Answer:
d = 12.5
Step-by-step explanation:
Second term = a + d
Third term = a + 2d
a + d + a + 2d = 27
2a + 3d = 27
Fourth term = a + 3d
Fifth term = a + 4d
a + 3d + a + 4d = 77
2a + 7d = 77
2a + 3d = 27 (1)
2a + 7d = 77 (2)
Subtract (1) from (2) to eliminate a
7d - 3d = 77 - 27
4d = 50
Divide both sides by 4
d = 50/4
= 12. 5
d = 12.5
Substitute d = 12.5 into (1)
2a + 3d = 27
2a + 3(12.5) = 27
2a + 37.5 = 27
2a = 27 - 37.5
2a = -10.5
a = -10.5 / 2
= -5.25
a = -5.25
The common difference of the sequence is 12.5.
Given that,
The sum of the 2nd and 3rd terms of an arithmetic sequence is 27,
And the sum of the 4th and 5th terms is 77.
We have to determine,
The common difference of the sequence?
According to the question,
Let d is the common difference of the sequence,
The second term to the arithmetic series is,
[tex]\rm Second \ term= a+d[/tex]
And the third term to the arithmetic series is,
[tex]\rm Third \ term= a+2d[/tex]
The sum of the second and third terms of the sequence is 27.
[tex]\rm Second \ term + third \ term = 27\\\\a+d + a+2d = 27\\\\2a + 3d = 27[/tex]
The fourth term to the arithmetic series is,
[tex]\rm fourth \ term= a+3d[/tex]
And the fifth term to the arithmetic series is,
[tex]\rm fifth \ term= a+4d[/tex]
The sum of the fourth and fifth terms of the sequence is 77.
[tex]\rm fourth\ term + fifth \ term = 77\\\\a+3d + a+4d = 77\\\\2a + 7d = 77[/tex]
On solving both the equations,
[tex]\rm 2a + 3d = 27\\\\2a + 7d = 77[/tex]
Subtract equation 1 from equation 2,
[tex]\rm 2a + 3d - (2a + 7d) = 27-77\\\\2a +3d -2a-7d = -50\\\\-4d = -50\\\\d = \dfarc{-50}{-4}\\\\d = \dfrac{25}{2}\\\\d = 12.5[/tex]
Hence, The required common difference of the sequence is 12.5.
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On a coordinate plane, a straight red line with a positive slope, labeled g of x, crosses the x-axis at (negative 3, 0) and the y-axis at (0, 3). A straight blue line with a positive slope, labeled f of x, crosses the y-axis at (0, negative 3) and the x-axis at (1, 0). Both lines intersect at (3, 6).
Which statement is true regarding the functions on the graph?
f(6) = g(3)
f(3) = g(3)
f(3) = g(6)
f(6) = g(6)
Answer:
f(3)=g(6)
Step-by-step explanation:
The statement is true regarding the functions on the graph is f of 3=g of 3. The correct option is B.
What is a Function?A function assigns the value of each element of one set to the other specific element of another set.
Given two function f(x) and g(x) which intersect at (3, 6).
Now, when two functions intersect then it means that there is a value of x for which the value of both the functions is equal. This value of x and y is the point at which the two functions intersect.
Hence, the statement is true regarding the functions on the graph being
f of 3=g of 3.
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How would you explain to someone the rules of a horizontal translation where we are subtracting from the inputs(within the parenthesis) before evaluating the function
Answer:
Ok, we know that we can write a horizontal translation as:
y' = f(x - A)
where if A is positive, this moves the graph of f(x) A units to the right.
Why is this?
Ok, let's compare:
y = f(x)
and
y' = f(x - A)
in y, when x = 0 we have f(0).
While to have this same point in y', we need to evaluate in x = A.
f(A - A) = f(0).
Then the value f(0) is now at x = A, this means that the point moved A units to the right.
And you can do this for all the values, so you will find that the entire graph of f(x) has ben moved A units to the right.
Please help!!! Look at the attachment
Option D is the correct answer
Each year the seventh graders who study life science participate in a special field trip to the city zoo in 2010 the school paid $1,260 for 84 students to enter the zoo in 2011 the school paid $1,050 for 70 students to enter the zoo in 2012 the school paid $1,395 for 93 students to enter the zoo is the price the school pays each year in entrance fees proportional to the number of students entering the zoo explain why or why not
Answer:
Yes, the price the school pays each year in entrance fees is proportional to the number of students entering the zoo
Step-by-step explanation:
Relationships between two variables is proportional if their ratios are equivalent.
In 2010, the school paid $1,260 for 84 students to enter the zoo.
Ratio of the price the school pays each year in entrance fees to the number of students entering the zoo = [tex]1260:84=15:1[/tex]
In 2011, the school paid $1,050 for 70 students to enter the zoo.
Ratio of the price the school pays each year in entrance fees to the number of students entering the zoo = [tex]1050:70=15:1[/tex]
In 2012, the school paid $1,395 for 93 students to enter the zoo.
Ratio of the price the school pays each year in entrance fees to the number of students entering the zoo = [tex]1,395:93=15:1[/tex]
As [tex]1260:84=1260:84=1,395:93=15:1[/tex],
the price the school pays each year in entrance fees is proportional to the number of students entering the zoo.
Answer:
yes
Step-by-step explanation:
the price the school pays each year in entrance fees is proportional to the number of students entering the zoo.
What is 12 divided by 2.5?
Answer:
4.8
Step-by-step explanation:
Just divide
Answer:
4.8
Step-by-step explanation:
Which describes the graph of y= (x+ 6)²+ 1? A. Vertex at (-6,-1) B. Vertex at (-6, 1) C. Vertex at (6, 1) D. Vertex at (6,-1)
Answer:
B
Step-by-step explanation:
Answer:
B- Vertex at (-6,1)
Step-by-step explanation:
Rhone purchases eggs from a local dairy farm. He finds 3 broken eggs. He uses half the remaining eggs to bake a few pancakes. If 5 eggs remain now, how many eggs did Rhone purchase from the farm?
Answer:
He bought 13 eggs
Step-by-step explanation:
Lets make a equation:
X-3 /2=5
That means 5 times 2+3 would be X. 5 times 2=10 plus 3=13
The required number of eggs that Rhone purchased is given as 13.
Given that, Rhone purchases eggs from a local dairy farm. He finds 3 broken eggs. He uses half the remaining eggs to bake a few pancakes, at the end, 5 eggs remain now, how many eggs did Rhone purchase from the farm is to be determined.
What are equation models?The equation model is defined as the model of the given situation in the form of an equation using variables and constants.
Here,
Let the number of eggs be x,
Now,
3 eggs were found broken, the remaining eggs = x - 3,
He uses half the remaining eggs to bake a few pancakes and 5 eggs were left,
So,
X-3 /2=5
x = 10 + 3
x = 13
Thus, the required number of eggs that Rhone purchased is given as 13.
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HELP
the temperature in Alaska was -13 at 7:00am. By noon, the temperature was 5. How much did the temperature change?
I BEG ANYONE PLS SAVE ME WITH THIS QUESTION ITS MY LAST ONE PLSS
Answer:
21
Step-by-step explanation:
hope this helps.....
What is the chemical formula for copper(ll) sulfate?
A) CuSO4
B) Cu2SO4
C) CuS
D) Cu2S
[help pls]
what pets do you have
Answer:
a goldish!
Step-by-step explanation:
Answer:
2 ferrets a dog and 2 cats
Step-by-step explanation:
What is the remainder? –10 –7 7 10
Answer: C
Step-by-step explanation:
Which equation describes the line with slope of 3 and
containing the point (-3,-2)?
y = -1/3x-3
y = 1/3x - 1
y = 3x – 2
y = 3x + 7
Option D is the correct answer, y = 3x + 7
The line is y=3x+7
Given that the point is (-3, -2) and slope=m=3.
Using the point slope formula we get:
[tex]y-\left(-2\right)=3\left(x-\left(-3\right)\right)\\y+2=3\left(x+3\right)\\y+2=3x+9\\y=3x+7[/tex]
The line is y=3x+7
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Abc is similar to DEF. Which statement is true
Answer:
Can u right the answers out pls i cant see them
Step-by-step explanation:
Find the slope between the two points on the line: (1.-19) (-2,-7)
Answer:
The answer of the question is -4
Answer:
-4
Step-by-step explanation:
SOMEONE PLEASE HELP ME ON THIS!!!,
Answer:
did u just forget to attach a pic
Step-by-step explanation:
Willie and his two friends earn money mowing lawns in their neighborhood. On Saturday, they mowed two lawns and were paid 28$. If wille and his friends split the earnings equally, which expression does not equal how much wille will receive from working on Saturday
Answer:3/28
Step-by-step explanation:
If the original lengths of the graph below are multiplied by 3, will the new drawing be a reduction or enlargement?
Answer:
enlargement
Step-by-step explanation:
Please Help !!!
Sam found that if the product of 5 and a number is increased by 40, the
result is 121 more than the product of 2 and the number. What is the
number?
Answer:
the number is 45
Step-by-step explanation:
HELP AND PLEASE HURRRY
The Lanier band is raising money for their annual trip. They are selling insulated cups for $25 each and have already made $1500. They need to make at least $10,000 to go on the trip. Which inequality represents the situation?
A. 25x + 1500 ≤ 10,000
B. 25x+ 10,000 ≤ 1500
C. 25x + 1500 ≥ 10,000
D. 25x + 10,000 ≥ 1500
Answer:
25x + 1500 < 10,000
They have to make at least $10,000 to go on the trip.
The cups are $25 each, so it would be 25x.
In addition to that, $1500 has already been made.
= 25x + 1500 < 10,000
A
PLEASE HELP
PLEASE HELP
solve
Answer:
the answer is 32 S=32
Step-by-step explanation:
you have to find s right so you do 162-130 =32 or 130+32=162...
30 gallons to 40 gallons
Answer:
10 or 70
Step-by-step explanation:
10= 40-30=10
70=40+30=70
Which awnser choice is a solution to the equation 3x-2=7
Answer:
x=3
Step-by-step explanation:
Answer:
x=3
Step-by-step explanation:
X=3 because you would add 2 to seven Which equals 9. Then you would divide 9 by 3 which equals the answer 3.
Toby the Tiger makes $25 an hour selling cereal. Write an equation to
describe the proportional relationship between the amount of hours that
Toby works and the amount of money that Tony earns. (Hint: Make Table)
*
y=5x
y=15x
y=35x
y=25x
Answer:
I think it is y=25x
Step-by-step explanation:
Since Tony the Tiger makes $25 an hour, in 2 hours, he would make $50. Both of them, when divided, equal 25, the constant of proportionality.
Is this a function or non function?
Answer:
yes it is a function
Step-by-step explanation:
A function can only cross the y-axis once. If it crosses any y-axis more than once, it is not a function. This starts at 0 and will continue on to positive infinity. It will never cross the same y-axis twice. So yes, it is a function.
A spinner is divided into 5 uneven sections, which are labeled red, blue, green, yellow, and orange. Ricardo spun the spinner 120 times. The results are Red: 35 Blue: 36 Green: 32 Yellow: 8 Orange: 9 Based on the different data, what is the probability ricardo will soon blue on his next spin?
Answer: 3/10
Step-by-step explanation: It's 3/10 because the total amount when you add all the numbers together is 120, and since he spins it 120 times, we could assume that 36 would be the amount of times that it would land on it based on the data given. We're not done yet though. You do 36/120 to get the probability, and you simplify it to get 3/10.
The probability that Ricardo spins blue on his next spin is 0.3
We could use the principle of experimental probability to determine the probability of spinning blue on next spin :
Given that :
Red: 35
Blue: 36
Green: 32
Yellow: 8
Orange: 9
Experimental probability = (number of times event occur / total number of trials)
Total number of trials = (35 + 36 + 32 + 8 + 9) = 120
The experimental probability of spinning blue is thus :
(Number of blue spins / total number of spins)
= 36 / 120
= 0.3
The probability of spinning blue on next spin is 0.3
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Which of the following values are solutions to the inequality - 5 < 9 - 6x ?
Answer: x < 7/3
Step-by-step explanation: Use a number line for a visual
Which two statements are advantages of online banking?
Answer:
B and C
Step-by-step explanation:
that sounds right anyway
Carly,Brandon and Wyatt gather and shell walnuts for their grandfather. Carly gathers 3.5 pounds of walnuts.Brandon collects 3.75 pounds of walnuts and Wyatt collects 2 1/4 pounds. If they place all of the walnuts in one basket and each shells the same amount of walnuts, how many pounds will each person shell ?
Answer
9.5
Step-by-step explanation:
The graph shows equivalent ratios. Frank plotted another point with a y-value of 18. What is the x-value of that point?
x =
Answer:
x - 6
took the assignment
Step-by-step explanation:
Answer:
6
Step-by-step explanation:
The area of the base of a square notepad is 2.25 square inches. What is the length of one side of the base of the notepad?
Answer:
1.5 inches
Step-by-step explanation:
Because the base of the notepad is a square, that means that each side of the base would be equal. Since the area is 2.25 square inches, and each side would have to be equal, the equation to solve would be x*x = 2.25, or x^2=2.25. So, you just take the square root of both sides, and x=1.5 inches. Each side of the notepad would be 1.5 inches.
Answer: 1.5 inches
Step-by-step explanation:
:)