Answer:
The sum of first eighteen terms of the arithmetic sequence is [tex]\mathbf{S_{18}=1638}[/tex]
Option B is correct option.
Step-by-step explanation:
We need to find the sum of the first eighteen terms of the arithmetic sequence whose nth term is an = 15 + 8n
The formula used to calculate sum of arithmetic sequence is: [tex]S_n=\frac{n}{2}(a_1+a_n)[/tex]
Finding a₁ by putting n=1
[tex]a_n=15+8n\\a_{1}=15+8(1)\\a_{1}=15+8\\a_{1}=23[/tex]
We have [tex]a_1=23[/tex]
Finding 18th term n=18
[tex]a_n=15+8n\\a_{18}=15+8(18)\\a_{18}=15+144\\a_{18}=159[/tex]
So, the sum of first eighteen terms of the arithmetic sequence is:
[tex]S_n=\frac{n}{2}(a_1+a_n)\\S_{18}=\frac{n}{2}(a_1+a_{18})\\S_{18}=\frac{18}{2}( 23+159)\\S_{18}=9(182)\\S_{18}=1638[/tex]
So, the sum of first eighteen terms of the arithmetic sequence is [tex]\mathbf{S_{18}=1638}[/tex]
Option B is correct option.
order 6 9/10 6 19/80 6 3/4 least you greatest
Answer:
6 9/10, 6 3/4, 6 19/80
Step-by-step explanation:
it is the ordre r r my duuuud
Please Help Me Please Ill mark brainiest
Answer:
1. Similar by AAA (3 angles equal)
2. Similar by SSS (3 sides proportionate)
3. Similar by SAS ( 2 side proportionate and equal angle in between)
what does d/dx (-8x - 643)=
Evaluate the expression "12 - (-36) / -6"
Answer:
ah bbhgggvgujjbgg
hhhjj
Ramon drove 425 miles on 15 1/2 of gas. How many miles per gallon did he drive?
Answer: If half a gallon is 15 then just multiply 15 with 2.
Step-by-step explanation:
Answer:
He drove 27[tex]\frac{13}{31}[/tex] miles per gallon.
Step-by-step explanation:
15[tex]\frac{1}{2}[/tex] gas = 425 miles
[tex]\frac{31}{2}[/tex] gas = 425 miles
31 gas = 425 × 2
= 850 miles
1 gallon = 850 miles ÷ 31
1 gallon = 27[tex]\frac{13}{31}[/tex] miles
Sally is currently in a city that is 100 ft below sea level. She then drives to a new city 50 ft above sea level. What integer represents the total distance sally drove
Answer:
I think the answer is -50.
Step-by-step explanation:
50 feet below sea level. First, look for key words. The word “below” means you will need to use a negative integer. The answer is -50.
if (81)^p = 43,046,721, what is the value of p?
Answer:
P = 4
Step-by-step explanation:
81 x 81 x 81 x 81 = 43,046,721
Which of the following expressions is NOT a perfect square trinomial?
Answer:
2
Step-by-step explanation:
Complete the point-slope equation of the line through ( 6 , 4 ) and (7, 2)
What lever has resistance between the axis (fulcrum) and the force (effort)? A. first B. second C. third D. fourth Please select the best answer from the choices provided. A B C D
Answer:
B. Second
Step-by-step explanation:
Levers are defined as the simple machine, which consists of a rod fixed at a pivot, load, and fulcrum. The levers are classified into first class, second, and third class.
What is lever?A lever is a simple machine made of a rigid beam and a fulcrum. The effort (input force) and load (output force) are applied to either end of the beam. The fulcrum is the point on which the beam pivots. When an effort is applied to one end of the lever, a load is applied at the other end of the lever.
here, we have,
The difference between different types of levers are:
1. In the first-class levers, the fulcrum is present between the load and effort. The mechanical advantage can be greater, less, or equal to 1.
2. The second class levers, the load is present between the fulcrum and effort. The mechanical advantage is always greater than the 1.
3. The third class levers, the effort is present between the fulcrum and load. The mechanical advantage is always less than 1.
Thus, the correct answer is Option 1.
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complete question:
What distinguishes first class levers from both second and third class levers? A. The fulcrum is between the load and effort. B. There is a fulcrum on both sides of the load. C. Greater effort is required to move the load. D. The first class lever is not found in the human body. Please select the best answer from the choices provided. A B C D.
Which of the following values of x make the following functions equal? y =4x+6 and y=5x+3
3
2
4
1
Answer:
The value of x that makes both functions. y = 4·x + 6 and y = 5·x + 3 equal is;
x = 3
Step-by-step explanation:
The given functions are;
y = 4·x + 6 and y = 5·x + 3
For the functions to be equal, we have that the y values are equal, therefore;
y = y and 4·x + 6 = 5·x + 3, which gives;
4·x + 6 = 5·x + 3
5·x - 4·x = 6 - 3
∴ x = 3
Therefore, the value of x that makes both functions. y = 4·x + 6 and y = 5·x + 3 equal is x = 3.
Answer:
x=3
Step-by-step explanation:
Which of the following is a second degree trinomial? 3x + 8 -4x2 - 6x + 7 6x4 + 4x2 - 7 5x2 + 10
Answer:
the first one
Step-by-step explanation:
because it is
A line passes through the point (-2,3) and has a slope of 5/2
Write an equation in SLOPE-INTERCEPT form for this line.
Answer:
y = 5/2x + b
3= 5/2(-2) + b
3= -5 + b
3 + 5 = b
b = 8
y = 5/2x + 8
The equation in slope-intercept form is y= 5/2x + 8.
What is Slope?A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes. y and x are the net changes in the y and x coordinates, respectively. Therefore, it is possible to write the change in y coordinate with respect to the change in x coordinate as,
m = Δy/Δx where, m is the slope
Given:
Slope = 5/2
and, point (-2, 3).
Using Slope- intercept form
y = mx + b
y= 5/2x + b
As, the line passes through (-2, 3)
3 = 5/2(-2) + b
3 = -5 + b
b= 8
So, the Equation of line is y= 5/2x + 8.
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Show the next three fractions equivalent to 12 in the list.
12, −1−2, −3−6, . . .
A.
−510, −714, −918
B.
−48, −510, −612
C.
−5−10, −7−14, −9−18
D.
−4−8, −5−10, −6−12
Answer:
its c not sure
Step-by-step explanation:
help with these please im sorry I wanna save points
x + 9 = -2
Could someone please help me with this problem?
Answer:
x = -11
Step-by-step explanation:
First, you have to isolate x to one side. To do this, you have to subtract 9 on both sides like this
x + 9 - 9 = -2 - 9
So this will now be
x = -11
There you go!
Answer:
x=-11
Step-by-step explanation:
x+9=-2
-9 -9
---------------
x=-11
Plzz help e for brainliest if 2 people answer
Answer:
B
Step-by-step explanation:
Answer:
B
Step-by-step explanation:
Please help I will mark brainliest
What is the solution to the equation -4(2x + 3) = 2x + 6 - (8x + 2)?
A. x = -10
B. x = -8
C. x = - 5/2
D. x = -4/7
Answer:
B. x = -8
Step-by-step explanation:
-4(2x + 3) = 2x + 6 - (8x + 2)
-8x -12 = 2x + 6 - 8x -2
(now, "-8" in both terms is cancelled):
-12 = 2x + 6 - 2
(leave 2x alone in second term):
-12 -6 +2 = 2x
-16 = 2x
-16/2 = x
-8 = x
Justine lives in an apartment while attending college. Her monthly rent last year was $680, but this year she has to pay $800 per month. By what percent did her monthly rent increase from last year to this year?
Answer:
6,528,000
Step-by-step explanation:
Multiply 800 by 12. Then multiply the number by 680. And there u go.
6,528,000
The percent did monthly rent increase from last year to this year is 17.6%
Last year Justine paid $680 in rent while this year she paid $800 in rent
The increase in rent = $800 - $680 = $120
The percentage increase in rent = ($120/$680) * 100% = 17.6%
The percent did monthly rent increase from last year to this year is 17.6%
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The linear equation c = 0.1998s + 76.4520 models the number of calories, c, in a beef hot dog as a function of the amount of sodium s, in milligrams, in the hot dog. What is the slope, and what does it mean in this context?
Answer:
The slope of the linear equation is 0.1998, and it means that the calories in a beef hot dog is increasing with the rate of 0.1998 calories per milligram of sodium.
Step-by-step explanation:
Using y = mx + b, we know that m represents the slope.Looking at the equation of c = 0.1998s + 76.4520, our m is equal to 0.1998.This slope means that the rate is increasing by 0.1998 calories for every milligram of sodium.What’s the perimeter
Whats 5000+35548-455x4534+38534x233=?
Answer:
6,956,000
Do all the operations in order by following the PEMDAS method.
Please help me out!
Answer:
5[tex]\sqrt{8}[/tex], 40/3, [tex]\sqrt{170}[/tex]
Step-by-step explanation:
[tex]\sqrt{170}[/tex]= 13.03840481
5[tex]\sqrt{8}[/tex] = 14.14213562
40/3 = 13.33...
what are the x and y intercepts of the graph of -7x+4y=-14
Answer:
The answer is (2, -7/2)
A fish tank contains 600 gallons of water when full. The tank
contains a permanent hole, which causes the tank to leak at a
constant rate of 12 gallons each week. Let w be the number of
weeks. Which of the following expressions describe the number of
gallons left in the tank after any given number of weeks.
a. 600 + 12w
b. 600 - 12w
c. 12 -600w
d. 12 + 600w
Answer: 600 - 12w
Step-by-step explanation:
From the question, we are informed that a fish tank contains 600 gallons of water when full and that the tank
contains a permanent hole, which causes the tank to leak at a constant rate of 12 gallons each week.
If the number of weeks is represented by w, then the expression that describe the number of gallons left in the tank after any given number of weeks will be:
= 600 - 12w
For example let's say the number of weeks is 5 weeks. Using the expression,
600 - 12w
= 600 - 12(5)
= 600 - 60
= 540 gallons
There'll be 540 gallons after 5 weeks.
50°
850
53 + x
I need to find the value of x and without saying x =
v=r-s/2 solve for r
Answer:
r=v + [tex]\frac{s}{2}[/tex]
Step-by-step explanation:
v=r-[tex]\frac{s}{2}[/tex]
v+[tex]\frac{s}{2}[/tex]=r
On solving for r, we get -
[tex]$r=v+\frac{s}{2}[/tex]
We have the following expression -
[tex]$v=r-\frac{s}{2}[/tex]
We have to solve for r.
Solve for x (at k = 2) :log ( [tex]\frac{\pi }{x}[/tex] ) = k
On solving -
log(π) - log(x) = k
log(x) = k - log(π)
log(x) = 2 - log(π)
log(x) = 2 - 0.497
log(x) = 1.503
x = 31.84
According to the question, we have -
[tex]$v=r-\frac{s}{2}[/tex]
On solving for r, we get -
[tex]$r=v+\frac{s}{2}[/tex]
Hence, we get - [tex]$r=v+\frac{s}{2}[/tex].
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What si the equation in slope intercept form of the line that passes through the points (-4,2) and (12,6)
Answer:
b = -12
Step-by-step explanation:
In order to find the slope intercept you must first find the slope of the given points.
[tex]-4,2 = 12,6[/tex]
[tex]S=\frac{y2-y1}{x2-x1}[/tex]
Substitute:
[tex]\frac{12--4}{6-2}[/tex]
[tex]12--4=12+4=16[/tex]
[tex]6-2=4[/tex]
[tex]S=\frac{16}{4}[/tex]
Now find the slope intercept
[tex]16\div4=4[/tex]
[tex]SI=y=mx+b[/tex]
Substitute:
[tex]12=4\times6+b[/tex]
Solve:
[tex]4\times6=24[/tex]
[tex]12=24+b[/tex]
Subtract 24 on both sides:
[tex]12-24=-12[/tex]
[tex]x=-12[/tex]
[tex]y=-12[/tex]
Hope this helps.
Math often shows up in sports in ways that we don’t realize. Take for example the baseball diamond. It is actually a square with the bases set at a 90 degree angles. If the bases are 90 feet apart, how far is it from home plate to second base? Round to the nearest tenth.
Distance between home plate and second base: ____________________ feet
Group of answer choices
90
127.3
63.6
145
Answer:
Distance between home plate and second base = 127.3 ft (Approx)
Step-by-step explanation:
Given:
Base distance = 90 ft
Find:
Distance between home plate and second base
Computation:
Distance between home plate and second base = √90²+90²
Distance between home plate and second base = √8100 + 8100
Distance between home plate and second base = √16200
Distance between home plate and second base = 127.3 ft (Approx)