The nth term of the given geometric sequence, 3, 12, 48, 192, . . . , is a(n) = 3[4^(n - 1)], where a(n) is the nth term.
A geometric sequence refers to a sequence of numbers, which the next term is obtained by multiplying the previous term with a constant, called a ratio.
a(n) = a r^(n-1)
Where:
a(n) = nth term
a = first term
r = ratio
Given the geometric sequence 3, 12, 48, 192, . . .
Find the ratio,
r = a(n)/a(n-1)
r = a(2)/a(1)
r = 12/3
r = 4
Notice that the ratio between two succeeding terms is always 4.
Substitute the value or r and the first term to the formula to determine expression for the nth term.
a(n) = a r^(n-1)
a(n) = 3[4^(n - 1)]
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Find the 17 th term of each sequence. a₁₈ = -9, d = -11
The 17 th term of each sequence. a₁₈ = -9, d = -11 is [tex]a_{17}[/tex] = -185.
What is a sequence?a₁₈ = -9, d = -11 is
[tex]a_{17}[/tex] = -9 + (16)(-11)
[tex]a_{17}[/tex] = -185.
succession: the doing of one thing after another. A list of books is presented in alphabetical order. a succession of sonnets that is continuous or connected. a later event, outcome, or repercussion; something that happens after.
A series of numbers is an ordered list. The three dots signify moving forward in the set pattern. Each digit in the sequence is referred to as a word. The first term in the list is 1, followed by the second by 3, the third by 5, and so on.
Arithmetic sequences, geometric sequences, quadratic sequences, and special sequences are the four primary categories of distinct sequences you need to be familiar with.
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Which of the following expressions shows how to rewrite 4 − 5 using the additive inverse and displays the expression correctly on a number line?
The expression that shows how to rewrite 4 − 5 using the additive inverse is (a)
How to determine the expression that shows how to rewrite 4 − 5 using the additive inverse?The expression is given as
4 - 5
The law of additive inverse states that
x + (-x) = 0
This means that x and -x are additive inverses
Using the above as an illustration,
4 - 5 can be rewritten as 4 + (-5)
And the above implies that the number line moves 4 points to the right and 5 points to the left
Hence, the expression that shows how to rewrite 4 − 5 using the additive inverse is (a)
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The circle below is centred at O.
a) Work out the size of angle x.
b) Which of the circle theorems below allows
you to calculate this angle?
O
X
Not drawn accurately
31°
The perpendicular line from the centre of a circle to a chord
bisects the chord
Two tangents that meet at a point are the same length
The angle at the circumference in a semicircle is a right angle
Opposite angles in a cyclic quadrilateral add up to 180°
The angle between the tangent and the radius at a point
on a circle is 90°
Answer:
[tex]\textsf{a)} \quad x = 59^{\circ}[/tex]
[tex]\textsf{b)} \quad \boxed{\begin{minipage}{8.5 cm}\sf The angle between the tangent and the radius at a point \\on a circle is $90^{\circ}$.\end{minipage}}[/tex]
Step-by-step explanation:
Part (a)As two sides of the triangle inside the circle are the radius of the circle, the triangle is an isosceles triangle.
Therefore, its two base angles are 31°.
The tangent of a circle is:
A straight line that touches the circle at only one point.Always perpendicular to the radius.Therefore:
[tex]\implies x + 31^{\circ} = 90^{\circ}[/tex]
[tex]\implies x +31^{\circ}-31^{\circ}= 90^{\circ} - 31^{\circ}[/tex]
[tex]\implies x = 59^{\circ}[/tex]
Part (b)The circle theorem that allows you to calculate angle x is:
[tex]\boxed{\begin{minipage}{8.5 cm}\sf The angle between the tangent and the radius at a point \\on a circle is $90^{\circ}$.\end{minipage}}[/tex]
Rex and Samir participated in a walkathon. Rex walked for 1 2/3 hours, and Samir walked for 3 1/3 hours. complete the comparison. Samir walked _____ times ad many hours as Rex walked.
Samir walked 2 times as many hours as Rex walked.
What is ratio?A ratio can be defined as the comparison of two or more numbers on the basis of their sizes in relation to each other.
It also indicates how many times one number contains another.
Given that;
Rex walked = 1 2/3 hours = 5/ 3 hoursSamir walked = 3 1/3 = 10/ 3 hoursTo determine the ratio, we have to divide Samir's walking hours by Rex's working hours
= 10/ 3 ÷ 5/ 3
Take the inverse of the divisor and multiply
= 10/ 3 × 3/ 5
= 2 hours
Thus, Samir walked 2 times as many hours as Rex walked.
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How many times does your heart beat per second
Answer:
The average heart beats 80 - 90 timers per minute. In 1 second it beats 1.33 1.5 times
Step-by-step explanation:
Quora
The height of a thrown football, in feet after t seconds is given by h(t) =-16^2+48^t+6. How many seconds does it take for the balls to reach maximum height after it is thrown?
Answer:
I don't know rjdjdjjdjddjidis
[tex]If BD=3, then CD= [blank] −−−.Enter your answer as the number that correctly fills in the blank.[/tex]
The value of the triangle side segment CD is; 3
How to use triangle congruence postulate?
The HL Congruence Postulate states that if the hypotenuse and leg of one right triangle are congruent to the hypotenuse and leg of another right triangle, then the two triangles are congruent.
Now, in this question, we are told that BA ≅ CA. Thus, by applying HL congruence postulate, we can say that;
BD = CD
Also, AD = AD due to reflexive property of congruence.
We are given that BD = 3. Thus, CD = 3
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decimals equivalent to 8.1
Answer:
8.10 & 8.100
Hope this helps ^^
Have a good day <3!
pls answer this question als0oo
I am doing a test and have no idea how to do this
Answer:
x squared
Step-by-step explanation:
x squared and the rest =1
(k)(k − k + h); use h = -2, and k = 6
Answer:-12
Step-by-step explanation:
6(6-6+ -2)
6(-2)
-12
b. Explain how your answer to part (a) relates to the explicit formula a n = a+(n-1) d
My answer to part (a) relates to the explicit formula in an n = n+6 n a= n+6 n.
a= n+6 n
Step-by-step explanation:
n=an−1−5
Step 1: Flip the equation.
an−6=n
Step 2: Add 6 to both sides.
an−6+6=n+6
an=n+6
Step 3: Divide both sides by n.
an n = n+6 n a= n+6 n
What is explicit formula?An arithmetic sequence has the explicit formula a = a + (n - 1)d, and each term of the sequence may be computed without knowing the values of the previous terms. The nth term of an arithmetic, geometric, or harmonic series is usually the explicit formula.
The formal equations for L-functions in mathematics are Riemann's zeta function and links between sums over an L-complex function's number zeroes and sums over prime powers.
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Find the center and the radius of each circle. x²+y²=2
The equation of the circle x^2 + y^2 = 2 has a radius of √2 and a center located at (0 , 0).
The standard form of the equation of 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.
On the other hand, the general form of the equation of circle is given by
x^2 + y^2 + Dx + Ey + F = 0
where D = -2h, E = -2k, and F = h^2 + k^2 -r^2.
If the equation of the circle, x^2 + y^2 = 2, is in standard form, then
h = 0
k = 0
r = √2
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& Check
# 18 1
The function b(x)= |x-45] represents the absolute deviation (in inches) of a boy's height x (in inches) from the average height of boys in a kindergarten class. The
function g(x)= |x-44| represents the absolute deviation (in inches) of a girl's height x (in inches) from the average height of girls in a kindergarten class. Compare
the absolute deviations for a boy and a girl who are both 43 inches tall.
I don't know lol ididjdjdj
What do you notice about the measures of anges the are side by side?
they add up to 180 degrees
r^2 + 5x– 14
factor
Answer:
it is not factorable
Step-by-step explanation:
Which line is parallel to the line 5 x+6 y=30 ?
f. 5 x+9 y=30
g. 9 x+6 y=30
h. 5 x+6 y=9
i. 6 x+5 y=30
The equation of the line h. 5x + 6y = 9 is parallel with the equation of the line 5x + 6y = 30.
Two lines are parallel with each other if they do not intersect no matter how much you extend both lines. Parallel lines have equal slopes.
The slope, m, determines the steepness of a line. It can be measured by the vertical distance from one point to another divided by the horizontal distance of the same points. In an equation in slope-intercept form, y = mx + b, the slope, m is the coefficient of x.
Determine the slope of the given line and each given choices by transforming each into slope-intercept form.
5x + 6y = 30
6y = -5x + 30
y = -5/6 x + 30/6
y = -5/6 x + 5
m = -5/6
f. 5x + 9y = 30
9y = -5x + 30
y = -5/9 x + 30/9
y = -5/9 x + 10/3
m = -5/9
g. 9x + 6y = 30
6y = -9x + 30
y = -9/6 x + 30/6
y = -3/2 x + 5
m = -3/2
h. 5x + 6y = 9
6y = -5x + 9
y = -5/6 x + 9/6
y = -5/6 x + 3/2
m = -5/6
i. 6x + 5y = 30
5y = -6x + 30
y = -6/5 x + 30/5
y = -6/5 x + 6
m = -6/5
Since h. 5x + 6y = 9 has a slope of -5/6 and equal to the slope of the given line, then they are parallel lines.
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1/16 to the power of 2
Answer: 0.00390625
Step-by-step explanation:
Answer:
The answer is 1/256 :)
Step-by-step explanation:
This one is actually quite simple! All you need to do is multiply 1/16 by 1/16! 1 x 1 is 1 of course, and 16 x 16 is 256. I've attached an image to help break it down even further. (credit to cymath.com)
Hope this helps!
Write an equation of a parabola with vertex at the origin and the given focus. (0,6)
Answer:
27273763hebvrhejwj27222
Need help asap please
Answer:
1) the center is (3,4), radius is 3. 3) ( x − 2 )^2 + ( y − 14 )^2 = 9, 5) the center is (12,5), the radius is 4
Step-by-step explanation:
For the graphs just look for the middle point, and thats essentially your center, and the radius is how many units the edge of the circle is to the center. So for 1 the center would be (3,4) and the radius 3. For problem 3 use the equation ( x − a )^2 + ( y − b )^2 = r^2, where you substitute the radius for r, your x center coordinate as a, and your y coordinate as b. In problem 5, use 12 as your x value for the center coordinate, and 5 as your y value. Then just take the root of 16 to get your radius, and apply that to the other problem. Hope this helps :)
6 4 0,409, 210
onas period
ones
The number name for this number is six hundred forty million, four hundred
nine thousand, two hundred ten.
1Expanded form is a way to write a number as the sum of each
digit multiplied by its place value. Fill in the blanks to write the
number in expanded form.
The expansion of 6 4 0,409, 210 is given below with the solution.
What does "expanded form" mean?The division of numbers into groups according to place value, such as ones, tens, hundreds, thousands, ten thousand, and so on, results in the expanded form of the number. The expanded version of the number is the one that is represented by the sum of each digit times its place value.
6 4 0,409, 210 = 6 × 10,00,00,000 + 4 × 100,00,000 + 0 × 10,00,000 + 4 × 100,000 + 0 × 10,000 + 9 × 1000 + 2 × 100 + 1 ×10 + 1 × 0
A number is displayed in expanded form according to the place values of its digits.
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I'm more sophisticated than my little sister. I save my money in a bank account that pays
me 3% interest on the money in the account at the end of each month. (If I take my money
out before the end of the month, I don't earn any interest for the month.) I started the
account with $50 that I got for my birthday. How much money will I have in the account at
the end of 10 months? How many months will it take to have at least $100? Justify your
answer with a mathematical model of the problem situation.
The amount of money after 10 months will be $67.2. The number of months (n) that it takes to have at least $100 will be 2 years or 24 months.
What is compound interest?A loan or deposit's interest is computed using the starting principle and the interest payments from the ago decade as compound interest.
We know that the compound interest is given as
[tex]\rm A = P \left (1 + r \right ) ^{t}[/tex]
Where A is the amount, P is the initial amount, r is the rate of interest, and t is the number of months.
I keep my savings in a bank account that, at the end of each month, gives me 3% interest on the balance. (If I withdraw my funds before the end of the month, I forfeit the interest I would have accrued.) I opened the account using the $50 I received as a birthday gift.
The amount of money after 10 months will be
A = 50 (1 + 0.03)¹⁰
A = 50(1.03)¹⁰
A = 50 x 1.344
A = $67.2
The number of months (n) that it takes to have at least $100 will be
100 = 50 (1.03)ⁿ
2 = (1.03)ⁿ
n ln 1.03 = ln 2
n = ln 2 / ln 1.03
n = 23.5 ≈ 24 months or 2 years
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Find the sum of each finite series. Σ¹° n = 1 (3 n-4)
The sum of the given finite series is 125
The given finite series is:
[tex]\sum\limits^{10}_{n=1} {(3n-4)}[/tex]
Use the properties of sum operator:
[tex]\sum\limits^{10}_{n=1} {(3n-4)}=\sum\limits^{10}_{n=1} {3n}-\sum\limits^{10}_{n=1} {4}[/tex]
Calculate each term on the right side:
[tex]\sum\limits^{10}_{n=1} {4}=4+4+...+4=10\times4=40[/tex]
[tex]\sum\limits^{10}_{n=1} {3n}=3\sum\limits^{10}_{n=1} {n}[/tex]
= 3.(1 + 2 + 3 + ... + 10)
The series in the brackets is an arithmetic series with :
the first term: a(1) = 1
the last term: a(10) = 10
the common difference: d = 2 - 1 = 1
Use the sum formula for arithmetic series:
S(n) = n/2 [a(1) + a(n)]
S(10) = 10/2 [1 + 10]
=5 . 11 = 55
Therefore,
[tex]\sum\limits^{10}_{n=1} {3n}=3\times{55}=165[/tex]
Combine the sum:
[tex]\sum\limits^{10}_{n=1} {3n}-\sum\limits^{10}_{n=1} {4}=165-40[/tex]
= 125
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In the regular polyhedron described below, all faces are congruent polygons. Use a system of three linear equations to find the numbers of vertices, edges, and faces.
Every face has five edges and every edge is shared by two faces. Every face has five vertices and every vertex is shared by three faces. The sum of the number of vertices and faces is two more than the number of edges.
A normal polyhedron shape is defined as a polyhedron having a symmetry group that acts transitively on the flags. Regular polyhedral are highly symmetrical because they are all edge-transitive, corner-transitive, and face-transitive. Many different equivalent definitions are used in classical contexts. There are many definitions in mathematics defining a regular polyhedron, and is that the faces of a polyhedron are nothing but congruent regular polygons that are constructed in the same way around each vertex of the polyhedron. So the polyhedron having faces/sides that are congruent with regular polygons and the exact number of faces that meet at each vertex is called a regular polyhedron.
Euler's polyhedron formula describes the relationship between the number of vertices, edges, and faces of a three-dimensional polyhedral shape.
V-E+F=2 gives Euler's polyhedron formula.
Where V-corner, E-edge, F-face.
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Jenny's Bakery sells carrot muffins at 2 each. The electricity to run the oven is 120 per day and the cost of making one carrot muffin is 1.40 . How many muffins need to be sold each day to break even?
If Jenny's Bakery sells carrot muffins at 2 each and the electricity to run the oven is 120 per day and the cost of making one carrot muffin is 1.40, then the number of muffins needed to be sold each day to break even is equal to 200.
The number of muffins needed to be sold each to break even can be determined by forming a linear equation.
A linear equation, sometimes also referred to as a first-degree equation can be described as an equation that contains variables that have the maximum power of not more than one.
The linear equation for this problem will be,
Cost of electricity to run the oven + Cost of making x number of muffins = Sale price of x number of muffins
120 + 1.40 (x) = 2 (x)
Here x is equal to the number of muffins
Rearranging the equation,
120 = 2(x) - 1.40 (x)
120 = 0.6 (x)
120/0.6 = x
x = 200
Hence, 200 muffins are needed to be sold each day to break even.
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ASAP Please
Three of the angles in a quadrilateral are 100°, 65° and 100°.
a. Show how you can calculate the fourth angle.
b. Suggest which type of quadrilateral this shape may be.
a. 95 b. kite
Step-by-step explanation:
a. all quadrilaterals add up to 360° angle with all angles, so 100+100+65=265, 360-265=95.
b. most quadrilaterals have 2 pairs of 2 equilateral angles, and this is one of the only ones that doesnt.
Answer:
a) 95°
b) Kite
Step-by-step explanation:
Part (a)Theorem: Interior angles of a quadrilateral sum to 360°.
Given angles:
100°65°100°Let x be the unknown angle.
⇒ 100° + 65° + 100° + x = 360°
⇒ 265° + x = 360°
⇒ 265° + x - 265° = 360° - 265°
⇒ x = 95°
Therefore, the fourth angle is 95°.
Part (b)A kite is a quadrilateral that has one pair of congruent opposite angles.
Therefore, as two of the interior angles of the given quadrilateral are equal, the shape may be a kite.
In a class of 28 sluderds, 14 take physics and
22 take mathematics. The students in the class
take at least one of the two subjects;
Calculate how many
students take both subjects
It can be solved using a Venn diagram. Total 8 students took both subjects.
Describe the Venn diagram.A Venn diagram uses overlapping circles or other shapes to represent the relationships between two or more groups of objects. They typically serve to attractively organize objects, highlighting both the similarities and differences between the components. In the fields of mathematics, statistics, logic, education, linguistics, computer science, and business, Venn diagrams are extensively utilized.
It can be solved using a Venn diagram as
14 students take Physics, 6 students take mathematics and the rest 8 take both subjects.
where, 14(Physics) + 6(mathematics) + 8(both) = 28 (which is the total no. of students).
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Suppose you use the origin to test whether a linear equation is a direct variation function. Does this method work? Support your answer with an example.
The linear equation with a direct variation function always passes through the origin.
What are direct variation functions?
The direct variation function defines a linear function of the form y = kx, where y varies as a multiple of x and x 0. These always follow the origin test.
Calculation
Yes, the method will always work because the linear equations having direct variations are those equations which always pass through the origin.
For example: If we consider an equation y = 3x. Then, it will always pass through the origin as y changes with respect to some multiples of x.
Hence, the direct variation function always passes through the origin.
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Solve each equation for y .
-10 y=5 x
y = -x/2 is the value of y in the equation -10 y=5 x
⇒ -10 y=5 x
⇒ y = -5x/10
⇒ y = -x/2
How to solve an equation?To solve linear equations, utilize the steps that are provided below.
Remove parentheses from each side of the equation and combine similar terms to make it simpler.To separate the variable term on one side of the equation, use addition or subtraction.To find the variable, use division or multiplication.The common denominator can be multiplied by each side of the equation to eliminate fractions.Lets take an example of solve z for 7z – (3z – 4) = 12
Here is no multiplication or division, so this will be easy to solve
⇒ 7z – (3z – 4) = 12
⇒ 7z – 3z + 4 = 12
⇒ 4z = 12 – 4
⇒ 4z = 8
⇒ z = 8/4
⇒ z = 2
See, that was so simple, using the mentioned methods, every linear equation can be solved easily.
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the question is hard
The correct completion of the given two column proof is as below.
How to carry out a Two column proof?
From the given two column proof, the correct way to complete it is;
Statement 1; m║n
Reason 1; Given
Statement 2; ∠3 and ∠6 are same side interior angles
Reason 2; Definition of Same side interior angle theorem
Statement 3; ∠3 and ∠6 are supplementary
Reason 3; Definition of Supplementary
Statement 4; m∠3 + m∠6 = 180°
Reason 4; Same side interior angle theorem
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