Answer:
10
Step-by-step explanation:
Remember that the formula for the sum of an arithmetic series is:
[tex]S=\frac{k}{2}(a+x_k)[/tex]
Where k is the number of terms, a is the initial term, and x_k is the last term of the series.
We essentially want to find k, the number of terms, given that the sum S is equal to 105. So, substitute 105 into our equation:
[tex]105=\frac{k}{2}(a+x_k)[/tex]
To do so, we need to final term x_k. We don't know what it is yet, but that doesn't matter. All we need to do is to write it in terms of k. First, remember that the standard form for the explicit formula of an arithmetic sequence is:
[tex]x_n=a+d(n-1)[/tex]
Where a is the first term, d is the common difference, and n is the nth term.
From our sequence, we can see that the first term is -3.
Also, we can determine that our common difference is +3, since each subsequent term is 3 more than the previous one. -3+3 is 0, 0+3 is 3, 3+3 is 6, and so on.
Therefore, our explicit formula is:
[tex]x_n=-3+3(n-1)[/tex]
Therefore, our final term, x_k, will be if we substitute k for n. So, we can acquire the equation:
[tex]x_k=-3+3(k-1)[/tex]
Now that we know what x_k is, we can substitute that into our original equation:
[tex]105=\frac{k}{2}(a+x_k)[/tex]
Substitute the equation into x_k. Also, let's substitute -3 (our first term) for a. So:
[tex]105=\frac{k}{2}(-3+(-3+3(k-1)))[/tex]
And now, all we have to do is to solve for k.
First, distribute the 3:
[tex]105=\frac{k}{2}(-3+(-3+3k-3))[/tex]
Add within the parentheses:
[tex]105=\frac{k}{2}(3k-9)[/tex]
Multiply both sides by 2. This removes the fraction on the right:
[tex]210=k(3k-9)[/tex]
Distribute. We will get a quadratic:
[tex]210=3k^2-9k[/tex]
So, let's solve for k. Let's divide everything by 3:
[tex]70=k^2-3k[/tex]
Subtract 70 from both sides:
[tex]0=k^2-3k-70[/tex]
Factor. We can use -10 and 7. So:
[tex]0=(k-10)(k+7)[/tex]
Zero Product Property:
[tex]k-10=0\text{ or } k+7=0[/tex]
Solve for k for each equation:
[tex]k=10\text{ or } k=-7[/tex]
-7 doesn't make sense (we can't have -7 terms). Remove that solution. So, we are left with:
[tex]k=10[/tex]
Therefore, the number of terms we have in our series for our sum to be 105 is 10.
And we're done!
4x + y = 2
I need to solve the literal equation for y.
Answer: y=2−4x
Step-by-step explanation:
When solving for y in this problem(4x+y=2) we need to get y by itself in the equation. To do this we need to move 4x over to the right side of the equation. To do this we subtract, 4x from both sides of the equation.
Please help with my music math
A mixed number can have the same value as an improper fraction. True False
Answer:
true
Step-by-step explanation:
a mixed number can have the same value as an improper fraction but never as an proper fraction
Solve for g.
C=1/2gq
Answer:
[tex] g = \frac{2c}{q}[/tex]
Step-by-step explanation:
[tex]c = \frac{1}{2} gq \\ 2c = gq \\ \huge \red{ \boxed{ g = \frac{2c}{q} }}[/tex]
Answer:
g = 2C/q
Step-by-step explanation:
C * (2) = 1/2gq * (2)
2C / q= gq / q
2C/q = g
which ordered pair is not a solution to this system?
x+y > 3
x + 2y > 5
Answer:2,2
Step-by-step explanation:
I guess
In an arithmetic progession T7 =20 and T13 =38,. Find the first term and the common difference.
$20,000 was invested in a 3-year simple interest money market account. After 3 years,
the account balance was $32,000.
What was the interest rate for the account?
Step-by-step explanation:
Amount = principal + S. I.
S. I. = p * t * r / 100
32000 = 20000 + 20000 * 3 * r / 100
12000 = 600 r
r ( Rate of interest) = 20 %
. When the process of solving a linear inequality results in the variable being eliminated with a false statement remaining, what does this mean about the solution set of the inequality?
Answer:
No Solution
Step-by-step explanation:
When we solve linear inequalities using any one the methods such as
1) Elimination or
2) Substitution
And we get the variable eliminated with a false statement remaining, this means there is no solution.
In other words the solution does not exist or the solution is not possible in the given range or the values given are false.
But when the values are true we get a solution for the variable solved.
In the elimination method we eliminate the same terms by addition or subtraction after making them equal.
And the substitution method requires putting the values of one variable in place of another.
Here is the question 20 points and brainlest but I want a detailed answer
Answer:
18.75 sq.feet
Step-by-step explanation:
According to the question
1 card = 18 sq.in
150 cards = 150 * 18
= 2700 sq.in
= 18.75 sq.feet
If 9 (x) = – 5x2 – 4x + 19 find f (–3)
Answer:
- 14
Step-by-step explanation:
[tex]f(x) = - 5 {x}^{2} - 4x + 19 \\ plug \: x = - 3 \\ f( - 3) = - 5 {( - 3)}^{2} - 4( - 3) + 19 \\ f( - 3) = - 5 \times 9 + 12 + 19 \\ f( - 3) = - 45 + 31 \\ f( - 3) = -14[/tex]
(7x+40)+(6x+43)=180 x? Z?
[tex](7x + 40) + (6x + 43) = 180\\7x + 40 + 6x + 43 = 180\\7x + 6x = 180 - 40 - 43\\13x = 97\\x = \frac{97}{13}[/tex]
I'm not sure what you mean by Z but x is [tex]\frac{97}{13}[/tex]
What is the length of EF?
6 units
10
8 units
7 units
10%
-2 0
-2-
2 units
H Н
-4
G
-6
-B
10
Answer:
7
Step-by-step explanation:
An executive committee consists of 15 members: 7 men & 8 women. 5 members are selected at random to attend a meeting in Hawaii. The names are drawn from a hat. What’s the probability that all 5 selected are women?
Answer:
1.8%
Step-by-step explanation:
(8c5 * 7c0)/15c5
= 0.018
This is the answer which I get when I solve this... cross check the calculations once.
Name 4 noncoplanar points.
Answer:
RPVN
Step-by-step explanation:BRBR
AHHHH please help answer and I’ll give you points
Answer: Yes She is correct
Step-by-step explanation:
Help solve step by step please? 3/7➗4/5=
Answer:
15/28
Step-by-step explanation:
Step-by-step explanation:
3/7 divided by 4/5
Find the reciprocal of 4/5 which is 5/4
Multiply 3/7 by 5/4
3*5= 15 which is the numerator
7*4=28 which is the denominator
so the final answer is 15/28
a. {1, 2, 3, 4, 5} = {x | x E N and x < 5}
True or False
Answer:
true
i just anwwsered this one in my lessons
A perfect square ends with the same two digits. How many possible values of this digit are there?
Answer:
A perfect square is a whole number that is the square of another whole number.
n*n = N
where n and N are whole numbers.
Now, "a perfect square ends with the same two digits".
This can be really trivial.
For example, if we take the number 10, and we square it, we will have:
10*10 = 100
The last two digits of 100 are zeros, so it ends with the same two digits.
Now, if now we take:
100*100 = 10,000
10,000 is also a perfect square, and the two last digits are zeros again.
So we can see a pattern here, we can go forever with this:
1,000^2 = 1,000,000
10,000^2 = 100,000,000
etc...
So we can find infinite perfect squares that end with the same two digits.
7/8 divided by 6 help me NOW please
Answer:
0.14583333333
Step-by-step explanation:
0.14583333333
Find the inverse of s.
= {(-2, -7), (0, -3), (2, 1), (4, 5), (5, 7)}
Answer:
( − 7 , − 2 ) , ( − 3 , 0 ) , ( 1, 2 ) , ( 5 , 4 ) , ( 7 , 5 )
From: iOE Your friend
:D :) *Be awesome.Be You*
A ____ is written as an if-then statement A.conjecture B.counterexample C.conditional D.negation
Answer: C
Definition of a conditional:
A conditional statement is a statement that can be written in the form “If P then Q,” where P and Q are sentences. For this conditional statement, P is called the hypothesis and Q is called the conclusion. Intuitively, “If P then Q” means that Q must be true whenever P is true.
Can anybody please help me out with this problem I would really appreciate it so much . Please and thank you
"Supplementary" angles add up to 180°.
Opposite angles are supplementary, so . . .
(12x - 4) + (19x - 2) = 180°
Clear the parentheses: 12x - 4 + 19x - 2 = 180°
Add up all the x's on the left side: 31x - 4 - 2 = 180°
Add up the plain old numbers on the left side: 31x - 6 = 180°
Add 6 to each side: 31x = 186°
Divide each side by 31 : x = 6°
Well ! Now that you know that x = 6° . . .
Angle EPC is (12x - 4)°
That's (12·6 - 4)°
Which is (72 - 4)°
Which is 68°
V=1/3(pie)r(squared)h Need to isolate h.
Answer:
[tex]\frac{v}{\frac{1}{3}\pi^{2}}=h[/tex]
Step-by-step explanation:
Divide V by everything you don't need on the right side.
So, You should end up with
[tex]\frac{v}{\frac{1}{3}\pi^{2}}=h\\[/tex]
Cheri paid $6.50 for the bunch of grapes with the weight of 2.5 pounds. What is the price per pound?
please help me and also show work plz
Answer:
[tex]\boxed{k = -6}[/tex]
Step-by-step explanation:
[tex]13 +\frac{k}{3} =11[/tex]
→ Multiply everything by 3
[tex]39 + k = 33[/tex]
→ Minus 39 from both sides to isolate k
[tex]k = -6[/tex]
What is the property of (4y + 1) x 0 =0
Answer: Zero Property
Step-by-step explanation:
Of 150 goldfish in the fish pound, 27 are red. What percentage of goldfish are red?
To get the percent, divide 27 by 150 then multiply the quotient by 100.
(27 / 150) * 100 = 18%
Bentley signed up for a streaming music service that costs $13 per month. The service allows Bentley to listen to unlimited music, but if he wants to download songs for offline listening, the service charges $0.75 per song. How much total money would Bentley have to pay in a month in which he downloaded 10 songs? How much would he have to pay if he downloaded s songs
Answer:
multiply 0.75 × 10 = 7..50
Write a ratio for the following description: Kaleel made three times as many baskets as John during a basketball practice.
Answer:
3:1
Step-by-step explanation:
If John makes 3, Then Kaleel makes 9, If John makes 1, Then Kaleel makes 3.
3a − 2a + 4 = 16 Solve for a.
Answer:
a=12
Step-by-step explanation:
[tex]3a-2a+4=16\\\\(3a-2a)+4=16\\\\(3-2)a+4=16\\\\1a+4=16\\\\a+4-4=16-4\\\\a=12[/tex]