Point B has coordinates (1,2). The x-coordinate of point Ais - 11. The distance between point A and
point B is 13 units. What are the possible coordinates of point A?
4x^2+2x-1=0 in quaratic equations
Answer:
Step-by-step explanation:
"quaratic" should be "quadratic."
The coefficients of this quadratic are 4, 2 and -1. Thus, the discriminant is
b^2 - 4ac, or here, 4 - 4(4)(-1) = 20
Since the discriminant is positive, our quadratic has two real, different roots.
-2 ± (√4)(√5)
The roots are: x = ---------------------
2(4)
-1 ± √5
This reduces to x = ---------------
8
Seats in a theater are curved from the front row to the back. The front row has 10 chairs, the second has 16 and the third has 22, and so on.
A. Write a recursive rule for this series
B. Write an explicit rule for this series
C. Using the explicit formula, find the number of chairs in row 5
D. The auditorium can hold 17 rows of chairs. Write a sigma notation for this series, and then use either series formula to calculate how many chairs can fit in the auditorium
Answer:
The first term is 10.
The second term is 16
The third term is 22.
We can see that the first term plus 6, is:
10 + 6 = 16
Then the first term plus 6 is equal to the second term.
And the second term plus 6 is:
16 + 6 = 22
Then the second term plus 6 is equal to the third term.
A) As we already found, the recursive rule is:
Aₙ = Aₙ₋₁ + 6
B) The explicit rule is:
Aₙ = A₁ + (n - 1)*6
Such that A1 is the first term, in this case A₁ = 10
Then:
Aₙ = 10 + (n - 1)*6
C)
Now we want to find A₅, then:
A₅ = 10 + (5 - 1)*6 = 34
There are 34 chairs in row 5.
D)
Here we have 17 rows, then we can have 17 terms, this means that the total number of chairs will be:
C = A₀ + A₁ + ... + A₁₆
This summation can be written as:
∑ 10 + (n - 1)*6 such that n goes from 0 to 16.
The formula for the sum of the first N terms of a sum like this is:
S(N) = (N)*(A₁ + Aₙ)/2
Then the sum of the 17 rows gives:
S(17) = 17*(10 + (10 + (17 - 1)*6)/2 = 986 chairs.
There are total 986 chairs in the considered auditorium and there are 34 chairs in the fifth row.
The recursive rule for this series is: [tex]T_n = T_{n-1} + 6[/tex]The explicit rule for this series is: [tex]T_n = 6n + 4[/tex]What is recursive rule?A rule defined such that its definition includes itself.
Example: [tex]F(x) = F(x-1) + c[/tex] is one such recursive rule.
For this case, we're provided that:
Seats in rows are 10 in front, 16 in second, 22 in third, and so on.
10 , 16 , 22 , .....
16 - 10 = 6
22 - 16 = 6
...
So consecutive difference is 6
If we take [tex]T_i[/tex] as ith term of the series then:
[tex]T_2 - T_1 = 6\\T_3 - T_2 = 6\\T_4 - T_3 = 6 \\T_5 - T_4 = 6\\\cdots\\T_{n} - T_{n-1} = 6[/tex]
Thus, the recursive rule for the given series is [tex]T_{n} - T_{n-1} = 6[/tex] or [tex]T_n = T_{n-1} + 6[/tex]
From this recursive rule, we can deduce the explicit formula as:
[tex]T_n = T_{n-1} + 6\\T_n = T_{n-2} + 6 + 6\\\cdots\\T_n = T_{n-k} + k \times 6\\T_n = T_1 + 6(n-1)\\T_n = 10 + 6(n-1) \: \rm (as \: T_1 = 10)\\[/tex]
Thus, the explicit rule for this series is [tex]T_n = 10 + 6(n-1)[/tex]
For 5th row, putting n = 5 gives us:
[tex]T_n = 10 + 6(n-1) = 6n + 4\\T_5 = 6(5) + 4 = 34[/tex]
If the auditorium has 17 rows, then total chairs are:
[tex]T = T_1 + T_2 + \cdots + T_{17} = \sum_{n=1}^{17} T_n\\\\T = \sum_{n=1}^{17} (10 + 6(n-1))\\\\T = \sum_{n=1}^{17} (6n + 4)\\\\T = 6\sum_{n=1}^{17} n + \sum_{n=1}^{17}4 = 6\sum_{n=1}^{17} n + 4 \times 17\\\\T = 6\left( \dfrac{17(18)}{2}\right) + 68 = 918 + 68\\\\T = 986[/tex]
(it is because [tex]\sum_{k=1}^n k = 1 + 2 + \cdots + n = \dfrac{n(n+1)}{2}[/tex] )
Thus, there are total 986 chairs in the considered auditorium. There are 34 chairs in the fifth row. The recursive rule for this series is: [tex]T_n = T_{n-1} + 6[/tex] The explicit rule for this series is: [tex]T_n = 6n + 4[/tex].
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Need someones help on this!
Answer this question please
Hannah had 30 dollars to spend on 3 gifts. She spent 8 7 10 dollars on gift A and 4 2 5 dollars on gift B. How much money did she have left for gift C? Solve
Answer: [tex]\$16\dfrac{9}{10}[/tex]
Step-by-step explanation:
Given
Hannah had 30 dollars
Money spent on gift A
[tex]8\ \dfrac{7}{10}=\dfrac{8\times 10+7}{10}=\dfrac{87}{10}[/tex]
money spent on gift B
[tex]4\ \dfrac{2}{5}=\dfrac{22}{5}[/tex]
Money spent on gift C
[tex]\Rightarrow \text{Total-Money spent on (A+B)}\\\\\Rightarrow 30-\dfrac{87}{10}-\dfrac{22}{5}=30-\dfrac{87}{10}-\dfrac{44}{10}\\\\\Rightarrow \dfrac{300-87-44}{10}=\dfrac{169}{10}\\\\\Rightarrow \$16\ \dfrac{9}{10}[/tex]
An English teacher reviewed 2/3 of an essay in 1/4 of an hour. At this rate, how many essays can she review in 1 hour?
Answer: 2 2/3
Step-by-step explanation:
Answer:
2 2/3
Step-by-step explanation:
What is the length of AC
A)72
B)8
C)None of these
D)136
E)132
F)96
Factor the expression using the GCF.
42 – 12 =
Answer:
30
Step-by-step explanation:
Well 42
-
12
30
Will mark brainliest for the **CORRECT** answer!
Answer:
4x + 12x = 320
16x = 320
x = 20
Step-by-step explanation:
This is because the diagram shows 4x + 12x and the total being, 320.
4x + 12x = 16x
and 320/16 = 20
so x = 20
hope this helped :)
3 of the 100 digital video recorders (DVRs) in an inventory are known to be defective. What is the probability you randomly select an item that is not defective?
Answer:
97/100
Step-by-step explanation:
Probability calculates the likelihood of an event occurring. The likelihood of the event occurring lies between 0 and 1. It is zero if the event does not occur and 1 if the event occurs.
For example, the probability that it would rain on Friday is between o and 1. If it rains, a value of one ids attached to the event. If it doesn't a value of zero is attached to the event.
Probability that the DVRs is not faulty = total number of faulty videos / total number of videos
total number of faulty videos = 100 - 3 = 97
total number of videos = 100
97/100
help me out and ill give brainliest
Answer:
C
Step-by-step explanation:
Y= MX (The Slope which is Rise/Run) minus 2 (The Y-Intercept).
Solve each equation mentally
5
7
9
4
In percents?
Answer:
Convert the decimal to a percentage by multiplying the decimal by
100 .
500%
700%
900%
400%
Use the box method to distribute and simplify (2 + 1)(2x - 3). Drag and drop the
terms to the correct locations of the table.
Answer:
2x^2-x-3
(2x)(-3)
(x)
(1)
Step-by-step explanation:
Distribute
(2x^2) (-3x)
(2x) (-3)
please help.
I need which letters to click
MULTIPLICACIÓN Y DIVISIÓN DE NÚMEROS ENTEROS
11. -2115 ÷ -9 =
12. 7854 ÷ -34
13. 3425 × -4 =
14. -7 × 5 × -3 =
15. 12 × -7 × 9 =
Andrea constructed a triangle. Angle 1 and 3 are the same size and angle 2 has a measurement of 70 degrees. What is the measurement of angle 1 and 3
Answer:
Step-by-step explanation:
By triangle sum theorem,
Sum of all angles of a triangle is 180°.
m∠1 + m∠2 + m∠3 = 180°
(m∠1 + m∠3) + m∠2 = 180°
2(m∠1) + 70° = 180° {Given → m∠1 = m∠3]
2(m∠1) = 110°
m∠1 = 55°
Therefore, m∠1 = m∠3 = 55°
Can you help me for these 3 questions.
Answer:
Step-by-step explanation:
1) a + a
2) 2n+4 = 6n
3) 1
4n = 4
n = 1
HELP ASAP!!! select all the descriptions that apply to the transformation!
Answer: A and B
Step-by-step explanation:
The shape is moving from right to left and down
Please Help!!! Unit 8: Right Triangles & Trigonometry Homework 6: Trigonometry Review
The value of x from the figure is [tex]cos^-1(\frac{14}{13} )[/tex]
Triangles and AnglesFrom the given diagram, we have the following
Adjacent = 14Hypotenuse = 13The required angle is x
Using the SOH CAH TOA identity
[tex]cos \theta =\frac{adj}{hyp}\\ cos \theta =\frac{14}{13}\\ \theta = arccos(\frac{14}{13} )[/tex]
Hence the value of x from the figure is [tex]cos^-1(\frac{14}{13} )[/tex]
Learn more on SOH CAH TOA here: https://brainly.com/question/22307176
Drag the operations signs to make the number sentence true. Use each operation sign once. +–×÷ 4 (3 2) 6 1 = 14
Answer: its 4x(3+2)-6÷ 1=14
Step-by-step explanation: in the picture
please help!! i will give brainliest.
Answer:
3/10 inches apart
Step-by-step explanation:
total miles based on 2" equals 33 miles can be found by solving this proportion:
2/33 = 6/x
2x = 198
x = 99
99 miles divided by 11 rest stops means each stop is 9 miles apart
now use new ratio of 1" equals 30 miles
1/30 = x/9
30x = 9
x = 9/30 or 3/10 inches
A farmer wants to seed and fence a section of land. Fencing costs $27 per yard. Grass seed costs $2 per square foot. How much does it cost to fence and seed the pasture? (No links)
Answer:
she have 29 seed for the pasture
18+2 =20
Because 18 is 2 numbers away from 20
Answer:
Yes, that is correct.
Step-by-step explanation:
Please show me step by step how to do this
Answer:
The next three terms of the sequence are 17, 21 and 25.
The 300th term of the sequence is 1197.
Step-by-step explanation:
The statement describes an arithmetic progression, which is defined by following formula:
[tex]p(n) = p_{1}+r\cdot (n-1)[/tex] (1)
Where:
[tex]p_{1}[/tex] - First element of the sequence.
[tex]r[/tex] - Progression rate.
[tex]n[/tex] - Index of the n-th element of the sequence.
[tex]p(n)[/tex] - n-th element of the series.
If we know that [tex]p_{1} = 1[/tex], [tex]n = 2[/tex] and [tex]p(n) = 5[/tex], then the progression rate is:
[tex]r = \frac{p(n)-p_{1}}{n-1}[/tex]
[tex]r = 4[/tex]
The set of elements of the series are described by [tex]p(n) = 1 + 4\cdot (n-1)[/tex].
Lastly, if we know that [tex]n = 300[/tex], then the 300th term of the sequence is:
[tex]p(n) = 1 + 4\cdot (n-1)[/tex]
[tex]p(n) = 1197[/tex]
And the next three terms of the sequence are:
n = 5
[tex]p(n) = 1 + 4\cdot (n-1)[/tex]
[tex]p(n) = 17[/tex]
n = 6
[tex]p(n) = 1 + 4\cdot (n-1)[/tex]
[tex]p(n) = 21[/tex]
n = 7
[tex]p(n) = 1 + 4\cdot (n-1)[/tex]
[tex]p(n) = 25[/tex]
The next three terms of the sequence are 17, 21 and 25.
The 300th term of the sequence is 1197.
A builder has an 6-acre plot divided into 1 4 -acre home sites. How many 1 4 -acre home sites are there?
Complete question :
A builder has an 6-acre plot divided into 1/4 -acre home sites. How many 1/4 -acre home sites are there?
Answer:
24 home sites
Step-by-step explanation:
Given :
Total size of land = 6 - acre
Size of each home site = 1/4 acre
Number of home sites obtainable from the 6-acre land :
Total size of land ÷ size of each home site ;
6 ÷ 1/4
6 * 4/1
= 24
Hence, 24 home sites are on the plot of land.
What does this equal to
|9-14|
Answer:
5
Step-by-step explanation:
An absolute value is NEVER negative.
|9 - 14| = |-5| = 5
Answer: 5
What is AB?
Triangle ACB is right angle triangle. The length of AC is 12 and BC is 35.
Answer:
the answer is 35
Step-by-step explanation:
because if BC is 35 that means AB will have to be that same because it's a triangle
The required value of AB is 33 units for the given right triangle.
What is the right triangle?A right triangle is defined as a triangle in which one angle is a right angle or two sides are perpendicular.
Triangle ACB is a right-angle triangle. The length of AC is 12 and BC is 35.
Pythagoras's theorem states that in a right-angled triangle, the square of one side is equal to the sum of the squares of the other two sides.
Assume BC is the hypotenuse,
Since this is a right triangle, use the formula AB² + AC² = BC² and substitute values of AC = 12 and BC = 35.
AB² + AC² = BC²
AB² + (12)² = (35)²
AB² + 144 = 1225
AB² = 1225 -144
AB² = 1081
AB = 32.8785
Rounded to two decimal places,
AB = 33 units
Therefore, the required value of AB is 33 units.
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WILL GIVE BRAINLIEST PLEASE HELP ASAP, BEST ANSWER GETES BRAINLIEST. NOT A SCAM AND ITS NOT CAP WHAT SO EVER
Answer:
A. 60 + x = 90
Step-by-step explanation:
Complementary angles add up to 90 degrees so
60 + x = 90
Answer:
The answer is A: 60 + x = 90
Step-by-step explanation:
Complimentary angles are two angles that add up to 90, so the equation 60 + x = 90 is what you need to use to find the complimentary angle. I hope this helps :)
