A) The problem statement tells you it is a geometric sequence, so you know each term is some multiple of the one before. The first terms of the sequence are given, so you know the first term. The common ratio (the multiplier of interest) is the ratio of the second term to the first (or any term to the one before), -6/2 = -3.
So, the recursive definition is ...
... a_1 = 2
... a_n = -3·a_(n-1)
B) The explicit formula is, in general, ...
... a_n = a_1 · r^(n -1)
where r is the common ratio and a_1 is the first term. Filling in the known values, this is ...
... a_n = 2·(-3)^(n-1)
Answer:
a1=2
an=(an-1)(-3)
Step-by-step explanation:
Hope it helps. :)
A line has __________ dimension and is usually represented with two arrowheads.
one
two
three
Points that lie in the same plane are known as ___________ points.
collinear
coplanar
coordinate
1. A line has only a length dimension. It has no width or height. It is a one-dimensional object.
2. Points on the same line are collinear. On the same plane, they are called coplanar. Coordinates locate a point relative to some measurement reference.
PLZ HELP WILL MARK BRAINLEST SOLVE FOR X
[tex]\frac{x}{8} + 19 = 30[/tex] - subtract 19 from both sides
[tex]\frac{x}{8} = 11[/tex] - multiply both sides by 8
[tex]x = 88[/tex]
In this equation, x = 88.
If f(x) is a third degree polynomial function and g(x) = f(–2x), which of the following is NOT true?
f(x) and g(x) have the same x-intercepts.
f(x) and g(x) have the same y-intercepts.
f(2) = g(–1)
f(x) and g(x) have the same number of zeros
Answer:
f(x) and g(x) have the same x-intercepts (is not true)
Step-by-step explanation:
g(x) is a reflection across the y-axis and a horizontal compression of f(x). In general those transformations will move the x-intercepts. (The y-intercept and the number of x-intercepts will remain unchanged.)
_____
Comment on the question/answer
f(x) = x^3 is a 3rd degree polynomial. When transformed to g(x) = -8x^2, its only x-intercept (x=0) remains the same. The answer above will not apply in any instance where the only x-intercept is on the line of reflection. (The question is flawed in that it does not make any exception for such functions.)
The ratio AB to CB is
Answer:
1/3
Step-by-step explanation:
The ratio of AB to CB
AB/CB
3/9
Simplifying by dividing the top and bottom by 3
1/3
In kite JKLM , MJ=JK and ML=KL . Diagonals JL¯¯¯¯¯ and MK¯¯¯¯¯¯¯ intersect at point P, m∠MLK=48∘ , and m∠JKM=30∘ . What is m∠JML ?
Answer:
96°
Step-by-step explanation:
ΔKLM is isosceles, so base angle KML will be half the supplement of ∠MLK, or ...
.... ∠KML = (180° -48°)/2 = 66°
ΔKJM is also isosceles, so base angle JMK will be the same measure as ∠JKM, 30°.
∠JML = ∠JMK + ∠KML = 30° +66°
∠JML = 96°
Which expression represents the phrase?
Answer:
It would be C
Here's Why:
Sum means addition"Seven times the sum of a number" meaning a number times another number which represents 7nCarter has balance of -2,096.37 on his bank loan.He makes a payment and subtracts $500 of his debt.Then he decides to make a monthly payment to subtract $250 of the debt each month.What is the least number of months that Carter needs to make the monthly payment to pay off the original debt? Explain your thinking
7 months
Step-by-step explanation:After Carter makes his $500 payment, the balance on the loan is -1596.37. We want to find the number of months (m) such that ...
... -1596.37 +250m ≥ 0
... m ≥ 1596.37/250 . . . . add 1596.37, divide by the coefficient of m
... m ≥ 6.4
The least number of months that is more than 6.4 is 7 months.
_____
Comment on this answer
Carter's loan balance may also be affected by interest charged on the loan amount. We don't expect those charges to be so high as to require an additional month's payment.
(4x10^6) - (2x10^5)
Simplify!
the perimeter of a rectangle whose sides are lengths ( 4z + 3 ) units and ( 3z + 5 ) units
Answer:
14z + 16 is your perimeter
Step-by-step explanation:
To solve the perimeter, add all sides together. Note that in a rectangle, the opposite sides are congruent and parallel to each other.
Let Perimter = p
p = 2(4z + 3) + 2(3z + 5)
Simplify. Distribute the numbers.
2(4z + 3) = 8z + 6
2(3z + 5) = 6z + 10
Simplify. Combine like terms
p = 8z + 6 + 6z + 10
p = 14z + 16
14z + 16 is your perimeter
~
30 ounces = how many pounds and ounces
Answer: " 1 lb , 14 oz. " .
_________________________________________________
Step-by-step explanation:
_________________________________________________
Note the exact conversion: " 16 oz. = 1 lb. " .
→ {that is: " 16 ounces = 1 pound " .}.
_________________________________________________
30 oz. * ( 1 lb / 16 oz). = [tex]\frac{30}{16}[/tex] lbs. ;
= (30/2) / (16/2) lbs.
= (15 / 8) lbs. ;
_________________________________________________
1
8 ┌ 15
- 8
7 ;
______________________
The answer is equal to: " 1 7/8 lbs. " .
→ (1 lb) + (7/8) (lb). ;
______________________
→ (7/8) lb. = how many "oz." ??
_______________________
Note the exact conversion: " 1 lb. = 16 oz. " .
_______________________
→ [tex]\frac{7 lb}{8}[/tex] * [tex]\frac{16 oz}{1 lb}[/tex] ;
= [tex]\frac{7}{8} * \frac{16}{1}[/tex] oz. ;
→ The "8" cancels to a "1" ; and the "16" cancels to a "2" ;
→ {since: " {16 ÷ 8 = 2 } " ;
and: {since: " {8 ÷ 8 = 1 } " .
_______________________________________________
→ So we can rewrite as:
_______________________________________________
→ [tex]\frac{7}{1} * \frac{2}{1}[/tex] oz. ;
= { 7 * 2 } oz. ;
= 14 oz.
_______________________________________________
→ So:
_______________________________________________
→ " 30 oz. " = " (1 lb) + (7/8) lb. " ;
= " 1 lb. + 14 oz. " ;
= " 1 lb , 14 oz. " .
_______________________________________________
→ The answer is: " 1 lb , 14 oz. " .
_______________________________________________
Let us check our answer:
→ Does: " 1 lb. + 14 oz. = ? 30 oz. ? " ;
_______________________________________________
Note the exact conversion: " 1 lb. = 16 oz. " .
_______________________________________________
→ Does: " 16 oz. + 14 oz. = ? 30 oz. ?? " ;
_______________________________________________
₁
16 oz
+ 14 oz
30 oz.
_______________________________________________
→ Does: " 30 oz. = ? 30 oz. ? " ??? ; → Yes!
_______________________________________________
Hope this helps!
Best wishes to you in your academic endeavors
— and within the "Brainly" community!
_______________________________________________
Plz Help ASAP WILL MARK BRAINIEST Solve for x:
Answer:
The correct answer is 5.34
Step-by-step explanation:
you can double check this by multiplying .6 and 8.9
Answer:
x = 5.34
Step-by-step explanation:
x/ .6 = 8.9
We want to solve for x, which means we want x by itself.
Multiply each side by .6
x/ .6 * .6= 8.9 * .6
x = 5.34
A computer printer cost $100. Ink cartridges for the printer cost $25 each. How could you determine the overall cost of printer?
Answer: does the printer come with a starter pack of ink? how many ink cartridges does it take? A standard printer takes pink, blue, black, and yellow.
Step-by-step explanation:
1) $100 for printer
2) $25 for each cartridge
total cost if take 4 cartridges:
$200
Answer:
25*x+100
Step-by-step explanation: You do 25 multiplied by the number of cartridges (x) and then add 100 for the cost of the printer. For example, if you buy 5 cartridges, it would be, 25*5+100 and then it would equal 225 or 225 dollars for the overall cost of the printer.
Pat bounces a basketball 25 times in 30 seconds. At that rate, approximately how many fimes will Pat bounces the ball in 150 seconds?
Answer:
125 times
Step-by-step explanation:
Set up the proportion
25 times/ 30 seconds = x / 150 seconds Multiply by 150
25 * 150 / 30 = x
3750 / 30 = x
x = 125
He will be able to bounce the ball 125 times
Answer:
The ball will bounce 125 times
Step-by-step explanation:
We can use ratio's to solve this problem. I will put how many times the basketball is bounced on top and how many seconds on the bottom.
25 times x times
------------- = ----------------
30 seconds 150 seconds
Using cross products
25 * 150 = 30 * x
Divide each side by 30
25*150/30 =30*x/30
25 * 5 = x
125 =x
once out of every two weeks of the year would be how may days through out the year
Answer:
26 most years; 27 some years
Step-by-step explanation:
1 day out of 14 is 1/14 of the number of days in a year.
The number of days in a year depends on the year or years you're talking about. In all cases, there are not an integer number of weeks in a year, so days are left over. 365/14 = 26 1/14.
For example, if you're concerned with every other Monday, most years, there will be 26 of them, but every few years there will be 27. Over a period of 800 years, there will be exactly 71 years with 27 days of interest instead of 26. 800 is not divisible by 71, so the spacing will be uneven.
2x 2 - 4x + 6 = 0 is in general form.
2x² - 4x + 6 = 0 /:2
x²-2x+3=0
Δ=(-2)²-4·1·3=4-12=-8<0
x∈∅
False. A, B, and C does not have a greatest common factor of 1 which means this ewuation is not in general form.
If f(x) = x^3 – x^2 – 3, which of the following is equal to g(x) = f(2 – x)?
–x^3 + 5x^2 – 8x + 1
–x^3 + 7x^2 – 16x – 15
x^3 + 5x^2 + 8x + 1
x^3 – 7x^2 + 16x – 15
Answer:
–x^3 + 5x^2 – 8x + 1
Step-by-step explanation:
You can observe that expanding f(2-x) will give you a sum that includes (2-x)³, so will have a -x³ term. This narrows the choices to one of the first two.
If x=0, then you have ...
... f(2) = 2^3 -2^2 -3 = 8 - 4 - 3 = 1 . . . . corresponds to the first selection
_____
Worked in detail
f(2-x) = (2-x)³ -(2-x)² -3 . . . . substitute 2-x for x in the expression for f(x)
... = (2³ -3·2²x +3·2x² -x³) -(2² -2·2x +x²) -3
... = -x³ +5x² -8x +1 . . . . . matches the first selection
_____
Using ...
... (a+b)³ = a³ + 3a²b +3ab² +b³
... (a+b)² = a² +2ab +b²
the temperature in Tampa was 55°F at 5a.m . It rose 7°every hour for the next 2 hours and then rose 8° every hour for 3 hours after that. It then remained constant until 3p.m. what was the temperature at noon.
Answer:
93 °F
Step-by-step explanation:
At 7 am, the temperature was 55 °F + 2×7 °F = 69 °F.
At 10 am, the temperature was 69 °F + 3×8 °F = 93 °F.
Since the temperature was constant until 3 pm, it was 93 °F at noon.
Quadrilateral QRST has two pairs of congruentes sides, but it is not a parallelogram. What figure is it? What further condition would have to satisfy to be a parallelogram?
Answer:
The correct answer is: [C]:
________________________________________________
" {The figure is a kite. To be a parallelogram, it would have to have pairs of opposite congruent sides, not just congruent sides. } ."
________________________________________________
Step-by-step explanation:
________________________________________________
Note that "all" squares are "parallelograms" ; and that "all" rectangles are
"parallelograms" ;
yet: "Not All parallelograms" are "squares" or "rectangles".
________________________________________________
The question asks:
________________________________________________
"Quadrilateral QRST has two pairs of congruent sides, but it is not a parallelogram.
What figure is it?
What further condition would have to satisfy to be a parallelogram? " .
________________________________________________
So; we can rule out:
________________________________________________
"Answer choices:
[A]: "The figure is a square..." ;
________________________________________________
[B]: "The figure is a rectangle..." ; AND :
________________________________________________
[D]: "The figure is a square..." .
________________________________________________
We are left with:
________________________________________________
Answer choice: [C]:
________________________________________________
" { The figure is a kite. To be a parallelogram, it would have to have pairs of opposite congruent sides, not just congruent sides. } " .
________________________________________________________
The frequency (F) and length (L) of a wave are related by the following formula: F x L = 3.0 x 1010. Consider that the wavelength of violet light is 1.3 x 10−8. What is the frequency of violet light?
Answer:
2.3 × 10^18
Step-by-step explanation:
Your formula tells you ...
... F × (1.3 × 10^-8) = 3.0 × 10^10
Dividing by the coefficient of F, you have ...
... F = 3.0/1.3 × 10^(10-(-8))
... F ≈ 2.3 × 10^18
Trevon is making payments on a car that costs $26,555. He makes 36 equal payments. If he rounds the equal payments up to the nearest whole dollar, about how much will he overpay after 36 months? Show your work to justify your answer.
Answer:
$13
Step-by-step explanation:
$26,555 ÷ 36 = 737.6388889 ≈ $738 per month
36 × 738 = $26,568
= $13
Answer:
$13 will be overpaid after 36 months if payments are rounded of to nearest whole number dollar.
Step-by-step explanation:
We are given the following in the question:
Total cost of car = $26,555
Number of equal installments made = 36
Payment of 1 installment =
[tex]\displaystyle\frac{\text{Toatl cost}}{\text{Number of installments}} = \frac{26555}{36} = 737.6389\$[/tex]
Rounding of to nearest whole number, payment of one installment = $738
Value of 36 installments of $738 each =
[tex]36\times 738 = 26568\$[/tex]
Money overpaid after 6 months =
[tex]26568 - 26555 = 13\$[/tex]
Thus, $13 will be overpaid after 36 months if payments are rounded of to nearest whole number dollar.
find the value of x.
Answer:
71.79 degrees
Step-by-step explanation:
The cosine is (adjacent side to angle) / (hypotenuse)
so the cosine of x = 5/16
to get x you multiply cosine by its inverse
(cos^-1 x)(cos x) = (cos^-1 x)(5/16)
= 71.79 degrees
Select linear or nonlinear to correctly classify each function.
Answer:
okiii i got the answers right here i hope this helps!
Step-by-step explanation:
oki so for the first one liner
the second it non liner
third is also non liner
and the lasst one is liner
Your class wants to know to most typical age of student in your class. It collects the ages of all students and the teacher. Which measures of central tendency would give you the best typical student age
Answer:
Median.
Step-by-step explanation:
Assuming the teacher is not of similar age to the students, their higher age would pull the mean higher than if the teacher were not included, where the median would not be pulled by this extreme value.
If (2−√3) is a root of a polynomial with integer coefficients, which of the following must be another root?
2√3
√3−2
2+√3
3−√2
Answer:
2+√3
Step-by-step explanation:
We know that roots with square roots come in pairs
so if we have a+ sqrt(b), we will also have a - sqrt(b)
Since one of the roots is 2 -sqrt(3), it must have another root of 2+ sqrt(3)
The conjugate of the root (2-√3) for a polynomial with integer coefficients is (2+√3), which must also be a root of the polynomial.
If (2-√3) is a root of a polynomial with integer coefficients, then by the Conjugate Root Theorem (which is a consequence of the Complex Conjugate Root Theorem), if the polynomial has real coefficients and a non-real root, then its complex conjugate must also be a root. However, since √3 is a real number and our expression involves only real numbers, in this context, we look for the conjugate in terms of radicals. Thus, the conjugate of (2-√3) would be (2+√3), which must also be a root of the polynomial.
The other options given, such as 2√3, √3-2, and 3-√2, do not satisfy the criteria of being the conjugate of (2-√3). They might be roots of some polynomial, but without the constraint of integer coefficients or known conjugate pairs, we cannot confirm that.
Simplify (2p+3)2 - (2p-3)2 (Give proper detailed answer with all steps)
Answer:
[tex]24p[/tex]
Step-by-step explanation:
There's a very useful pattern in factoring and multiplying binomials called a difference of squares, and it looks like this:
[tex](x+y)(x-y)=x^2-y^2[/tex]
We can use this difference of squares to factor the expression we've been given, setting [tex]x=2p+3[/tex] and [tex]y=2p-3[/tex] to obtain the expression
[tex](2p+3)^2-(2p-3)^2=[(2p+3)+(2p-3)][(2p+3)-(2p-3)][/tex] (1)
tackling each of the multiplicands on the right:
[tex](2p+3)+(2p-3)=2p+2p+3-3=4p[/tex] (Left)
[tex](2p+3)-(2p-3)=2p-2p+3-(-3)=3+3=6[/tex] (Right)
This simplifies the expression on the right of (1) to [tex]4p\cdot6[/tex], or simply [tex]24p[/tex].
a random generator is used to select an integer from 1 to 3 inclusive. What is the difference between the estimated probability that a 3 is generated and the actual probability that a 3 is generated?
1 2 3 3 3 2 2 1 1 1 2 3 1 1
A. 0.29
B. 0.33
C. 0.05
D. 0.04
Answer:
option no D
Step-by-step explanation:
AS it given that it is a random generator
so it will generate random integers between 1 and 3
so
possible sample space = {1,2,3}
Total no of out comes = 3
Estimated probability that 3 will occur will be obtained by dividing total no of outcomes with total no of possible events to occur
as the occurrence of event is only 1
so
Estimated probability = 1 /3 = 0.33333
Now
The experiment is performed
total outcomes = 14
Total no of like able events that 3 occurred = 4
Actual probability = 4 / 14
= 0.2857
Difference between actual and estimated probability is = 0.3333-0.2857
=0.0421
≅0.04
which is option D
Final answer:
The actual probability of a 3 being generated is 1/3, and the estimated probability from the given sequence is 4/14. The difference between the two probabilities is roughly 0.05, which corresponds to answer choice C.
Explanation:
The question refers to the probability of a random generator selecting the number 3 from a set of integers ranging from 1 to 3, where each number has an equal chance of being selected. The actual probability of the random generator selecting a 3 is 1/3, as there are three possible outcomes and each is equally likely. To find the estimated probability, we can look at the frequency of the number 3 in the provided set of generated numbers: (1 2 3 3 3 2 2 1 1 1 2 3 1 1). In this set, there are 4 occurrences of the number 3 out of 14 total numbers. Therefore, the estimated probability is 4/14 or approximately 0.2857. The difference between the estimated and actual probabilities is 0.3333 (actual) - 0.2857 (estimated) = 0.0476. When rounded to two decimal places, the difference is approximately 0.05. Thus, the correct answer to the question would be C. 0.05.
Evaluate the expression 8 to the second power + 3.8 - 10 * 2
Answer:
47.8
Step-by-step explanation:
8^2+3.8-10*2
64+3.8-20
47.8
if x equals 8 and y equals 0 are the lines perpendicular? Yes or no?
Answer:
yes it's perpendicular line
Step-by-step explanation:
A punter kicks a football upward with an initial velocity of 48 feet per second. After how many seconds does the ball hit the ground? Use the formula h=rt−16t2, where h represents height in feet and r represents the initial velocity (rate) in feet per second.
A. 3
B. 6
C. 8
D. 12
A. 3
Step-by-step explanation:Fill in the given values in the formula (h=0, r=48) and solve for t.
... 0 = 48t -16t²
... 0 = 16t(3 -t)
This is true for t = 0 and for t = 3.
The ball will take 3 seconds to hit the ground.
Answer:
A.3
Step-by-step explanation:
Please help me answer this question, thank youuu