===========================================
Explanation:
There are a few approaches. Here's one way to solve.
Let d be the common difference between the terms.
We add d to each term of this arithmetic sequence to get the next term.
First term = mSecond term = 12 = m+dThird term = n = (m+d)+d = m+2dFocusing on the second equation, we can solve for d like so
m+d = 12
d = 12-m
This is then plugged into the third equation
n = m+2d
n = m+2(12-m)
n = m+24-2m
n = 24-m
Therefore,
m+n = m+(24-m) = 24
It turns out that it doesn't matter what m and n are because m+n is always equal to 24 in this case.
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A more concrete example:
Let's say m = 2. We won't set up n just yet but we'll be able to compute it fairly soon.
Since m = 2, this means d = 12-m = 12-2 = 10. This is the gap between adjacent or neighboring terms.
If d = 10, then the third term must be n = 12+d = 12+10 = 22
We can then see that m+n = 2+22 = 24
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I'll do another example:
m = 5
d = 12-m = 12-5 = 7
n = 12+d = 7 = 19
m+n = 5+19 = 24
Whenever in doubt, or if you get stuck, it helps to come up with actual numeric values to hopefully clear things up.
-----------------
An alternative way to get the answer:
Let's try to determine what m+n is actually saying. We have 12 right in the middle of the first term (m) and third term (n). Because the gap between the numbers is the same (that being d), we know that 12 is the midpoint of m and n. It might help to draw out a number line to see what's going on.
The midpoint of m and n is (m+n)/2
Set this equal to 12 and isolate the "m+n"
(firstTerm+thirdTerm)/2 = second term
(m+n)/2 = 12
m+n = 2*12
m+n = 24
So in general, if the first three terms of the arithmetic sequence are m, k, n, then m+n = 2k.
a.) x ≥ 2
b.) x > 2
c.) x < 2
d.) x ≤ 2
Answer:
x < 2
Step-by-step explanation:
There is an open circle at 2 so that means it is not equal to
The line goes to the left so x is less than 2
x < 2
Answer:
c.) x < 2
Step-by-step explanation:
open circle means > or <
the line is going to the left, meaning < or ≤
from this, we know the inequality is x < 2
I need help with can someone help me out
area of circle= 22/7×6×6
= 22/7×36
= 3.1×36
= 113.14
Answer:
[tex]36\pi[/tex]
Step-by-step explanation:
[tex]a = {6}^{2} \times \pi = 36\pi[/tex]
Solve for 2. Round to the nearest tenth, if necessary.
59
K
58°
M
圆
Submit Answer
Answer: 0
PLSSSS HELP
Answer:
x ≈ 94.4
Step-by-step explanation:
Using the tangent ratio in the right triangle
tan58° = [tex]\frac{LM}{KL}[/tex] = [tex]\frac{x}{59}[/tex] ( multiply both sides by 59 )
59 × tan58° = x , then
x ≈ 94.4 ( to the nearest tenth )
Help me answer this, Thank you
Answer:
Step-by-step explanation:
rotate it in a full circle
Which function shows a fabric with a price of $1.25 per square yard?
A table showing Price of Fleece with five columns and two rows. The first row, Square Yards, has the entries, 1, 2, 3, 4. The second row, Price, has the entries, $1.25, $2.00, $2.75, $3.50.
A table showing Price of Fleece with five columns and two rows. The first row, Square Yards, has the entries, 1, 2, 3, 4. The second row, Price, has the entries, $0.25, $1.25, $2.25, $3.25.
A coordinate plane showing Price of Fleece. The x-axis shows Number of Square Yards and the y-axis shows Price in dollars. A line starts at (0, 0) and passes through (5, 4) and ends (10, 8).
A coordinate plane showing Price of Fleece. The x-axis shows Number of Square Yards and the y-axis shows Price in dollars. A line starts at (0, 0) and passes through (4, 5) and ends (8, 10).
Answer:
D
Step-by-step explanation:
Took the test
Brainliest pls
Answer:
D
Step-by-step explanation:
E 2020
Solve for U 11+15u=-7+13u
Help fast please
Answer:
-9
Step-by-step explanation:
11+15u=-7+13u
or, 15u-13u = -7-11
or, 2u = -18
or, u = -9
Answered by GAUTHMATH
Please help cause if you dont you will get a beatboxbattle lol.
Answer:
14
Step-by-step explanation:
2a -b
Let a = 9 and b = 4
2(9) - 4
Multiply first
18-4
14
The population of a place in a particular year increased by 15% next year it decreased by 15%. Find the net increase or decrease percent in the initial population
Answer:
there was a decrease of 2.25%
Step-by-step explanation:
Let me illustrate with an example
Assume the population is 100
percentage increase = 100 + 15 = 115% = 1.15%
Population after 15% increase = 100 x 1.15 = 115
Percentage decrease = 100 - 15 = 85% = 0.85
Population after 15% decreases 115 x 0.85 = 97.75
rate of increase = (97.75 / 100) - 1 = -2.25%
Select all the expressions equivalent to 2(x + 3)
2(x + 3) = 2x + 6
1. Correct - 2 * (x + 3) = 2x + 6
2. Correct - (x + 3)2 = 2x + 6
3. Correct - 2x + 6
4. Incorrect - 2x + 3
5. Incorrect - 2x + 3
6. Incorrect - 3x + 6
Hope this helps!
1000000+200000=?
fun for me
Answer:
1,200,000
Step-by-step explanation:
hope i helped
Answer:
1.200.000
Step-by-step explanation:
[tex]thankyou[/tex]
Three dressers are placed side by side. One dresser is 5 feet 5 inches wide, another is 5 feet 10 inches wide, and the third is 3 feet 11 inches wide. How wide are they combined?
Answer:
15 feets 2 inches
Step-by-step explanation:
Given the widths :
1st dresser = 5 feets 5 inches
2nd dresser = 5 feets 10 inches
3rd dresser = 3 feets 11 inches
Their combined width is :
5ft + 5ft + 3 ft + 5in + 10in + 11in
13 feets 26 inches
Recall :
1 foot = 12 inches
26 inches = 26/12 feets = 2 feets 2 inches
Hence,
13 feets + 2feets 2 inches
Combined width = 15 feets 2 inches
Find the value of k for which the following system of equations has infinite solution. 5x +2y=k,10x +4y=3
Answer:
k=3/2 or 1 1/2
Step-by-step explanation:
Answer 3/2
Step-by-step explanation:
Question 1 (1 point)
The perimeter of an iPad Air is 820 mm. Its length is 100 mm less than twice the
width.
If x = the length of the iPad Air and y = the width of the iPad Air, the linear system of
equations that could be used to model this situations is,
2x + 2y = a
bx = cy-d
The value of a is:
Answer:
a is the perimeter which is given as 820 mm.
Step-by-step explanation:
Perimeter, P = 820 mm
Length is 100 m less than twice of width
let the length is x and the width is y.
So,
x = 2 y - 100
P = 2 (x + y)
820 = 2 (2y - 100 + y)
410 = 3 y - 100
3 y = 510
y = 170 mm
x = 2 x 170 - 100 = 240 mm
The equation is
2 x = 2 y = a
where, a is the perimeter which is given as 820 mm.
find the missing side lengths
Answer:
a = 17
b = 17
Answered by GAUTHMATH
Use the substitution method to find the solution for the system of equations. Write the answer as an ordered pair. 3x+2y=23 (1/2)-y=4
Answer:
x = 7.75 y = -0.125
Step-by-step explanation:
3x + 2y = 23 1/2x - y = 4
2(1/2x - y) = (4)2 1x - 2y = 8
3x + 2y = 23
+ 1x - 2y = 8
4x = 31
x = 7.75
3(7.75) + 2y = 23
23.25 + 2y = 23
2y = -0.25
y = -0.125
The cost of carpeting a sqaure yard is $9.10. How much does it cost to carpet 12.5 square yards?
Answer:
113.75$
Step-by-step explanation:
I. When a square yard = 9.10
so 1 * 9.1 = 9.1
if 12.5 square yard
then 12.5 * 9.1 = 113.75$
If the area of a rectangular field is x2 – 3x + 4 units and the width is 2x – 3, then find the length of the rectangular field.
Answer:x²-3 x+4/ 2x-3 units
Step-by-step explanation:
Area = Length * Width sq. units
x^2 - 3x + 4 = Length * 2x - 3
=>Length = x^2- 3 x + 4/ 2 x − 3 units
Giải phương trình lượng giác cơ bản sinx=cos2x
Answer:
Step-by-step explanation:
Solve the following, where 0° < θ < 360°.
If cos θ=2/3 and tan θ<0
Find θ.
Answer:
The angle θ = 312°.
Step-by-step explanation:
0° < θ < 360°
If cos θ = 2/3 and tan θ < 0
As cos θ is positive and tan θ is negative so the angle is in fourth quadrant.
cos θ = 2/3
θ = 312°
this graph represents the function f(x)=4sin(x) which statement is true about this function
Answer:
A
Step-by-step explanation:
The function is increasing in the interval in A because as the x-values increase so do the y-values on the graph, which can be shown by the graph sloping upwards at that specific section.
The graph of a function is increasing on the interval (3π/2, 2π) option (A) is correct.
What is trigonometry?Trigonometry is a branch of mathematics that deals with the relationship between sides and angles of a right-angle triangle.
We have given a graph of a trigonometric function,
As we know, the trigonometric function is sinusoidal in nature, and it has a domain of all real numbers and lies between the [a, a]where is the amplitude of the function.
The trigonometric ratio is defined as the ratio of the pair of a right-angled triangle.
From the graph, the function is increasing from 3π/2 to 2π
The graph slopes upward at that particular segment, indicating that the function is increasing in the interval in A as the x-values increase and the y-values on the graph follow suit.
Thus, the graph of a function is increasing on the interval (3π/2, 2π) option (A) is correct.
Learn more about trigonometry here:
brainly.com/question/26719838
#SPJ5
find the missing side of the triangle.
Find the volume of the cylinder. Round to the nearest tenth.
Answer:
V = 56.5 mi^3
Step-by-step explanation:
The volume of a cylinder is given by
V = pi r^2 h where r is the radius and h is the height
V = pi ( 3)^2 (2)
V = 18 pi
Letting p = 3.14
V = 56.52 mi^3
Rounding to the nearest tenth
V = 56.5 mi^3
Fill in the missing statements and reasons in the proof
Answer:
1. Given
2. Vertical angle theorem
3. AB≅DB, EB≅CB, m<ABC≅m<DBE
4. △ABC ≅ △DBE
Hope this helps :D
What is the range of the absolute value function shown in the graph?
A. 3 ≤ y < ∞
B. -∞ < y ≤ 3
C. -6 ≤ y < ∞
D. -∞ < y < ∞
Answer:
C
Step-by-step explanation:
as we can see on the graph, the lowest y value is the vertex/corner at x=3, y=-6.
all other y values are above (=are larger) that level.
and it goes up without appearant limit, so up to infinity.
Can someone help me with this? 20 points
Answer:
Step-by-step explanation:
Triangle ABC is a 45-45-90 right triangle. That means that segment BC also measures 10.
The big triangle as a whole is a 30-60-90. The side length across from the 30 degree angle is 10, so the whole length of BD is 10√3. However, since we already have the length of BC as 10, then segment CD measures
10√3 -10 which is 7.32
. Tập nghiệm của bất phương trình
1 5
1 1
x x
x x
là:
Answer:
pnj hnu n
126
11
yes ......
....
.
..
x u g
*** I NEED HELP PLEASE HELP YOUR GIRL OUT LOL**
Identify the segment parallel to the given segment
Answer:
parallel segments in order: CB, CA, CO, AN, BA, NO
1. Find the sum of csc230° and cot2 45°.
Answer:
5
Step-by-step explanation:
Based on the given conditions, formulate
Evaluate the expression:
Calculate the power:
Calculate the first two terms:
Answer:
what is the electrical work done in a circuit
Answer:
a open and close switch and a condentation out put.
Instructions: Find the missing side. Round your answer to the nearest tenth.
54°
29
Answer:
x = 23.5
Step-by-step explanation:
Since this is a right triangle, we can use trig functions
sin theta = opp / hyp
sin 54 = x / 29
29 sin 54 = x
x=23.46149
To the nearest tenth
x = 23.5
