Answers
Answer:
[tex]A\text{ : a}_1\text{ = 9 , a}_n\text{ = a}_{n-1}\text{ + 6}[/tex]Explanation:
Here, we want to get the formula that could be used to represent the rule of the sequence
From the given terms:
4th term is 9 and the 5th term is 15
6th term is 21, 7th is 27 and 8th is 33
What this means is that the difference between each of the terms is 6
Hence, we add 6 to the current term to get the next term
Thus:
[tex]a_n\text{ = a}_{n-1}\text{ + 6}[/tex]Now, to get the first term, we can see that we are 3 differences away from the 3rd term
Hence, the value of the first term will be:
[tex]9-6(3)\text{ = -9}[/tex]Thus, we have the first term as -9
Related Questions
a1=-4; an= an-1+11What is the iterative rule for the arithmetic sequence above?
Answers
a1 = -4, means the first term of the sequaence = -4
In the arithmetic sequence, there is a common difference between each two consecutive terms
We can find this difference from the given rule
an = a n-1 + 11
an-1 is the previous term of an
11 is the common difference
The rule of the sequence is
[tex]a_n=a+(n-1)d[/tex]a is the first term
d is the common difference
n is the position of the term
Substitute a by -4
d by 11
[tex]a_n=-4+(n-1)11[/tex]Multiply the bracket by 11
[tex]\begin{gathered} a_n=-4+n(11)-1(11)_{} \\ a_n=-4+11n-11 \end{gathered}[/tex]Add the like terms -4 and -11
[tex]a_n=11n-15[/tex]The rule of the sequence is a(n) = 11n - 15
Two angles are supplementary. One angle measures 9x+9 degrees and the other measures 7x-5 degrees. Determine the measure of both angles.
Answers
108º and 72º
1) If two angles are supplementary then
α+β =180º
2) So we can write out:
(9x +9) + (7x -5) = 180º
9x+7x +9-5 = 180º
16x +4 = 180º
16x = 176º
16x/16 =176/16
x= 11
2.2) If x= 11 then we can plug into that and find out the measures of those angles this way:
9(11) +9 = 99 +9 = 108º
7(11) -5 = 77 -5 = 72º
3) Hence, the angles are 108º and 72º, note that 108 +72 = 180º
Write the system of inequality for thisparagraph:The ninth graders are hosting the nextschool dance. They would like to make atleast a $500 profit from selling tickets.The ninth graders estimate that at most300 students will attend the dance. lheywill earn $3 for each ticket purchased inadvance and $4 for each ticket purchasedat the door.
Answers
1) We can write out the following system of inequalities:
[tex]\begin{gathered} \begin{matrix}\end{matrix}3x+4y\ge500 \\ x+y\leq300 \end{gathered}[/tex]The first inequality refers to the profit from selling tickets, where x is the profit from tickets, and the second one refers to the maximum number of students that will be at the party.
Do you know the Distance formula?
Answers
The distance between two points (x1, y1) and (x2, y2) is given by the formula below:
[tex]d=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]For example, the distance between the points (2, 4) and (3, 8) is given by:
[tex]undefined[/tex]You have a frame that holds 8 pictures.you fill 1/4 of the frame.how many pictures do you put in the frame?explained
Answers
2 pictures.
1) Considering that a frame is rectangular as well as each picture. We're dealing with the area of a rectangle and proportionality.
2) If I fill 1/4 and the whole frame holds 8, then I can state that:
[tex]8\times\frac{1}{4}=2[/tex]Therefore I put into the frame 2 pictures because 2 pictures are equivalent to 1/4 of the area of that frame.
Find the measure of angle A for the triangle shown.oThe value of angle A is
Answers
The sum of the internal angles of a triangle must be equal to 180 degrees. We were given two of the angles and need to calculate the last one, to do that we will solve the following equation:
[tex]\measuredangle A+\measuredangle B+\measuredangle C=180[/tex]Applying the data from the triangle we have:
[tex]\begin{gathered} \measuredangle A+100+47=180 \\ \measuredangle A+147=180 \\ \measuredangle A=180-147 \\ \measuredangle A=33 \end{gathered}[/tex]The angle A measures 33 degrees.
You have a cup with 17 coins inside. The total inside the cup is $5.50. Determine how many half dollars and quarters are inside the cup.
Answers
Let x be the number of half dollar and y, the number of quarter dollar
Thus,
[tex]x+y=17\text{ -----eq i)}[/tex]Half dollar is 50cent, quarter dollar is 25cents,
Thus,
[tex]0.5x+0.25y=5.50\text{ -----eq i}i)[/tex]Solving the two(2) equations simultaneously; we have:
From eq i)
[tex]\begin{gathered} x+y=17 \\ x=17-y\text{ -----eq }iii) \end{gathered}[/tex]Put eq iii) into ii), we have:
[tex]\begin{gathered} 0.5x+0.25y=5.50 \\ 0.5(17-y)+0.25y=5.50 \\ 8.5-0.5y+0.25y=5.50 \\ 8.5-0.25y=5.50 \\ 8.5-5.50=0.25y \\ 0.25y=3 \\ y=\frac{3}{0.25} \\ y=12 \end{gathered}[/tex]From eq iii)
[tex]\begin{gathered} x=17-y \\ x=17-12 \\ x=5 \end{gathered}[/tex]Hence, there are 5 half dollars and 12 quarter dollars inside the cup
what is the verbal expression for 5+2x
Answers
we have the following:
[tex]5+2x[/tex]therefore, the verbal expression is five plus two times x
how tall is Raj? Round answer to two decimal places.Raj is ____ feet tall.
Answers
Given the information on the picture, we have the following right triangle:
then, to find the height, we can use the tangent function to get the following:
[tex]\begin{gathered} \tan (32)=\frac{\text{opposite side}}{adjacent\text{ side}}=\frac{h}{10} \\ \Rightarrow h=10\cdot\tan (32)=6.25 \\ h=6.25 \end{gathered}[/tex]therefore, Raj is 6.25 feet tall
How many solutions does the equation (2 sin x + 1)(sin x – 1) = 0 have over the interval 0 ≤ x < 2π?
Answers
The initial equation is
[tex](2\sin x+1)(\sin x-1)=0[/tex]We can expand this expression as shown below
Answer the word problem #7 as seen in the picture please.
Answers
369.6 ft
7) We can sketch this out to better grasp it:
We can then, calculate the height, by making use of a trigonometric ratio tangent:
[tex]\begin{gathered} \tan (73)=\frac{h}{113} \\ 3.2708\cdot113=h \\ h=369.6 \end{gathered}[/tex]2) Hence, the height of that Building is approximately 369.6 ft
Solve for n.25n−3=5n+8 Enter your answer in the box.n =
Answers
Solution:
Consider the following equation:
[tex]25n\text{ - 3 = 5n +8}[/tex]putting together like terms, this equation is equivalent to:
[tex]25n\text{ -5n = 8}+3[/tex]this is equivalent to:
[tex]20\text{ n = 11}[/tex]solving for n, we get:
[tex]n\text{ = }\frac{11}{20}=0.55[/tex]so that, we can conclude that the correct answer is:
[tex]n\text{ = }0.55[/tex]what is the length of segment AB in the triangle shown below?
Answers
Given:
BC = 8 inches
AC = 17 inches
Let's solve for length of segment AB.
To solve for AB, apply Pythagorean theorem.
We have:
[tex]AC^2=BC^2+AB^2[/tex]Now, rewrite the equation for AB:
[tex]AB^2=AC^2-BC^2[/tex]Plug in the values:
[tex]\begin{gathered} AB^2=17^2-8^2 \\ \\ AB^2=289-64 \\ \\ AB^2=225 \end{gathered}[/tex]Take the square root of both sides:
[tex]\begin{gathered} \sqrt{AB^2}=\sqrt{225} \\ \\ AB=15 \end{gathered}[/tex]Therefore, the length of AB is 15 inches.
ANSWER:
15 inches
3 + 0.1 + 0.006 make it into a decimal
Answers
Explanation:
To add the decimal we can rewrite the number 3 and 0.1 as:
3 = 3.000
0.1 = 0.100
Because we can add zeros after the decimal point without change the number.
Now, we can add the decimals as follows:
x=_-b+_√b2-4ac -2a i need help
Answers
solution
[tex]x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}\text{ (1)}[/tex]When we have a quadratic equation in the following form:
[tex]ax^2+bx+c=0[/tex]And we want to find the roots we can use the quadratic formula given by (1)
what is the y intercept of the equation? -10x -15y =60
Answers
Let's begin by listing out the information given to us:
[tex]-10x-15y=60[/tex]We will proceed by making y the subject of the equation so as to conform it to the general linear equation formula
[tex]\begin{gathered} y=mx+b \\ where\colon b=y-intercept \\ \\ -10x-15y=60 \\ \text{Add 15y to both sides, we have:} \\ -10x-15y+15y=60+15y \\ -10x=15y+60 \\ \text{Subtract 60 from both sides, we have:} \\ -10x-60=15y\Rightarrow15y=-10x-60 \\ 15y=-10x-60 \\ \text{Divide through by 15, we have:} \\ \frac{15y}{15}=-\frac{10}{15}x-\frac{60}{15} \\ y=-\frac{2}{3}x-4 \\ \text{Comparing }y=-\frac{2}{3}x-4\text{ with }y=mx+b \\ b=-4 \\ \therefore\text{The }y-intercept\text{ is }4 \end{gathered}[/tex]8 is added to the square of a number The quotient of 2 and the sum of a number and 1Need help
Answers
Let' call x to the unknown number.
8 is added to the square of a number is equivalent to: 8 + x²
The quotient of 2 and the sum of a number and 1 is: 2/(x + 1)
The graph below shows a proportional relationship between x and y.yWhat is the constant of proportionality, ?T
Answers
Answer:
0.5
Explanation:
To determine the constant of proportionality, we pick two points on the graph.
When x=0, y=0
When x =1, y=0.5
[tex]\begin{gathered} \text{Slope, m=}\frac{0.5-0}{1-0} \\ =0.5 \end{gathered}[/tex]The constant of proportionality is 0.5
(8 - (-1)Step 2 of 4: Find (g - (-1)Enable Zoom/Pan8(x) = -x-210-5-5f(x) = 2x + 1
Answers
Answer:
[tex](g-f)(-1)\text{ = 0}[/tex]Explanation:
Here, we want to calculate (g-f)(-1)
We start by subtracting f(x) from g(x)
Then we proceed to substitute -1 for x
Mathematically, we have that as:
[tex]\begin{gathered} -x-2\text{ -\lparen2x+1\rparen} \\ -x-2-2x-1\text{ = -x-2x-2-1 = -3x-3} \end{gathered}[/tex]Now, we substitute -1 for x as follows:
[tex]\begin{gathered} -3(-1)\text{ - 3} \\ =\text{ 3-3 = 0} \end{gathered}[/tex]1)How many ounces are equal to 7 pounds?
Answers
We are asked to find out how many ounces are there in 7 pounds?
Answer:
112 ounces are equal to 7 pounds.
Explanation:
Recall that 1 pound is equal to 16 ounces.
[tex]1lb=16oz[/tex]Please note that lb is the short form for pounds and oz is the short form for ounces.
To convert the 7 pounds into ounces, multiply the 7 pounds by 16.
[tex]7\cdot16oz=112oz[/tex]Therefore, 112 ounces are equal to 7 pounds.
Divide the monomials 20m^5n^2/30m^3n^9
Answers
Answer
[tex]\frac{2m^2}{3n^7}[/tex]Explanation
Given monomials:
[tex]\frac{20m^5n^2}{30m^3n^9}[/tex]Using division law of indices:
[tex]\begin{gathered} \frac{20}{30}\times\frac{m^5}{m^3}\times\frac{n^2}{n^9}=\frac{2}{3}\times m^{5-3}\times n^{2-9} \\ =\frac{2}{3}\times m^2\times n^{-7} \\ \end{gathered}[/tex]Now, using the negative exponent law of indices, we have:
[tex]\frac{2}{3}\times m^2\times\frac{1}{n^7}=\frac{2\times m^2\times1}{3\times n^7}=\frac{2m^2}{3n^7}[/tex]
Solve (-2,5) and (2,1) as an equation in point slope form for the second point
Answers
Slope - Intercept Form of a Line:
y = mx + b
where m is the slope and b the y - intercept.
Given the points: (-2, 5) and (2, 1):
To find m:
[tex]\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1} \\ m=\frac{1-5}{2+2} \\ m\text{ = -1} \end{gathered}[/tex]To find b:
1 = -1(2) + b
b = 1 + 2
b = 3
EQUATION OF THE LINE:
y = -x + 3
Fill in the blanks so the left side is a perfect square trinomial. That is, complete the square.x² + 8/9x+__ = (x+__)^2
Answers
Given:
There are given the equation:
[tex]x^2+\frac{8}{9}x+()=(x+())^2[/tex]Explanation:
According to the question:
We need to find the missing terms:
So,
From the equation:
[tex](x+\frac{4}{9})^2=x^2+\frac{2.x.4}{9}+(\frac{4}{9})^2[/tex]Then,
[tex]\begin{gathered} (x+\frac{4}{9})^2=x^2+\frac{2.x.4}{9}+(\frac{4}{9})^2 \\ =x^2+\frac{8x}{9}+\frac{16}{81} \\ =x^2+\frac{8}{9}x+\frac{16}{81} \end{gathered}[/tex]Final answer:
Hence, the missing value is shown below:
[tex]x^2+\frac{8}{9}x+\frac{16}{81}=(x+\frac{4}{9})^2[/tex]what is the equation of the line that passes through the points (2,-2) and has a slope of -1/2
Answers
Given the point (2,-2) and the slope m = -1/2, we can find the equation of the line using the point-slope formula:
[tex]\begin{gathered} (x_0,y_0)=(2,-2)_{} \\ m=-\frac{1}{2} \\ Equation\colon \\ y-y_0=m(x-x_0) \\ \Rightarrow y-(-2)=-\frac{1}{2}(x-2)=-\frac{1}{2}x+\frac{2}{2}=-\frac{1}{2}x+1_{} \\ \Rightarrow y+2=-\frac{1}{2}x+1 \\ \Rightarrow y=-\frac{1}{2}x+1-2=-\frac{1}{2}x-1 \\ y=-\frac{1}{2}x-1 \end{gathered}[/tex]therefore, the equation of the line is y = -1/2x -1
What is the volume of a right circular cylinder with a base diameter of 10 meters and a height of 10 meters?
Answers
ANSWER
250π cubic meters
EXPLANATION
The volume of a cylinder is,
[tex]V=B\cdot h[/tex]Where B is the area of the base and h is the height. Since the base is circular, the area is,
[tex]B=\pi\cdot r^2[/tex]Where r is the radius.
In this case, we know that the height is h = 10 meters and the diameter is d = 10 meters, so the radius is,
[tex]r=\frac{d}{2}=\frac{10m}{2}=5m[/tex]And the volume is,
[tex]V=\pi\cdot5^2m^2\cdot10m=\pi\cdot25\cdot10\text{ }m^3=250\pi\text{ }m^3[/tex]Hence, the volume of this cylinder is 250π m³.
Every year, the students at a school are given a musical aptitude test that rates them from 0 (no musical aptitude) to 5 (high musical aptitude). This year's results were:Aptitude Score012345Frequency 042375The median aptitude score: ____________________
Answers
1) Let's set a table for that to better visualize what's in the question:
Based on that table, we can list the scores as:
1 1 1 1 2 2 3 3 3 4 4 4 4 4 4 4 5 5 5 5 5
Therefore, there are 24 scores.
2) Since 24 is an even number let's find the average of the 12th and 13th data points:
[tex]Md=\frac{4+4}{2}=4[/tex]Thus, the median (middle number) is 4
can you pls help me i am unsure of how to solve this
Answers
Since the profit in the first week is $70
Since it increases by $15 each week, then
We can solve it as an arithmetic progression
P = a + (n -1)d, where
a is the profit in the 1st week
d is the value of increasing each week
n is the number of the week
a = 70, d = 15, and n = 12 (12th week)
Substitute these values in the rule above
P = 70 + (12 - 1)(15)
P = 70 + 11(15)
P = 70 + 165
P = 235
The profit during the 12th week is $235
Solve. Remember to use the order of operations, radical36 radical16
Answers
Shena, this is the solution to question 15:
√25 √9
5 * 3
15
In case there is a minus sign, this is the answer:
√25 - √9
5 - 3
2
However, I do not see 15 as one of the available options, but I do see 2.
polygon abcde shown in the coordinate plane find the area of the figure Answer choices: 32466072
Answers
We have to calculate the area of the polygon.
To do that we divide the polygon in known figures of which we can calculate the area.
Then, the area of the polygon will be the sum of the areas of its parts.
We can then divide the polygon as:
We can add the areas of the three figures as:
[tex]\begin{gathered} A=A_1+A_2+A_3 \\ A=\frac{3*4}{2}+\frac{6*4}{2}+4*\frac{9+5}{2} \\ A=\frac{12}{2}+\frac{24}{2}+4*7 \\ A=6+12+28 \\ A=46 \end{gathered}[/tex]Answer: the area is 46 square units.
What do I do next? Long division 459 divided by 2?
Answers
Answer:
To divide 459 by 2 by long division method.
we have that,
Division is one of the four basic mathematical operations. In math, long division is a method for dividing large numbers into steps or parts, breaking the division problem into a sequence of easier steps. It is the most common method used to solve problems based on division.
we get,
we get,
229.5 as the quotient.
Answer is: 229.5