write the first five terms of the geometric sequence with a1=-2 and common ratio r=-5/2
Answers
Answer:
option D
Step-by-step explanation:
First term is -2
common ratio = -5/2
To get second term we multiply first term -2 by common ratio -5/2
[tex]-2 * \frac{-5}{2} =\frac{10}{2} = 5[/tex]
To get third term we multiply second term 5 by common ratio -5/2
[tex]5 * \frac{-5}{2} =\frac{-25}{2}[/tex]
To get fourth term we multiply third term -25/2 by common ratio -5/2
[tex]\frac{-25}{2}*\frac{-5}{2} =\frac{125}{4}[/tex]
Option D is correct
The first five terms of the geometric sequence with a first term of -2 and a common ratio of -5/2 are -2, 5, -12.5, 31.25, and -78.125.
To find the terms of a geometric sequence, we start with the first term and multiply each subsequent term by the common ratio. In this case, the first term, a1, is -2 and the common ratio, r, is -5/2.
The first term (a1) is -2
The second term (a2) is -2*(-5/2) = 5
The third term (a3) is 5*(-5/2) = -12.5
The fourth term (a4) is -12.5*(-5/2) = 31.25
The fifth term (a5) is 31.25*(-5/2) = -78.125
Therefore, the first five terms of the sequence are -2, 5, -12.5, 31.25, and -78.125.
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Related Questions
x+2= √2 solve for x will give brainliest
Answers
Answer:
Our answer is [tex]x=-2+\sqrt{2}[/tex].
Step-by-step explanation:
To solve for x, we need to isolate the variable. We can do so by subtracting 2 to both sides.
[tex]x+2=\sqrt{2} \\x+2-2=-2+\sqrt{2} \\\\x=-2+\sqrt{2} \\[/tex]
Our answer is [tex]x=-2+\sqrt{2}[/tex].
To find the decimal, calculate with a calculator.
Use the dot product to find |v| when v=(-8,2)
Answers
Answer:
2√17
Step-by-step explanation:
V = (-8, 2)
|v| = √((-8)^2 + 2^2)
= √(64 + 4)
= √68
= √4* √17
= 2√17
Answer:
= 2 sqrt(17)
Step-by-step explanation:
To find the magnitude of v using the dot product
|v| = sqrt(v1*v1 + v2*v2)
= sqrt( -8*-8 + 2*2)
= sqrt(64+ 4)
= sqrt(68)
= sqrt(4*17)
= sqrt(4) sqrt(17)
= 2 sqrt(17)
On Friday, 537 people attended a play. On Saturday, 812 people attended the same play. About how many more people attended the play on Saturday than on Friday? Hiw did u estimate? Show your work
Answers
Answer:
275
Step-by-step explanation:
To find out how many more, we find the difference between the two values. We use the math operation subtraction to find the difference.
Friday had 537 and Saturday had 812. We subtract 812-537= 275.
275 more people attended Saturday than Friday.
Find the next two terms of the sequence: 80, ?40, 20, ?10, ______, ______. A) 20, 40 B) 1 2 , 1 4 C) 5, ? 5 2 D) ?30, ?40
Answers
Answer:
5, 5/2
Step-by-step explanation:
80, 40, 20, 10, ______,
80/40 = 2
40/20 = 2
We are dividing by 2 each time
10/2 =5 so the next term is 5
5/2 = 5/2
Can someone help me with these please?
Answers
Point-slope form: y-y1 = m(x-x1)
Standard form: ax + by = c
Slope-intercept form: y = mx+b
Start by finding the slope. We know it is negative since the line is decreasing. The slope is -4/3.
To create point-slope form, we need to get one point from the graph. Let's use (3,0).
[tex]y = -\frac{4}{3}(x-3)[/tex]
To create slope-intercept form, we need the slope and the y-intercept. The y-intercept is the point where our equation crosses the y-axis. For this equation, it is 4.
[tex]y = -\frac{4}{3}x + 4[/tex]
To get standard form, solve the equation in terms of C.
Point-slope form: y = -4/3(x-3)
Slope-intercept form: y = -4/3x + 4
Standard form: 4/3x + y = 4
Jim drank 2/5 of his water bottle and John drank 3/10 of his water bottle. How much did the both boys drink?
Answers
1. Convert 2/5 into 4/10
2. Add 4/10 and 3/10
If U = {natural numbers less than 20} and N = {factors of 18}, what is N
Answers
N={1,2,3,6,9,18}
This is from the answer key to this question;
N= {4, 5, 7, 8, 10, 11, 12, 13, 14, 15, 16, 17, 19.}
HELP!!!!!! I believe its B but I am not sure! :(
Answers
Answer:
A
Step-by-step explanation:
When solving for x as an exponent, we need to use logarithms in order to undo the operation and rearrange the terms. We use log rules to bring down the exponent and solve. Logarithms are the inverse operations to exponents and vice versa. We have one special kind of logarithm called the natural logarithm whose base is e. We write it as ln. Since our base is e here, we will use the natural logarithm to rearrange and isolate x.
[tex]e^{4x-1} =3[/tex]
We begin by applying the natural logarithm to each side.
[tex]ln(e^{4x-1}) =ln(3)[/tex]
Log rules allow use to rearrange the exponent as multiplication in front of the log.
[tex](4x-1)ln(e) =ln(3)[/tex]
ln e as an inverse simplifies to 1.
[tex](4x-1)(1)=ln(3)[/tex]
We now apply the inverse operations for subtraction and multiplication.
[tex]4x-1+1=1+ln(3)\\4x=1+ln(3)\\\frac{4x}{4} =\frac{1+ln3}{4} \\x =\frac{1+ln3}{4}[/tex]
Option A is correct.
25 POINTS! EXPLAIN FOR BRAINLIEST/THANK YOU.
Answers
By the polynomial remainder theorem, a polynomial [tex]p(x)[/tex] has a factor of [tex]x-c[/tex] if [tex]p(c)=0[/tex]. So all you need to do is check the value of [tex]f(x)[/tex] at [tex]x=1,3,-3,5,-5[/tex]. You should get
[tex]f(1)=-96[/tex] (so [tex]x-1[/tex] is NOT a factor)
[tex]f(3)=-96[/tex] (so [tex]x-3[/tex] is NOT a factor)
[tex]f(-3)=f(5)=f(-5)=0[/tex] (so the last three options are factors)
Answer:
the answer is c and yeah
Step-by-step explanation:
Kris has a box of 8 crayons. Silvia, s box has 6 times of many crayons as Kris box . How many crayons are in sylvia box
Answers
6•8=48
Hat is the position of 7 in the number 876,543? A. The ten-thousands place B. The hundreds place C. The tens place D. The thousands place
Answers
find the sum of the geometric series. 14-7+(7/2)-(7/4)+
Answers
28/3
Explanation:
Common ratio of the series is −12. Using formula for sum of an infinite geometric convergent series a1−r, the required sum would be 141+12=283
What is the growth factor of the following example? Assume time is measured in the units given.
Water usage is increasing by 3% per year.
Answers
Answer:
The growth factor is option c. 1.03 per year
Step-by-step explanation:
Growth rate: r = 3% = 3 / 100 → r = 0.03
Growth factor: b = 1+r
Replacing r by 0.03 in the formula above:
b = 1+0.03
b = 1.03
Answer: The growth factor is 1.03 per year
In triangle LNP, R is the centroid and LO = 30. Find LR and RO. Enter the answers as numbers.
Answers
Answer:
[tex]|LR|=20[/tex]
[tex]|RO|=10[/tex]
Step-by-step explanation:
The centroid divides the median in the ratio [tex]2:1[/tex].
Thus [tex]|LR|:|RO|=2:1[/tex]
This implies that,
[tex]|LO|:|RO|=3:1[/tex]
We were given that,
[tex]|LO|=30[/tex]
We substitute this value to obtain,
[tex]30:|RO|=3:1[/tex]
or
[tex]\frac{30}{|RO|}=\frac{3}{1}[/tex]
We cross multiply to get,
[tex]3|RO|=30\times 1[/tex]
We divide through by 3, to get,
[tex]|RO|=10[/tex]
We can observe from the diagram that
[tex]|LR|+|RO|=|LO|[/tex]
[tex]|LR|+10=30[/tex]
[tex]|LR|=30-10[/tex]
[tex]|LR|=20[/tex]
Ron buys pens from a store. 3 packs of blue pens cost $22.50 and 4 packs of black pens cost $34.00. How much would it cost Ron to buy 2 packs of blue pens and 3 packs of black pens?
Answers
How do the graphs of these function compare to one another?
Answers
Algebraic Expressions Write each phrase as an algebraic expression. 5 subtracted from y
Answers
List the first four terms of a geometric sequence with t 1 = 4 and t n = -3t n-1 .
Answers
[tex]t_1=4\\t_n=-3t_{n-1}\\\\t_2=-3\cdot4=-12\\t_3=-3\cdot(-12)=36\\t_4=-3\cdot36=-108[/tex]
Consider the scatter plot.
Scatter plot with line of best fit of y equals 0.75x plus five.
The line of best fit is y = 0.75x + 5.
Choose the best representation for the slope.
The slope of the line of best fit shows that each additional minute, the distance increases by 0.75 feet.
The slope of the line of best fit shows that each additional minute, the distance decreases by 5 feet.
The slope of the line of best fit shows that each additional minute, the distance decreases by 0.75 feet.
The slope of the line of best fit shows that each additional minute, the distance increases by 5 feet.
Answers
Answer:
The correct answer option is: The y-intercept of the line of best fit shows that when time started, the distance was 5 feet.
Step-by-step explanation:
We are given a scatter plot with a best fit line as shown on the given graph.
The equation of the best fit line is given by:
y = 0.75x + 5
So with the help of the equation and by looking at the given graph, we can conclude about the representation of the y intercept that the the y-intercept of the line of best fit shows that when time started, the distance was 5 feet.
Since the distance shown on the y axis is already 5 when the time started at 0 minutes.
There are 64 pretzels in a 16-ounce bag of chocolate covered pretezel. What is the rate of pretzels per ounce?
Answers
What is an equation of the line that is parallel to y=4x-1 and that passes through the point (-3,5)?
A. y=4x-3
B. y=4x+5
C. y=4x+17
D. y=-4x+17
Answers
Answer:
C. y=4x+17
Step-by-step explanation:
If we want to find a line parallel to y =4x-1, the slopes will have to be the same because parallel lines have the same slope. Knowing y= mx+b we know the slope of the old line is 4, so the slope of the parallel line is 4.
If we know the slope of the line and a point, we can use the point slope form of a line
y-y1 = m(x-x1)
y-5 = 4(x--3)
y-5=4(x+3)
Distribute the 4
y-5 = 4x+12
Add 5 to each side
y-5+5 = 4x+12+5
y = 4x+17
Answer: The answer is C. y=4x+17
Step-by-step explanation:
The other person was correct and i got an A<3
Someone please help with these questions
Answers
Question 4:
Statement Reason
1. [tex]\overline{AC}[/tex] and [tex]\overline{BD}[/tex] bisect at O 1. Given
2. O is the midpoint of [tex]\overline{AC}[/tex] and [tex]\overline{BD}[/tex] 2. Definition of bisector
3. [tex]\overline{AO}[/tex] ≅ [tex]\overline{CO}[/tex] and [tex]\overline{BO}[/tex] ≅ [tex]\overline{DO}[/tex] 3. Definition of midpoint
4. ∠AOB ≅ ∠COD 4. Vertical Angle theorem
5. ΔAOB ≅ ΔCOD 5. SAS postulate
6. ∠A ≅ ∠C 6. CPCTC
*****************************************************************************
Question 5:
Statement Reason
1. [tex]\overline{BD}[/tex] ≅ [tex]\overline{BC}[/tex] and [tex]\overline{AD}[/tex] ≅ [tex]\overline{CD}[/tex] 1. Given
2. [tex]\overline{BD}[/tex] ≅ [tex]\overline{BD}[/tex] 2. Reflexive Property
3. ΔABD ≅ ΔCBD 3. SSS Postulate
4. ∠1 ≅ ∠2 and ∠3 ≅ ∠4 4. CPCTC
5. [tex]\overline{BD}[/tex] bisects ∠ABC and ∠ADC 5. Definition of angle bisector
Solve 14.2 divided by 0.5 dhow your work and explain how you new where thr decamal point whas going to be
Answers
Final answer:
To solve the division problem 14.2 divided by 0.5, you can use the long division method. The quotient is 28.4.
Explanation:
To solve the division problem 14.2 divided by 0.5, we can perform the long division method. Here's the step-by-step process:
Place the dividend, 14.2, inside the division bar.Place the divisor, 0.5, outside the division bar.Divide the first digit of the dividend, which is 1, by the divisor. The result is 2.Write down the quotient, 2, above the division bar.Multiply the quotient, 2, by the divisor, 0.5, which gives you 1.Subtract the product, 1, from the first digit of the dividend, 1, which gives you a remainder of 0.Bring down the next digit, which is 4, from the dividend.Divide the new dividend, 4, by the divisor, 0.5. The result is 8.Write down the new quotient, 8, next to the previous quotient.Multiply the new quotient, 8, by the divisor, 0.5, which gives you 4.Subtract the product, 4, from the new dividend, 4, which gives you a remainder of 0.Since there is no remainder anymore, the division is complete. The final quotient is 28.4. Therefore, 14.2 divided by 0.5 is equal to 28.4.
Ms.Rochelle wants to put her 29 students into groups of 6. How many groups of 6 can she make? If she puts any remaining students in a smaller group, how many students will be in that group?
Answers
Answer:
A. 4 groups of 6 students in each group.
B. The smaller group will have 5 students.
Step-by-step explanation:
We have been given that Ms.Rochelle wants to put her 29 students into groups of 6.
A. To find the number of groups of 6 that can be made from 29 students, we will find the greatest multiple of 6 from 29.
Multiples of 6 are: 6, 12, 18, 24, 30, 36,...
We can see that the greatest multiples of 6 in 29 in 24.
[tex]\text{Number of groups that can be made with 29 students}=\frac{24}{6}[/tex]
[tex]\text{Number of groups that can be made with 29 students}=4[/tex]
Therefore, Ms. Rochelle can form 4 groups from 29 students with 6 students in each group.
B. To find the number of students in small group, we will subtract 24 from 29.
[tex]\text{Number of students in the small group}=29-24[/tex]
[tex]\text{Number of students in the small group}=5[/tex]
Therefore, If Ms. Rochelle puts any remaining students in a smaller group, the number of students in smaller group will be 5.
HELPP! Calculate S22 for the arithmetic sequence in which a12=2.4 and the common difference is d=3.4
Answers
Answer:
S22 for the arithmetic sequence is:
First option: 15.4
Step-by-step explanation:
a12=2.4
d=3.4
S22=?
Sn=(a1+an)n/2
n=22
S22=(a1+a22)22/2
S22=(a1+a22)11
ak=aj+(k-j)d
a12=a1+(12-1)d
2.4=a1+11(3.4)
2.4=a1+37.4
Solving for a1: Subtracting 37.4 both sides of the equation:
2.4-37.4=a1+37.4-37.4
Subtracting:
-35=a1
a1=-35
a22=a12+(22-12)d
a22=2.4+10(3.4)
a22=2.4+34
a22=36.4
S22=(a1+a22)11
S22=(-35+36.4)11
S22=(1.4)11
S22=15.4
Find X
I have no idea how to make it
Answers
Answer: 5
Step-by-step explanation:
The length of the midsegment is one-half the length of the base. So,
Base = 2(midsegment)
7x + 1 = 2(4x - 2)
7x + 1 = 8x - 4
1 = x - 4
5 = x
Justin's rice ball recipe uses 100 grams of rice to make 11 rice ball. Justin has 700grams of rice. How many rice balls can Justin make with 700 grams of rice?
Answers
Answer: I TINK 77 rice balls
Step-by-step explanation:
Answer:77
Step-by-step explanation:
Someone help me please 30 points
Answers
Answer:4.-37 5.-6 6.-33 11.-20 12.-16
13.19
Step-by-step explanation:
Answer:
1. -41
2. -40
3. -4
4. -37
5. -24
6. -33
8. -47
9. 14
10. 59
11. -20
12. -16
13. 19
Need help fast please
Answers
Answer:
13. The slope for a line that is perpendicular to the line y=4x+8 is -1/4
14. The slope for a line that is perpendicular to the line x=-6 is 0
15. The equation for a line that is perpendicular to the line 8x-4y=12 and passes through the origin is y = - (1/2) x
16. The equation for a line that is perpendicular to the line y=-(1/3)x and passes through the point (0,-10) is y=3x-10
Step-by-step explanation:
13. What is the slope for a line that is perpendicular to the line y=4x+8?
y=mx+b
Comparing with the form slope-intercept, the slope of the given line is the coefficient of x, then the slope of the given line is 4.
A line perpendicular to y=4x+8 must have a slope opposite and inverse, then:
Slope of the perpendicular = - 1/4
14. What is the slope for a line that is perpendicular to the line x=-6?
The line x=-6 is a vertical line. A line perpendicular to the line x=-6 must be a horizontal line (Angle=0°), then:
Slope of the perpendicular = tan Angle = tan 0° = 0
15. Write the equation for a line that is perpendicular to the line 8x-4y=12 and passes through the origin.
8x-4y=12
Isolating y: Subtracting 8x both sides of the equation:
8x-4y-8x=12-8x
-4y=-8x+12
Dividing all the terms by -4:
-4y/(-4)= -8x/(-4)+12/(-4)
y=2x-3
The slope of the given line is 2
The slope of the perpendicular is m=-1/2 (opposite and inverse to the slope of the given line)
The perpendicular passes through the origin:
P1=(0,0)=(x1,y1)→x1=0, y1=0
Using the equation point - slope:
y-y1=m(x-x1)
Replacing the known values:
y-0=(-1/2)(x-0)
y=(-1/2)x
16. Write an equation for a line that is perpendicular to the line y=-(1/3)x and passes through the point (0,-10).
The slope of the given line is -(1/3)
The slope of the perpendicular is m=3/1→m=3 (opposite and inverse to the slope of the given line)
The perpendicular passes through the point:
P1=(0,-10)=(x1,y1)→x1=0, y1=-10
Using the equation point - slope:
y-y1=m(x-x1)
Replacing the known values:
y-(-10)=3(x-0)
y+10=3x
Isolating y: Subtracting 10 both sides of the equation:
y+10-10=3x-10
y=3x-10
The slope of the line below is-1/7Write a point-slope equation of the line using the coordinates of the labeled point.
Answers
Answer:
While you do not have the coordinates included, you can use the point-slope form of the equation and input the slope. This would be:
y - y1 = -1/7(x - x1)
In this equation, simply put the ordered pair in at x1 and y1. This will give you the full point-slope equation.