Arithmetic sequence is done by adding or subtracting the difference. The 12th term of the arithmetic sequence will be 58.
What is the arithmetic sequence?The arithmetic sequence is the series of numbers where every two consecutive terms have the same difference between them.
We know that the nth term of an arithmetic sequence is given as,
[tex]a_n = a_1 + (n-1)d[/tex]
Also, we are given two functions adding the two functions we get,
[tex]f(x) + g(x)\\\\ = 25 + 3(n-1)[/tex]
comparing the sum we get with the arithmetic sequence formula for nth term, we will understand that,
[tex]a_1 + d(n-1)\\25+3(n-1)[/tex]
therefore,
a₁ = 25
and d = 3
that means the first term of the sequence is 25 while the difference between the two terms is 3.
Now, substituting the values in the formula we will get that the 12th terms of the sequence can be written as,
[tex]a_n = a_1 + (n-1)d\\\\a_{12} = 25 + (12-1)3\\\\a_{12} = 25 + 33\\\\a_{12} = 58[/tex]
Hence, the 12th term of the arithmetic sequence will be 58.
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use the distributive property to rewrite this equation.
11x(3x+4y)
Solve the inequality
Answer:
[tex]x\leq 6[/tex]
Step-by-step explanation:
[tex]\frac{3x}{2} \leq 9[/tex]
multiply by 2 to cancel
[tex]3x\leq 18[/tex]
Divide by 3:
[tex]x\leq 6[/tex]
Hope this helps
what is the slope that connects the two points ( -1,-2) and (4,4)
8th grade math.
Answer:
6/5
Step-by-step explanation:
rise/run
I hope this is right! :D
Answer:
The slope would be 6/5
hello can someone help me with this factoring problem? thank you!
Please help me I really need help ?
Answer:
1. 1/5 1/3 4/6
2. 3/5 3/4 7/8
3. 87 nickels
4. 150 minutes
5. 2
6. 3/4
Step-by-step explanation:
1. least to greatest: 1/5 1/3 4/6
2. least to greatest: 3/5 3/4 7/8
3. 1 nickel = 5 cents
So 485 ÷ 5 = 87 nickels
4. Total number of minutes = 50 x 2 = 150 minutes
5. A composite number is a whole number that can be made by multiplying other whole numbers.
3 x 3 = 9 ⇒ composite number
3 x 5 = 15 ⇒ composite number
3 x 7 = 21 ⇒ composite number
Therefore 2 is NOT a composite number (it is a prime number)
6. 6/8 = 3/4
An article reports "attendance dropped 2% this year, to 3750." What was the attendance before the drop?
Answer:
7,500 was the attendance before the drop.
Step-by-step explanation:
3750 x 2
Surface Area of Cylinder=2πrh+2πr2
Where r is the radius of the cylinder and h is the height of the cylinder.
Find the surface area when r is 8 inches and h is 8 inches.
A. 160π in²
B. 154π in²
C. 288π in²
D. 256π in²
Answer:
D. [tex]256\pi\ in^2[/tex]
Step-by-step explanation:
To do this, we need to plug in the given values into the equation:
[tex]SA=2\pi rh+2\pi r^2\\SA = 2\pi 8(8)+2\pi 8^2\\SA=2\pi 64+2\pi 64\\SA=128\pi + 128\pi\\SA=256\pi \ in^2[/tex]
Given cos0=3/4 and angle 0 is in Quadrant I, what is the exact value of sin 0 in
simplest form? Simplify all radicals if needed.
Answer:
sinθ=√7/4
Step-by-step explanation:
Here,
cosθ=3/4
b/h=3/4
b=3 and h=4
Using Pythagoras theorem,
h²=p²+b²
4²=p²+3²
16-9=p²
p=√7
Now,
sinθ=√7/4
The area of a rectangle is 168 cm^2. The rectangle has a perimeter of 52 cm. What are the dimensions of the quadrilateral?
Answer:
12 cm by 14 cm
Step-by-step explanation:
The area is given by ...
A = LW
The perimeter is given by ...
P = 2(L +W)
Substituting the given values, we have ...
168 = LW
52 = 2(L +W)
The second equation can be used to find an expression for L:
26 = L +W . . . . . divide by 2
L = 26 -W . . . . . subtract W
Using this in the first equation, we have ...
168 = (26 -W)(W)
W² -26W +168 = 0
Factors of 168 are ...
168 = (-1)(-168) = (-2)(-84) = (-3)(-56) = (-4)(-42) = (-6)(-28) = (-7)(-24)
= (-8)(-21) = (-12)(-14)
Only the last factor pair (-12, -14) has a sum of -26, so the equation factors as ...
(W -12)(W -14) = 0
Solutions are W=12, and W=14. The corresponding values of L are 14 and 12.
The quadrilateral has dimensions of 12 cm and 14 cm.
The stigma is the opening in a flower through which pollen moves to fertilize the eggs. Which characteristic would be most helpful to the stigma in capturing pollen?.
Answer:
having a sticky surface
Step-by-step explanation:
Just took the tests
What is the measure of angle 1?
Answer:
88
Step-by-step explanation:
92 and angle 2 are corresponding and 180-92= 88
Write a word problem that must be solved with division and includes 2/7 as the dividend and 4 as the divisor.
The word problem that must be solved with division and includes 2/7 as the dividend and 4 as the divisor is that John wants to buy a 4 yards cloth qnd there are pieces of 2/7 yards each. How many pieces will he buy?
How to calculate the value?In this case, it should be noted that division is used.to separate into different parts.
Therefore, John wants to buy a 4 yards cloth qnd there are pieces of 2/7 yards each.
The pieces to be bought will be:
= 4 ÷ 2/7
= 4 × 7/2
= 14
He'll buy 14 pieces.
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Help me with this question please this is due today
please can you help me on this mathswacth question?
Answer:
84 cm
Step-by-step explanation:
the area of a parallelogram is the how tall is it times it by the how long the base
(H x B)
the answer is 84 cm
Ryan works at the car wash making $5. 30 per hour plus tips. Last week Ryan worked 32 hours and earned $403. How much in tips did Ryan make last week? a. $86. 40 b. $148. 00 c. $169. 60 d. $233. 40 Please select the best answer from the choices provided A B C D.
Answer:
d. $233.40
Step-by-step explanation:
you solve this by first multiplying Ryan's hourly rate($5.30) by how many hours he worked last week(32 hours)
5.30*32=169.6
then you take that number and subtract it from how much he earned($403) and the resulting number will be what he made in tips
403-169.9=233.40
Answer:
d. $233.40
Step-by-step explanation:
pay for 32 hours
= $5.30 × 32
= $169.60
tips = $403 - $169.60
= $233.40
HELP ASSAAPPP
The first term of a geometric sequence is 3, and the common ratio is 3.
What is the 7th term of the sequence?
Please help solve this 6r-r+4
Answer:
5r+4
Step-by-step explanation:
Let's simplify step-by-step.
6r−r+4
=6r+−r+4
Combine Like Terms:
=6r+−r+4
=(6r+−r)+(4)
=5r+4
Please help quick !
Answer:
10 A. Quadrent 2
10 B. Quadrent 3
Step-by-step explanation:
Image
Can you figure out what the answer is here?
Answer:
Triangle = 10
Circle = 5
Two halves of Square = 2
Fourth answer: 20
Step-by-step explanation:
Figuring out the triangle first is easiest because since 3 triangles make 30, then each triangle must be 10.
Now, we have our second equation become 10 + C + C = 20, and we get C=5 after solving for the value of the circle.
Our third equation will be 5 + S + S = 13, which becomes 5+2S=13, 2S=8, and then S=4, so the value of a square is 4
Our fourth equation will be 10 + 5*(1/2)(4) = ?, and we see that half of 4 is 2, so we have 10 + 5(2) = 10 + 10 = 20 as our answer.
The value of the given expression x + yz will be 20.
What is the solution to the equation?The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.
Let 'x' represents an equilateral triangle, 'y' represent a circle, and 'z' represents the right triangle. Then the equations are given as,
x + x + x = 30
3x = 30
x = 10
x + y + y = 20
10 + 2y = 20
y = 5
y + 2z + 2z = 13
5 + 4z = 13
z = 2
Then the value of the expression is calculated as,
x + yz = 10 + 5 × 2
x + yz = 10 + 10
x + yz = 20
The value of the given expression x + yz will be 20.
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Anyone able to help me with this???? Need it ASAP!! Please and thank youuu
Answer:
(4, -3)
Step-by-step explanation:
Rewrite equations:
x−2y=10;6x+3y=15
Step: Solvex−2y=10for x:
x−2y=10
x−2y+2y=10+2y(Add 2y to both sides)
x=2y+10
Step: Substitute2y+10forxin6x+3y=15:
6x+3y=15
6(2y+10)+3y=15
15y+60=15(Simplify both sides of the equation)
15y+60+−60=15+−60(Add -60 to both sides)
15y=−45
15y
15
=
−45
15
(Divide both sides by 15)
y=−3
Step: Substitute−3foryinx=2y+10:
x=2y+10
x=(2)(−3)+10
x=4(Simplify both sides of the equation)
Therefore answer: is
x=4 and y=−3
Hope it helps!
A spinner is shown.
Red
Violet
Orange
Indigo
Yellow
Blue
Green
The spinner arrow is spun 150 times
Ahout how many times will the spinner arrow stop on Blue or Green?
Answer:
43
Step-by-step explanation:
Total number of different colors = 7
Probability of spinner landing on blue = 1/7
Probability of spinner landing on green = 1/7
Probability of spinner landing on blue OR green = 1/7 + 1/7 = 2/7
if the spinner is spun 150 times,
Number of times spinner will land on green or blue = Probability of spinner landing on blue OR green x 150
= 2/7 x 150
= 42.85714...
= 43 (rounded to the nearest whole number)
Answer:
Approximately 43 timesStep-by-step explanation:
Number of sections is 7
Probability of each section is 1/7
Probability of blue or green:
P(blue or green) = 2*1/7 = 2/7Spinner nun 150 times, number of stops on blue or green:
N = 2/7*150 = 42.86 ≈ 43 (rounded up)write 8029.85 in scientific notation
Help me please????????
A rectangular box is 1m long and 75 cm high. if the volume of the box is 375000cm³,find the width of the box
Answer:
width = 50 cm
Step-by-step explanation:
The volume (V) of a rectangular box is calculated as
V = lwh ( l is length, w is width and h is height )
Since V is given in cm³ then dimensions must be in cm
l = 1 m = 100 cm , then
100 × w × 75 = 375000
7500w = 375000 ( divide both sides by 7500 )
w = 50
the width of the box is 50 cm
The two triangles below are similar. What is the perimeter of triangle XYZ?
Answer:
24 units
Step-by-step explanation:
create a proportion:
15/20 = 6/XY
cross-multiply:
15·XY = 120
XY = 8
15/25 = 6/YZ
cross-multiply:
15·YZ = 150
YZ = 10
Perimeter:
6 + 8 + 10 = 24
What is the slope of the line that passes through the points (1, -7) and (-2,-7)? Write your answer in simplest form.
Answer:
0
Step-by-step explanation:
its a straight line horizontally
(PLEASE HELP!) (IM GIVING GOOD POINTS!)
Yutto is writing a paper, and he notices he can write 1.25 pages every 2 hours. He estimates he can finish the six-page paper in 6 hours.
Is his estimate reasonable, why or why not?
No, he incorrectly rounded 1.25 to 2.No, he incorrectly rounded 1 point 2 5 to
No, he incorrectly rounded 6 to 6.5.No, he incorrectly rounded 6 to
Yes, he correctly rounded 1.25 to 2.Yes, he correctly rounded 1 point 2 5 to
Yes, he found the exact time.
Answer:
No, he incorrectly rounded 1.25 to 2
Step-by-step explanation:
hope this helps :)
Answer:
No, he incorrectly rounded 1.25 to 2
Step-by-step explanation:
To find out how many pages Yutto writes in 1 hour we divide
1.25/2=0.625
Now we multiply
0.625×6=3.75
3.75≠6
So now we know that Yutto was incorrect so we can eliminate the last two options. Now how did he get his original estimate? For option A,
1.25 is rounded to 2
2/2=1
1×6=6
So the answer is A
In a concert band, the probability that a member is in the brass section is
0.50. The probability that a member plays trombone, given that he or she is in
the brass section, is 0.24.
What is the probability that a randomly selected band member is in the brass
section and plays trombone?
A. 0.74
• B. 0.26
O C. 0.48
D. 0.12
Answer:
D
Step-by-step explanation:
the odds are less than .24 so it must be 0.12
If a plane can travel 480 miles per hour with the wind and 420 miles per hour against the wind, find the speed of the wind and the speed of the plane in still air.
a. The speed of the wind is 30 mph
b. The speed of the plane in still air is 450 mph
Let
V = speed of plane in still air and v = speed of wind.The required equationsSince the plane can travel 480 miles per hour with the wind, we have that
V + v = 480 (1)
Also, the plane travels 420 miles per hour against the wind, we have that
V - v = 420 (2)
a. Speed of the windThe speed of the wind is 30 mph
subtracting equations (1) and (2), we have
V + v = 480 (1)
-
V - v = 420 (2)
2v = 60
v = 60/2
v = 30 mph
So, the speed of the wind is 30 mph
b. Speed of the plane in still air
The speed of the plane in still air is 450 mph
Substituting v into equation (1), we have
V + v = 480 (1)
V + 30 = 480
V = 480 - 30
V = 450 mph
So, the speed of the plane in still air is 450 mph
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Mario has gross biweekly earnings of $784. 21. By claiming 1 more withholding allowance, Mario would have $13 more in his take home pay. How many withholding allowances does Mario currently claim? a. 3 b. 4 c. 5 d. 6 Please select the best answer from the choices provided A B C D.
The number of withholding allowances which Mario currently claim for her gross biweekly earnings of $784. 21 is 4.
What is federal income tax?Federal income tax is the tax which is used to develop and run the city or country and charged on the citizen residing there .
Mario has gross biweekly earnings of $784.21. By claiming 1 more withholding allowance, Mario would have $13 more in his take home pay.
The value $784.21 lies between $780 and $800. Here, in the problem, the Mario can claim $13 more in his take home pay.
Form, the table of Federal income tax, the calculated amount will be,
[tex]n=20-7\\n=13[/tex]
Now, again from the table, Mario still claim 4 withholding allowances currently.
The number of withholding allowances which Mario currently claim for her gross biweekly earnings of $784. 21 is 4.
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