Recursive formula of an arithmetic sequence is given by the expression,
[tex]T_n=a+(n-1)d[/tex]
Where, [tex]T_n=[/tex] nth term
[tex]a=[/tex] First term of the sequence
[tex]n=[/tex] Number of term
[tex]d=[/tex] Common difference
Therefore, number of sticks in the 6th pattern are 32.
And number of sticks in the nth pattern are [tex]T_n=5n+2[/tex]
From the picture attached,
Number of sticks in 1st pattern = 7
Number of sticks in 2nd pattern = 12
Number of sticks in 3rd pattern = 17
Sequence formed is 7, 12, 17..... nth term
This sequence has a common difference of 5 in each successive term so it will be an arithmetic sequence.
Therefore, nth term of the sequence will be,
[tex]T_n=a+(n-1)d[/tex]
[tex]T_n=7+(n-1)5[/tex]
[tex]T_n=5n+2[/tex]
If [tex]n=6,[/tex]
[tex]T_n=7+(6-1)5[/tex]
[tex]T_n=7+25[/tex]
[tex]T_n=32[/tex]
Learn more,
https://brainly.com/question/1606280
Which equation can be used to find 40 percent of 25? StartFraction 25 divided by 1 Over 40 divided by 1 EndFraction = StartFraction 25 Over 40 EndFraction StartFraction 100 times 4 Over 40 times 4 EndFraction = StartFraction 400 Over 16 EndFraction StartFraction 40 times 4 Over 25 times 4 EndFraction = StartFraction 160 Over 100 EndFraction StartFraction 40 divided by 4 Over 100 divided by 4 EndFraction = StartFraction 10 Over 25 EndFraction
Answer:
d
Step-by-step explanation:
Answer:
I think it's D
Step-by-step explanation:
Sorry if im wrong.
Write the equation of the line that passes through the point (8, -2) and whose slope is 1/4
Step-by-step explanation:
y + 2 = 1/4(x - 8)
y +2 =1/4x - 2
y = 1/4x - 4
Which is equivalent to 4V91/2
Answer:
B.
Step-by-step explanation:
= [tex]\sqrt[4]{9} ^{x/2}[/tex]
= Since [tex]\sqrt[4]{} = 1/4[/tex]
= So, [tex]9^{1/4*x/2}[/tex]
= [tex]9^{\frac{x}{8}[/tex]
Answer:
option B
Step-by-step explanation:
[tex](\sqrt[4]{9})^{\frac{1}{2}x} =(9^{\frac{1}{4}})^{\frac{1}{2}x}\\\\=9^{\frac{1}{4}*\frac{1}{2}x}\\\\=9^{\frac{1}{8}x}[/tex]
2x-4=-4x+6
What value of x makes the equation true
A x=5/3
B x=-5/3
C x=5
D x=-5
Answer: 5/3
6x = 10
x=10/6
x=5/3
Answer:
x = 5/3
Step-by-step explanation:
2x-4=-4x+6
Add 4x to each side
2x+4x-4=-4x+4x+6
6x -4 = 6
Add 4 to each side
6x -4 +4 = 6+4
6x = 10
Divide each side by 6
6x/6 = 10/6
x = 5/3
Merryvale Orchards sold 85 bags of oranges yesterday. Each bag contained 32 oranges. Round each number to the nearest ten to estimate the number of oranges sold
Answer:
2720 oranges were sold
What is the length of ED
Answer:
ED ≈ 2.6 units
Step-by-step explanation:
Using the Sine rule in Δ DEF
[tex]\frac{FD}{sin115}[/tex] = [tex]\frac{ED}{sin20}[/tex]
[tex]\frac{6.95}{sin115}[/tex] = [tex]\frac{ED}{sin20}[/tex] ( cross- multiply )
ED sin115° = 6.95 sin20° ( divide both sides by sin115° )
ED = [tex]\frac{6.95sin20}{sin115}[/tex] ≈ 2.6 ( to the nearest tenth )
A jar contains 4 red marbles, 6 blue marbles, 3 yellow marbles, and 5 green marbles. If one marble is randomly selected, what is the probability that it is red or green?
Answer:
1/2
Step-by-step explanation:
4 red marbles, 6 blue marbles, 3 yellow marbles, and 5 green = 18 marbles
P( red or green) = red or green / total
= (4+5) / 18
= 9/18
=1/2
Answer:
50%
Step-by-step explanation:
4 red + 5 green = 9 marbles
total marbles = 18 marbles
9 is 50% of 18
How many moles of sulfate will be formed if you start with 2.80 moles of sodium hydroxide and you have an excess of sulfuric acid
Answer:
1.4 mol
Step-by-step explanation:
2NaOH + H2SO4 -----> Na2SO4 + 2H2O
from reaction 2 mol 1 mol
given 2.8 mol x
x = (2.8*1)/2 = 1.4 mol
The LCM of three numbers is 7920 and their GCD is 12. Two of the numbers are 48 and 264. Using factor notation find the third number if one of its factors is 9.
Answer:
The third number is 180.
Step-by-step explanation:
Let the third number be 9x where x is an integer.
48 = 2*2*2*2*3
264 = 2*2*2*3*11
9x = 3*3*x
2*2*2*2*3*3*11*x = 7920y where y is an integer
1584x = 7920y
so x = 7920y / 1584= 5y.
Now the GCD is 12 so x must have 4 as one of its factors.
Also x is a multiple of 5 so it could be 20 then y would be 4.
If x = 20 then the third number is 9*20 = 180.
This checks out OK.
What’s the answer I need help plssssssssss
Answer:
[tex]\frac{\sqrt[3]{19} }{\sqrt[3]{x} }[/tex]
So A is the answer
Step-by-step explanation:
[tex]y=\frac{19}{x^3}\\\mathrm{Interchange\:the\:variables}\:x\:\mathrm{and}\:y\\x=\frac{19}{y^3}\\\mathrm{Solve}\:x=\frac{19}{y^3}\:\mathrm{for}\:y\\y=\sqrt[3]{\frac{19}{x}}\\\sqrt[3]{\frac{19}{x}}\\\frac{\sqrt[3]{19} }{\sqrt[3]{x} }[/tex]
a food manufacturer recently developed a new preservative to extend the shelf life of its perishable food items. It makes two batches of the perishable items. The preservative is added only to the second batch. After some time, researcher compares the shelf life of the batches. which method is the researcher applying?
Answer:
The researcher is using the Experiment method
Step-by-step explanation:
Plato
Answer:
Experiment
Step-by-step explanation:
PLATO/Edmentum
I GOT IT RIGHT!!!
For which table would 70 be the missing value,x?
It is C
The Stone and Pounds
Answer:
c
Step-by-step explanation:
What are the domain and range of f(x) = |x + 6|?
Answer:
The domain is (-∞,∞)
The range is [0,∞)
Step-by-step explanation:
The graph will be a V shape facing upwards with a vertex of (-6,0)
Answer:
Domain = (-∞,∞)
Range = [0,∞)
Step-by-step explanation:
Anyone know this ? Need help :(
Answer:
19
Step-by-step explanation:
We can multiply the exponents, giving us 19 ^ (1/9 * 9) = 19 ^ 1 = 19.
Answer:
19
Step-by-step explanation:
(19^1/9)^9
19^(1/9*9)
19^1
19
Can someone help me with this please
3 lines are shown. A line with points M, H, K intersects a line with points J, H, L at point H. A line extends from point H to point P between angle K H J. Angle M H L is 140 degrees and angle K H P is 20 degrees. What is mAnglePHJ? 100° 120° 140° 160°
Answer:
The answer is 120 degrees
Step-by-step explanation:
your welcome!!!!!!!!!!!!
Answer:
120
Step-by-step explanation:
edge 2022
If you add the digits in a two-digit number and multiply the sum by 7, you get the original number. If you reverse the digits in the two-digit
number, the new number is 18 more than the sum of its two digits. What is the original number?
O A 42
B. 24
C. 64
D.46
E.36
Answer: A - 42
Step-by-step explanation:
Let x= ones digit, y=tens digit
1st (original number) :
7(x+y)=10y + x
2nd (new number by reversing the digits): 18+x+y=10x+y
simplifying:
1st condition: 6x=3y
2nd condition: x=2
substituting x=2 to 6x=3y
y=4
Answer:
The answer is 42 but let me tell you this question made my brain cell work an all nighter from how bad I am at riddles LOL
Step-by-step explanation:
What is the product? Assume x greater-than-or-equal-to 0 (StartRoot 3 x EndRoot + StartRoot 5 EndRoot) (StartRoot 15 x EndRoot + 2 StartRoot 30 EndRoot)
Answer:
[tex]3\sqrt5 x+ \sqrt x (6 \sqrt{10} +5\sqrt{3}) +10 \sqrt6[/tex]
Step-by-step explanation:
To find the product :
[tex](\sqrt{3x} +\sqrt5)(\sqrt{15x} +2\sqrt{30})[/tex]
[tex]\sqrt{3x}(\sqrt{15x} +2\sqrt{30}) +\sqrt5(\sqrt{15x} +2\sqrt{30})\\\Rightarrow \sqrt{3x}\times \sqrt{15x} +\sqrt{3x}\times 2\sqrt{30} +\sqrt5 \times \sqrt{15x} +\sqrt5\times 2\sqrt{30}\\\Rightarrow \sqrt{45} \times x + 2 \sqrt{90x} + \sqrt{75x} + 2 \sqrt{150}\\\Rightarrow \sqrt{5 \times 9} \times x + 2 \sqrt{9\times 10x} + \sqrt{25 \times 3x} + 2 \sqrt{25 \times 6}\\\Rightarrow 3\sqrt5 x+ 2 \times 3 \sqrt{10x} +5\sqrt{3x} +2 \times 5 \sqrt6\\\Rightarrow 3\sqrt5 x+ 6 \sqrt{10x} +5\sqrt{3x} +10 \sqrt6[/tex]
[tex]\Rightarrow 3\sqrt5 x+ \sqrt x (6 \sqrt{10} +5\sqrt{3}) +10 \sqrt6[/tex]
Some identities used:
1. [tex](a+b)(c+d) = a (c+d) + b(c+d)[/tex]
2. [tex]\sqrt9 =3[/tex]
3. [tex]\sqrt{25} =5[/tex]
4. [tex]\sqrt x \times \sqrt x=x[/tex]
5. [tex]\sqrt a \times \sqrt b = \sqrt{ab}[/tex]
So, the solution is [tex]3\sqrt5 x+ \sqrt x (6 \sqrt{10} +5\sqrt{3}) +10 \sqrt6[/tex]
Answer:it’s b
Step-by-step explanation:
On edge
Which division problem would have an estimated quotient of 3.5 if the divisor and dividend were rounded to the nearest whole number?
Answer:
Step-by-step explanation:
Weren't there possible answer choices from which to choose? If so, please share them.
7 3 + 4
-- is equivalent to ---------- and has an estimated (and exact) quotient of 3.5.
2 2
If the divisor (2) and the dividend (7) were rounded to the nearest whole number (which would be 7), the estimated quotient would still be 3.5.
Answer:
7 3 + 4
-- is equivalent to ---------- and has an estimated (and exact) quotient of 3.5.
2 2
Step-by-step explanation:
How many solutions does this linear system have?
Y= -1/2x + 4 x + 2y=-8
Answer:
No solutions
Step-by-step explanation:
[tex]y=-\dfrac{1}{2}x+4 \\\\x+2y=-8[/tex]
Substitute:
[tex]x+2(-\dfrac{1}{2}x+4)=-8\\\\x-x+8=-8\\\\8=-8[/tex]
This system has no solutions.
Hope this helps!
What is the probability brittnie gets at least 35 hits in her next 100 at bats? (round to 3 decimal places.)?
Answer:
0.350
Step-by-step explanation:
Probability is defined as the chances that an event will occur or not occur. The entire idea of probability has to do with 'chance' events. Thus, the probability that an event will surely occur is 1, while the probability that an event will never occur is zero. Probabilities range between 0-1.
Probability of an event is obtained from
Probability= expected outcome/total number of outcomes
In this case,
Expected outcome= 35
Total number of outcomes = 100
Probability= 35/100= 0.350
A brick weighs w
kg. Write an expression for the weight of 2 bricks
Answer:
2w
Step-by-step explanation:
weight of 1 brick = w
so to find the weight of 2, times it by 2, which leaves you with 2w
Find the surface area of the composite solid.
PLZ HELP
Answer:
613.5 m^2
Step-by-step explanation:
The area of the base is
A = 1/2 bh
= 1/2 (10) (8.7) =43.5 m^2
We have three sides with all the same area
The area of one side is 10 * 16 = 160
3 * 160 = 480 m^2
Now to the top
We have 3 sides with the same area
The area of one side
A = 1/2 bh
A = 1/2 (10) (6)
= 30 m^2
3* 30 = 90
Add all the areas together to get the total surface area
43.5 m^2+ 480 m^2 + 90 m^2
613.5 m^2
Answer:
[tex]\Huge \boxed{\mathrm{613.5 \ m^2 }}[/tex]
[tex]\rule[225]{225}{2}[/tex]
Step-by-step explanation:
We can find the total surface area by adding the surface area of the triangular prism with the surface area of the triangular pyramid at the top.
Surface area of the triangular prism:
10 × 8.7 × 1/2 + 16 × 10 × 3
⇒ 523.5
Surface area of the triangular pyramid:
6 × 10 × 1/2 × 3
⇒ 90
Adding the surface areas:
523.5 + 90
⇒ 613.5
[tex]\rule[225]{225}{2}[/tex]
Which fraction is equivalent to StartFraction 2 Over 6 EndFraction? StartFraction 3 Over 7 EndFraction, because StartFraction 2 Over 6 EndFraction = StartFraction 2 + 1 Over 6 + 1 EndFraction = StartFraction 3 Over 7 EndFraction StartFraction 3 Over 9 EndFraction, because StartFraction 2 Over 6 EndFraction = one-third and One-third = StartFraction 3 Over 9 EndFraction StartFraction 3 Over 12 EndFraction, because StartFraction 2 Over 6 EndFraction = one-third and One-third = StartFraction 3 Over 12 EndFraction StartFraction 3 Over 8 EndFraction, because StartFraction 2 Over 6 EndFraction = one-half = StartFraction 2 + 1 Over 6 + 2 EndFraction = StartFraction 3 Over 8 EndFraction
Question:
Which fraction is equivalent to [tex]\frac{2}{6}[/tex]?
- [tex]\frac{3}{7}[/tex] because [tex]\frac{2}{6}= \frac{2 + 1}{6 + 1}[/tex]
- [tex]\frac{3}{9}[/tex] because [tex]\frac{2}{6}= \frac{1}{3}[/tex] and [tex]\frac{1}{3} = \frac{3}{9}[/tex]
- [tex]\frac{3}{12}[/tex] because [tex]\frac{2}{6}= \frac{1}{3}[/tex] and [tex]\frac{1}{3} = \frac{3}{9}[/tex]
- [tex]\frac{3}{8}[/tex] because [tex]\frac{2}{6}= \frac{1}{2} = \frac{2+1}{6+2} = \frac{3}{8}[/tex]
Answer:
- [tex]\frac{3}{9}[/tex] because [tex]\frac{2}{6}= \frac{1}{3}[/tex] and [tex]\frac{1}{3} = \frac{3}{9}[/tex]
Step-by-step explanation:
Two fractions are said to be equal if and only if they give the same value when simplified.
The equivalent of [tex]\frac{2}{6}[/tex] is as explained in the selected option;
First, divide numerator and denominator by 2
[tex]\frac{2/2}{6/2}[/tex]
Then simplify
2/2 = 1 and 6/2 = 3; So;
[tex]\frac{2/2}{6/2} = \frac{1}{3}[/tex]
Multiply numerator and denominator by 3
[tex]\frac{1*3}{3*3} = \frac{3}{9}[/tex]
Hence, [tex]\frac{2}{6}[/tex] is equivalent to [tex]\frac{3}{9}[/tex]
Answer:
B
Step-by-step explanation:
StartFraction 3 Over 9 EndFraction, because StartFraction 2 Over 6 EndFraction = one-third and One-third = StartFraction 3 Over 9 EndFraction
Choose the most appropriate name for the function described below.
The temperature of the coffee depends on the number of minutes it sits on
the desk.
Answer:
D. Temperature(minutes), or t(m)
Step-by-step explanation:
Option D is the correct answer.
( D.temperature(minutes), or t(m) )
Step-by-step explanation:
We are given that:
The temperature of the coffee depends on the number of minutes it sits on the desk.
i.e. the temperature(t) of coffee is a function of time in minutes (t).
i.e. times is a independent variable and temperature is a dependent variable.
Hence, the most appropriate name for the function described below is:
temperature(minutes), or t(m).
Hence, option D is correct.
Answer:
Temperature is the answer
Step-by-step explanation:
I got it right
To solve the equation, Antwan uses the distributive property, combines like terms, then uses the addition and subtraction properties of equality to isolate the variable term on one side of the equation and the constant term on the other side. What are the possible values of the constant after Antwan has completed these steps?
3 (1/3x + 1) + 4 = -1 - 4 (x + 3)
A.) –3 or 3
B.) –3 or 5
C.) –20 or 5
D.) –20 or 20
Answer:
the answer is D
Step-by-step explanation:
i only need help with B
Answer:
it will take 3 sticks to make pattern n
_
| |
Can someone please help me I’m stuck I don’t know what
Answer:
x = 7.5
Step-by-step explanation:
Given BE is parallel to CD and intersects the other 2 sides, it divides those sides proportionally, that is
[tex]\frac{AE}{ED}[/tex] = [tex]\frac{AB}{BC}[/tex] , substitute values
[tex]\frac{10}{8}[/tex] = [tex]\frac{x}{6}[/tex] ( cross- multiply )
8x = 60 ( divide both sides by 8 )
x = 7.5
A plumber charges $70 per hour plus $40 for the call. What does he charge for 4 hours of work? Use x to represent the hours of work.
Answer:
Step-by-step explanation:
70x4 is 280 plus 40 is 320.
Answer:
$320
Step-by-step explanation:
(4 x $70) + $40 is the equation
$280 + $40 = $320
$320
Question 3: Marla bought one necklace and two bracelets for $67.50. Use the following information to determine the amount she paid for each bracelet: The price of the necklace was $27. The bracelets were both the same price. Enter your numerical answer only in the box; do not include the dollar sign.
Answer:
Each bracelet costs 20.25
Step-by-step explanation:
Here's what was given in the equation:
Total Price: $67.50
Price of necklace: $27
We can subtract the $27 from the $67.50 to get $40.5
Since we know that both bracelets are the same price we can divide the $40.5 by 2 to get two of the exact same prices. The result is $20.25 for each bracelet.
Hope this helps
Answer:
20.25
Step-by-step explanation:
Took test got it right.