Sum of first 7 terms of an AP = 49.
Sum of first 17 terms = 289
Find:the sum of first 30 term
Solution:We know that,
Sum of first n terms of an AP – S(n) = n/2 * [ 2a + (n - 1)d ]
Hence,
→ 7/2 * [ 2a + (7 - 1)d ] = 49
→ 2a + 6d = 49 * 2/7
→ 2( a + 3d ) = 14
→ a + 3d = 14/2
→ a + 3d = 7 -- equation (1)
Similarly,
→ 17/2 * [ 2a + 16d ] = 289
→ 17/2 * 2 * (a + 8d) = 289
→ a + 8d = 289 * 2/17 * 1/2
→ a + 8d = 17 -- equation (2)
Subtract equation (1) from (2).
→ a + 8d - (a + 3d) = 17 - 7
→ a + 8d - a - 3d = 10
→ 5d = 10
→ d = 10/5
→ d = 2
Substitute the value of d in equation (1).
→ a + 3 * 2 = 7
→ a = 7 - 6
→ a = 1
Now,
Sum of first 30 terms = 30/2 * [ 2(1) + (30 - 1)(2) ]
→ S(30) = 15 (2 + 58)
→ S(30) = 15 * 60
→ S(30) = 900
Therefore, the sum of first 30 terms of the given AP is 900.
I hope it will help you.
Regards.
answer refer in pic siso
What is the slope of the graph below?
Answer:m=-1/2
Step-by-step explanation:
can someone help me x -y =1
and can yall explain how you solved it
Answer:
x = 1 + y
Step-by-step explanation:
add y to both sides, and that is basically it
3/4 + 5/6 divided by 2/3
Answer:
2
Step-by-step explanation:
Answer:
Hello
Step-by-step explanation:
The awnser to your question is 2
I need help with 9and 10 pleas
HELPP PLZ (12 points btw)
Which of the following is most likely the next step in the series?
20 POINTS!! HELP ME PLZZ I NEED HELP WITH THIS!!
Answer:
0.22222222
Step-by-step explanation:
Hope this helps!!!
Answer:
0.22222222
Step-by-step explanation:
you have to divide 2 by 9.
28 > m - 4
Solve the equation
Answer:
m<32
Step-by-step explanation:
You add 4 to both sides to isolate the variable which in this case is m this gives you 32>m, then you can just flip the equation.
Answer: m < 32
Step-by-step explanation:
28 > m - 4
Add 4 to both sides:
32 > m
Flip the inequality so m is in front:
m < 32
Hope this helps!
Scott High School is holding a fundraiser and plans to use 1/2 of the money collected to build a new library. Of the money directed towards building the new library, 5/8 will go towards purchasing computers. What fraction of the money raised will go towards purchasing computers for the library?
Answer:
[tex]Computer = \frac{5}{16}[/tex]
Step-by-step explanation:
Given
[tex]Library = \frac{1}{2}[/tex]
[tex]Computers = \frac{5}{8}[/tex] of library.
Required
Determine the fraction going towards computer purchase.
We have:
[tex]Computers = \frac{5}{8}[/tex] of library.
This can be rewritten as:
[tex]Computers = \frac{5}{8}[/tex] * library.
Substitute [tex]Library = \frac{1}{2}[/tex]
So, we have:
[tex]Computer = \frac{5}{8} * \frac{1}{2}[/tex]
[tex]Computer = \frac{5}{16}[/tex]
Hence:
The fraction is [tex]\frac{5}{16}[/tex]
What is the constant in the expression? 4x - 1*
O 4
O -4
O 1
O -1
Answer:
-1
Step-by-step explanation:
-1 is the constant in the expression 4x - 1
Answer:
-1
Step-by-step explanation:
as it got no variables to it.
NEED HELP ASAP!!!!! WILL GIVE BRAINLIEST!!
2+2
Answer:
2+2=4
Step-by-step explanation:
You've got this man.
Answer:
4
Step-by-step explanation:
( worth 74 points and brainliest pls help)
Answer:
40 CMStep-by-step explanation:
If you check the measurement
of the other line, it will NOT match the one
on the side. It is a few centimeters bigger than the bottom.
hope this helps! <3
Answer:
[tex]\Large \boxed{\sf 40}[/tex]
Step-by-step explanation:
The triangle is a right-angled triangle
Use Pythagorean Theorem formula to solve for hypotenuse
[tex]\displaystyle c=\sqrt{a^2+b^2}[/tex]
Substitute in the values
[tex]\displaystyle c=\sqrt{24^2+32^2}=40[/tex]
Simply the expression below .
8+ ( 15 - 3 ) + 4
help please .
Answer:
24
Step-by-step explanation:
8+ ( 15 - 3 ) + 4
8+12+4
20+4
24
-7+0.3(-4x+20)+8.8x simplified
can somebody help me pleaseee ?? it’s due soon & im stuck .
Answer:
a. lenqth=32 , width=2
b. m∠p=100 m∠Q=50 m∠R=30
c. XY=20 YZ=12
d.m∠1=90 m∠2=90
Step-by-step explanation:
a. the area of a rectangle is length×width so to find the possible sizes for L and W we need to list the factors (multiplication of two numbers to get 64) of 64, which are,
1 AND 64 (this answer is suitable but it's better to choose another
one if available for more accuracy)
2 AND 32 (this is a good answer to use)
4 AND 16 (this one already used in the question)
8 AND 8 (this answer will be wrong as the sizes need to be different because it's a rectangle but it will be good for square)
SO we will choose 2 AND 32 for the answer and we can put them in any order we want.
b. first of all acute angles are angles measured less than 90 degrees. so to have at least one angle not acute we use measures up to 90 degrees.
I will put one answer as 100 degrees (note you can use any number above 90 to not be an acute angle) and the other answers will be two numbers add up to be 80 degrees (and again you can choose any numbers for that).
c. the two answers should add up to be 32 so for this counterexample we can choose any two numbers to have the sum of 32 (remember that 16+16 already chosen in the question.
d. two supplementary angles are two angles add up to be 180 degrees so for this question we need to find two angles sum to 180 and not obtuse (that mean 90 degrees or less) and the only answer can appear is 90+90=180.
The following are the last 10 run scores Colin got in cricket:
1, 25, 27, 3, 23, 25, 5, 9, 26, 27
a) Work out Colin's mean score.
b) Colin plays cricket again on Sunday. He gets 5 runs.
What is his new mean score?
Give your answers as decimals
Answer:
a) 18.8
b) 20
I hope this helps :) Let me know if it's right!
Answer:
17.1
Step-by-step explanation:
Given parameters:
Scores of Colins:
1, 25, 27, 3, 23, 25, 5, 9, 26, 27
A. Colin's mean score;
The mean is the sum of all values divided by the number of values in a given set;
Mean = [tex]\frac{1 + 25 + 27 + 3 + 23 + 25 + 5 + 9 + 26 + 27}{10}[/tex]
Mean = [tex]\frac{171}{10}[/tex]
Mean score = 17.1
9 is 10 times the value of the 9 in 329,513
2 is 110 the value of the 2 in 7,562
6 is 110 the value of the 6 in 4.68
Answer:
498,173.26.
Step-by-step explanation:
The place value of 9 in the number 3, 29,513 = 9000
In the required number,
Place value of 9 is 10 times of the value of 9 in 329, 513 = 9000 * 10 = 90,000
The value of 2 is one-tenth of 2 in 7562 = 2/10 = 0.2
The value of 6 is one-tenth value of 6 in 4.68 = 0.60/10 = 0.06
Thus, the required number would be 498,173.26 as the other numbers do not justify the above conditions of having 9 at ten thousand place, 2 at tenth, and 6 in hundredth place.
helpppp. I need to answers and its rotating around the orgin.
Find the value of x.
2x x
Answer:
2x²
Step-by-step explanation:
2xx
=2*x*x
=2*x2
=2x2
A scared tarantula was able to go a distance of 20 meters in 6 seconds. What was its
average speed?
Answer:
3.33 m/s
Step-by-step explanation:
speed = [tex]\frac{meters}{seconds} > \frac{20}{6} = 3.33[/tex]
help me solve for the red variable
Answer:
i just need points
Step-by-step explanation:
HELP! Please include the steps you took as I don't fully understand how to do this!
[tex]22x-17=12x+8[/tex]
Select all that apply.
Which decimals in the list are repeating decimals?
5/6
4/15
3/5
1 3/4
1/3
4/1,000
Answer:
5/6 4/15 1/3
Step-by-step explanation:
the answers are above
Answer:
the repeating decimals are in 5/6 4/15 1/3
Step-by-step explanation:
to find them you would just divide them for example 5/6, you would divide the 5 by the 6
While on spring break, Kayla decided she wanted to go parasailing She was held at a constant angle above the water by a large tow rope attached to the back of the boat. The length of the tow rope is 240 meters. If the angle of the rope keeps Kayla at a horizontal distance of 181 meters away from the boat, how high above the boat is Kayla?
Answer:
157.6m
Step-by-step explanation:
Given
Horizontal distance = 181m
Length of the rope =240m
To know how high above Kayla was, we will use the Pythagoras theorem.
According to the theorem;
d² = x²+y²
x is the horizontal distance
y is the vertical distance
d is the length of the rope
Substitute
240² = 181²+y²
y² = 240²-181²
y² = 24839
y = √24839
y = 157.6m
Hence the boat is 157.6m above Kayla
Flavia needs to build a fence around her dog house, as illustrated on the coordinate grid below. If each unit represents 1 foot, what is the total length of Flavia’s fence in feet?
Answer:
I would say your answer is (D
9) Draw a graph of the linear equation y= -2/-5x +3
12c - 4c + 18 = 50 solving for variable
Answer:
c=4
Step-by-step explanation:
subtract 50-18= 32
then subtract 12c-4c= 8c
8c=32
divide 8c by 32 which gives you
c=4
Answer:
[tex]:\implies \sf 12c - 4c + 18 = 50 \\ \\ \\ [/tex]
[tex]:\implies \sf 8c = 50 - 18 \\ \\ \\ [/tex]
[tex]:\implies \sf 8c = 32 \\ \\ \\ [/tex]
[tex]:\implies \sf c = \frac{32}{8} \\ \\ \\ [/tex]
[tex]:\implies \underline{ \boxed{\textsf { \textbf{c = 4}}}} \\ \\ \\ [/tex]
What’s the value of X ?
Answer:
x=25
Step-by-step explanation:
Isolate the variable by dividing each side by factors that don't contain the variable.
(2x+2)+(5x+3)=180
Which one?
A. B. C. or D?
Answer: c
Step-by-step explanation: distribute -7p by multiplying it by 8p first, which gives you -56p squared. Then multiply the -7p by -1 which gives you 7p as the two negatives will cancel out.
Find the value of each variable.
Answer:
19. x = 65
20. x = 12
21. x = 35, y = 85
Step-by-step explanation:
19. 2x -10 = 120
2x (-10 + 10) = (120 +10)
2x/2 = 130/2
x = 65
20. 2x + 4x + 108 = 180
6x + (108 - 108) = (180 - 108)
6x/6 = 72/6
x = 12
21. 2x + 25 = 3x - 10
2x + (25 - 25) = 3x (- 10 - 25)
(2x - 3x) = (3x - 3x) - 35
-x/-1 = -35/-1
x = 35
3x - 10 + y = 180
3(35) - 10 + y = 180
105 - 10 + y = 180
(95 - 95) + y = (180 - 95)
y = 85
please help me? im desperate!
Answer:
The same sign
Step-by-step explanation: