The formula to calculate the 10th term of a Geometric Progression is :
=> [tex]a_{10} = a.r^{9}[/tex]
The formula to calculate [tex]n^{th\\}[/tex] term in a given Geometric progression is
=> [tex]a_{n} = a.r^{n-1}[/tex]
Where a1 = a, r is a common ratio defined by the ratio of any two successive terms r = a2/a1, and n is the term to be found.
In the given sequence, we have the first term i.e. a = -3, n = 10,
common ratio => r = a2/a1 => r = -2
Calculating using the G.P. formula for the 10th term
=> [tex]a_{10} = a.r^{9}[/tex]
=> [tex]a_{10} = (-3).(-2)^{(10-1)}[/tex]
=> [tex]a_{10\\}[/tex] = (-3)(-512) = 1536
The 10th term for this sequence will be 1536.
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A surveyor needs to find the distance from point A to point B across a canyon. She places a stake at A, and a coworker places a stake at B on the other side of the canyon. The surveyor then locates C on the same side of the canyon as A such that CA ⊥ AB. A fourth stake is placed at E, the midpoint of CA. Finally, a stake is placed at D such that CD ⊥ CA and D,E, and B are sited as lying along the same line.
a. Explain how the surveyor can use the triangles formed to find AB.
The surveyor can find AB if he finds CD as CD = AB.
What actually means by a triangle's congruency?Two triangles are said to be congruent if their three corresponding sides are equal and their three corresponding angles are equal in size.These triangles can be moved, rotated, flipped, and turned to appear identical.If they are readjusted, they will coincide.Two triangles are congruent if they satisfy all five congruence conditions.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,
First, connect B and D and make a square ACDB with BC as a diagonal.
In triangle ACB and DCB:So, ACB ≅ DCB under SAS condition.
Therefore, the surveyor can find AB if he finds CD as CD = AB.
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3 2/5 + 9 1/10 ?????…?.?
Answer: 25/2
Step-by-step explanation:
coverting the mixed numbers into improper fractions we get
17/5+91/10
getting a common denominator and adding the numerators we get 125/10
then we can simplify, which gets 25/2
Write an equation in point-slope form for each pair of points. (1,10) and (5,42)
The point slope form of (1,10) and (5,42) is (y - 10) = 8(x - 1).
How to find the point slope form?A straight line is represented using its slope and a point on the line using point slope form. In other words, the point slope form is used to determine the equation of a line whose slope is "m" and passes through the point (x1, y1).
given that
the coordinates points are (1, 10) and (5,42)
(x1,y1) = (1,10)
(x2, y2) = (5,42)
The formula of point-slope is
(y - y1) = m(x - x1)
Here,
x1 = 1 and y1 = 10 but we don't know the value of m.
now,find the value of m using the following formula
[tex]m = \frac{(y2 - y1)}{(x2 - x1)} [/tex]
now, substitute the values, we get
[tex]m = \frac{(42 - 10)}{(5 - 1)} [/tex]
[tex]m = \frac{30}{4} [/tex]
m = 8
so, the value of m is 8.
substitute these values into the point-slope formula
(y - 10) = 8(x - 1)
Hence, the point slope form of (1,10) and (5,42) is (y - 10) = 8(x - 1).
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HELP ASAP
(−2x − 13) + (19 + 5x)
Answer:
3x+6
Step-by-step explanation:
Let's simplify step-by-step.
−2x−13+19+5x
=−2x+−13+19+5x
Combine Like Terms:
=−2x+−13+19+5x
=(−2x+5x)+(−13+19)
=3x+6
Find the sum of each infinite geometric series. 6+5+ 25/6 + . . .
The sum of the infinite geometric series 6+5+ 25/6 + . . is S = 36
The given geometric series is:
6 + 5 + 25/6 + . . .
The common ratio (r) of a geometric series is given by:
r = a(n) / a(n - 1)
Notice that in the given series:
a(1) = 6
a(2) = 5
a(3) = 25/6
Hence, the common ratio is
r = a(2) / a(1) = 5/6
Since 0 < r < 1, the series is convergent and the sum exists.
Use the sum formula:
S = a(1) / (1 - r)
Substitute a(1) 6 and r = 5/6 into the formula:
S = 6 / (1 - 5/6)
= 6 / (1/6)
= 36
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Chris buys an item for $6.43. He gives the cashier a $50 bill. How much money should Chris get back
Answer:
43.57
Step-by-step explanation:
subtract 6.43 from 50
Answer: 43.57
Step-by-step explanation: 50 dollars minus 6 dollars and 43 cents and it gives you 43.57
Melanie spent half of her allowance going to the movies. She washed the family
car and earned nine dollars. What is her weekly allowance if she ended with
seventeen dollars?
Answer:43
Step-by-step explanation:
(9+17)x2
HELP ME WITH THIS QUESTION PLS PLS
Answer: 49
Step-by-step explanation:
A=πr^2
A=π(7)^2
A=49π in^2
Answer: 49
Answer:
154 Inches square.
r=7
area= πr^2
= 22/7* 49
= 154
The total entrance fee for a group of 4 adults and 3 children to a water park is $220.
The total fee for a group of 2 adults and 1 child is $98. Determine the entrance fee for
an adult and the entrance fee for a child.
What does the solution represent in terms of this situation?
The entrance fee in the water park for the adult $37 and for the child are $24.
What basically is a two-variable linear equation?The maximum power of a variable in a linear equation of two variables is one.
A linear equation with two variables raised the same power is a two-variable equation.It is written as ax + by + c = 0, where a, b, and c have all become real numbers, but a and b remain not equal to zero.3x + 9y = 5 and -x + 8y = 6 are both two-variable linear equations.Now, for the question's given condition;
Let the cost for the adult is 'x'.
Let the cost for the child is 'y'.
The total cost for entrance fee is $220.
The group of 4 adults and 3 children costs 220.
4x + 3y = 220 ........equation 1
The group of 2 adults and 1 child costs $98.
2x + y = 98 .........equation 2
Use elimination method to solve the equations;
x = 37 and y = 24.
Therefore, the entrance fee in the water park for the adults is $37 and for the child us $24.
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y varies directly with x . Explain your answer.If x is doubled, what happens to y ?
If x is doubled then the value of y is also doubled.
What is direct variation?A sort of proportionality known as "direct variation" occurs when one quantity immediately changes in response to a change in another variable. This suggests that if one number increases, the other quantity will also rise proportionately. Similar to the last example, if one quantity declines, the other amount likewise declines. The link between direct variation and the graph will be linear, resulting in a straight line.
As y varies directly with x,
Using direct variation,
which implies y = kx
if x is doubled,
y = 2kx,
This implies that if x is doubled then the value of y is also doubled.
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Write an algebraic expression.
7. Bobby ran 4 miles and will run 3 miles a day from now on. Jack ran 6 miles and will
run 5 miles a day from now on.
a. Create an algebraic expression that represents the amount of miles that Bobby & Jack
will run together. Simplify, if possible.
b. Determine how many miles they will run after 8 days.
From the situation described, it is found that:
a) The linear function that represents the amount of miles that Bobby & Jack will run together is T(x) = 2(4x + 5).
b) They will have run 74 miles after 8 days.
What is a linear function?A linear function is modeled by:
y = mx + b
In which:
m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.For both Bobby's and Jack's function, we have that:
The amount that they have ran is the intercept.The daily amount that they will run is the slope.Hence the functions for the number of miles they will have run after x days are given by:
B(x) = 4 + 3x.J(x) = 6 + 5x.The total amount is:
T(x) = B(x) + J(x)
T(x) = 4 + 3x + 6 + 5x
T(x) = 8x + 10.
T(x) = 2(4x + 5).
After 8 days, the number of miles they will have run is:
T(8) = 2(4 x 8 + 5) = 2 x 37 = 74.
They will have run 74 miles after 8 days.
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The ratio of the measure of the angles of a triangle is 1: 2: 3 . The length of the shortest side is 8 . What is the perimeter of the triangle?
The perimeter of the triangle is 37.86
Given,
The ratio of the measure of the angles of triangle = 1:2:3
Let the angles be taken as x, 2x, 3x.
Total angle of a triangle is 180°.
We can now find x.
x + 2x + 3x = 180°
6x = 180°
x = 180°/6 = 30°
x = 30°
2x = 2 × 30° = 60°
3x = 3 × 30° = 90°
Let the sides of the triangle be a, b, c.
The length of the shortest side is given = 8
Lets take a as 8.
We can use Trignometric Formulas here:
Trignometric Formulas:
sin θ = [tex]\frac{opposite side}{hypotenuse}[/tex]
cos θ = [tex]\frac{adjacent side}{hypotenuse}[/tex]
tan θ = [tex]\frac{opposite side}{adjacent side}[/tex]
By using sin rule we can find other sides.
That is,
sin 30° = opposite side / hypotenuse
sin 30° = a/b
sin 30° = 8/b
b = 8 × sin 30°
b = 16
Next,
sin 60° = opposite side / hypotenuse
sin 60° = c/16
c = sin 60° × 16
c = 13.86
Now we can find the perimeter of the triangle = a + b + c
= 8 + 16 + 13.86
= 37.86
The perimeter of the triangle is 37.86
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Tionna wants to replicate a painting in an art museum. The painting is 3 feet wide and 6 feet long. She decides on a dilation reduction factor of 0.25. What size paper should she use? F. 4 in.× 8in. H. 8 in. × 16 in. G. 6 in. × 12in. J. 10 in. ×20 in.
10in × 20in is size paper should she use. That is, option J . 10in × 20in is the correct answer.
What are examples of linear equations?
Ax + By = C is the usual form for two-variable linear equations. A standard form linear equation is, for instance, 2x+3y=5. When an equation is given in this format, finding both intercepts is rather simple (x and y). When attempting to solve systems involving two linear equations, this form is also quite helpful.The given size of the painting is 3 feet wide and 6 feet long.
The value of 1 foot in inches,
1 foot = 12inches.
The size of the painting is 36 inches wide and 72 inches long.
width is, ( 0.25 × 36 ) = 9 inches. So option F . 4in × 8 in is not the answer and
the length is, ( 0.25 × 72 ) = 18 inches. So option G 6in × 12in and H. 8inch × 16 in are not the possible choices.
So, the reduced dimensions of the dilated painting are 9 inches wide and 18 inches long.
That is, option J . 10in × 20in is the correct answer.
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what are two different methods for solving a real-world problem that can be represented by an equation
Subtraction Property of Equality and Addition Property of Equality are two different approaches to resolving a real-world problem that can be depicted by an equation.
What is defined as the Addition Property of Equality?When the identical quantity is added to the both sides of an equation, it generates an equivalent equation, according to the addition property of equality.
2 = 1+1, for example, is an equation given that both the right and left sides of the equal sign symbolize the number 2. However, by adding the number 3 to both sides, this same new equation 2 +3 = 1 + 1 + 3 is founded. As a result of the Addition Property of Equality, if a = b, then a + c = b + c.What is defined as the Subtraction Property of Equality?To maintain equality, if we deduct a number from one side of the equality, we must subtract the very same number from the opposite side of the equality.
Consider the equation X = Y. If a real number 'b' is deducted from the LHS of X = Y, we should then subtract b from Y, so X - b = Y - b. As a result, the formula is as follows:X = Y : X - b = Y - bThus, Subtraction Property of Equality as well as Addition Property of Equality are two different ways of solving a real-world problem that may be represented by an equation.
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Simplify each sum or difference. State any restrictions on the variables.
x / 3x + 9 - 8/x² + 3x
Simplification of the equation [tex]\frac{x}{3x+9}- \frac{8}{x^{2} +3x}[/tex] is equal to (x² -24)/ 3x(x+3), restriction on the variables are x ≠0 , x≠ -3.
As given in the question,
Given equation [tex]\frac{x}{3x+9}- \frac{8}{x^{2} +3x}[/tex]
Simplify the given equation,
x/ 3(x+3) - 8/x(x+3)
= (x² - 24) / 3x(x+3)
Restriction on the variables for the above equation is,
x≠ 0 , x≠ -3
Therefore, simplification of the equation [tex]\frac{x}{3x+9}- \frac{8}{x^{2} +3x}[/tex] is equal to (x² -24)/ 3x(x+3), restriction on the variables are x ≠0 , x≠ -3.
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Given the following triangle, find c.
1. 12
2. 18/17
3. 6/17
4. 3√34
Answer:
Step-by-step explanation:
4.
do A squared plus B squared equal C squared, you should get [squared root[ of 306 then simplify it to 3 squared root 34 by using the family tree
Solve each system by substitution. 3x+5y=13 , 2x + y = 4
The solution of the system of equations involving 3x + 5y = 13 and 2x + y = 4 is (1 , 2).
A system of linear equations is a set of two or more equations which includes common variables. To solve system of equations, we must find the value of the unknown variables used in the equations that must satisfy both equations.
There are three methods that can be used to solve system of linear equations.
1. Elimination
2. Substitution
3. Graphing
Using substitution method, given two linear equations in x and y,
3x + 5y = 13 (equation 1)
2x + y = 4 (equation 2)
Using the second equation, find the value of one variable, lets say y, in terms of the other.
2x + y = 4 (equation 2)
y = 4 - 2x
Substitute the equation of y to the first equation.
3x + 5y = 13 (equation 1)
3x + 5(4 - 2x) = 13
3x + 20 - 10x = 13
Combining all terms containing the variable x on one side and the constants on the other side of the equality, and solving for x.
3x + 20 - 10x = 13
3x - 10x = 13 - 20
-7x = -7
x = 1
Substitute the value of x in the equation of y.
y = 4 - 2x
y = 4 - 2(1)
y = 4 - 2
y = 2
Hence, the solution of the given system of equations is (1 , 2).
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How do I Evaluate 16 2/3?
Answer:
6.34960 correct to 5 decimal places.
Step-by-step explanation
16 ^ 2/3
= cube root of 16^2
∛(16^2)
= ∛(256)
= 6.349604208.
The 2 in the 2/3 means the square of 16, and the 3 in 2/3 mean 16^1/3
which is the same as the cube root.
The evaluation of mixed fractions [tex]16\dfrac{2}{3}[/tex] in improper fractions using the simplification rule is [tex]\dfrac{50}{3}[/tex].
The combination of a proper fraction and a whole number is called a mixed fraction.
When the numerator is greater than the denominator, such type of fraction is called an improper fraction.
To evaluate [tex]16 \dfrac{2}{3}[/tex] , convert the mixed number to an improper fraction and then simplify it.
Multiply the whole number [tex](16)[/tex] by the denominator [tex](3)[/tex] and add the numerator [tex](2)[/tex].
[tex](16 \times 3 )+ 2 \\= 48 + 2\\ = 50[/tex]
The sum is written with the denominator [tex]3[/tex] as [tex]\dfrac{50}{3}[/tex] .
The evaluation of mixed fractions [tex]16\dfrac{2}{3}[/tex] in improper fractions is [tex]\dfrac{50}{3}[/tex].
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What is the algebraic expression for "the sum of a number and 4"?
A. 4-z
B. 4/z
C. z+4
Answer:
C. z + 4
Hope this helps :)
Step-by-step explanation:
When it says "sum," it means the answer to 2 number that you add. The first number will be unknow which z will stand for, and the second number is 4 since it was stated in the statement, "the sum of a number and 4."
A garden is in the shape of a square with a perimeter of
32
feet. The garden is surrounded by two fences. One fence is around the perimeter of the garden, whereas the second fence is
2
feet from the first fence on the outside. If the material used to build the two fences is
$
1.18
per foot, what was the total cost of the fences?
Answer:
Step-by-step explanation:
32 / 4 = 8 = length or width (because it is a square both are the same)
8 + 2 = 10
10 + 10 + 10 + 10 = 40 (perimeter of outer fence)
32(1.18) + 40(1.18) = $84.96
can someone help me with this
We have given the expression -13y + 7 -11 - 4y to write as sum which is
-13y + 7 +(-11) + (-4y).
What is an mathematical expression?A mathematical expression is a phrase that includes at least two numbers or variables, at least one arithmetic operation, and the expression itself. Any one of the following mathematical operations can be used. (Number/variable, Math Operator, Number/variable) is the order in which an expression is composed.
Arithmetic operators and numbers make up a mathematical numerical expression. No equality or inequality symbols, or unidentified variables, are present.
Indeterminate variables, integers, and arithmetic operators make up an algebraic expression. Neither equality nor inequality symbols can be found in it.
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7. What's the sum of 2 and 24?
A. 10/20
B.
C. %20
D. %10
Answer:26
Step-by-step explanation:it's 26
Answer:
26
Step-by-step explanation:
You add 24 + 2 = 26 ( SUM means to ADD )
Ross joined a 30 week weight loss challenge. he lost 10.4 pounds int eh first 4 weeks if he maintains this rate of weight loss how many pounds will eh lose at the end of the 30 week challenge
Answer: 78 pounds
Step-by-step explanation:
10.4/4 = 2.6
2.6 * 30 = 78
Find the arithmetic mean a n of the given terms. a n₋₁ = 4, a₊₁ = -3
The arithmetic mean a n of the given terms a n₋₁ = 4, a₊₁ = -3 is [tex]a_{n}[/tex] = 1/2.
What is arithmetic mean?an=a1+d(n−1) by using this formula the arithmetic mean a n of the given terms are
[tex]a_{n}[/tex] = (-3 + 4)/2
[tex]a_{n}[/tex] = 1/2
The sum of a set of numbers divided by the total number of numbers in the set is known as the arithmetic mean or arithmetic average in mathematics and statistics.
The arithmetic mean can be calculated as one approach. Divide the total by the total number of values after adding up all the values. Add the numbers together, for instance: a + b + c + d and so on, if there is a set of "n" numbers.
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Assume an initial starting ft of 290 units, a trend (tt) of eight units, an alpha of 0.40, and a delta of 0.50. if actual demand turned out to be 278, calculate the forecast for the next period.
The forecast for the next period when the actual demand turned out to be 278 will be 294 units.
What is the forecast?The method of forecasting entails creating assumptions based on historical and current data. These might then be contrasted with what transpires.
Ft = 290, Tt = 8, α = 0.40, δ = 0.50, At = 278. Then the forecast for the next period will be
FITt = Ft + Tt
= 290 + 8
= 298 units
Ft + 1 = FITt + α(At − FITt)
= 298 + 0.40(278 − 298)
= 298 − 8
= 290 units
Tt + 1 = Tt + δ(Ft + 1 − FITt)
= 8 + 0.50(290 − 298)
= 8 − 4
= 4 units
FITt + 1 = Ft + 1 + Tt + 1
= 290 + 4
= 294 units
The forecast for the next period will be 294 units.
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What is the graph solution of 1 + k ≥ 4 or 9 + k < 2? ( I don't understand in how to solve this, if possible please do a step by step or at least explain how you got your answer.
Using the concept of the or operation, the solution of the given inequality in the number line is given at the graph in the end of the answer.
What is the result of the or operation between sets?The or operation between sets has as a result all the elements that belong to at least one of the sets.
For this problem, we have two inequalities:
1 + k ≥ 49 + k < 2.Then we solve the inequality then apply the or operation between them.
The solutions to the inequalities are given as follows:
1 + k ≥ 4 -> k ≥ 3 (numbers to the right of k = 3, with a closed interval).9 + k < 2 -> k < 2- 9 -> k < -7(numbers to the left of k = -7, with an open interval).The or operation will involve both the numbers to the left of k = -7 and the numbers to the right of k = 3 being plotted on the number line, as shown in the graph at the end of the answer.
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what is 5u+10u for math 8?
Answer:
(5+10)u
= 15u
is the solution
The graph below shows how the number of donations to a charity affects the expected total value of those donations.
In October, the charity received 60 donations.
If the graph continues in the same way, what is the expected total value of the donations in October?
I can't answer it but i hope someone else does :)
Maybe the answer - But there are limits depending on whether you donate the funds to a “50% charity” or a “30% charity.” As the name implies, the total deduction for gifts to 50% charities cannot exceed 50% of a taxpayer's adjusted gross income (AGI). Accordingly, donations to 30% charities are limited to 30% of AGI.
This line graph shows the United States population from 1800 to 2000. A graph titled U S population has year on the x-axis, and millions of people on the y-axis. A line increases from 0 in 1800 to 300 in 2000. What was the population in the year 2000? about 50 million about 100 million about 200 million about 300 million
In the line graph it represents us to infer that the U.S. population in 2000 was about 300 million.
What is graph?A graph contains data of which input maps to which output.
Analysis of this leads to the relations which were used to make it.
For example, if the graph of a function is rising upwards after a certain value of x, then the function must be having increasingly output for inputs greater than that value of x.
WE have been given graph that titled U S population has year on the x-axis, and millions of people on the y-axis. A line increases from 0 in 1800 to 300 in 2000.
The line graph showed that:
The U.S. population was under 50 million in 1800
It increased exponentially after 1880
It reached around 300 million in 2000
The U.S. has seen its population rise exponentially over the last century such that; over 300 million and it was around the year 2000 that this milestone was reached.
Therefore U.S. population in 2000 was around 300 million.
In the line graph it represents us to infer that the U.S. population in 2000 was about 300 million.
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Answer:
300 million is ur answer:)
Step-by-step explanation:
Write the equation of the circle that passes through the given point and has a center at the origin. (Hint: You can use the distance formula to find the radius.) (√3, 0)
The equation of the circle that passes through the point (√3 , 0) and has a center at the origin is x^2 + y^2 = 3.
Using the distance formula, get the radius of the circle by solving for the distance between the center and the point (√3 , 0).
radius = distance = √(x2 - x1)^2 + (y2 - y1)^2
radius = √(√3 - 0)^2 + (0 - 0)^2
radius= √3
The standard form of the equation of the 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.
Given the radius and center of the circle, substitute these values to the standard form of the equation of the circle.
(x - h)^2 + (y - k)^2 = r^2
where (h , k) = (0 , 0)
r = √3
(x - 0)^2 + (y - 0)^2 = (√3)^2
x^2 + y^2 = 3
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