Answer:
The ratio of the first term to the common difference is 1 : 2
Step-by-step explanation:
The rule of the sum of the AP is
[tex]S_{n}=\frac{n}{2}[2a+(n-1)d][/tex] , where
a is the first number
d is the common difference
n is the position of the number
∵ [tex]S_{10}[/tex] = 4 × [tex]S_{5}[/tex] ⇒ (1)
→ Find [tex]S_{10}[/tex] and [tex]S_{5}[/tex]
∵ In [tex]S_{10}[/tex] n = 10
∴ [tex]S_{10}=\frac{10}{2}[2a+(10-1)d][/tex]
∴ [tex]S_{10}=5[2a+9d][/tex]
∴ [tex]S_{10}[/tex] = 10a + 45d ⇒ (2)
∵ In [tex]S_{5}[/tex] n = 5
∴ [tex]S_{5}=\frac{5}{2}[2a+(5-1)d][/tex]
∴ [tex]S_{5}=2.5[2a+4d][/tex]
∴ [tex]S_{5}[/tex] = 5a + 10d ⇒ (3)
→ Substitute (2) and (3) in (1)
∵ 10a + 45d = 4[5a + 10d]
∴ 10a +45d = 20a + 40d
→ Subtract 40d from both sides
∴ 10a + 45d - 40d = 20a + 40d - 40d
∴ 10a + 5d = 20a
→ Subtract 10a from both sides
∴ 10a - 10a + 5d = 20a - 10a
∴ 5d = 10a
→ Divide both sides by 5
∴ d = 2a
→ That means d is twice a or a is half d
∴ a : d = 1 : 2
The ratio of the first term to the common difference is 1 : 2
To rent a bike, Max pays a flat rate of $5 plus an hourly rental fee. The graph shows the amount, C, in dollars, that Max pays based on the number of hours, t, that Max rents the bike. What is the rate of change in the cost to rent the bike with respect to the number of rental hours?
$5 per hour
$2.50 per hour
$2 per hour
$7.50 per hour
Answer:
C
Step-by-step explanation:
The rate of change in the cost to rent the bike with respect to the number of rental hours will be $2.5 per hour so option (B) will be correct.
What is a linear function?A straight line on the coordinate plane is represented by a linear function.
A linear function always has the same and constant slope.
The formula for a linear function is f(x) = ax + b, where a and b are real values.
In another word, a linear function is a function that varies linearly with respect to the changing variable.
The rate of change is also called the slope of the function.
Since it is a linear function so slope will remain constant.
Slope = difference in ys coordinate/difference in xs coordinate
Slope = (30-5)/(10-0) = 2.5
Hence "The rate of change in the cost to rent the bike with respect to the number of rental hours will be $2.5 per hour".
For more about the linear function,
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Solve the Inequality algebraically.
4|7 – x|– 5 > 15
Answer:
Step 1: Add 5 to both sides.
4(|−x+7|)−5+5>15+5
4(|−x+7|)>20
Step 2: Divide both sides by 4.
4(|−x+7|)÷4 > 20÷4
|−x+7|>5
Step 3: Solve Absolute Value.
|−x+7|>5
We know either−x+7>5 or −x+7<−5
−x+7>5(Possibility 1)
−x+7−7>5−7(Subtract 7 from both sides)
−x>−2
−x -1 > -2-1(Divide both sides by -1)
x<2
−x+7<−5(Possibility 2)
−x+7−7<−5−7(Subtract 7 from both sides)
-x-1 > -2-1( Divide both sides by -1)
x<2
−x+7<−5(Possibility 2)
−x+7−7<−5−7(Subtract 7 from both sides)
−x-1 < −12-1 (Divide both sides by -1)
x>12
Hope this helps!
A delivery truck driver charges a fixed base price of $6 for 2 miles. After 2 miles, he charges an additional $2 for every mile. After 6 miles, he
charges an additional S4 for every mile.
Describe the cost of the delivery truck between 1 mile and 2 miles.
Answer:
the anser is 3 for one mile and 6 for two
Step-by-step explanation:
he charges 6 2 miles so have of six is 3 so one mile is 3$ and 2 is 6 they add the extra stuff to confuse you
What is the equation in slope-intercept form of the line that passes through the points(−4,2) and (12,6)
carlos biked 139/8 miles on Saturday and 135/7 miles on sunday which day did he ride further and by how much
Answer: Sunday by 2 miles
Step-by-step explanation:
Answer: sunday
Step-by-step explanation:
As the lighted part of the moon appears to get smaller, we say that the moon is _______.
Question 2 options:
waxing
swelling
disappearing
waning
Answer:
i pretty sure it is waxing
Step-by-step explanation:
!!!!Translate the sentence into an inequality!!!!!
The sum of 9 and x is greater than or equal to 27.
Answer:
I got you my man 9 is greater than.
Step-by-step explanation:
2 1/3 × 3 1/5 what is the simplified answer because im stuck....
Answer:
[tex] 7 \frac{7}{15} [/tex]
Step-by-step explanation:
[tex]2 \frac{1}{3} \times 3 \frac{1}{5} \\ \\ = \frac{2 \times 3 + 1}{3} \times \frac{3 \times 5 + 1}{5} \\ \\ = \frac{6 + 1}{3} \times \frac{15 + 1}{5} \\ \\ = \frac{7}{3} \times \frac{16}{5} \\ \\ = \frac{7 \times 16}{3 \times 5} \\ \\ = \frac{112}{15} \\ \\ = 7 \frac{7}{15} [/tex]
A kilobyte is 210 bytes and a megabyte is 220 bytes. How many kilobytes are in a megabyte?
Answer: 1.05 bytes (1.04761905)
Explanation: The operation to use when you need to find how much of something is in another is division. And since we're trying to find out how many kilobytes are in a megabyte, you'd need to divide 220 by 210. After doing so, you should get a quotient of 1.04761905. When a remainder is present, you can round it up. I chose to round up by the nearest hundredth. Therefore, there are 1.05 kilobytes in a megabyte.
I hope this helped!
Good luck <3
Problem 5
Please help
what is the slope of the line ? (100 points)
Answer:
y ≈ 4x + -2
Step-by-step explanation:
Answer: 8/2 or 4
Step-by-step explanation:
What is 2(n-3) = 4n +1
Answer:
n=-3.5
Step-by-step explanation:
my picture look at it. the answer is wrong but it's the same steps.
Answer:
n = (-3.5)
Step-by-step explanation:
. The wheel is divided into eight same-sized sections, and three of those sections represent winning a gift certificate. Assuming the wheel is fair, approximately how many gift certificates are likely to be won if 528 customers spin the wheel
The probability of winning is 3/8 since there are 3 winning spaces out of 8 total.
We expect to have (3/8)*528 = 198 winners
Note how if we had 198 winners out of 528 total players, then the empirical probability of winning is 198/528 = 3/8
all of the following are possible effects of increased global temperatures except
Answer:
Cold fronts or blizzards
Step-by-step explanation:
The length of an actual tunnel is 480 miles. If one inch represents 80 miles, what is the length of the tunnel on a scale drawing
Answer:
8in
Step-by-step explanation:
start by dividing 480mi by 60mi and you get 8in
check your answer by multiplying 60x8
The two lines intersected by the transversal are barrel. What is the value of x?
A. 9
B. 7
C. 11
D.29
What are 2 other names for line QR
Answer:
QR and RQ are the other two names of QR.
If my answer helped, please mark me as the brainliest!!
Thank You!!
Answer:
Step-by-step explanation:
rq and qr
Andrea has 8 red buttons and 9 blue buttons. How many buttons does Andrea have?
Answer:
17 buttons
Step-by-step explanation:
Answer: 17
Step-by-step explanation:
8 + 9 = 17
what’s The definition of linear in Math
Answer: Linearity is the property of a mathematical relationship that can be graphically represented as a straight line. Linearity is closely related to proportionality. Examples in physics include the linear relationship of voltage and current in an electrical conductor, and the relationship of mass and weight.
Hope this helped!
Sending U good luck!
Dave and his brother Theo are selling cookies by the pound at the school bake sale. Dave sold 14.84 pounds of cookies and Theo sold 21
pounds of cookies. How many pounds did they sell altogether?
Answer:
35.84
Step-by-step explanation: add together 14.84 and 21 pounds of cookies
Answer:
35.84 pounds
Step-by-step explanation:
You would do 14.84 and 21.00 (because you line up the decimals) then just add how you normally would
II. The train and roller coaster will arrive back at their stations at the same time. If the train had a .15 mile head start and is traveling at a speed of .65 miles per minute, and the roller coaster is travelling at an average speed of .78 miles per minute, how long before they both arrive at the station?
Answer:
1 minutes 9sec
Step-by-step explanation:
given data
Train
let the distance be x
distance covered by train= (15+x)miles
speed of train=65mile per minute
time t=?
we know that speed= distance/time
distance= speed*time
15+x=65t----------------------1
Roller coaster
distance=x miles
speed= 78miles per minutes
time t=?
we know that speed= distance/time
distance= speed*time
x=78t----------------------2
put x=78t in equation 1 we have
15+78t=65t
78t-65t+15=0
13t=-15
t=15/13
t=1.15====1miin 9sec
so it will take 1minutes 9sec
How do I solve x + 4 = -x - 4
Answer:
x = -4
Step-by-step explanation:
x + 4 = -x - 4
Get x on one side by adding x to both:
2x + 4 = -4
Subtract 4 from both sides:
2x = -8
Divide both sides by 2 to get x alone:
x = -4
Can someone help me urgently
Answer:
which answer did you need help with
Step-by-step explanation:
i dont see what your inquiring about
Anna goes to the bank 3 times one day to withdraw $10 each time. The next day, she deposits $32. Find and solve an expression to find the change in her account.
Answer:960 day 3 =
d a y=
10 =
d a y =
32 =
Step-by-step explanation:
How many 4 digit numbers are there which are divisible by 2?
Answer:
There are 100 different 4-digit numbers that are divisible by 2
Step-by-step explanation:
And so any multiples of that will be divisible by 2, 3, 5 and 9.
-16 + (-11)
Please help
Answer:
-27
Step-by-step explanation:
-16 + (-11) = (16×-1) + (11×-1) = -(16 + 11) = (27 × -1) = -27
_____________________
Since both numbers are negative, when adding them, just pretend they are both positive, and then make your answer negative.
Answer:
-27
Step-by-step explanation:
(-16),-17,-18,-19,-20,-21,-22,-23,-24,-25,-26,-27
What are the coordinates of the image of D'E'F'G' after a rotation of 90º counterclockwise? The coordinates of the pre-image DEFG are D(2,0) E(2,2) F(5,2) G(5,1)
Given:
The coordinates of the pre-image DEFG are D(2,0) E(2,2), F(5,2), G(5,1).
To find:
The coordinates of the image of D'E'F'G' after a rotation of 90º counterclockwise.
Solution:
If a figure is rotated 90º counterclockwise, then
[tex](x,y)\to (-y,x)[/tex]
Using this rule, we get
[tex]D(2,0)\to D'(0,2)[/tex]
[tex]E(2,2)\to E'(-2,2)[/tex]
[tex]F(5,2)\to F'(-2,5)[/tex]
[tex]G(5,1)\to G'(-1,5)[/tex]
Therefore, the coordinates of the image of D'E'F'G' after a rotation of 90º counterclockwise are D'(0,2), E'(-2,2), F'(-2,5) and G'(-1,5).
Logan and his children went into a restaurant and where they sell drinks for $3 each and tacos for $2 each. Logan has $35 to spend and must buy at least 12 drinks and tacos altogether. If Logan decided to buy 5 drinks, determine all possible values for the number of tacos that he could buy.
Answer: if he buys 5 drinks he can buy 10 tacos
Step-by-step explanation:
2m + 3m² - 4m
Simplify pls
Answer:
2m+3m2=5m2-4m=1m2
1m2 answer
0= 4y + 6 + 2v
Could I get some help with this?