3. The sum of the second term and the ninth term of an arithmetic sequence is -5. The sum of the third and fourth terms of the same sequence is 7. Find the first term of the sequence.
Answer:
First term of the sequence is [tex]11[/tex]
Step-by-step explanation:
Let [tex]a[/tex] be the first term and [tex]d[/tex] be the common difference
We have
The sum of the second term and the ninth term of an arithmetic sequence is [tex]-5[/tex]
[tex]a+(2-1)d+a+(9-1)d=-5\\\\2a+9d=-5---eqn1[/tex]
The sum of the third and fourth terms of the same sequence is [tex]7[/tex]
[tex]a+(3-1)d+a+(4-1)d=7\\\\2a+5d=7---eqn2[/tex]
eqn 1 - eq2
[tex]4d=-12\\\\d=-3[/tex]
Substituting in eqn 1
[tex]2a+9\times -3=-5\\\\2a=22\\\\a=11[/tex]
First term of the sequence is [tex]11[/tex]
What is an equation of the line that passes through the points (4, -1) and (-8, -7)?
Answer:
y=-1/2x - 3
I think this is it, its been a while though.
i wake up at 6:00 am gianna wakes up 35 minutes later john wakes up 7 minutes before gianna at what time does john wake up
Find the number of minutes Hohn wakes up after you:
35 minutes - 7 minutes = 28 minutes
6:00 am + 28 minutes = 6:28 am
John wakes up at 6:28am
Answer: 6:28am
Step-by-step explanation: If you wake up at 6 and Gianna wakes up 35 mins later then Gianna woke up at 6:35. If John wakes up 7 mins before Gianna the 35mins -7mins=28. So John woke up at 6:28 am.
Hi, I have a question it is kinda hard but I think i got it, if it's wrong plz tell mee
Solve for X
5-x+6=4
X=3
5-x + 6 = 4
Combine like terms:
11-x = 4
Subtract 11 from both sides
-x = -7
Divide both sides by -1
X = 7
Answer: x = 7
Solve for X
5-x+6=4
Answer:-x = 7
Explanation:-=> 5-x + 6 = 4
=> (5+6)-x = 4
=> 11-x = 4
(subtract both the sides by 11)
=> -x = -7
(divide both the sides by -1)
=> x = 7
Can someone help me with this please?
Write the converse of the following statement. Then determine its validity.
a. If the diagonals of a parallelogram are congruent, then the parallelogram is a rectangle.
b. If a parallelogram is a rectangle, then the diagonals are congruent. TRUE.
c. If a parallelogram is a rectangle, then the diagonals are congruent. FALSE.
d. If the diagonals of a parallelogram are not congruent, then the parallelogram is not a rectangle. FALSE.
d. If a parallelogram is not a rectangle, then the diagonals are not congruent. TRUE.
The converse and the validity of the statement is:
If a parallelogram is a rectangle, then the diagonals are congruent. TRUE.The statement is given as:
If the diagonals of a parallelogram are congruent, then is the parallelogram is a rectangle
Considering the following statement
If a then b
Its converse is:
If b then a
So, the converse of the given statement is:
If a parallelogram is a rectangle, then the diagonals are congruent.
The diagonals of a rectangle are true.
Hence, the validity is true.
So, the true statement is (b)
Read more about converse statements at:
https://brainly.com/question/4421013
Using the GCF you found in Part b re write 35 +63 factor one factor is the GCF and the other is the sum of the two numbers that do not have a common factor show your work
Answer:
7(9 + 14)
Step-by-step explanation:
The Greatest Common Factor of 35 and 63 is 7; both 35 and 63 are evenly divided by 7. Thus, 35 + 63 can be rewritten as 7(5) + 7(9), or 7(14)
So 35 + 63 = 7(9 + 14)
Answer:
= 98
Step-by-step explanation:
Find the value of theta, to the nearest hundredth if cos they have is -0.7 and theta is in quadrant 2
Step-by-step explanation:
if I understand you correctly, then
cos(theta) = -0.7
then Theta = 134.427004...°
and that is rounded 134.43°
Help Plssss it is due tommorrow!!!!! I think it is A i am not sure help
Answer: congruent bases
Step-by-step explanation:
what makes a trapezoid a trapezoid is that the bases are different! the side on top and bottom are different.
Need help on HS geometry
Answer:
RS = 46 , RT = 38
Step-by-step explanation:
A segment joining the midpoints of 2 sides of a triangle (mid segment) is half the length of the third side, then
RS = 2 × UW = 2 × 23 = 46
RT = 2 × VW = 2 × 19 = 38
Solve
x ^ 4 -8x ^ 2 – 9 = 0
Answer: 0 is the answer
Step-by-step explanation: your welcome its 0
help please anybody hmm
Answer:
94.6-18.8=75.8
75.8 is the answer
Step-by-step explanation:
Hope this helps
May i get braineist pls?
solve for x: 2-3(2x-2)=17
Answer:
x = - 1.5
Step-by-step explanation:
2 - 3(2x - 2) = 17 ← distribute parenthesis
2 - 6x + 6 = 17 , simplify
8 - 6x = 17 ( subtract 8 from both sides )
- 6x = 9 ( divide both sides by - 6 )
x = [tex]\frac{9}{-6}[/tex] = - [tex]\frac{3}{2}[/tex] = - 1.5
1/2 + (-7) – 2 1/2 - (-2)
Choose the graph that matches the following system of equations:
x + y = 4
2x + 3y = 18
Picture of coordinate plane with line y equals negative x plus 4 and line y = equals negative 2 thirds x plus 6. They intersect at negative 6, 10.
Picture of coordinate plane with line y equals x minus 4 and line y equals negative 2 thirds x plus 6. They intersect at 6, 2.
Picture of coordinate plane with line y equals x minus 4 and line y equals negative 2 thirds x minus 6. They intersect at negative 1.2, negative 5.2.
Picture of coordinate plane with line y equals x plus 4 and line y equals negative 2x plus 6. They intersect at 0.67, 4.67.
Answer:
Line x-intersect: -6
y-intersect: 10
Step-by-step explanation:
X + y = 4
x = 4-y
2(4-y) + 3y = 18 (substitution)
8-2y+3y = 18
y = 18-8
y = 10
x + 10 = 4
x = -6
Which expression is equivalent to 6x-9/3
Answer:
option A is the answer 2x-3
Answer:
2x-3
Step-by-step explanation:
(6x-9)/3
This can be simplified to
6x/3 - 9/3
2x -3
How many Match sticks will be In Image 6?
Answer:
19
Step-by-step explanation:
A shop has a sale that offers 20% off all prices.On the final day reduce all the sale prices by 25%.Linz buys a radio on the final day.Work out the overall percentage reduction on the price of the radio
Answer:
40%
Step-by-step explanation:
Original price = x
Sale = 20% off
20% / 100 = 0.2 to convert from a percent to a decimal
Sale = x - 20% of x = x - 0.2x = 0.8x
Sale price = y = 0.8x
Reduction of sale prices = 25% = 0.25
Reduction = y - 25% of y = y - 0.25y = 0.75y
End price in terms of original price (x):
0.75y = 0.75(0.8)x
= 0.6x
End price = 0.6 or 60% of original price, coming out to a 100-60 = 40% overall percentage reduction
SOMEONE HELP!!!!!!!!!!!!!!!!!!!! I would give more points but there are people who just write random things for an answers that isnt correct just to get points.
Answer:
a) 320 is correct
b) 20 more 18 year old students
Step-by-step explanation:
a) 320 is correct
b) 20 more 18 year old students: The only information we have in the 25 - 35 minute time frame is the data for 30 minutes:
12 years: 40 students
18 years: 60 students
Difference = 20 more 18 year old students than 12 year old students spent spent time on social media for 25 - 35 seconds.
HEPL!! due in 2 hours so please help or attempt! I came up with 5 different answers and don't know which one is the actual answer!!
Answer:
Original Price = $23
Step-by-step explanation:
$5.75 is the price after a discount of 75%
Let the original price be x and x is 100% of the price
5.75 = 100%x - 75%x
5.75 = 25%x
The new price is 25% of the original because you are subtracting 75%
25% is also written as 0.25
5.75 = 0.25x
x = 5.75/0.25
x = 23
The original price is 23
-Chetan K
26=7(g−9)+1226, equals, 7, left parenthesis, g, minus, 9, right parenthesis, plus, 12
An 18-foot ladder is leaning against a wall. The bottom of the ladder is 4.5 feet from the base of the wall.
How high up the wall does the ladder reach? Round your answer to the nearest tenth, if necessary.
A
13.5 feet
B
18.6 feet
o
С
22.5 feet
D
17.4 feet
Answer:
d
Step-by-step explanation:
use Pythagoras theorem
that is a²+b²=c²
so 4.5²+b²= 18²
rearrange to b²=18²-4.5²
so you get b=
[tex] \sqrt{303.75} [/tex]
that is equal to 17.42842506
Once the prompt in image is read answer choices are:
A. -0.9
B. -0.4
C. 0.4
D. 0.9
which function describes the arithmetic sequence shown -5,-7,-9,-11,-13
Answer:
[tex]n(x)=x-2[/tex]
Step-by-step explanation:
You can notice that between each of the arithmetic sequence there is a addition of 2. So we know that to add a 2 to get the next value. We can write it as n(x) where n is a function where x is the number:
n is the function and x repersent the number which is givenWe can write this function as: [tex]n(x)=x-2[/tex]So if we input x = -5 we will get -7. If we input -11 we get -13.
round 0.006772 to 1 significant figure
Answer:
0.007
Step-by-step explanation:
0's before other numbers are non-significant. Then you just round your number.
Hope that helps
What is the factored form of n3+512 (pleas help fast)
A- (n-8)(n^2+8n+64)
B- (n+4)(n^2-4n+128)
C- (n-4)(n^2+4n+128)
D- (n+8)(n^2-8n+64)
Answer:
Since both terms are perfect cubes, factor using the sum of cubes formula,
a³+b³=(a+b)(a²-ab+b²) where
a=n and b=8
(n+8)(n²-8n+64)
Answer
(n+8)(n²-8n+64)
hi
have a good day
thank me later
Carryonlearing
Answer:
Step-by-step explanation:
The only one that has a chance of being correct is D. That's because the first term is correct and you have to assume that the second one is as well.
cubrt(512) = 8
The first term is (n + 8)
The second term is (n^2 - 8*n + 8^2) = n^2 - 8n + 64
All the other answers have the wrong first term
A: it should be n + 8 not n - 8
B and C are both wrong because the cube root of 512 is 8 not 4.
please help! i need for this to be done.
Solve.
t+7.45=1334
Enter your answer as either a decimal or a mixed number in simplest form in the box.
t =
Answer:
t = 6.3
Step-by-step explanation:
t + 7.45 = 13 [tex]\frac{3}{4}[/tex] = 13.75 ( subtract 7.45 from both sides )
t = 6.3
i keep this all day what is 6 + 6 × 6 + 6 ÷ 6=
Answer:
43
Step-by-step explanation:
6 + 6 × 6 + 6 ÷ 6
using BIDMAS, we do the division first
6÷6=1
then multiplication
6×6=36
leaving us with:
6+36+1=43
Hopefully this helped- have a good day)
Let's do
6+6×6+6÷66+36+17+3643Done!
Help ME!
Question 1: Evaluate the expression:
2+5⋅8
Question 8: 10÷(3−1⋅2)
Option answers for Question 8: 4, 10, 10/4, and 2.5
Answer:
Q1: 42
Q8: 10
Step-by-step explanation:
PEMDAS
Find the slope of the line (-3,-2),(1,-2)
Answer:
0
Step-by-step explanation:
The y-axis is the same so the slope has to be zero, since the line is not going vetrically anytime on the graph