find the nth term of the following sequence
4, 7, 12, 19, 28
Answer:
[tex]n^2+3[/tex]
Step-by-step explanation:
4, 7, 12, 19, 28
The differences are 7-4=3, 12-7=5, 19-12=7, 28-19=9.
This is an arithmetic sequence since the differences are constant.
There must be [tex]n^2[/tex] in the nth term.
These are the next terms in the sequence:
4, 7, 12, 19, 28, 39, 52, 67, 84, 103, 124, 147, 172, 199, 228, 259, 292, 327, 364, 403, 444, 487, 532, 579, 628, 679, 732, 787, 844, 903, 964, 1027, 1092, 1159, 1228, 1299, 1372, 1447..
[tex]n^2 +c=4[/tex]
[tex]1^2+c=4[/tex]
[tex]c=4-1[/tex]
[tex]c=3[/tex]
Therefore, the nth term is [tex]n^2+3[/tex].
Answer:
nth term = n^2 + 3.
Step-by-step explanation:
4 7 12 19 28
The differences are in an arithmetic sequence so this is a quadratic sequence,
- the differences are 3, 5, 7, 9... which is an A.S.
The common difference of the A.S. is 2 so there is n^2 in the formula for the nth term.
By inspection , we see that each term is 3 more than the term number squared.
1^2 + 3 = 4
2^2 + 3 = 7
3^2 + 3 = 12
4^2 + 3 = 19 and so on.
We know that central angles are congruent, because it is given. We can say that segments AO, CO, BO, and DO are congruent because . Then by the congruency theorem, we know that triangle AOC is congruent to triangle BOD. Finally, we can conclude that chord AC is congruent to chord BD because .
Answer:
because they have the same shape and size, or if one has the same shape and size as the mirror image of the other.
Step-by-step explanation:
Answer:
Complete the missing parts of the paragraph proof.
Proof:
We know that central angles
✔ AOC and BOD
are congruent, because it is given. We can say that segments AO, CO, BO, and DO are congruent because
✔ all radii of a circle are congruent
. Then by the
✔ SAS
congruency theorem, we know that triangle AOC is congruent to triangle BOD. Finally, we can conclude that chord AC is congruent to chord BD because
✔ CPCTC.
how many times do you need to add 5 to 17 to reach the product of 6 and 7
Answer:
5
Step-by-step explanation:
The product of 6 and 7 is 42.
Let x be the number of times needed to add 5 to 17 to reach 42.
17 + 5x = 42
5x = 42 - 17
5x = 25
x = 5
Answer: I’m pretty sure it’s 5
Step-by-step explanation:
is xsquare+1/xsquare equal5 is quadratic or not
Answer:
Yes, it is a quadratic equation.
Step-by-step explanation:
Let's solve it to make it a quadratic equation:
=> [tex]\frac{x^2+1}{x^2} =5[/tex]
=> x²+1 = 5x²
=> 5x²-x²-1 = 0
=> 4x²-1 = 0
Comparing it with the standard form of quadratic equation i.e.
[tex]ax^2+bx+c = 0[/tex]
So, we get
a = 4 , b = 0 and c = -1
So, yes. It is a quadratic equation and it is a pure quadratic equation since b is equal to 0.
A car increases, then decreases, its speed. Which table could represent the speed of the car?
6
43
5
45
5
45
7
41
7
49
9
43
9
47
o
6
47
Time (min)
Speed (mph)
Time (min)
Speed (mph)
Time (min)
Speed (mph)
Time (min)
Speed (mph)
N00
il colloll
100
5
45
6
45
7
45
41
5
45
6
43
7
41
9
41
41
Answer:
The speed increases (45—>47—>49) then decreases (48—>47) over time.
Step-by-step explanation:
The table that represents the speed of the car that increases and decreases as time increases is Table B.
Option B is the correct answer.
What is speed?Speed is the ratio of the given distance and time.
It shows how fast an object is moving at a given time.
The formula is Distance / Time.
We can find the distance or time when the required values is given using this formula.
We have,
From the table,
We see that,
Time 5 6 7 8 9
Speed 45 47 49 48 47
This indicates that,
As time increases, the speed increased from 5 minutes to 7 minutes and decreases from 7 minutes to 9 minutes.
Thus,
The table that represents the speed of the car that increases and decreases as time increases are in Table B.
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Estimate 6 8 9 ( 1 9 10 ) by rounding to the nearest whole number. The estimate is the actual product because
Answer:
[tex]6\frac{8}{9} (1\frac{9}{10}) = 13[/tex]
Step-by-step explanation:
Given
[tex]6\frac{8}{9} (1\frac{9}{10})[/tex]
Required
Estimate
To do this; we start by converting both fractions to improper fraction
[tex]6\frac{8}{9} (1\frac{9}{10})[/tex]
[tex]\frac{62}{9} (1\frac{9}{10})[/tex]
[tex]\frac{62}{9} (\frac{19}{10})[/tex]
Open Bracket
[tex]\frac{62}{9} * \frac{19}{10}[/tex]
Combine to form a single fraction
[tex]\frac{62 * 19}{9 * 10}[/tex]
Multiply numerators and denominators
[tex]\frac{1178}{90}[/tex]
Convert fraction to decimal
[tex]13.0888888889[/tex]
Approximate to nearest whole number
[tex]13[/tex]
Hence, [tex]6\frac{8}{9} (1\frac{9}{10}) = 13[/tex]
Answer:
First box: 14
Second box: greater than
Third box: both factors were rounded up.
Step-by-step explanation:
I JUST DID IT AND GOT IT RIGHT!
HOPE IT HELPS!
Approximately how many liters are in 18 quarts?
Answer:
18 liquid quarts ≈ 17 litres
Answer:
18 us liquid quart =17.034 liters
Step-by-step explanation:
1) 1 us liquid quart = 0.946 liter
2) Multiply 0.946 *18 = 17.034
The numerator of a fraction is 2 less then its denominator. If 2 is subtracted from the numerator and 1 is the added to the denominator then the fraction becomed 1/2. Find the fraction.
Answer:
Probably, 3/1.
Step-by-step explanation:
Just do the reverse of the instructions and you get your answer.
1+2=3
2-1=1
Gretta created some figures that she calls reebs What attribute do these reebs have in common?
Answer:
Reebs have 1 right angle
Step-by-step explanation:
Look at all the reebs. They all have 1 right angle!
Answer:
C
Step-by-step explanation:
Four lines extend from point K. The space between lines K J and K N is 58 degrees. The space between lines K N and K M is 61 degrees. The space between lines K M and K L is 61 degrees. Which statement must be true about the diagram? Point K is a midpoint of Line segment J L. mAngleJKN = One-halfmAngleJKM Ray KM is an angle bisector of AngleNKL. JK = One-halfKL
Answer:
Ray KM is an angle bisector of [tex]\angle NKL[/tex].
Step-by-step explanation:
Given that there are 4 lines that are extended from a point K.
Angle between KJ and KN is [tex]58^\circ[/tex] i.e. [tex]\angle JKN =[/tex] [tex]58^\circ[/tex]
Angle between KN and KM is [tex]61^\circ[/tex] i.e. [tex]\angle NKM =[/tex] [tex]61^\circ[/tex].
Angle between KM and KL is [tex]61^\circ[/tex] i.e. [tex]\angle MKL =[/tex] [tex]61^\circ[/tex]
Please refer to the attached image for the conditions and dimensions of angles given in the question statement.
Now, let us have a look at the options given:
1. Point K is a midpoint of Line segment JL
JL is not a straight line first of all, and secondly there is no condition given about the line segments.
So, it is incorrect.
2. [tex]m \angle JKN = \dfrac{1}{2}m \angle JKM[/tex]
[tex]\angle JKN =[/tex] [tex]58^\circ[/tex] and
[tex]m \angle JKM =58+61=139^\circ\\\Rightarrow \dfrac{1}{2} m \angle JKM = 64.5^\circ[/tex]
So, it is also incorrect.
3. Ray KM is an angle bisector of [tex]\angle NKL[/tex].
Ray KM divides the [tex]\angle NKL[/tex] into two equal angles [tex]\angle NKM =[/tex] [tex]61^\circ[/tex] and [tex]\angle MKL =[/tex] [tex]61^\circ[/tex] so it is correct.
The given line passes through the points (-4, -3) and (4.
1)
What is the equation, in point-slope form of the line that is
perpendicular to the given line and passes through the
point (-4, 3)?
V-3 -2(x+4)
3-
2-
+
Oy-3 =-{(x+4)
Ov-3 = {(x + 4)
-2
y-3 =2(x + 4)
-3
(-3)
9514 1404 393
Answer:
y -3 = -2(x +4)
Step-by-step explanation:
The slope of the given line is ...
m = (y2 -y1)/(x2 -x1)
m = (1 -(-3))/(4 -(-4)) = 4/8 = 1/2
The perpendicular line will have slope -1/(1/2) = -2.
__
The point-slope equation of the line with slope m through point (h, k) is ...
y -k = m(x -h)
For point (-4, 3) and slope -2, the equation is ...
y -3 = -2(x +4)
4x= 2y + 38; 2 - 3y=x
Simultaneous equation please help
Answer:
x = 59/7, y = -15/7
Step-by-step explanation:
4x= 2y + 38;
2 - 3y=x
We can substitute for x in the first equation since the second equation is solved for x
4(2-3y) = 2y+38
Distribute
8 - 12y = 2y+38
Add 12y to each side
8-12y+12y = 2y+12y+38
8 = 14y+38
Subtract 38 from each side
-30 = 14y
Divide by 14
-30/14 = y
-15/7 = y
Now solve for x
2 - 3y = x
2 - 3*-15/7 = x
2 +45/7 = x
14/7 + 45/7 = x
59/7 =x
P(X< ) 1-P(X> ) A softball pitcher has a 0.626 probability of throwing a strike for each curve ball pitch. If the softball pitcher throws 30 curve balls, what is the probability that no more than 16 of them are strikes? Fill in the blanks below to represent the probability
Answer:
19.49% probability that no more than 16 of them are strikes
Step-by-step explanation:
Binomial probability distribution
Probability of exactly x sucesses on n repeated trials, with p probability.
Can be approximated to a normal distribution, using the expected value and the standard deviation.
The expected value of the binomial distribution is:
[tex]E(X) = np[/tex]
The standard deviation of the binomial distribution is:
[tex]\sqrt{V(X)} = \sqrt{np(1-p)}[/tex]
Normal probability distribution
Problems of normally distributed samples can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
When we are approximating a binomial distribution to a normal one, we have that [tex]\mu = E(X)[/tex], [tex]\sigma = \sqrt{V(X)}[/tex].
In this problem, we have that:
[tex]n = 30, p = 0.626[/tex]
So
[tex]\mu = E(X) = np = 30*0.626 = 18.78[/tex]
[tex]\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{30*0.626*0.374} = 2.65[/tex]
What is the probability that no more than 16 of them are strikes?
Using continuity correction, this is [tex]P(X \leq 16 + 0.5) = P(X \leq 16.5)[/tex], which is the pvalue of Z when X = 16.5. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{16.5 - 18.78}{2.65}[/tex]
[tex]Z = -0.86[/tex]
[tex]Z = -0.86[/tex] has a pvalue of 0.1949
19.49% probability that no more than 16 of them are strikes
Can I have some help please? Thanks!
Answer:
(22/7)/6=0.523809
Step-by-step explanation:
V=4/3πr^3
V=4/3π(1/2)^3=π/6
or (22/7)/6=0.523809
Please help help❤️help me it would mean a lot
Answer:
B. points C, F and G
Step-by-step explanation:
B. Points G C F
What is the range of this function?
If point OR=20 and point PR=5, what is OP(geometry)? please show work
Answer:
The length of OP is 25.
Step-by-step explanation:
The data provided is:
OR = 20
PR = 5
Assume that OR and PR are straight lines.
O_____________________R______P
Compute the length of OP as follows:
OP = OR + PR
= 20 + 5
= 25
Thus, the length of OP is 25.
What else would need to be congruent to show that ABC= A DEF by SAS?
B
E
Given:
AC DF
ZCZE
А
O A. BC = EF
O B. ZCEF
O C. ZAŁ ZD
O D. AC = DF
Answer:
A.
Step-by-step explanation:
BC ≅ EF
BC needs to be congruent to EF to show that ΔABC ≅ ΔDEF by SAS(Side -Angle-Side) Postulate.
x is equal to ____ degrees. Angle Y measures _____ degrees.
Answer:
x=62 and y=246
Step-by-step explanation:
x was given in the figure so x=62. and y=4x-2 so you substitute x by 62
y=4x-2
y=4*62-2
y=248-2=246
Please help with answers A and B :)
cereal is on sale for $3.60 for a 9-ounce box. what is the price per ounce?
Answer:
$0.40 per oz
Step-by-step explanation:
given that the cereal is $3.60 for a 9 oz box
i.e
9 oz ----> costs $3.60
1 oz ----> costs $3.60 ÷ 9 = $0.40
hence the unit rate is $0.40 per oz
Answer:
0.40 per ounce
Step-by-step explanation:
The question asks is to find the unit rate, or price per ounce.
To find this, we need to divide the price by the number of ounces.
price/ ounces
It costs $3.60 for 9 ounces of cereal.
$3.60/9 ounces
Divide $3.60 by 9 (3.60/9=0.4)
$0.4/ounce
It costs $0.40 per ounce of cereal.
What is being constructed based on the markings in the following diagram?
Inscribed regular hexagon
inscribed equilateral triangle
perpendicular line through a point off a line
perpendicular line through a point on a line
thank you :)
Answer:
perpendicular line through a point on a line
Step-by-step explanation:
The circle centered at C seems intended to produce point D at the same distance as point B. That is, C is the midpoint of BD.
The circles centered at B and D with radius greater than BC seems intended to produce intersection points G and H. (It appears accidental that those points are also on circle C. As a rule, that would be difficult to do in one pass.)
So. points G and H are both equidistant from points B and D. A line between them will intersect point C at right angles to AB.
Segment GH is perpendicular to AB through point C (on AB).
Answer:
Perpendicular line through a point on a line
Step-by-step explanation:
What is the value?
I’m so stuck :/
Answer:
15
Step-by-step explanation:
do PEMDAS
do parenthesis first so -3^2 plus 3 times 2
then do exponents so 9 plus 3 times 2
then multiplication so 9 plus 6
then addition so 15
hope this helps
Answer:
Hey!
Your answer is 15!!
Step-by-step explanation:
IF YOU NEED A FURTHER EXPLANATION PLS LET ME KNOW!
HOPE THIS HELPS!!
Write a mathematical sentence that expresses the information given below.
Use g as your variable name. If necessary:
type < = to mean <
or > Fito mean >.
The number of gallons of gas that were in the tank plus 13 more adds up to
76 gallons.
Answer:
g + 13 = 76
Step-by-step explanation:
We are told to use the variable "g" for the number of gallons of gas in the tank. When we add 13 to that, we are told the sum is 76. When all numbers are in gallons, this translates to ...
g + 13 = 76
Daniel expanded the expression as shown. Negative 2 (Negative 8 x minus 4 y + three-fourths) = negative 10 x minus 8 y minus 1 and one-fourth What errors did he make? Select three options.
Answer:
16x + 8y -3/2
Step-by-step explanation:
The expression can be represented mathematically as follows.
-2(-8x - 4y + 3/4) = - 10x - 8y - 1 1/4
-2(-8x - 4y + 3/4) = - 10x - 8y - 5/4
The first way to solve this expression is by opening the bracket by multiplying the outside values by the inner values.
-2(-8x - 4y + 3/4)
Multiply -2 by all the values in the brackets
-2 × - 8x = 16x not - 10x
-2 × - 4y = 8y not -8y
-2 × 3/4 = -6/4 = - 3/2 not -5/4
Bringing the value together the expected answer will be 16x + 8y -3/2 and not - 10x - 8y - 5/4.
Answer
A, B, and C
Step-by-step explanation:
Hope this helps!
In the first half of a basketball game, a player scored 9 points on free throws and then scored a number of 2-point shots. In the second half, the player scored the same number of 3-point shots as the number of 2-point shots scored in the first half. Which expression represents the total number of points the player scored in the game?
This question is incomplete
Complete Question
In the first half of a basketball game, a player scored 9 points on free throws and then scored a number of 2-point shots. In the second half, the player scored the same number of 3-point shots as the number of 2-point shots scored in the first half. Which expression represents the total number of points the player scored in the game?
a) 2x + 3x + 9
b) 2x + 3 + 9
c) 2x + 3x + 9x
d) 2 + 3x + 9
Answer:
a) 2x + 3x + 9
Step-by-step explanation:
Let the number of points shots a player scores = x
In a free throw, the player scored 9 points = 9
The player also scored a number of 2-point shots = 2x
In the second half, the player scored the same number of 3-point shots as the number of 2-point shots scored in the first half = 3x
The expression represents the total number of points the player scored in the game =
2x + 3x + 9
Which graph shows the line y- 1 = 2(x + 2)?
Answer:
Graph C
Step-by-step explanation:
The slope is 2 and to find the numbers in the equation are actually the opposite of what they appear, making the point (-2,1).
7th grade math I needs some help
Answer:
Step-by-step explanation:
To find 5e. El change, find the difference between week 1 and 1.
56.92-(-16.54) = 56.92+16.54 = -73.46.
Note: this is negative, because we are calculating the difference.
Hope this helps
If 96 out of 200 pet owners own cats, what fraction and what percentage of
pet owners do not own cats?
Check all that apply.
A. 52%
104
IL B.
200
C. 48%
D. 0.52%
E 96 help ASAP plz
200
Answer:
A. 52% and B. 104/200
Step-by-step explanation:
To find the answer, we first have to find how many pet owners own cats. As percentages are x/100, when we have x/200 we divide the numerator and denominator by 2 to bring the fraction to 48/100. (96/200 divided by 2 equals 48/100). Now that we have the percentage of pet owners that own cats (48%), we need to find how many do not own cats. To do so, we just subtract 100-48 to get 52. Then, we do the same to the fraction of 96/200. (200-96 = 104). This brings our answers to A. 52% and B. 104/200
The percentage of owners that do not own cat is 52%
What are percentages?A percentage is a number or ratio that can be expressed as a fraction of 100. If we have to calculate percent of a number, divide the number by the whole and multiply by 100. Hence, the percentage means, a part per hundred. The word per cent means per 100. It is represented by the symbol “%”.
Given here, 96 out of 200 pet owners own cats then the owners who do not own cat are 104
Therefore the number of non cat owners in percentage terms is
= (104/200) ×100
= 52.5%
Hence, the answer is 52.5%
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find the smallest square number that is divisible by each of the number 8,12,18 and 30
Answer:
3600.
Step-by-step explanation:
8 = 2*2*2
12= 2*3
18= 2*3*3
30 = 2*3*5
The lowest common multiple of the these is
2 * 2 * 2 * 3*3* 5 = 360.
So the smallest square number = 2*2*2*2*3*3*5*5
(We make all the sets of factors a square).
So it's 16 * 9 * 25 = 3600.
Answer:
3600
Step-by-step explanation: