An arithmetic progression has the first term as x and the common difference as d.
a)Write down in terms of x and d, the 3rd, 9th and 25th terms of the progression (1mark)
b)The progression is increasing and the 3rd 9th and 25th terms forms the first three consecutive terms of a geometric series.If the sum of the 7th and twice the 6th term of the arithmetic progression is 78.Calculate the first term and the common difference of the AP
KINDLY DO NOT ATTEMPT IF YOU DO NOT KNOW⛔
Answer:
First term: 6
Common difference: 15/4
Step-by-step explanation:
General form of arithmetic progression:
[tex]a_n=a+(n-1)d[/tex]
(where [tex]a[/tex] is the initial term and [tex]d[/tex] is the common difference between terms)
Question (a)
[tex]\implies a_3=a+(3-1)d=a+2d[/tex]
[tex]\implies a_9=a+(9-1)d=a+8d[/tex]
[tex]\implies a_{25}=a+(25-1)d=a+24d[/tex]
Question (b)
General form of a geometric progression: [tex]a_n=ar^{n-1}[/tex]
(where [tex]a[/tex] is the initial term and [tex]r[/tex] is the common ratio)
Therefore, the first three terms of a geometric series are:
[tex]a_1=ar^0=a[/tex]
[tex]a_2=ar^1=ar[/tex]
[tex]a_3=ar^2[/tex]
To find the common ratio:
[tex]r=\dfrac{ar^2}{ar}=\dfrac{ar}{a} \implies \dfrac{a_3}{a_2}=\dfrac{a_2}{a_1}[/tex]
If the 3rd 9th and 25th terms of an arithmetic progression form the first three consecutive terms of a geometric series, then inputting these into the above formula for r:
[tex]\implies \dfrac{a+24d}{a+8d}=\dfrac{a+8d}{a+2d}[/tex]
[tex]\implies (a+24d)(a+2d)=(a+8d)(a+8d)[/tex]
[tex]\implies a^2+26ad+48d^2=a^2+16ad+64d^2[/tex]
[tex]\implies 10ad=16d^2[/tex]
[tex]\implies 10a=16d[/tex]
The 6th and 7th terms of the arithmetic progression are:
[tex]a_6=a+5d[/tex]
[tex]a_7=a+6d[/tex]
If the sum of the 7th and twice the 6th term of the arithmetic progression is 78, then:
[tex]\implies a_7+2(a_6)=78[/tex]
[tex]\implies (a+6d)+2(a+5d)=78[/tex]
[tex]\implies 3a+16d=78[/tex]
Substituting [tex]10a=16d[/tex] into [tex]3a+16d=78[/tex] and solving for a:
[tex]\implies 3a+10a=78[/tex]
[tex]\implies 13a=78[/tex]
[tex]\implies a=6[/tex]
Substituting [tex]a=6[/tex] into [tex]3a+16d=78[/tex] and solving for d:
[tex]\implies 3(6)+16d=78[/tex]
[tex]\implies 16d=60[/tex]
[tex]\implies d=\dfrac{15}{4}[/tex]
Mary and Philip are in a race. Mary runs 5.47 meters per second and Philip runs 6.59 meters per second. How much farther ahead is Philip after 12 seconds?
Answer:
Philip, after 12 seconds, is 13.44 meters farther ahead after 12 seconds
Step-by-step explanation:
Philip
6.59 x 12 = 79.08
Mary
5.47 x 12 = 65.64
79.08 - 65.64 = 13.44
Can someone please help me I will give a lot of points and a brainliest
Answer:
(m+n-1)√pStep-by-step explanation:
we'll arrange the equation in an order↝m√p + n√p -√p
now, we'll isolate the common variable in the equation↝√p(m+n-1)
now, we'll match our answer with the given options↝(m+n-1)√p = √p(m+n-1)
↝(m-n+1)√p ≠ √p(m+n-1)
↝(m-n-1)√p ≠√p(m+n-1)
hence, option 1st is correct ✓
Option A
Let's verify
[tex]\\ \rm\Rrightarrow (m+n-1)\sqrt{p}[/tex]
a(b+c)=ab+ac[tex]\\ \rm\Rrightarrow m\sqrtp}+n\sqrt{p}-\sqrt{p}[/tex]
Hence verified
Look at the Picture below.
Answer:
153.86Step-by-step explanation:
[tex]area = \pi {r}^{2} \\ = 3.14 \times {7}^{2} \\ = 3.14 \times 49 \\ = 153.86 \: {km}^{2} \\ [/tex]
A circle has a radius of 6 yards. A sector of the circle that is 12. 56 yards² is painted. What is the angle measurement of the painted sector?
A. 9 degrees
B. 11 degrees
C. 40 degrees
D. 45 degrees
Answer:
your answer is D.45 degrees
. The total distance from Keith's home to the office,
then to the gym, and then back home is 44 miles,
The distance from his home to the office is 6 miles
more than the distance from the office to the gym,
The distance from the gym to the office is 2 miles
less than the distance from the gym to his home,
Find the distances between each location, then
classify the triangle,
Answer:
the total distance from the home to the office is 52 m
What is the vertex of a parabola represented by the equation f(x) = −2(x − 4)2 − 7?
Answer:
4,-7
Step-by-step explanation:
Giving brainliest answer correct pls!
Answer:
Step-by-step explanation:
woven blanket at - 1003 feet.
21 plus 4x equal 61 what equal 61
Answer:
x = 10
Step-by-step explanation:
61 - 21 = 40
40 / 4 = 10
x = 10
Example on how to solve
Answer:
x = -1, y = 2
Step-by-step explanation:
plug the first equation into the second to get: 4x-20x=16
simplify: -16x=16
therefore, x = -1, and y = 2
Select the correct statements that correspond to the question. Thank you!
A couch and coffee table cost a total of $996. The cost of the couch is two times the cost of the coffee table. Find the cost of each item.
Answer: the cost of the couch is 664 and the cost of the coffe table is 332
Step-by-step explanation:
X is the cost of the coffee table and 2x is the cost of the couch (which is two times more than the coffee table)
2x + x = $996
3x = $996
x = 996/ 3
x = $332 (this is what the coffee table cost)
2x => 2(332)
2x => $664 (the cost of the couch which is two times the cost of the coffee table)
together, $332 + $664 = $996 total
Simplify 3(x-2)
3x+6
3x-6
3x+2
3x-2
Answer:
3(x-2)
=3x-6
by using BODMAS
Add:
(2^3 − + 4) + (5^2 − 6 + 3)
Answer:26!
Step-by-step explanation:
((23) - 4) + ((52 - 6) + 3)
(23 - 4) + 22
26
Hope this helps! ^w^
Help it’s due by Thursday
Answer:
10 is B. 9 is 28.8
Step-by-step explanation:
Simplify a/3a + 2a/3a fraction
SOLUTION:
=) (a + 2a)/3a
=) 3a/3a
=) 1
i need help with this question
Answer:
no haha
Step-by-step explanation:
find the length of the missing side in the triangle below
give answer to one decimal place :))
Which of the following situations or activities involve permutation?
a. matching shirts and pants
b. forming different triangles out of 5 points on a plane, no three of which are collinear
c. assigning telephone numbers to subscribers
d. forming a committee from members of a club
Question
You divide two polynomials and obtain the result 5x2−13x+47−102x+2. What is the dividend?
Answer:
5x2−115x+49
Step-by-step explanation:
hope it helps
5x²-115x+49 is the required dividend.
What is dividend?A dividend is a number that is being divided, if 2x is a dividend and 2 is a divisor, then it gives remainder 2, when 2x is divided by 2.
The given polynomial is,
5x²-13x+47-102x+2
To find dividend, simplify this polynomial,
5x²-115x+49
This is the required dividend.
To learn more about Dividend on:
https://brainly.com/question/21291606
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How to find the unknown constant between two expressions.
Answer:
Step-by-step explanation:
This is called a 'System of equations'.
Say that you have these two expressions, and the unknown is "b".
5b = y
4b+2 = y
Now we can solve two ways; graph it or solve it.
Solving it, we can see that they both equal y, so:
5b=4b+2
move 4b to the left side by subtraction:
(5b-4b) =2
b = 2
let's see what y equals when b = 2
5 * 2 = y
10 = y
Graphing it we see they intersect, or solve at
(2,10) or b=2, y=10
Hope this helps!
What numbers go in the boxes?
For second one
Vertex is (-3,0)
Axis of symmetry=x=-3There is only one x intercepts
Only one real root is -3Answer:
vertex = (-3, 0)
axis of symmetry: x = -3
one real root at x = -3
Step-by-step explanation:
The vertex is the turning point of the curve (so the maximum point for parabolas that open downwards, and the minimum point for parabolas that open upwards)
The axis of symmetry is the vertical line that goes through the vertex of a parabola. So this will be the line of the x-value of the vertex.
The roots of a parabola are the points where the curve intersects (or touches) the x-axis.
First graph
vertex = (3, -4)
axis of symmetry: x = 3
roots: x = 1, 5
Second graph
vertex = (-3, 0)
axis of symmetry: x = -3
one real root at x = -3
What is the correct justification for the first step in solving this
equation? 3(x - 4) + 1 = 12x *
-
O Addition Property
O Division Property
O Commutative Property
O Distributitive Property
Answer:
Distributitive Property
Step-by-step explanation:
The correct justification for the first step in solving the provided equation is that the first step should be distributive Property
What is the property of equality?Property of equality says that by performing any mathematical operation, of both sides of a expression does not change the original value of the equation.
The equation given in the problem is,
[tex]3(x - 4) + 1 = 12x[/tex]
To solve the above equation, we need to open the brackets of the equation. To do this, we need to use the distributive property of the equality.
This can be done by multiplying the number 3 inside the bracket (x-4). This operation simplify the equation, to solve it further. Therefore,
[tex]3x - 3\times4 + 1 = 12x\\3x - 12 + 1 = 12x[/tex]
Hence, the correct justification for the first step in solving the provided equation is that the first step should be distributive Property.
Learn more about the property of equality here;
https://brainly.com/question/1601404
12x + 4 divided by 4 plus 20x + 5 divided by 5
PLEASE SOMEONE HELP ME FIND THE AMOUNT
Answer:
$1248
Step-by-step explanation:
I = 960 x 3 x 0.1
= 2880 x 0.1
= $288
Amount
= 960 + 288
= $1248
The measurement of one angle of a right triangle is 61°
What is the measurement of the third angle?
Enter your answer in the box.
Answer:
58
Step-by-step explanation:
61+61=122
180-122=58
3rd angle is 58°
A box has 3 one-dollar bills, 2 five-dollar bills, 2 ten-dollar bills, and 1 twenty-dollar bill. A student selects one bill from the box at random.
PART A Develop a probability model to compare the probability of selecting $5 to the probability of selecting $10. Explain.
PART B how does the probability of selecting $1 compare to the probability of selecting $20? explain
Answer and explanation:
There's 3 one dollar bills
2 five dollar bills
and 2 ten dollar bills
and 1 twenty dollar bill
3+2+2+1=8
Part A: The probability of selecting 5 is 2/8 and the probability of selecting 10 is also 2/8 and both of them are the same, 1/4.
Part B: The probability of selecting a one dollar bill is 3/8 and the probability of selecting a twenty dollar bill is 1/8 because there are 3 one dollar bills in 8 bills and 1 twenty one dollar bill in 8 bills only.
Estimate the amount of the tip by rounding the bill to the nearest dollar before calculating.
20% tip on a bill of $59.77
Answer:
$12 would be the correct answer :)
PLS HELP DUE TODAY 11:59
Use the two images of the houses to answer the following questions. Number your answers.
1. Are the lengths of one house proportional to the lengths of the other house? Why or why not?
2. How can you use scale factors to show that the homes are or are not proportional?
3.what role does surface area take in the building of a house
4.what advantages exist for a house with a large amount of surface area exposed to the elements? EXPLAIN
Simplify the expression. 2y−5(y−3)=
Answer:
-3y -15
Step-by-step explanation:
2y - 5(y-3) = 2y -5y - 15
= -3y -15
Your welcome, and feel free to comment if you need have any questions!
The simplified value of the expression, 2y−5(y−3) using the Distributive property is 15- 3y.
Given Expression:
2y−5(y−3)
Using Distributive property
[tex]{\text} a *(b+c) = (a *b) + (a*c)[/tex]
So, applying the Distributive property in the expression 5(y - 3) gives
5(y - 3) = 5y - 15
Substituting the value 5y - 15 in 2y−5(y−3) as
2y−5(y−3) = 2y - (5y-15)
= 2y - 5y + 15
Now, operating the simplified value is
2y−5(y−3) = 15 - 3y
Thus, the simplified expression is -3y + 15.
Learn more about Expression here:
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