Jordan will hike a 10 mile trail at a rate of 2 mi/h. Write a linear equation to represent the distance of the trail that Jordan still has to hike after x hours. What does the y-intercept of the equation represent?
Answer:
y = 10 -2x; 10 is the length of the trail
Step-by-step explanation:
Jordan's remaining distance starts at 10 miles, and decreases 2 miles each hour:
y = -2x +10
The y-intercept is the length of the trail.
Find a general term a, for the sequence whose first four terms are given.
1 /1,1/4,1/9,1/16
Answer:
an = 1/n^2
Step-by-step explanation:
We notice that the denominators are the squares of successive integers. The general term will be ...
[tex]\boxed{a_n=\dfrac{1}{n^2}}[/tex]
The fifth term of a geometric sequence is 32 and the eighth term is 4.
(a) Find the ratio. (2 marks)
(b) Find the first term. (2 marks)
(C) Find the sum of the first 50 terms of the sequence. (3 marks)
What is the first term?
Answer:
a. 1/2
b. 512
c. 1024
Step-by-step explanation:
The nth term of a geometric progression can be written as;
Tn = ar^n-1
where a is the first term, r is the common ratio and n is the term number
From the question;
Fifth term = ar^4 = 32
Eight term = ar^7 = 4
a. We want to find the common ratio
What to do here is that we can divide the 8th by the 5th term
ar^7/ar^4 = 4/32
r^3 = 1/8
r^3 = (1/2)^3
Thus r = 1/2
b. First term
we can make a substitution in any of the two given terms
Let’s use the fifth term
ar^4 = 32
a * (1/2)^4 = 32
a * 1/16 = 32
a = 16 * 32
a = 512
C. Sum of the first 50 terms
To calculate this, we use the sum of terms formula
Sn = a(1- r^n)/1-r
a = 512 , n = 50 and r = 1/2
Making the substitution;
Sn = 512(1-(1/2)^50)/1-1/2
Kindly note that (1/2)^50 will be infinitesimally small and will be close to zero
So we can approximate (1/2)^50 to be zero
Hence;
Sn = 512(1-0)/0.5
Sn = 512/0.5
Sn = 1024
3/2a-8=11 URGENT ANSWERRRRRRR
Answer:
38/3
Step-by-step explanation:
3/2a-8=11
3/2a=19 add 8 to each side
i forget the rest of the steps smh
Answer:
38/3
Step-by-step explanation:
3/2A-8=11
3A/2=11+8
3A/2=19 CROSS MULTIPLY
3A=38
A=38/3
Mr.Joseph recently received a notice that his average gas and electric bill would increase at the beginning of the year. He went online to see the amount of his last 12 bills. If his average bill over the past 12 month goes up 17%, what can he expect to pay on average next year.
Answer:
about 2,546
Step-by-step explanation:
Please help me with this question ASAP Inequalities 9+3/5x>81/5
Answer:
9+3/5x-(81/5)=0
Step-by-step explanation:
Kyle has $25 and gets a job walking Chihuahuas for $2 per hour. Sophia has $4 and walks Rottweilers for $9 per hour. How many hours will they both have to work to have the same amount of money?
Answer:
3 hours
Step-by-step explanation:
Let k represent Kyle's balance after h hours. Let s represent Sophia's balance after h hours. Then we have ...
k = 25 +2h
s = 4 +9h
We want to find h so that k=s:
25 +2h = 4 +9h
21 = 7h . . . . . subtract 4+2h
3 = h . . . . . . . divide by 7
If both work 3 hours, they will have the same amount of money.
Which sets of ordered pairs show equivalent ratios use the grid to help you check all that apply
Answer:
(2,2), (4,4), (6,6)
Step-by-step explanation:
2×1= 2
2×2 = 4
2×3 = 6
Answer:
2nd and 4th options are correct choices.
Step-by-step explanation:
From the incomplete picture given below, we have:
2nd = (2,2), (4,4), (6,6)
4th = (4,1), (8,2), (12,3)
Enjoy!
A ten-pin boeling ball has the volume of about 5374 cm^3. A cadlepin bolwing ball has a volume of about 48 in^3. About how much greater is the volume of ten-pin bowling ball than the volume of candlepin bowling ball.
Answer: 16122/144= 111.95
Step-by-step explanation: 5374cm^3=16122 48in^3=144= 111.95
what is 6.257 x 10^-7
Answer:
-62570000
Step-by-step explanation:
6.257× -10000000
-62570000
The property can be used to remove the parentheses in the expression 1.7(x + 9).
Answer: Distributive property
pleseeeeeeeeeeeeeee helllllllppppp fassttttty pleaseeeeeeeee
Answer:
0.10
Step-by-step explanation:
[tex]0.15 = \frac{15}{100} \\ 0.40 = \frac{40}{100} \\ 0.35 = \frac{35}{100} \\ [/tex]
Since all of them have the denominator as 100,
the total no. of sweets must be 100. So,
No of strawberries= 100-15-40-35
= 10
p(taking a strawberry sweet)= 10/100
= 0.10
Answer:
0.10
Step-by-step explanation: did work
i need help im to lazy right now (5y+3)(3y-6
Answer:
15y²-21y-18
Step-by-step explanation:
(5y+3)(3y-6)15y²-30y+9y-1815y²-21y-182x−1=34x+9
can someone solve this ?
Answer:
25
Step-by-step explanation:
9+25=34
What value of q satisfies this equation?
59 + 5q = 159 - 11
Answer:
0,454
Step-by-step explanation:
= 59 + 5q = 159q - 11
= 5q - 159q = 11 + 59
= 154q = 70
= q = 70 : 154
= q = 0,454
Answer:
89/5 or 17.8
Step-by-step explanation:
Write 821 in scientific notation
Answer:
8.21 x 102
Step-by-step explanation:
cus thats the answer
What is the best estimate for the value of the expression?
[34/8 - 16/3] -14/9
O -3
O -2 1/2
O 7
O 7 1/2
Answer:
-2 1/2
Step-by-step explanation:
Answer:
B
Step-by-step explanation:
-2 1/2
how do you solve 7 - x = -11 * EXTRA POINTS
Answer:
X = -18
Step-by-step explanation:
7-18=-11
7 - 5/2 (8r - 6) + 2r =32
Answer:
r=-5/9
Step-by-step explanation:
Factor out the 2 from the expression
Reduce the numbers with the greatest common factor 2
Distribute the 5
Add Like terms
And then divide to get r
X+y=-4
2x+4y=-12
Stop by substitution
Answer:
X=4-y
2(4-y)+4y=12
8-2y+4y=12
2y=12-8
2y=4
y=4/2
y=2
x=4-y
x=4-2
x=2
help me i have no clue
Answer:
It seems like D if I eyeball it.
solve this equation 3/10x-4=40-2x
I Am Pretty Sure The Answer Is x=440/23
Hope This Help's
) A train leaves Hamilton at 9.50 am and arrives in Wellington at 7.25pm. Work out, in hours and minutes, the time taken for this journey.
this is your answer.............
if it is 9:39 what time would it be a hour and a half later
Answer:
It would be 11:09
Answer:
11:09
Step-by-step explanation:
30 mins after 9:30 is 10pm,add an hour that's 11 pm plus the 9 additional minutes its 11:09
Solve the system of linear equation. 2x-5= 14
3x+2y = 40
Answer:
x=9.5, y=5.75
Step-by-step explanation:
2x-5=14, 3x+2y=40
focus on 2x-5=14 first:
2x-5=14 (add 5 to both sides) 2x=19(divide both sides by 2) x=9.5
Now subtitute x into the second equation and find y:
3(9.5)+2y=40(simplify) 28.5+2y=40(subtract 28.5 on both sides) 2y=11.5(divide both sides by 2) y=5.75
Two rectangles are similar. If the height of the first rectangle is 3 inches, and the height of the second rectangle is 9 inches, by what factor was the first rectangle changed?
Answer:
3.2
Step-by-step explanation:
3.2/1
1) 3(3x - 4) = -2(1 – 4x)
Answer:
x = 10
Step-by-step explanation:
3(3x - 4) = -2(1 - 4x)
9x - 12 = -2 + 8x
9x - 8x = -2 + 12
x = 10
Hope this helps!
Explain what mistake was made in the problem below and what should be the
right answer.
Student Work:
2(x + 4) – 8 = 3x+10-4
2x + 8–8 = 3x + 6
2x = 3x + 6
- 3x – 3x
X = 6
Answer:
Instead of moving the 3x to the opposite side of the equation they moved the 2x. And the correct answer is x=-6 not x=6.
Step-by-step explanation:
Student Work:
2(x + 4) – 8 = 3x+10-4
2x + 8–8 = 3x + 6
2x = 3x + 6
- 3x – 3x
X = 6
My work:
2(x+4)-8=3x+10-4
2x+8-8=3x+6
2x=3x+6
-x=6
x=-6
Can someone please check this chart I made for me?
Answer:
I think it's great.
Good job!
3/4 of a cup of pasta sauce for every 12 ounces whats the unit rate
Answer:
the unit rate is 1/4 every 4 ounces
Step-by-step explanation:
12/3=4 3/3=1 so 1/4 of a cup every 4 ounces.