Answer:
10
Step-by-step explanation:
30 -2
28 -3
25 -4
21 -5
16 -6
= 10
Answer:
10
Step-by-step explanation:
Given the sequence 30, 28, 25, 21, 16, you want to know the next number.
DifferencesFirst differences between successive terms are ...
28 -30 = -2
25 -28 = -3
21 -25 = -4
16 -21 = -5
These are not constant, so this is not an arithmetic sequence. However, we notice the second differences are constant:
-3 -(-2) = -1
-4 -(-3) = -1
-5 -(-4) = -1
ApplicationThis observation tells us the next second difference is ...
-5 +(-1) = -6
And the next number in sequence is ...
16 +(-6) = 10
The next number is 10.
__
Additional comment
When a sequence of numbers is described by a polynomial or exponential, looking at differences (and their differences) can help determine the degree of the polynomial, or the common ratio of the exponential.
Here, the second differences are constant, so a second-degree (quadratic) polynomial will describe the sequence. The polynomial describing this sequence is ...
a(n) = 31 -(n)(n+1)/2
A local deli kept track of the sandwiches it sold for three months. The polynomials below model the number of sandwiches sold, where s represents days. Ham and Cheese: 4s^3-28s^2+33s+250Pastrami: -7.4s^2+32s+180Write a polynomial that models the total number of these sandwiches that were sold.
we are given that the following polynomials model the number of sandwiches sold per day:
[tex]\begin{gathered} HC=4s^3-28s^2+33s+250 \\ P=-7.4s^2+32s+180 \end{gathered}[/tex]The total amount of sandwiches is equivalent to the sum of both polynomials:
[tex]4s^3-28s^2+33s+250-7.4s^2+32s+180[/tex]Associating like terms:
[tex]4s^3+(-28s^2-7.4s^2)+(33s+32s)+(250+180)[/tex]Adding like terms:
[tex]4s^3-35.4s^2+65s+430[/tex]Since we can simplify any further, this is the polynomial that models the total amount of sandwiches.
in the diagram triangle JKL and is inscribed in the circle and Arc JL = 62 degrees what is angle L
SOLUTION
m < L = ?
m < J = 62 degrees
m < L + 62 + 90 = 180 ( Sum of angles in a triangle )
m < L + 152 = 180
m < L = 180 - 152
I inserted a picture of the question Please don’t ask tons of questions. & please state whether it’s a b c or d
As given by the question
There are given that the graph of the triangle.
Now,
According to the properties,
If the point (x, y) or (-x, y) rotated about the origin by the angle of 360 degrees.
That means,
There is no difference between rotating 360 degrees clockwise or anti-clockwise around the origin.
Then,
From the vertices of the triangle ABC is:
[tex]\text{A is (-6, 3), B is (-5, 7) and C is (-4, 3).}[/tex]Since the triangle map onto itself
[tex]\begin{gathered} A=A^{\prime} \\ B=B^{\prime} \\ C=C^{\prime} \end{gathered}[/tex]So, the triangle is rotated 360 degrees about the origin
Hence, the correct option is D.
Write the slope intercept equation through the point (1,2) and it’s parallel to the line y=1+4x
Given:
Line equation, y=1+4x
The point, (1,2)
To find the slope intercept form:
The general slope intercept form is, y=mx+b.
First to find m:
From the line equation,
y=4x+1
We have, m=4
Next to find b:
Substitute m=4, and (1,2) in the general intercept form is,
[tex]\begin{gathered} (2)=4(1)+b \\ 2=4+b \\ b=-2 \end{gathered}[/tex]Now, substitute m=4 and b=-2 in the slope intercept form
Thus, the slope intercept form is,
[tex]y=4x-2[/tex]Question60 is 40% of what number?
let the required number be x then
[tex]\begin{gathered} \frac{60}{x}\times100=40 \\ x=\frac{60}{40}\times100 \\ x=150 \end{gathered}[/tex]So 60 is 40% of 150.
10. Determine if the following sequence is arithmetic or geometric. Then, find the 67th term. 36, 30, 24, 18, ... a. arithmetic, -360 b. arithmetic, 12 c. geometric, -360 d. geometric, 12
hello
to determine if the sequence is arthimetic or a geometric progression, we check if a common difference or common ratio exists between the two sequence
the sequence is 36, 30, 24, 18,......
from careful observation, this is an arthimetic progression because a common difference exists between them
d = 30 - 36 = -6
or
d = 24 - 30 = -6
to find the 67th term, let's apply the formula
[tex]\begin{gathered} T_n=a+(n-1)d \\ T_{67}=a+(67-1)d \\ a=\text{first term = 36} \\ d=common\text{ difference = }-6 \\ T_{67}=36+(67-1)\times-6 \\ T_{67}=36+66\times-6 \\ T_{67}=36-396 \\ T_{67}=-360 \end{gathered}[/tex]A bag contains 5 red and 3 blue marbles. Two marbles are drawn simultaneously from the bag. DETERMIN the probability that at least one is red.
total number of balls = 5 + 3 = 8
The possibilities are:
RR (two red) and RB (one red and one blue)
RR and RB are mutually exclusive
P(RR) =
In the figure shown, what is mzA? Explain.57°; AABC is an isosceles triangle with base angles A and C. m2A = mc.B. 66; AABC is an isosceles triangle with base angles B and C. m2B = m_C = 57, and m2A + m2B + m2 = 180.C. 57. AABC is an equilateral triangle.
Since ABC is an isosceles triangle with sides AB=AC, then the angle ABC is the same as ACB, an it's equal to 57º.
Since all three internal angles should add up to 180º, then the angle BAC should have a measure of 180-2(57)=66º.
13 divided by 10 5/6
Answer:
the answer is 1 1/5
If y varies directly with x and y=12when.x=9 what is the value of x when y=36?
y varies directly with x
y=kx
y=12, x=9
12=k9
Solve for k:
12/9 =k
y= 12/9x
For y=36
36 = 12/9 x
Solve for x:
36 /(12/9)= x
27=x
x=27
Question 11:What is the maximum height of the driver off the diving board
To find the maximun height (y) given a quadratic equation as above you find the coordinates of the vertex (maximum or minimun point of a parabola)
1. Use the next formula to find the x- coordinate of the vertex
[tex]\begin{gathered} y=ax^2+bx+c \\ \\ x=-\frac{b}{2a} \end{gathered}[/tex][tex]\begin{gathered} x=-\frac{\frac{24}{9}}{2(-\frac{4}{9})} \\ \\ x=-\frac{\frac{24}{9}}{-\frac{8}{9}}=\frac{-24}{-8}=3 \end{gathered}[/tex]2. Use the value of x above to find y-coordinate in the vertex:
[tex]\begin{gathered} y=-\frac{4}{9}(3)^2+\frac{24}{9}(3)+12 \\ \\ y=-\frac{4}{9}(9)+\frac{72}{9}+12 \\ \\ y=-4+8+12 \\ \\ y=16 \end{gathered}[/tex]Then, the maximum height of the diver is 16 feetfind the coordinates of the midpoint of the line joining the points and show your work.
formula of midpoint
[tex](\frac{x1+x2}{2},\frac{y1+y2}{2})[/tex]the we replace (7,1) and (-1,3)
[tex](\frac{7+(-1)}{2},\frac{1+3}{2})[/tex]simplify to solve
[tex]\begin{gathered} (\frac{7+1}{2},\frac{4}{2}) \\ \\ (\frac{8}{2},\frac{4}{2}) \\ \\ (4,2) \end{gathered}[/tex]Midpoint is (4,2)
Graph
How many solutions does the following equation have? - 6(x + 7) = - 4x – 2 А. No solutions B.Exactly one solution C.Infinitely many solutions
ANSWER
Exactly one solution.
EXPLANATION
We are given the equation:
-6(x + 7) = -4x - 2
To find the number of solutions, we have to solve for x:
-6x - 42 = -4x - 2
Collect like terms:
-6x + 4x = 42 - 2
-2x = 40
x = 40 / -2
x = -20
Therefore, the equation has exactly one solution.
if the growth factor is 1.2, what is the growth rate
SOLUTION
Step 1 :
In this question, we are meant to know the relationship between Growth factor and Growth Rate.
Growth factor is the factor by which a quantity multiplies itself over time.
Growth rate is the addend by which a quantity increases ( or decreases ) over time.
Step 2 :
From the question, if the growth factor is 1.2 which is also 120 %,
then the growth rate will be ( 120 - 100 ) % = 20 % = 0. 2
CONCLUSION:
The Growth Rate = 0. 2
a rectangle with a area of s sq feet and a width of 6 in what is the length of the rectangle
The area of the reactangle is calculates using the following formula:
[tex]A=w\cdot l[/tex]Where
A: area
w: wisth
l: lenght
You can write this formula in terms of the length by dividing the Area by the width:
[tex]l=\frac{A}{w}[/tex]If the area is A=s feet² and the width is w=6 feet, then the length is
[tex]l=\frac{s}{6}[/tex]The test results for 4 students are 96 83 78 and 83. If one more student's test score of 87 is added, what would increase?A. median B. meanC. modeD. range
Mean will increase because 87 is greater than 83 and 78, then the eman will be greater
Write the equation for the trigonometric graph.y= 8cos(pi/40x)y= –8sin(pi/40x)y= –8cos(pi/40x)y= 8sin(pi/40x)
Solution
For this case we can verify the answer using the point x= 0 if we replace we got:
y=8 cos (pi/40* 0) = 8 cos (0) = 8
y= -8 sin (pi/40 *0)= -8 sin(0) = 0
y= -8cos(pi/40*0)= -8 cos (0)= -8
y= 8 sin (pi/40 *0)= 8 sin(0) = 0
Then the correct option would be:
y= -8cos(pi/40*0)
I was doing this with a tutor but there was a connection problem.
ANSWER:
[tex](x-3)^2+(y+7)^2=113[/tex]The point (7,6) is not on the circle
STEP-BY-STEP EXPLANATION:
(a)
The equation of the circle is given as follows:
[tex]\begin{gathered} (x-h)^2+(y-k)^2=r^2 \\ \text{ where (h,k) is the center and r is the radius } \end{gathered}[/tex]We replace to calculate the radius of the circle, like this:
[tex]\begin{gathered} \mleft(-4-3\mright)^2+\mleft(1-\mleft(-7\mright)\mright)^2=r^2 \\ (-7)^2+(8)^2=r^2 \\ r^2=113 \end{gathered}[/tex]Therefore, the equation would be:
[tex](x-3)^2+(y+7)^2=113[/tex](b)
We replace the point, and if the value is greater than the radius, it means that this point is not on the circle:
[tex]\begin{gathered} (x-3)^2+(y+7)^2\le113 \\ \text{ replacing:} \\ \mleft(7-3\mright)^2+\mleft(6+7\mright)^2\le113 \\ 4^2+13^2\le113 \\ 16+169\le113 \\ 185\le113 \end{gathered}[/tex]Therefore, the point (7,6) is not on the circle
Reduce to lowest term10\25
Answer:
2/5
Step-by-step explanation:
10 and 25 can both be divided by 5
10 divided by 5 equals 2
25 divided by 5 equals 5
Not a timed or graded assignment. Quick answer = amazing review :)
The question is given to be:
[tex]\sqrt[]{\frac{64}{100}}[/tex]Recall the rule:
[tex]\sqrt[]{\frac{a}{b}}=\frac{\sqrt[]{a}}{\sqrt[]{b}}[/tex]Therefore, the expression becomes:
[tex]\sqrt[]{\frac{64}{100}}=\frac{\sqrt[]{64}}{\sqrt[]{100}}[/tex]Recall that:
[tex]\begin{gathered} 8\times8=64,\therefore\sqrt[]{64}=8 \\ \text{and} \\ 10\times10=100,\therefore\sqrt[]{100}=10 \end{gathered}[/tex]Hence, the expression becomes:
[tex]\frac{\sqrt[]{64}}{\sqrt[]{100}}=\frac{8}{10}[/tex]Dividing through by 2, we have:
[tex]\frac{8}{10}=\frac{4}{5}[/tex]Therefore, the answer is:
[tex]\sqrt[]{\frac{64}{100}}=\frac{4}{5}[/tex]HELLPPPPLLPPPPPPPPPPPPPPP
Answer:
a²+13a+40
Step-by-step explanation:
Now the x in the function has been replaced into (a+5) :
(a+5)²+3(a+5) =
(a²+10a+25)+(3a+15) =
a²+13a+40
Hope this helped and have a good day
How do you convert 313313 yards to inches? Use the drop-down menus to explain your answer.Since there are inches in 11 yard, 313313 by .So, 313313 yards = inches.
Given:
[tex]3\frac{1}{3}\text{yards}[/tex]Aim:
We need to convert yards into inches.
Explanation:
[tex]3\frac{1}{3}\text{yards}=\frac{3\times3+1}{3}\text{ yards}[/tex]
[tex]3\frac{1}{3}\text{yards}=\frac{10}{3}\text{ yards}[/tex]
Recall that
[tex]1\text{ yard =}36\text{ inches}[/tex]Multiply 10/3 on both sides, we get
[tex]\frac{10}{3}\text{ yards =}\frac{10}{3}\times36\text{ inches}[/tex][tex]\frac{10}{3}\text{ yards=}120\text{ inches}[/tex][tex]3\frac{1}{3}\text{ yards =}120\text{ inches}[/tex]We know that
[tex]3\frac{1}{3}\times36=120[/tex]Final answer:
Since there are 36 inches in 1 yard.
[tex]\text{ multiply 3}\frac{1}{3}\text{ by 36.}[/tex][tex]\text{ So, }3\frac{1}{3}\text{ yards =}120\text{ inches}[/tex]Solve the following system using the substitution method. Enter your answer as an ordered pair in the form (x,y). 3x-2y=55x+10y=35
System of equations
• Equation 1
[tex]3x-2y=5[/tex]• Equation 2
[tex]5x+10y=35[/tex]Procedure
Solving the system by substitution.
0. Isolating ,x ,from equation 2:
[tex]5x=35-10y[/tex][tex]x=\frac{35}{5}-\frac{10y}{5}[/tex][tex]x=7-2y[/tex]2. Replacing the expression of x obtained in equation 1:
[tex]3\cdot(7-2y)-2y=5[/tex]3. Simplifying:
[tex]21-6y-2y=5[/tex][tex]-8y=5-21[/tex][tex]y=\frac{-16}{-8}[/tex][tex]y=2[/tex]4. Finally, we replace this value in the isolated expression of x and solve it:
[tex]x=7-2\cdot(2)[/tex][tex]x=7-4[/tex][tex]x=3[/tex]Answer: (3, 2)
4. Sales tax in a certain state is 5%. If the sales tax on a new boat was $400, what was the selling price of the boat?
Sales tax percentage = 5% = 5/100 = 0.05 (decimal form)
Sales tax amount = $400
Multiply the selling price of the boat (x) by the sales tax percentage in decimal form. That expression must be equal to 400.
0.05x = 400
Solve for x:
x = 400/ 0.05
x= $8,000
Which inequality is represented by the graph?
Answer:
it's option c ............
I child drinks 1 1/2 cups of milk twice a day.If a container of milk has 15 cups of milk remaining for the child to drink ,in how many days will the container be empty?
Data
Milk drank = 1 1/2 twice a day
Volume in a container = 15 cups
Number of days the contaier will be empty = ?
Procedure
To solve this problem just divide the volume of the container by the milk drank by the child.
As the child drinks 1 1/2 twice a day, the total milk drank in a day will be = 2 x 1 1/2 = 3
Division 15/3 = 5
Solution: The container will be empty in 5 days
which of the following lines is perpendicular to the equation given below?
Given data:
The given equation of the line is y=-2x+8.
The slope of the given line is -2.
The slope of the line perpendicular to it is,
[tex]\begin{gathered} m\times-2=-1 \\ m=\frac{1}{2} \end{gathered}[/tex]The standard equation of the line is,
[tex]y=mx+c[/tex]Here, m is the slope of the line.
The second option can be written as,
[tex]\begin{gathered} x-2y=8 \\ 2y=x-8 \\ y=\frac{1}{2}x-4 \end{gathered}[/tex]Thus, option (B) is correct.
Beth Johnson's bank card account charges 1.1% every month on the average daily balance as well as the following special fees:Cash advance fee: 2% ( not less than $2 nor more than $10)Late payment fee: $25Over-the - credit- limit fee $10In the month of June, Beth's average daily balance was $1886. She was on vacation during the month and did not get her account payment in on time, which resulted in a late payment and resulted in charges accumulating to a sum above her credit limit. She also used her card for five Cash advances of$100,while on vacation. Find the special fees charged to the account based on account transactions in that month. The special fees are?
List of special fees paid by Beth:
1.Late payment fee: $25.
2.Cash advance fee: $10.
2% of $100 multiplied by 5 is equal to (2/100)(100)(5) = 10.
3.Over-the - credit- limit fee: $10
The addition of the special fees is equal to $45. (After adding $25+$10+$10)
The answer $45.
A table is in the shape of a regularhexagon. The perimeter of the table is 12 ftfeet. What is the length of each side ofthe tableA 1 ftB 2 ftC 3 ftD 4 ft
Solution:
Given the shape of a hexagon;
The perimeter, P, of a hexagon is;
[tex]\begin{gathered} P=6s \\ \\ \text{ Where }s=side\text{ length} \end{gathered}[/tex]Given;
[tex]\begin{gathered} P=12ft \\ \\ s=\frac{12}{6}ft \\ \\ s=2ft \end{gathered}[/tex]CORRECT OPTION: B
x = -1,0,1,2,3.
P(X = x) 0.2, 0.2, 0.2, 0.2, 0.2. Find the value of P(X<3).
The value of the probability P(x < 3) is 0.8
How to determine the probability value?From the question, the table of values is given as
x = -1,0,1,2,3.
P(X = x) 0.2, 0.2, 0.2, 0.2, 0.2
To calculate the probability P(x < 3). we make use of the probability values where x is less than 3
This means that
P(x < 3) = P(-1) + P(0) + P(1) + P(2)
Substitute the known values in the above equation
So, we have
P(x < 3) = 0.2 + 0.2 + 0.2 + 0.2
Evaluate the sum
P(x < 3) = 0.8
Hence, the probability value is 0.8
Read more about probability at
https://brainly.com/question/24756209
#SPJ1