Step-by-step explanation:
a) We can find the iterative rule by first making a table of values.
n -> [tex]a_n[/tex]
1 -> 22
2 -> 28
3 -> 34
We see that [tex]a_n[/tex] increases by 6 each time. Hence, the iterative rule should have the term 6n. However, if we put 1 in for n, we get 6. We want 22-6=16 more than this, or [tex]6n+16[/tex]. This would work for any seat row we give.
b) Our iterative rule to get the number of seats is [tex]6n+16[/tex]. Since we know that this value is 100, we can put both equal to each other.
[tex]6n+16=100\\6n=84\\n=14[/tex]
Thus, the 14th row has 100 seats.
Answer:
(a) S_n = S_1 + 6 (n - 1)
(b) Row 14 has 100 seats
Step-by-step explanation:
(a) The arithmetic sequence would follow the iterative rule,
S_n = S_1 + 6 (n - 1) where S is the number of seats in row n, n is the row number, and S is the number of seats in row 1.
Row 1 = S_1 = 22
2 = S_2 = 28
3 = S_3 = 34
4 = S_4 = 40
|| || = 46
|| || = 52
|| || = 58
|| || = 64
|| || = 70
|| || = 76
|| || = 82
|| || = 88
|| || = 94
Row 14 = S_14 = 100
(b) 100=22+6(n-1) solve for n after setting S_n = 100
100 = 22 + 6_n - 6
84/6 = 6n/6 Row 14 has 100 seats
14 = n
please say thanks!
A lampshade made from a piece of sheet plastic has a radius of the inner circle to be 7cm and that of the outer circle is 28cm. if its arc subtends an angle of 315 degree at the center, what is the area of the plastic used to form the lampshade
The area of the plastic used to form the lampshade is 2021.25 square centimeters
How to determine the area of the plastic used to form the lampshade?The given parameters in the question are:
Outer radius, R = 28 cm
Inner radius, r = 7 cm
Angle, ∅ = 315
The area of the plastic used to form the lampshade is calculated using the following area of sector formula
A = ∅/360 * π(R² - r²)
Substitute the known values in the above equation
A = 315/360 * 22/7 * (28² - 7²)
Evaluate the exponents
A = 315/360 * 22/7 * (784 - 49)
Evaluate the difference
A = 315/360 * 22/7 * 735
Evaluate the product
A = 2021.25
Hence, the area of the plastic used to form the lampshade is 2021.25 square centimeters
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A regular hexagon has an apothem measuring 14 cm and an approximate perimeter of 96 cm. a regular hexagon has an apothem with length 14 centimeters and a perimeter of 96 centimeters. what is the approximate area of the hexagon?
The approximate area of the hexagon = 672 cm²
What is hexagon ?
In geometry, hexagon is a polygon with 6 sides. If the lengths of all the sides and the measurement of all the angles are equal, such hexagon is called a regular hexagon. In other words, sides of a regular hexagon are congruent.apothem of the hexagon = 14 cm
perimeter of the hexagon = 96 cm
Area of the hexagon = [(3√3) / 2] a² ; where a is the measure of the side
hexagon has 6 sides.
Perimeter = 6a
96 cm = 6a
96 cm / 6 = a
16 = a
There are 6 triangles in the hexagon .
Area of a triangle = (height * base) / 2
A = (14 cm * 16 cm) / 2
A = 224 / 2
A = 112 cm²
The approximate area of the hexagon = 112 cm² * 6 triangles = 672 cm²
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Answer: D). 672 cm2
Step-by-step explanation:
2(x+2y)^2 + 3(x+2y) +1
Answer:
[tex]3x+2y^2+2(x+y)+2y+1[/tex]
Step-by-step explanation:
1) Split the second term in [tex]2{(x+2y)}^{2}+3(x+2y)+1[/tex] into two terms.
1 - Multiply the coefficient of the first term by the constant term.
[tex]2\times1=2[/tex]
2 - Ask: Which two numbers add up to 3 and multiply to 2?
2 and 1.
3 - Split [tex]3x+2y[/tex] as the sum of [tex]2(x+y)[/tex] and [tex]x+2y[/tex].
[tex]2x+2y^2+2(x+y)+x+2y+1[/tex]
2) Collect like terms.
[tex](2x+x)+2y^2+2(x+y)+2y+1[/tex]
3) Simplify.
[tex]3x+2y^2+2(x+y)+2y+1[/tex]
Thank you,
Eddie
Find the value of each variable.
one of the properties of a cyclic quad (four sided shape in eucliean geometry) is that the opposite sides add up to 180°
So in this case to get x we= 180°-105°=285°
therefore x is 285°
HELPPP There are 30 pencils in a box (15 pairs). 2 pair(s) are yellow,
3 pairs are brown, and the rest are tan. What is the probability of
pulling out a brown pencil on the first draw?
Write your answer as a reduced fraction.
Answer:
1/10
Step-by-step explanation:
Probability= number of brown pencil/number of pencil in the box
3/30
=1/10
Answer: 1/5
Step-by-step explanation:
30/15 pairs is 2 pencils per pair. That means there are 4 yellow pencils, 6 brown pencils, and the rest are tan.
30-10=20. There are 20 tan pencils.
6/30 is the probability of a brown pencil being pulled out.
This simplifies to 1/5.
A rectangular prism with a square base is cut from the center of a triangular prism. each side of the square base measures 1.7 units.what is the volume of the shaded solid? round to the nearest tenth of a cubic unit.11.6 units345.4 units357.0 units368.6 units3
Rounding to the closest tenth of a cubic unit, the shaded solid's volume is 45.4 cubic units.
What is rectangular prism?The 3D shape of a rectangular prism has six rectangular faces. Multiply a rectangular prism's three dimensions—length, width, and height—to determine its volume. Cubic units are used to measure volume.
According to the given information:The following formula can be used to determine a rectangular prism's volume:
Vr = Height * Width * Length
Triangular prism volume Vt is determined by its base area and height.
concerning the rectangular prism;
Vr = 1.7 × 1.7 × 4
Vr = 11.56 units in 3
Regarding the triangular prism
Vt = 0.5 × 5.7 × 5 × 4
Vt = 57 unit3
Volume of the solid shaded by Vt - Vr
The solid's shaded volume is equal to 57 - 11.56.
The colored solid's volume is 45.44 cubic units.
Due to this, the shaded solid's volume, when rounded to the nearest tenth of a cubic unit, is 45.4 cubic units.
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Find the volume of the figure. Round your answers to the nearest tenth. It is recommended you use the π button on your calculator to solve.
The volume of the figure is 1, 005. 4 mi³
Volume of a cylinderNote that the figure is a cylinder
The formula for volume of a cylinder is given as;
Volume = πr²h
Where
h = height = 5 mi
r = radius = 8mi
Substitute into the volume
Volume = 3. 142 × 8 × 8 × 5
Volume = 1,005. 4 mi³
Thus, the volume of the figure is 1, 005. 4 mi³
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Find the value of x if a, b, and c are collinear points and b is between a and c. ab=x 6,bc=3x−5,ac=36−x
The value of x if a, b, and c are collinear points and b is between a and c : 7
What is collinear points?Collinear points are those that are situated on the same line of sight or within a single line. In Euclidean geometry, two or more points are said to be collinear if they are located on a line either close to or far from one another.
According to the given information:
if A, B, and C are col-linear points and B is between A and C
then
AB+BC=AC
AB=x+6
BC=3x-5
AC=36-x
substituting value:(x+6)+(3x-5)=36-x
(x+3x)+(6-5)=36-x
4x+1=36-x
4x+x=36-1
5x=35
x=35/5
x=7
The value of x is 7
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A salesperson has 7 customers in denver and 13 customers in reno. in how many different ways could she telephone?
If a salesperson has 7 customers in denver and 13 customers in reno then there are 20 different ways in which he can make calls.
Given that the salesperson has 7 customers in denver and 13 customers in reno.
We are required to find the number of ways in which he can make use of telephone.
Number of customers in denver=7
Number of customers in reno=13
Total customers=20
Since he can talk to one customer at one time and he can either choose customer from denver or reno, the number of ways by using combinations will be [tex]7C_{1}[/tex]+[tex]13C_{1}[/tex]
=7+13
=20 ways.
Hence if a salesperson has 7 customers in denver and 13 customers in reno then there are 20 different ways in which he can make calls.
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Find the measure of the third angle of a triangle if the measures of the other two angles are given. 35.5 and 82.6
Answer:
61.9°
Step-by-step explanation:
The angles of a triangle always add up to 180°. Using this information along with the values of two of the three angles, we can set up an equation to find the measure of the third angle.
Set up an EquationLet the measure of the third angle be represented as "x". The first angle + the second angle + the third angle must equal 180 therefore...
[tex]35.5+82.6+x=180[/tex]
Solve the EquationStart by adding the like terms on the left side of the equation:
[tex]118.1+x=180[/tex]
Then, subtract both sides by 118.1:
[tex]x=61.9[/tex]
Therefore the measure of the third angle of the triangle is 61.9°.
Using the online tool, find two different combinations of radius and height that produce two cylinders with nearly the same volume. Record the
dimensions and volumes of the two cylinders below.
The radii and the heights of the two cylinders are
Cylinder 1: Height = 6 and Radius = 5Cylinder 2: Height = 10 and Radius = 3.87How to determine the combinations of radius and height?The volume of a cylinder is
V = πr²h
When the volumes of two cylinders are almost equal, then it means that:
V1 ≈ V2
This gives
πr²h ≈ πR²H
Divide both sides by π
r²h ≈ R²H
Assume that r = 5 and h = 6
So, we have:
5² * 6 ≈ R²H
Evaluate the product
150 ≈ R²H
Assume H = 10
So, we have:
150 ≈ R² * 10
Divide by 10
R² ≈ 15
Take the square root of both sides
R ≈ 3.87
Hence, the radii and the heights of the two cylinders are
Cylinder 1
Height = 6 and Radius = 5
Cylinder 2
Height = 10 and Radius = 3.87
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Answer:
These radius and height values will produce the same volume:
radius = 6 units and height = 18 units
radius = 9 units and height = 8 units
5x(3x-10) + (2x-6)(3x+8)
Answer: 21[tex]x^{2}[/tex] - 52x - 48
Step-by-step explanation:
Using the expanding rule we get
5x * 3x - 5x * 10 + (6[tex]x^{2}[/tex] - 18x + 16x -48)
15[tex]x^{2}[/tex] - 50x + 6[tex]x^{2}[/tex] - 2x - 48
21[tex]x^{2}[/tex] - 52x - 48
Answer:
21x^2-52x-48
Step-by-step explanation:
5x(3x-10) + (2x-6)(3x+8)
Distribute
5x^2 -50x+6x^2-2x-48
Combine like terms
21x^2-50x-2x-48
21x^2-52x-48
You decide that you want to purchase a Tesla SUV. You borrow \$95,000 for the purchase. You agree to repay the loan by paying equal monthly payments of \$1,200 until the balance is paid off. If you're being charged 6\% per year, compounded monthly, how long will it take you to pay off the loan?
Using compound interest and a graphing calculator, it is found that it will take about 15 years for the loan to be paid off.
What is compound interest?The amount of money earned, in compound interest, after t years, is given by:
[tex]A(t) = P\left(1 + \frac{r}{n}\right)^{nt}[/tex]
In which:
A(t) is the amount of money after t years. P is the principal(the initial sum of money). r is the interest rate(as a decimal value). n is the number of times that interest is compounded per year.For this problem, the parameters are given as follows:
A(0) = 95000, r = 0.06, n = 12.
Hence the value of the loan after t years is:
[tex]A(t) = P\left(1 + \frac{r}{n}\right)^{nt}[/tex]
[tex]A(t) = 95000\left(1 + \frac{0.06}{12}\right)^{12t}[/tex]
[tex]A(t) = 95000(1.005)^{12t}[/tex]
You have monthly payments of $1,200, hence the amount paid after t years is:
P(t) = 12 x 1,200t = 14400t
Then we have to solve for:
A(t) = P(t)
[tex]14400t = 95000(1.005)^{12t}[/tex]
Which is solved in the graph below, meaning that it will take about 15 years for the loan to be paid off.
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Brett needs to put this equation x − 2y = 16 into function notation so that he can identify the rate of change and the y-intercept. How should he display it?
Rewrite x − 2y = 16 in slope-intercept form as y = 1/2x - 8.
Slope (m) = 1/2
Y-intercept (b) = -8.
What is the Slope Intercept Equation?The slope-intercept equation helps us to easily identify the rate of change/slope (m) and the y-intercept (b) of an equation. It is given as y = mx + b.
Given, x − 2y = 16, in order to identify the slope (m) and y-intercept (b), rewrite the equation in slope-intercept form:
x − 2y = 16
-2y = - x + 16
Divide both sides by -2
-2y/-2 = -x/-2 + 16/-2
y = 1/2x - 8
As a function it would be written as y = 1/2x - 8.
Slope (m) = 1/2
Y-intercept (b) = -8.
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List the sides in order from the smallest to the largest 83 56 41
the order from smallest to largest is:
41, 56, 83.
How to list from smallest to largest?
Here we have 3 values, that are:
{83, 56, 41}
To list it from smallest to largest, we first need to write the smallest number, which we can identify is 41.
Then the middle number. Which is 56, that is larger than 41 and smaller than 83.
Finally, the largest number, which is 83.
Then the order is:
41, 56, 83.
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H=(,),()
F=(),()
Help please asap
Thanks so much
From the representation, the point H and F on the rectangle are H(-3,3) and F(2,-2).
According to the statement
we have given that the a rectangle on the graph with the two given points and we have to find the another points of the graph.
So, to find the points of the rectangle
firstly the given points are:
E(2,3) And G(-2,-2) and we have to find the point H and F.
So, The point H :
For the point H the lines of rectangle meet with each other at the 3 from origin on the x axis to the negative side and at the 3 from origin on the y axis.
So, the point H become H(-3,3)
And for point F:
For the point F the lines of rectangle meet with each other at the 2 from origin on the x axis to the positive side and at the 2 from origin on the y axis on the negative side.
So, the Point F become F(2,-2).
So, From the representation, the point H and F on the rectangle are H(-3,3) and F(2,-2).
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I need to know how to solve this
The surface areas of two similar cylinders are 6cm² and 54cm².
i. Find the scale factor for the enlargement.
ii. If the larger cylinder has height 12cm, how high is the smaller one?
iii. What is the ratio of their volumes?
Answer:
3, 4, 27
Step-by-step explanation:
1) Area scale factor = 9
Length scale factor = 3 because √9
2) 12/3 = 4
3) 3³ = 27
From the figure below, identify all pairs of alternate interior and alternate exterior angles
A.
alternate exterior
exterior means outside
like a front entrance to a home
1. o & t
2. n & u
B.
alternate interior
interior means inside
like as if its inside a house
1. p & s
2. q & r
( p & s ) AND ( q & r ) both look like the letter Z
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Kwame must earn more than 16 1616 stars per day to get a prize from the classroom treasure box. Write an inequality that describes S SS, the number of stars Kwame must earn per day to get a prize from the classroom treasure box.
The inequality that describes the number of stars S that Kwame must earn per day to get a prize from the classroom treasure box is: S > 16.
What is the inequality that models this situation?The number of stars that he earns is represented by the variable S. He must earn more than 16 stars to earn a prize from the classroom treasure box, hence the inequality that represents the desired amount is given as follows:
S > 16.
Which is read as:
S is greater than 16, which is derived from the Fact that Kwame must earn more than 16 stars per day to get a prize, as stated in the problem.
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Quick algebra 1 question for 10 points!
Only answer if you know the answer, quick shout-out to tariqareesha2 and MrBrainly, tysm for the help!
Last one
Because if we simplify
(4x³y-6xy³)/2xy(2xy(2x²-3y²))/2xy2x²-3y²Verified
Answer:
D is the correct Answer.
Step-by-step explanation:
4x^3+-6xy^3
2xy
When dividing exponents you will subtract. Leaving you with 2x^3-3y^2.
Therefore your answer is D.
What is the X
3x +15 and 2x + 20
Answer:
x = 5Step-by-step explanation:
What is the X
3x +15 and 2x + 20
assuming that the question is an equation
3x + 15 = 2x + 20
3x - 2x = 20 - 15
x = 5
-----------------
check
3 * 5 + 15 = 2 * 5 + 20
30 = 30
the answer is good
A. Undefined b. Zero c.negative b. Positive
I believe the slope is negative. If it was positive then it would have been " / "
Answer:
C
Step-by-step explanation:
• A vertical line has an undefined slope
• A horizontal line has a slope of zero
• A line sloping downwards from left to right has a negative slope
• A line sloping upwards from left to right has a positive slope
-------------------------------------------------------------------
the line here slopes downwards from left to right and has a negative slope
There are 8 blue socks in Sean’s drawer. After he removes 3 blue socks and 4 non-blue socks, the probability to pick a blue sock at random becomes 1/7. How many non-bluesocks were in Sean’s drawer originally?
Answer:
34
Step-by-step explanation:
you first write the equation:
(8-3) / (8+x-7) = 1/7, where x is the number of non blue socks
so, 5/(1+x) = 1/7
1+x = 35, so x=34
The angle between the generator and the central axis of a double-napped cone is 60°. a plane intersecting the cone makes an angle of 50° with the central axis. which conic section is formed?
The right option is (c).
As a result of the plane intersecting the cone here at an angle of 50° being less than the angle between the generator and central axis at an angle of 50°, a conic section is created.
What is Hyperbola?A smooth curve in a plane known as a hyperbola is one whose geometric characteristics or equations for which it is the solution set characterize it. Two parts of a hyperbola, known as connected components or branches, are mirror reflections of one another and resemble two infinite bows.
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I understand that the question you are looking for is:
"The angle between the generator and the central axis of a double-napped cone is 60°. A plane intersecting the cone makes an angle of 50° with the central axis. Which conic section is formed?"
(a)circle
(b)ellipse
(c)hyperbola
(d)parabola
divide.
6 divided by 2 2/7
Answer:
2.625
Step-by-step explanation:
2 2/7 in decimal form is 2.2857
6 / 2.2857 = 2.625
A soccer team ordered 12 jerseys and 12 pairs of shorts, for a total of $156. Later, they had to order 4 more jerseys and 6 more pairs of shorts, for a total of $62.
The system of equations that can be used to find x, the cost of each jersey, and y, the cost of each pair of shorts is shown.
12x + 12y = 156
4x + 6y = 62
What is the cost of each jersey?
The cost of each jersey is $8 dollar and that of shorts is $5
System of equationThis are expression that contain unknown equation and two or more equation.
According to the question, a soccer team ordered 12 jerseys and 12 pairs of shorts, for a total of $156. Later, they had to order 4 more jerseys and 6 more pairs of shorts, for a total of $62.
The system of equation that represent the expression is given as;
12x + 12y = 156
4x + 6y = 62
____________
6x + 6y = 78
4x + 6y = 62
Subtract
6x-4x = 78 - 62
2x = 16
x = 8
since 4x + 6y = 62
2x+3y = 31
2(8) + 3y = 31
3y = 31-16
3y = 15
y = 5
Therefore the cost of each jersey is $8 dollar and that of shorts is $5
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How long does it take for millions of dollars worth of emerald transactions to occur in bogota? a year three months a day a week
Answer: It will be A Day
Step-by-step explanation:
Find the general equation of the plane through the point (3, 2, 5) that is parallel to the plane whose general equation is 2x 3y − z = 0.
The plane we want and the plane we're given are parallel, so they share the same normal vector. The normal to [tex]2x+3y-z=0[/tex] is the vector (2, 3, -1), since [tex](2,3,-1)\cdot(x,y,z)=0[/tex].
Then the plane we want has equation
[tex](2,3,-1) \cdot (x-3, y-2, z-5) = 0 \\\\ \implies 2(x-3) + 3(y-2) - (z-5) = 0 \\\\ \implies \boxed{2x + 3y - z = 7}[/tex]
Simplify the expression. h4(h3)–6
Answer:
[tex]h^7-6[/tex]
Step-by-step explanation:
1) Regroup terms.
[tex]h^4h^3-6[/tex]
2) Use Product Rule: [tex]x^ax^b=x^{a+b}[/tex].
[tex]h^{4+3}-6[/tex]
3) Simplify 4 + 3 to 7.
[tex]h^7-6[/tex]
