Answers
[tex] \bf\longrightarrow \large\frac{ \frac{ \frac{a( {r}^{4} - 1)}{ \cancel{r - 1}} }{a( {r}^{2} - 1) } }{ \cancel{r - 1}} = 10 \\ [/tex]
[tex]\bf\longrightarrow {r}^{4} - 1 = {10r}^{2} - 10[/tex]
[tex]\bf\longrightarrow {r}^{4} - {10r}^{2} + 9 = 0[/tex]
Put a = r²[tex]\bf\longrightarrow \: {a}^{2} - 10 {a}^{2} + 9 = 0[/tex]
[tex]\bf\longrightarrow \: a = \frac{10± \sqrt{100 - 36} }{2} = \frac{10±8}{2} [/tex]
a = 9 or a = 1r = 3 or r = 1 but r ≠ 1
[tex]\therefore[/tex] r = 3
[tex]\bf\longrightarrow \: a_3 = 54 \\ \bf\longrightarrow \: a {r}^{2} = 54 \\ \bf\longrightarrow \: a = \frac{54}{9} = 6[/tex]
Related Questions
What Two whole numbers have their first common multiple as 6
Answers
Answer:
2, 3
Step-by-step explanation:
The prime factorization of 6 is 2(3), so one possibility is 2 and 3.
Find the vertical asymptote(s) of f(x)=\frac{\left(x^{2}+3x+6\right)}{x^{2}-4}
x = −1, 2
x = −2, 2
x = 1, −2
x = −1, 1
Answers
Answer:
x = −2, 2
Step-by-step explanation:
[tex]f(x)=\frac{\left(x^{2}+3x+6\right)}{x^{2}-4}[/tex]
Find the horizontal asymptotes by comparing the degrees of the numerator and denominator.
Vertical Asymptotes:
x=−2,2Horizontal Asymptotes:
y=1
No Oblique Asymptotes
Full Explanation
The line x=L is a vertical asymptote of the function [tex] y=\frac{x^{2} + 3 x + 6}{x^{2} - 4}[/tex] if the limit of the function (one-sided) at this point is infinite.
In other words, it means that possible points are points where the denominator equals 0 or doesn't exist.
So, find the points where the denominator equals 0 and check them.
x=−2, check: [tex] \lim_{x \to -2^+}\left(\frac{x^{2} + 3 x + 6}{x^{2} - 4}\right)=-\infty [/tex]
Since the limit is infinite, then x=−2 is a vertical asymptote.
x=2, check: [tex]\lim_{x \to 2^+}\left(\frac{x^{2} + 3 x + 6}{x^{2} - 4}\right)=\infty[/tex]
Since the limit is infinite, then x=2 is a vertical asymptote.
Vertical asymptotes: x=−2; x=2
Jayne stopped to get gas before going on a road trip. The tank already had 4 gallons of gas in it. Which equation
relates the total amount of gasoline in the tank, y, to the number of gallons that she put in the tank, x?
Oy=4+x
Answers
The equation that relates the total amount of gasoline in the tank is;
y = x + 4.
What is defined as the linear equation?A linear equation is just an algebraic equation with only a constant and the first-order (linear) term of the form y=mx+b, for which m is the slope and b is the y-intercept. The above is sometimes referred to as a "linear equation of 2 factors," in which y and x are the variables.Although they can, it is often easier and faster to use a computational method to arrive at a numerical answer. The actual power of equations is they offer a very unique way to describe many different functions in the world.For the given question;
The amount of gasoline already present in tank is 4 gallons.
The number of gallons filled above the the previous gasoline is x.
Thus, now the total gasoline present in this tank is x + 4.
If y shows the total gasoline in tank;
Then,
y = x + 4.
Therefore, the total amount of gasoline present in tank is given by equation is; y = x + 4.
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Light travels at a speed of 299,792 kilometers per second. What is the speed of light, in miles per minute? (Round your answer to the nearest thousand) Note: There are 1.609 kilometers in a mile.
Answers
Answer:
11,179,000 mi/min
Step-by-step explanation:
You want the given speed of light expressed in miles per minute.
Units conversionTo convert the speed from km/s to mi/min, we need to multiply by factors of s/min and mi/km.
[tex]\dfrac{299792\text{ km}}{\text{s}}\times\dfrac{60\text{ s}}{\text{min}}\times\dfrac{1\text{ mi}}{1.609\text{ km}}=\dfrac{299792\cdot 60}{1.609}\,\dfrac{\text{mi}}{\text{min}}\\\\\approx\boxed{11,\!179,\!000\text{ mi/min}}[/tex]
Which of the following graphs best represents the solution to the pair of equations below? y = x + 1 y = −x − 1 A coordinate plane is shown with two lines graphed. One line passes through the y axis at 1 and the x axis at 1. The other line passes through the y axis at 1 and the x axis at negative 1. The lines intersect at 0 comma 1. A coordinate plane is shown with two lines graphed. One line passes through the y axis at 1 and the x axis at negative 1. The other line passes through the y axis at negative 1 and the x axis at negative 1. The lies intersect at negative 1 and 0. A coordinate plane is shown with two lines graphed. One line passes through the y axis at negative 1 and the x axis at negative 1. The other line passes through the y axis at negative 1 and the x axis at 1. The lines intersect at 0 comma negative 1. A coordinate plane is shown with two lines graphed. One line passes through the y axis at negative 1 and the x axis at 1. The other line passes through the y axis at 1 and the x axis at 1. The lines intersect at 1 comma 0.
Answers
The graph that best describes the equations y = x + 1 y = −x − 1 is: A coordinate plane is shown with two lines graphed. One line passes through the y axis at 1 and the x axis at negative 1. The other line passes through the y axis at negative 1 and the x axis at negative 1. The lies intersect at negative 1 and 0.
What is a graph?A graph is a pictorial representation of data used in several disciplines. Graphs makes it easier to understand how a particular data relates with the other.
There many types of graphs, the type used here is the that of a straight line. The graph would have to cut through based on the signs that it has in the equation. That is if it is negative or positive.
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The Vasquez family visit their grandmother every three weeks and host a neighborhood party every eight weeks. Every 16 week, the Vazquez family takes a day to go hiking. After how many weeks will the Vasquez family both visit their grandmother and host the neighborhood party? After how many weeks will all three events occur?
Answers
The number of weeks whwn the Vasquez family both visit their grandmother and host the neighborhood party is 24 weeks.
The weeks will all three events occur is 48 weeks.
How to calculate the value?From the information, the Vasquez family visit their grandmother every three weeks and host a neighborhood party every eight weeks.
Therefore, this situation is just to find the least common factor of 3 and 8. This is 24
Therefore, the number of weeks whwn the Vasquez family both visit their grandmother and host the neighborhood party is 24 weeks.
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i need help this is mad confusing
Answers
Answer:
Natural number are the numbers: 1, 2, 3... (The ... means the pattern continues. These were the first numbers that you learned about when you were little.
The whole numbers at the number 0 to the list. 0,1,2,3,...
Integers are the whole numbers and their opposites. Zero is not positive or negative. ...,-3, -2 -1 , 0, 1, 2, 3,.... The list does not include numbers like 1/2 or .75
Rational numbers are numbers that can be written as an integer/ integer. This would include numbers like 1/2 and .75 because you can write .75 as 75/100(an integer over and integer.
Step-by-step explanation:
Do not get frustrated. They are just asking for definitions of different classes of numbers.
Solve 2l2x-1l-2=12 Show all work
Answers
Answer:
Solution
x= 2l (2) 14+l
Step-by-step explanation:
Divide both sides
2l
2
2l
2
x
=
2l
2
14+l
Translate the following into a math expression:
three more than twelve times a number
A: (x+3) 12
B: x/3+12
C: 12x+3
D: 3x/12
Answers
Answer ANSWER (x+3) 12
Step-by-step explanation:
Opposites
For problems 12-14, describe the similarities and differences between the expressions.
12. -3 and -(3)
13. -1(7) and -(7)
14. -2(4) and -(2•4)
Answers
The similarities between the expressions in all the three problems is that after opening brackets both of the expressions are the same.
How to check if two expressions are similar?Two expressions are similar if their values after solving are equal.
12. -3 and -(3)
Here, when we open the bracket for -(3), we obtain -3 which is the same as the first expression.
13. -1(7) and -(7)
Solving for the first expression, we get -1×7 = -7 and
-(7) = -7.
We can see that both expressions are similar.
14. -2(4) and -(2•4)
Solving -2(4), we get -2×4 = -8
And, -(2·4) = -(8) which is the same as -8
Hence, both expressions are similar.
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what are 3 budget planning tips
Answers
The three budget planning tips can be , to be aware of your net income , listing your monthly expenses and making adjustments.
What is a budget ?
A budget is an estimation of revenue and expenses over a specified future period of time.
We know that budgets can be created for an individual, a team of individuals, a business, a government, or pretty much anything else that generates and spends money.
The 3 budget planning tips can be as follows.
1.
First tip is to be aware of your net income. Finding out how much money you have coming in is the first step in making a budget. Setting up a budget is a crucial part of managing your finances and spending patterns. So , you must figure out how much money you are spending in order to develop a budget.
2.
Second tips can be to list your monthly expenses. The monthly expenses can be many such as rent payments , loan payments , insurances and utilities.
3.
Making adjustments is a third planning suggestion. You just compare your monthly expenses and net income. You'll need to alter your spending if you find that your expenses exceeds your income.
Therefore , the three budget planning tips can be , to be aware of your net income , listing your monthly expenses and making adjustments.
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solve x- 9y =20 for y
Answers
Which expressions are equal to 0 when x=-1? Check all that apply.
4(x + 1)
(4x + 5)
4(x - 1)
(5-4x)
4(x-(-1))
(4x + 5)
4 (x + (-1))
(4x + 5)
O4(x + 1)
(5 - 4x)
Answers
Each month, Braxton uses an average of 8 ounces of lotion. Calculate Braxton's total monthly savings if he purchases the brand that has the lowest price per ounce versus the highest price per ounce.
Brand A: 24 ounces for $3.30
Brand B: 40 ounces for $4.60
a $0.18
b $0.75
с $1.30
d $1.50
Answers
Option a: Broxton have a monthly savings of $0.18 if he purchases the brand that has the lowest price per ounce versus the highest price
Given,
Braxton’s average monthly usage of lotion = 8 ounces
The amount of two different brands of lotion are given:
Brand A: 24 ounces for $3.30
Brand B: 40 ounces for $4.60
We have to find the monthly savings of Braxton if he purchases the brand that has the lowest price per ounce versus the highest price:
We have to calculate amount for one ounce for the two brands given:
Brand A:
24 ounces for $3.30
Amount for one ounce = 3.30/24
Amount for one ounce = $0.1375
Brand B:
40 ounces for $4.60
Amount for one ounce = 4.60/40
Amount for one ounce = $0.115
Now, we have to calculate the amount for 8 ounces.
Brand A:
8 x 0.1375 = 1.1
$1.1 for 8 ounces of Brand A lotion.
Brand B:
8 x 0.115 = 0.92
$0.92 for 8 ounces of Brand B lotion.
Now, we have to calculate the savings:
Brand A – Brand B
1.1 – 0.92 = 0.18
That is, Broxton have a monthly savings of $0.18 if he purchases the brand that has the lowest price per ounce versus the highest price.
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A minor league baseball park has 7000 seats. Box seats cost $6, grandstand seats cost $4, and bleacher seats
cost $2. When all seats are sold, the revenue is $26,400. If the number of box seats is one-third the number of
bleacher seats, how many seats of each type are there? Give a complete sentence explaining what your answers
mean.
Answers
Taking into account the definition of a system of linear equations, the number of box seats is 400, the number of bleacher seats is 1200 and the number of grandstand is 5400.
System of linear equationsA system of linear equations is a set of two or more equations of the first degree, in which two or more unknowns are related.
Solving a system of equations consists of finding the value of each unknown so that all the equations of the system are satisfied. That is, the values of the unknowns must give the solution proposed in both equations.
Amount of seats of each typeIn this case, a system of linear equations must be proposed taking into account that:
"B" is the number of box seats."G" is the numer of grandstand seats."BL" is the number of bleacher seats.You know that:
A minor league baseball park has 7000 seats.Box seats cost $6, grandstand seats cost $4, and bleacher seats cost $2. When all seats are sold, the revenue is $26,400. The number of box seats is one-third the number of bleacher seats,So, the system of equations to be solved is
Equation 1: B + G + BL= 7000
Equation 2: 6B + 4G + 2BL= 26400
Equation 3: B= 1/3BL
There are several methods to solve a system of equations, it is decided to solve it using the substitution method, which consists of clearing one of the two variables in one of the equations of the system and substituting its value in the other equation.
In this case, replacing equation 3 in equation 1 and isolating the variable G, you get:
1/3BL + G + BL= 7000
4/3BL + G= 7000
G= 7000 - 4/3BL
Substituting this expression and equation 3 into equation 2 you get
6×1/3BL + 4×(7000 - 4/3BL) + 2BL= 26400
Solving:
2BL + 4×7000 - 4×4/3BL + 2 BL= 26400
2BL + 28000 - 16/3BL + 2 BL= 26400
2BL - 16/3BL + 2 BL= 26400 - 28000
-4/3BL= -1600
BL= (-1600)÷ (-4/3)
BL= 1200
Remembering that B= 1/3BL and G= 7000 - 4/3BL and replacing the value of BL you get:
B= 1/3BL= 1/3×1200 → B= 400
G= 7000 - 4/3BL= 7000 - 4/3×1200 → G= 5400
In summary, the number of box seats is 400, the number of bleacher seats is 1200 and the number of grandstand is 5400.
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Two planes, which are 2670 miles apart, fly toward each other. Their speeds differ by 90mph. If they pass each other in 3 hours, what is the speed of each?
400mph and 490mph
Answers
The speed of the fast plane is 490 mph while the speed of the slow plane is 400 mph
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Let x represent the speed of the fast plane and y represent the speed of the slow plane.
Their speeds differ by 90mph, hence:
x - y = 90 (1)
The planes meet after 3 hours, hence:
3x + 3y = 2670 (2)
From both equations:
x = 490, y = 400
The speed of the fast plane is 490 mph while the speed of the slow plane is 400 mph
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Use the diagram to find the angle measures that satisfy each case. Find the measures of all 4 angles if m<2-m<1=30 degrees
Answers
The measures of the angles are <1 = 85, <2 = 105, <3 = 85 and <4 = 105
How to use the diagram to find the angle measures that satisfy each case?The diagram that completes the question is added as an attachment
From the diagram, we have
<1 + <2 = 180 degrees --- supplementary angles
Given that
<2 - <1 = 30 degrees
Add the above equations
So, we have
2<2 = 210
Divide both sides by 2
<2 = 105
Substitute <2 = 105 in <2 - <1 = 30
So, we have
105 - <1 = 30
Evaluate
<1 = 85
Also, we have
<3 = <1
<4 = <2
This means that
<3 = 85
<4 = 105
Hence, the measures of the angles are <1 = 85, <2 = 105, <3 = 85 and <4 = 105
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PLEASE HELP WILL MAKE BRIANLIEST
Answers
Answer:
She scored 12
therefor she did pass
Step-by-step explanation:
CUTICLE
How many boys are there in an introductory geology course if 392 students are enrolled and there are five boys to every three girls?
Answer
How to enter your answer (opens in new window)
Answers
The number of girls is 147 and the number of boys is 245 in the introductory geology course
Students enrolled in the introductory geology course = 392 students
The ratio of boys to girls in the course = 5:3
Let the number of girls in the course be x, then the number of boys will be 392-x
Formulating the equation we get:
Number of boys/Number of girls = Ratio of boys/Ratio of girls
= 392-x/x = 5/3
= (392-x)*3 = 5x
= 1176-3x = 5x
=1176 = 8x
x = 147
Hence, the number of girls is 147 and the number of boys is 245
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Find the distance between the two points in simplest radical form.
(8, -4) and (3, 8)
Answers
Answer:
13
Step-by-step explanation:
[tex] \sqrt{ {(8 - 3)}^{2} + {( - 4 - 8)}^{2} } [/tex]
[tex] \sqrt{ {5}^{2} + {( - 12)}^{2} } [/tex]
[tex] \sqrt{25 + 144} = \sqrt{169} = 13[/tex]
Question 5:
Write each of the following numbers correct to 3 significant figures.
a) 37412
b) 84563
c) 261.42
d) 0.3684
e) 0.002615
f) 0.0025713
Answers
Following are the numbers correct to 3 significant figures
Answers to the following questions:
(1) Round to the needed significant figure: 37400;
(2) Round to the required significant figure: 84600;
(3) Round to the required significant figure: 261;
(4) Round to the needed significant figure: 0.00262
(5) Round to the required significant figure: 0.368
(6), round to the needed significant figure: 0.00257
What is meant by correct to significant figures?
The most significant number in the number is rounded up. Check the first non-zero digit if you want to round to one significant figure while doing so. If rounding to two significant numbers, have a look at the digit that comes after the first non-zero digit.
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53/2 = 18/x round to the nearest tenth where necessary
Answers
The solution to the given equation round to the nearest tenth as required in the task content is; 0.7.
What is the solution to the given equation as in the task content?According to the task content, the solution to the equation given is to be determined round to the nearest tenth.
On this note, the equation can be solved as follows;
53/2 = 18/x
By cross-multiplication; we have;
53 × x = 2 × 18
53x = 36
x = 36/53
x = 0.679
However, when round to the nearest tenth, x = 0.7.
Ultimately, The solution to the given equation round to the nearest tenth as required in the task content is; 0.7.
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-3(x+n)=x please help me
Answers
Answer:
x=− 3n/4
Step-by-step explanation:
Can someone help with the reason? The first one is given, after that- I have no clue.
Answers
Answer:
5x = 8(x - 3)
5x = 8x - 24 → Expand the brackets
-3x = -24 → Collect like terms ,which simply means that you'll transfer 8x to the other side , which will make it -8x
x = 8 → Divide both sides by the coefficient of x (3) : minus cancels minus; then 24 ÷ 3 = 8.
Referring to the figure,
to show the cost for various amounts of long distance calls, which of
the graphs shown shows the data on a 10-by-10 grid with the appropriate
scales?
a. Graph a c. Graph c
b. Graph b d. Graph d
Answers
Based on the figure, the graph that shows the data on long distance calls on a 10-by-10 grid with appropriate scales is Graph C.
Which graph is correct?The data is to be shown on a 10-by-10 grid which means that the range of numbers on the x and y axis should be between 0 and 10.
The scales should also be appropriate which means that Time (hours) should represent the x axis and Cost (dollars) should be on the y axis.
Only Graph C has this which makes it the right one.
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How do you find existence of inverse?
Answers
[tex]{\huge\color{black}{\boxed{\fcolorbox{green}{red}{꧁ANSWER꧂}}}}[/tex]
Existence of an Inverse
There are two numbers that f takes to 4, f(2) = 4 and f(-2) = 4. If f had an inverse, then the fact that f(2) = 4 would imply that the inverse of f takes 4 back to 2. On the other hand, since f(-2) = 4, the inverse of f would have to take 4 to -2.
What is the value of the expression below when w=4w=4? 9w-10 9w−10
Answers
Answer:
26
Step-by-step explanation:
The value equals 26
9 × 4 = 36
36 - 10 = 26
how many thousands multiplied by 3 will fit into 6912
Answers
2304 times 3 goes into 6912 and gives the remainder as 0.
The numerator number in the given division number 6912 by 3 is known as a dividend, and the denominator number is known as a divisor. As a result, 6912 is the dividend number and 3 is the divisor number.
Division is one of the four fundamental mathematical operations, along with addition, subtraction, and multiplication. Division is defined as the splitting of a large group into smaller groups so that each group has an equal number of items. In mathematics, it is an operation used for equal grouping and equal sharing.
Division is a basic arithmetic operation in which a larger number is divided into smaller groups with the same number of items. For example, how many total groups will be formed if 30 students must be divided into groups of 5 students for a sporting event? Such problems are easily solved by using the division operation. Here, we must divide 30 by 5. 30 5 = 6 will be the result. As a result, there will be six groups of five students each.
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The slope of the line that passing through (4,-3)and(8,6)
Answers
What is slope.
a surface of which one end or side is at a higher level than another; a rising or falling surface.
Formula of a slope
m= y2-y1/x2-x1
We have,
(4,-3) = X1 = 4 and y1= -3
(8,6) = x2 = 8 and y2 = 6.
Substitute
m= 6-(-3)/8-4
m= 9/5
So , slope of the line is 9/5.
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so does someone help me
Answers
Step-by-step explanation:
this is an exercise to take the logical definition of an operation and apply it.
we have first a triangle operation that simply stands for the sum of the 3 included values divided by 3.
in other words, FYI, it creates the mean value of 3 given numbers.
so, we need to calculate
mean value (7, 4, 4) + mean value (8, 2, 11).
(7 + 4 + 4)/3 + (8 + 2 + 11)/3 = 15/3 + 21/3 = 36/3 = 12
the second calculation is based on a table defining a new operation Delta :
2 Delta 2 = 20
2 Delta 5 = 5
2 Delta 3 = 5
5 Delta 2 = 3
5 Delta 5 = 10
5 Delta 3 = 23
3 Delta 2 = 3
3 Delta 5 = 2
3 Delta 3 = 50
so, now we need to use this to calculate
(5 Delta 2) Delta (2 Delta 3)
3 Delta 5
2
the result is 2.