Answer:
Common difference = 4
Position of 103 = 25th term
Step-by-step explanation:
a)
According to the given information:
[tex] a_3 + 20 = a_8[/tex]
[tex] a+ (3-1)d + 20 = a+ (8-1)d[/tex]
[tex] \cancel a+ 2d + 20 = \cancel a + 7d[/tex]
[tex] 2d + 20 = 7d[/tex]
[tex] 20 = 7d-2d[/tex]
[tex] 20 = 5d[/tex]
[tex] d = \frac{20}{5}[/tex]
[tex] \purple {\bold {d = 4}} [/tex]
Common difference = 4
b)
[tex] \because a_3 = 15....(given) [/tex]
[tex] \therefore a + (3-1)d = 15[/tex]
[tex] \therefore a + 2d = 15[/tex]
[tex] \therefore a + 2\times 4= 15[/tex]
[tex] \therefore a + 8= 15[/tex]
[tex] \therefore a = 15-8[/tex]
[tex] \red{\bold {\therefore a = 7}} [/tex]
[tex] \because a_n = a + (n - 1) d[/tex]
[tex] \therefore 103 = 7 + (n - 1)4 [/tex]
[tex] \therefore 103 - 7 = (n - 1)4 [/tex]
[tex] \therefore 96 = (n - 1)4 [/tex]
[tex] \therefore \frac{96}{4}= n - 1[/tex]
[tex] \therefore 24= n - 1[/tex]
[tex] \therefore 24+1= n[/tex]
[tex]\blue{\bold {\therefore n = 25}} [/tex]
So, the position of 103 in this sequence is 25th term.
Find the value of x.
106°
43°
X°
X =
Answer:
Maybe the figure of this question is a triangle.
If so...the answer comes something like this....
Hope it helps! :)
What are the domain and range of the function on the
graph?
What is the equation of the line that passes through the point (-4, -7) and has a
slope of ?
Answer:
the question seems incomplete
Color of socks
Number of socks
white
8
black
7
blue
2
brown
3
From the table, the ratio of white socks to brown socks is
Select two ratios equivalent to the ratio of white socks to brown socks.
32
A.13
B.15
41
C.32
12
D.40
15
Answer:
D.40:15 are equivalent to the ration of white socks to brown sock which is 8:3
Which expression is equivalent to 3x5−5x2(x3−2x)+3x3?
Answer:
19 × 2x
Step-by-step explanation:
3 × 5 − 5 × 2(3x − 2x) + 3 × 3 | Given
15 - 5 × 6x - 4x + 9 | Multiply and distribute.
19 × 6x - 4x | Add the numbers
19 × 2x | Combine like-terms.
Jericho takes 3 tests in one month. The number of correct answers and the total
number of questions on each test are shown in the table. List the tests in order
from the least percent of questions correct to the greatest percent of questions
correct. Show your work.
Answer:
you need to show the table for this question to get solved
Answer:
kiygtfrsass2EDWWQASDCfe
Step-by-step explanation:
Simplify
4y — 4ys + 2y – 5у — 54 – 34
Answer:
-4ys + y - 88
Step-by-step explanation:
When we have to simplify equations that have different variables, we always have to look at the like terms, which the like terms are ones that contain the same value and variable. So let's look at our equation :
4y — 4ys + 2y – 5у — 54 – 34
We can see three different terms here :
ys, y, and a constant term.
The rule is that we can only combine two properties that have the same like term, so in the equation :
4y — 4ys + 2y – 5у — 54 – 34
These have the same variable, therefore we can combine like terms.
4y + 2y - 5y
6y - 5y
y
Now implace it into the equation :
y — 4ys — 54 – 34
Onto the next property :
y — 4ys — 54 – 34
This is alone, therefore we can leave it :
y — 4ys — 54 – 34
These two are the same property, so do the following :
-54 - 34
-88
Impace into the equation :
y - 4ys - 88
Now that we have no same common like terms, we can order our equation to greatest value to least :
-4ys + y - 88
Evan subtracts 247 from 642 and get 395. What addition equation can he use to check his answer.
247+ ? =642
Answer:
Answer down below!
Step-by-step explanation:
When checking work, simply add your answer back in.
In this case, his answer was 395.
247 + 395 = 642
if he gets the same answer, then he is correct.
Help pleaseeeeee! i dont remember all of this
Answer:
35cm3
Step-by-step explanation:
7x5=35
Answer: The correct answer is 35. 7 * 5 = 35
Step-by-step explanation:
Solve the system by graphing
6x – 9 = y
y = -3x
i can graph but how do you solve it
Answer:
I love algebra anyways
The ans is in the picture with the steps how i got it
(hope this helps can i plz have brainlist :D hehe)
Step-by-step explanation:
What is the constant of proportionality in the equation y=\dfrac{5}{9}xy= 9 5 XY, equals, start fraction, 5, divided by, 9, end fraction, x?
Answer:
[tex]k=\dfrac{5}{9}[/tex]
Step-by-step explanation:
The given equation is :
[tex]y=\dfrac{5}{9}x[/tex] ...(1)
We need to find the constant of proportionality in the equation.
In this equation, y is directly proportional to x i.e.
y ∝ x
or
y = kx ...(2)
k is constant of proportionality
If we compare equation (1) and (2), we find that,
[tex]k=\dfrac{5}{9}[/tex]
So, the constant of proportionality is equal to [tex]\dfrac{5}{9}[/tex].
.What is the standard form of y – 8 = 2(x + 3)?
6th grade math help me pleaseee
Answer:
A) 3(2x-1) --> 6x - 3
B) 10(b+4c) --> 10b + 40c
C) 9(g-5h) --> 9g - 45h
D) 7(4n-5m-2) --> 28n - 35m - 14
E) a(b+c+1) --> ab + ac + a
F) (8j-3l+9)6 --> 48j - 18l + 54
G) (40s+100t)/10 --> 4s + 10t
H) (48p+24)/6 --> 8p + 4
I) (2b+12)/2 --> b + 6
J) (20r-8)/4 --> 5r - 2
K) (49g-7)/7 --> 7g - 1
L) (14g+22h) / 1/2 --> 28g + 44h
Find the marked prices of the following , given the percentage discount and the sale prices: part a: 12% discount , and the sale price $77
part b : 25% discount , and the sale price $123
Answer:
A) $87.5
B) $164
Step-by-step explanation:
A) Marked Price (Original Price)
= [tex]\frac{Sale Price}{1 -Discount}[/tex]
=[tex]\frac{77}{1-0.12}[/tex]
=87.5
B) Marked Price (Original Price)
=[tex]\frac{Sale Price}{1 -Discount}[/tex]
=[tex]\frac{123}{1-0.25}[/tex]
=164
Tax of northglenn city is calculated at 6.5%. Carlos is at a convenience store with his mom and needs to convert the percent the percent to a decimal to input it on his calculator. What decimal number should he use?
A triangle has side lengths of 6, 8, and 9. What type of triangle is it? right obtuse equiangular acute
Answer:
acute
Step-by-step explanation:
Answer:
It is an acute triangle
Step-by-step explanation:
If it is an acute triangle, a^2 + b^2 > c^2
If it is a right triangle, a^2 + b^2 = c^2
If it is an obtuse triangle, a^2 + b^2 < c^2
If it is an equilateral triangle, a = b = c
6^2 +8^2 ? 9^2
36+64 ? 81
100 ? 81
? is >, meaning it is an acute triangle.
what was an important concern for the founding fathers when drafting the articles confederation?
Answer: They wanted the government to not be too powerful, in other words they wanted the states to have more power
Step-by-step explanation:
if the length of a certain rectangle is decreased by 4cm and the width is increased by 3cm,a square with the same area would result.find the perimeter of original rectangle
Answer:
The perimeter is 50
Step-by-step explanation:
The original area is LW
The new area is (L-4)(W+3)
These areas are the same
1: (L-4)(W+3)=LW
You are also told that the new figure is a square, hence
2: (L-4)=(W+3)
Equation (2) implies
3: L=W+7
Substitute for L in Equation (1) and solve for W
(W+7-4)(W+3)=(W+7)W
W^2+3W+7W+21-4W-12=W^2+7W
6W+9=7W
W=9
Now use Equation (3) to solve for L
L=16
The perimeter is 2W+2L
P=18+32=50
HELP ME seriously i have 40 minutes left
Answer:
10 dollars less
Step-by-step explanation:
just trust me bro
find the volume of this prism
Answer:
i think it's 46.............
Look at the table below. For a certain tree, the table shows the relationship between the height of the tree in feet to its age in years.
What is the rate of change of the height of the tree to the age of the tree?
•The height of the tree increases by 2 feet for every year in the age of the tree.
•The height of the tree increases by 5 feet for every year in the age of the tree
•The height of the tree increases by 2 feet for every 5 years in the age of the tree.
•The height of the tree increases by 5 feet for every 2 years in the age of the tree.
Answer:
D
Step-by-step explanation:
The last option in the picture
7th grade please solve the problem above. Write a paragraph explaining how you found the solution you must include each step for solving please!!!
Answer:
x=0
Step-by-step explanation:
You must isolate the variable to solve for it, so subtracting 14 from the left is the first thing to do. This can be supported by using PEMDAS, whereas we are doing the inverse here to solve for something in the equation. This gives us 2x=0. Next, we have to divide by 2, which gives us x=0.
The perimeter of a square is given as 8x+20. Write two different expressions for the perimeter. Use factoring to write one of the expressoins. Are the expressions equivalen? Explain
Answer:
P = 4(2x + 5)
P = (2x + 5)+(2x + 5)+(2x + 5)+(2x + 5)
Step-by-step explanation:
Given that:
Perimeter of square = 4 * s
Where s = side length
If perimeter, P = 8x + 20
Then,
4s = 8x + 20
Divide both sides by 4
4s / 4 = (8x + 20) / 4
s = 2x + 5
P = 4s
P = 4(2x + 5)
Or
P = 2x + 5 in 4 places
P = (2x + 5)+(2x + 5)+(2x + 5)+(2x + 5)
A racing shell, which is a boat a crew team rows, moves 20 km/h in still water. During practice, the team rows 36 km against the current and 22 km with the current. Find the speed of the river current if the team rows a total of 3 hours.
Answer:
2 km/h
Step-by-step explanation:
Let x represent the speed of the river current, t₁ be the time spent rowing against the current and t₂ be the time spent rowing with the current.
Since the speed of the still water = 20 km/h.
The speed of rowing against the current = (20 - x)
The speed of rowing with the current = (20 + x)
We know that velocity = distance / time. Hence time = distance / velocity
t₁ = 36 / (20 - x)
t₂ = 22 / (20 + x)
but t₁ + t₂ = 3 hours
Therefore:
3 = 36 / (20 - x) + 22 / (20 + x)
multiply through by 400 - x²
3(400 - x²) = 36(20 + x) + 22(20 - x)
1200 - 3x² = 720 + 36x + 440 - 22x
3x² + 14x -40 = 0
This gives x = -6.7 or x = 2
x cannot be negative therefore x = 2 km/h
The speed of the river current is 2 km/h
Answer:
2km/h is correct
Step-by-step explanation:
The other guy is absolutely correct
6 times a number is equivalent to 28 less than 2 times the number. What is the number
Answer:
Step-by-step explanation:
2x+28<=6x
28<=4x
7<=x
In ΔHIJ, the measure of ∠J=90°, JI = 48, IH = 73, and HJ = 55. What is the value of the tangent of ∠H to the nearest hundredth?In ΔJKL, the measure of ∠L=90°, JL = 60, KJ = 61, and LK = 11. What ratio represents the tangent of ∠J?
Answer:
11:60
Step-by-step explanation:
In ΔHIJ, given the measure of ∠J=90°, JI = 48, IH = 73, and HJ = 55. We are to find tan<H
Using SOH CAH TOA
tan theta = opposite/adjacent
JI is the opposite (facing m<H)
HJ will be adjacent
tan m<H = JI/HJ
tan m<H = 48/55
tan m<H = 0.87 (to the nearest hundredth)
In ΔJKL, the measure of ∠L=90°, JL = 60, KJ = 61, and LK = 11. What ratio represents the tangent of ∠J?
Using SOH CAH TOA
tan theta = opposite/adjacent
LK is the opposite (facing m<J)
JL will be adjacent
tan m<J = LK/JL
tan m<H = 11/60
Hence the ratio that represents the tangent of ∠J is 11:60
A line contains the points (2,4) and (6,16). Write the linear function for the line in the form y=Mx+b
Answer:
y = 3x - 2
Step-by-step explanation:
Given the points :
(2,4) and (6,16).
x1 = 2 ; y1 = 4 ; x2 = 6 ; y2 = 16
Y = mx + b
m = slope
b = intercept
m = Rise / Run
Rise = y2 - y1 = 16 - 4 = 12
Run = x2 - x1 = 6 - 2 = 4
m = 12 / 4 = 3
Y = 3x + b
4 = 3(2) + b
4 = 6 + b
4 - 6 = b
b = - 2
Equation becomes ;
y = 3x - 2
if h (x) = |5x - 17|, find h(3)
Answer:
2
Step-by-step explanation:
5x - 17
5(3) - 17 = 15 - 17 = -2
let me know if its right or wrong
How to tell the difference between multiplication and division word problems?
Answer:
Multiplication is one of the four elementary mathematical operations of arithmetic, with the other ones being addition, subtraction and division. The result of a multiplication operation is called a product. And division is one of the four basic operations of arithmetic, the ways that numbers are combined to make new numbers. The other operations are addition, subtraction, and multiplication
Amber got a raise. Her hourly wage increased from $8 to $10 an hour. How much did amber's hourly wage increase.
Answer:
Her wage increased by $2 an hour
Step-by-step explanation:
Answer:
2 dollars.
Step-by-step explanation: