as 10 * 5
So, we have
10 * 5 = (5 + w)w
This means that
5 + w = 10
w = 5
Solve 5 + w = 10
w = 5
Substitute w = 5 in l = 5 + w
l = 5 + 5
l = 10
Hence, the width is 5 and the length is 10
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simplify 4/x+4 + x/x-4
A.Hint: Find the common denominator and then add.
The simplification of the given equation is (x² + 8x - 16)/(x-4)(x+4) by the method of LCM.
What is defined as the LCM?LCM is an abbreviation for least common multiple. The smallest number which is a multiple of both numbers is the least common multiple of them.For, the given equation;
4/(x+4) + (x/x-4)
To find the common denominator, use LCM; multiply a first term by (x-4)/(x-4) and the 2nd term by (x+4)/(x+4):
= (x-4)×4/(x-4)(x+4) + x×(x+4)/(x-4)(x+4)
The following step is to disperse the 4 (x-4) and x (x+4);
So you now have;
= (4x-16 + x² + 4x)/(x-4)(x+4)
Further simplify.
= (x² + 8x - 16)/(x-4)(x+4)
As, (x² + 8x - 16) is further not factor-able. So, the simplified form of the given equation is; (x² + 8x - 16)/(x-4)(x+4).
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The perimeter of an equilateral triangle is 15 inches more than the perimeter of a square, and the side of the triangle is 7 inches longer than the side of the square.
The length of the equilateral triangle side is 13 inches while that of the square is 6 inches.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Let x represent the side of the equilateral triangle and y represent the side of the square. Hence:
For the perimeter:
3x = 4y + 15
3x - 4y = 15 (1)
Also:
x = y + 7
x - y = 7 (2)
From the equations:
y = 6, x = 13
The length of the equilateral triangle side is 13 inches while that of the square is 6 inches.
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You have a puzzle with 36 pieces. Using the number of puzzle pieces on an edge, please describe the
domain (possible side lengths) and range (possible area).
Answer:there are 4 possible edges and issa 6x6 puzzle
Step-by-step explanation: clarify question or add screen shot?
A rectangle has a height of b^3+b^2b
3
+b
2
b, cubed, plus, b, squared and a width of b^2+7b+4b
2
+7b+4b, squared, plus, 7, b, plus, 4.
The area of the rectangle is equal to b² · (b + 1) · (b + 0.628) · (b + 6.372).
What is the area of the rectangle?
The area of the rectangle is equal to the product of the height and the width, each of them represented by polynomials. In this question we must apply algebraic handling to simplify the product of the two polynomials:
A = h · w (1)
Where:
h - Heightw - WidthIf we know that h = b³ + b² and w = b² + 7 · b + 4, then the area of the rectangle is:
A = (b³ + b²) · (b² + 7 · b + 4)
A = b² · (b + 1) · (b + 0.628) · (b + 6.372)
The area of the rectangle is equal to b² · (b + 1) · (b + 0.628) · (b + 6.372).
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Calculate and interpret the residual for the flower that had 2 tablespoons of sugar and looked fresh for 204 hours.
The Residual is -8.4 hours and the interpretation of the given residual is that the carnation stayed fresh for 8.4 hours less than expected based on how much sugar it received.
How to find the residual of a scatter plot?A residual plot is a type of scatter plot where the horizontal axis represents the independent variable, or input variable of the data, and the vertical axis represents the residual values.
Now, looking at the given residual plot and using a calculator online, we can say that the equation of the least squares regression line is;
y^ = 180.8 + 15.2x
Now, for 2 tablespoons of sugar , we have x = 2. Thus;
y^ = 180.8 + 15.2(2)
y^ = 212.4 hours
Residual for 204 hours is;
Residual = 204 - 212.4 = -8.4 hours
Thus, the interpretation of the given residual is that the carnation stayed fresh for 8.4 hours less than expected based on how much sugar it received.
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Complete question is;
Does adding sugar to the water in a vase help flowers stay fresh? To find out, two statistics students went to a flower shop and randomly selected 12 carnations. When they got home, the students prepared 12 identical vases with exactly the same amount of water in each vase. They put one tablespoon of sugarin 3 vases, two tablespoons of sugar in 3 vases, and three tablespoons of sugar in 3 vases.In the remaining 3 vases, they put no sugar. After the vases were prepared, the students randomly assigned 1 carnation to each vase and observed how many hours each flower continued to look fresh.
Calculate and interpret the residual for the flower that had 2 tablespoons of sugar and looked fresh for 204 hours.
Here are 4 triangles that have been transformed by a different transformation. Which transformation is a reflection? Can someone please help me with this
Answer:
choice 1 or A the first one
Step-by-step explanation:
pleaseee helpppp meeeee this is due sooonnnn
The midpoint of AB is M(0, -3)M(0,−3). If the coordinates of AA are (6, -5)(6,−5), what are the coordinates of BB?
Step-by-step explanation:
Mid point of AB is (0, -3)
Coordinate of A is (6, -5)
By using mid point formula, if P(x, y) and Q (x′, y′), then mid point of P= (x + x′)/2 , (y + y′)/2
So, ( 0, -3)= 6+x/2, -5+y/2
0=6+x/2
0=6+x, x = -6
and, -3= -5+y/2, -6= -5+y....
y = -1
so the coordinate is (-6, -1)
To find the midpoint of two points, we can use the following formula:
[tex]midpoint=(\dfrac{x_1+x_2}{2},\dfrac{y_1+y_2}{2})[/tex]
[tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] are two endpointsSolving the QuestionWe're given:
AA = (6, -5)AB = (0, -3)BB = [tex](x_2,y_2)[/tex]Plug the information into the formula:
[tex]midpoint=(\dfrac{x_1+x_2}{2},\dfrac{y_1+y_2}{2})\\\\(0,-3)=(\dfrac{6+x_2}{2},\dfrac{-5+y_2}{2})[/tex]
If [tex]\dfrac{6+x_2}{2}[/tex] must equal 0, then [tex]x_2[/tex] must be -6.
If [tex]\dfrac{-5+y_2}{2}[/tex] must equal -3, then [tex]-5+y_2[/tex] must equal -6, making [tex]y_2[/tex] equal to -1.
Therefore, BB is (-6,-1).
Answer(-6, -1)
Which expressions are equivalent to -9? Select all that are correct
The expressions that are equivalent to -9 are -(9) and -|9|
What are rational expressions?Rational expressions are expressions that are represented by the quotient of two polynomials or radicals. This means that, a rational expression is represented by a fraction whose numerator and denominator are polynomials or radicals
How to determine the expression?The expression is given as
-9
According to the identity law of algebra, we have the following equation
-x = -(x)
This means that
-9 = -(9)
Also, we have
-9 = -|9|
Hence, the expressions that are equivalent to -9 are -(9) and -|9|
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The balance sheet of Pacific Ocean Resort reports total assets of $720,000 and $870,000 at the beginning and end of the year,
respectively. The return on assets for the year is 21%.
Calculate Pacific Ocean's net income for the year.
Net income
Based on the return on assets of 21%, the net income of Pacific Ocean Resort for year is $166,950
What is return on assets?
The return on assets for the company is determined as the net income divided by the average total assets of Pacific Ocean Resort , bearing in mind that the average total assets is sum of the beginning and ending assets divided by 2
return on assets=net income/average total assets
return on assets=21%
net income=unknown
average total assets=($720,000+$870,000)/2
average total assets=$795,000
21%=net income/$795,000
net income=$795,000*21%
net income=$166,950
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Which type of data cannot be sorted?
Answer:
credit card an bank information
medical history
what is the least whole number that rounds to 230000 when rounded to the nearest ten thousand?
The least whole number that can be rounded to 230,000 is 225,000.
What is the least whole number?The ten thousand number (10,000) is usually the fifth digit in a number when counting from the right to the left. For example, in 132,456, 3 is the ten thousand number.
To round off to the nearest ten thousand, if the thousand digit is equal to or greater than 5 (i.e. 5,6, 7, 8, 9), 1 is added to the ten thousand digit and other numbers less than the ten thousand digit becomes 0. For example, when 234,612 is rounded to the nearest ten thousand, the number becomes 235,000.
If the thousand digit is less than 5 (i.e. 0, 1, 2, 3, 4), there is no change in the ten thousand digit other numbers less than the ten thousand digit becomes 0. For example, when 234,412 is rounded to the nearest ten thousand, the number becomes 234,000.
The numbers that can be rounded off to 230,000 are: 225,000, 226,000, 227,000, 228,000, 229,000, 230,000, 231,000, 232,000, 233,000, 234,000
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Question 1
The point (6, y) lies on the line
y = -8x + 2. Find y
Answer:
y=-50
Step-by-step explanation:
x=6
substitute x and u will find the answer
Austin mowed 8 lawns in 3 hours. At that rate, how long will it take him to mow 12 lawns?
Answer: 32 hours
Step-by-step explanation:
brain
Can someone please help me? I’m confused. I’ll give brainliest :)
the 3rd term of a linear sequence is 17. the 45th term is 269. determine the formula for the nth term.
Step-by-step explanation:
a linear or arithmetic sequence has a start value as first term, and then every following term is created by adding the same constant to the previous term.
a1 = a
a2 = a1 + c = a + c
a3 = a2 + c = a + c + c = a + 2c
a4 = a3 + c = a + c + c + c = a + 3c
...
as we can easily see
an = an-1 + c = a + (n-1)c
in our case
a3 = 17 = a + 2c
a = 17 - 2c
a45 = 269 = a + 44c = 17 - 2c + 44c = 17 + 42c
252 = 42c
c = 6
a = 17 - 2c = 17 - 2×6 = 17 - 12 = 5
so,
an = 5 + (n-1)×6
how much is this quarter
