Let [tex]a_n[/tex] denote the n-th term in the progression. So
[tex]a_n=a_{n-1}+d[/tex]
for some constant difference between terms d.
Solve for [tex]a_n[/tex] explicitly:
[tex]a_4=a_3+d[/tex]
[tex]a_5=a_4+d=a_3+2d[/tex]
[tex]a_6=a_5+d=a_3+3d[/tex]
and so on, up to
[tex]a_n=a_3+(n-3)d[/tex]
We're told that the third term is [tex]a_3=4m-2n[/tex], and the ninth term is [tex]a_9=2m-8n[/tex], and according to the recursive rule above, we have
[tex]a_9=a_3+6d[/tex]
Solve for d :
[tex]2m-8n=(4m-2n)+6d[/tex]
[tex]-2m-6n=6d[/tex]
[tex]d=-\dfrac{2m+6n}6=\boxed{-\dfrac{m+3n}3}[/tex]
At the restaurant, the cost of the meal before tax was
$40. The tax is 8.5%, and Sheri wants to leave at least
an 18% tip. Explain how to approximate the total cost of
the meal.
Answer:
so you add then multiply then subtract
Step-by-step explanation:
Answer:
First we estimate the percent's. 8.5% - 10%, 18% - 20%. Then we do the equation. If you add percent's you get 30% multiply that by 40 and you get 12. Add that to you problem and you get $52.
Step-by-step explanation:
Since the tax and gratuity were 4 and 8 dollars you can just add those up to the 40, but I did it another way.
This is the sample response if you want a better explanation.
The gratuity is about 20% of $40, which is $8. The tax is about 10% of $40, which is $4. So, the total cost is about $40 + $8 + $4 = $52.
Find the value of the missing side. a=9 b=12 c=
Answer:
a=9b=12c=15
Step-by-step explanation:
If boxes of chocolates contain chocolates in total, calculate how many chocolates boxes of chocolates will contain
4 divided by 1/5 plzzzz helppppppppppppppppppppppppp
Answer:
the answer is 20
Step-by-step explanation:
Answer:
Your answer is: 20
One of two or more expressions that are multiplied together to get a product.
Factor the numerator and denominator and cancel the common factors.
Step-by-step explanation:
Hope this helped : )
Which of the following sides are congruent?
Answer:
In these two parallelograms, the sides that are same are:
ST = WX
TU = XY
UV = YZ
SV = ZW
Therefore according to the question, the correct option is
d) ST = WX
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What is the square root of 4?
A. 3
B.67
C.2
D.1
Answer:
C. 2
Step-by-step explanation:
Because 4/2=2
Are there any outliers in the data?
Answer:
yes, there are a few outliers
Answer:
Yes
Step-by-step explanation:
30 is an outlier because it is much different from the other data points.
If f(–2) = 0, what are all the factors of the function f(x)=x3-2x2-68x-120 ? Use the Remainder Theorem.
Answer:
it would be option C) (x – 10)(x + 2)(x + 6)
Step-by-step explanation:
You have to divide x^3 -2x^2 -68x -120 by x + 2 to get x^2 - 4x -60 and then factor
The factors of the function are (x + 2)(x - 10)(x + 6).
What is a polynomial?Any expression which is formed by using constants, variables, and exponents is polynomial, it is solved with the help of mathematical operators. Polynomial is made by the parts "poly" and "nominal" here "poly" means many and "nomial" means terms.
Given f(-2) = 0
f(x) = x³ - 2x² - 68x - 120 .........(1)
one factor of function is x + 2
divide the function by x + 2
multiply x² by x +2
x²(x + 2) = x³ + 2x²
subtract the term from equation 1 we get,
x³ - 2x² - 68x - 120 - x³ - 2x²
= -4x² - 68x -120 ......(2)
now multiply -4x by x + 2
-4x(x + 2) = -4x² - 8x
subtract the term from equation 2 we get
-4x² - 68x -120 - (-4x² - 8x)
-60x - 120 ........(3)
again multiply -60 by (x + 2)
-60(x + 2) = -60x - 120
subtract from equation 3
-60x - 120 - (-60x - 120) = 0
The quotient we get from the division is,
x² - 4x - 60
here are the factors of x² - 4x - 60 = (x - 10)(x + 6)
Hence, the factors of polynomials are (x + 2)(x - 10)(x + 6).
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IM TIMED HELP PLS , solve the system of equations using substitution method , y = 2x + 8 , y = 4x - 2
Answer:
x=5, y=18
Step-by-step explanation:
y=2x+8
x= (y-8)/2
Substitute in second equation,
y= 4((y-8)/2) -2
y= 2(y-8)-2
y= 2y-16-2
16+2=2y-y
18=y
Replace y value in first equation to find x,
18= 2x+8
18-8=2x
10=2x
5=x
Find all zeroes of the function. Enter the real zeroes separated by commas.
Answer:
f(x)
=(x-4)[6(x^2)+23x+20]
=(x-4)(2x+5)(3x+4)
x=4,-2/5,-3/4
Help
(3x + 5) + (2x + 3)
1. What is the slope of the following equation? *
y= 3x - 3
A m=2
B m=1/2
Cm=3
Dm=-3
Six equilateral triangles are connected to create a regular hexagon. The area of the hexagon is 24a2 – 18 square units. Which is an equivalent expression for the area of the hexagon based on the area of a triangle?
6(4a2 – 3)
6(8a2 – 9)
6a(12a – 9)
6a(18a – 12)
Which expressions are equivalent to 2[3/4x+7]-3(1/2x-5)? Check all that apply
Answer:
B, C, E
Step-by-step explanation:
This is correct. Trust me.
Answer:B, C, E
Step-by-step explanation:
Ms. Smith has 132 stickers to give to her students. She has 25 students. If she gives the same number of stickers to each of her students, how many stickers will she have left over? *
Answer: 7
To find the remaining amount, we must multiply up to 132.
25 x 5 = 125
Subtract 125 from 132.
132 - 125 = 7
Answer = 7
The number of stickers Ms. Smith has leftover is 7.
Ms. Smith has 132 stickers and 25 students. She gives each student the same number of stickers. In order to determine the number of stickers she would have left, the number of stickers each student got has to be determined first. The stickers each student got can be determined by dividing the total number of stickers by the total number of stickers.
Total number of stickers each student got = total number of stickers / total number of students
132 / 25 = 5 (to the nearest whole number).
The total number of stickers distributed.
5 x 25 = 125.
The total amount of stickers left = 132 - 125 = 7 stickers.
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Which general rule maps abc onto a b c
6(1+x)+x=-14
Please help solve for x
Answer:
X is equal to -10
Step-by-step explanation:
#1. Multiply 6 to (1+x). Doing this makes this equation: 6+x+x=-14
#2. Move 6 to the other side of the equation, to the side of the answer and change its abbsolute value. Doing this will make x+x=-14-6.
#3. Simplify both sides. 2x=-14-6 ----> 2x=-20
#4. divide -20 by 2, this equals -10. x is equal to -10. WooHoo!
Answer:
Answer x=-[tex]\frac{20}{7}[/tex]
Step-by-step explanation:
6(1+x)+x=-14
(multiply bracket with 6)
6+6x+x=-14
(-6 for both sides)
6x+x=-20
(add x terms together)
7x=-20
(divide by 7 for both sides)
x=-[tex]\frac{20}{7}[/tex]
Which of the following numbers could be the probability of an event? 1, 1.39, -0.53, 0, 0.02, 0.26
Answers:
A) 1D) 0E) 0.02F) 0.26If x is a probability value, then [tex]0 \le x \le 1[/tex]
A probability of 0 means "impossible" while a probability of 1 means "100% certain".
what value of x will make the given triangles congruent?
Answer:
2
Step-by-step explanation:
Answer:
x = 10
Step-by-step explanation:
The hypotenuse of each of the triangles have to be equal
7x -5 = 4x+25
Subtract 4x from each side
7x -4x-5 = 4x+25-4x
3x -5 = 25
Add 5 to each side
3x-5+5 = 25+5
3x= 30
Divide by 3
3x/3 = 30/3
x = 10
Reuploaded for about the eighth time, these are the last points I have, please help, I am giving up 100 points. Find the minimum value of f(x, y) = 4x - 2y for the polygonal region determined by the feasible region.
Replace x and Y with the points and solve:
4x -2y
(-4,-1) = 4(-4) - 2(-1) = -16 +2 = -14
(-4,-4) = 4(-4) - 2(-4) = -16 +8 = -8
(2,-3) = 4(2) - 2(-3) = 8 + 6 = 14
(3,-5) = 4(3) -2(-5) = 12 +10 = 22
The minimum value ( lowest ) is -14, which would be (-4,-1)
How do I do this problem
A circular race track has a diameter of 120 ft.about how long would one lap of the track be
Answer:
The length of one lap of the track would be about 377 feet
Step-by-step explanation:
The length of any circular path is equal to the circumference of the circular pathThe circumference of a circle C = π d, where d is the lengths of its diameter∵ A circular race track has a diameter of 120 feet
→ That means the length of each lap equal the circumference of the track
∴ The length of one lap = C
∵ The diameter of the track is 120 feet
∴ d = 120 feet
∵ C = πd
∴ C = π(120)
→ Use π = 3.141
∴ C = (3.141)(120)
∴ C = 376.92 feet
→ Round it to the nearest whole number
∴ C ≅ 377 feet
∴ The length of one lap of the track would be about 377 feet
Write the standard form of the equation:
Slope= 3 y-intercept= -1
Answer:
y=3x-1
Step-by-step explanation:
y=mx+b
y=3x+b
y=3x-1
6 divided by 938 long division
What is the cardinal number of the set containing all negative integers greater than −8?
Answer: positive 7
Step-by-step explanation:
Cardinal number of the set containing all negative integers greater than −8 is 7.
What are cardinal number?In mathematics,cardinal numbers or cardinals for short, are generalization of the natural numbers used to measure the cardinality of sets. The cardinality of a finite set is a natural number: the number of elements in the set.
Now the given set is all negative integers greater than -8.
Let S be the set,so
S = {-7,-6,-5,-4,-3,-2,-1}
now to find the cardinality, we see that set S has 7 elements.
Cardinality of Set S is 7.
Hence, cardinal number of the set containing all negative integers greater than −8 is 7.
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Mrs. Santos can cook the menu for a party in 4 hours. Mr. Salonga can work to fast as she can. If they work together to cook, how many hours will it cake them to finish cooking.
2 hours and 40 minutes
Step-by-step explanation:
Let a be Mrs Santos
Let b be Mr. Salonga
Mrs. Santos can cook the menu for a party in 4 hours
a = 4 hours
Mr. Salonga can work twice as fast as she can.
b = 2 ( 4) = 8 hours
The word time formula is
1/a +1 /b = 1/t
Where t is the total time
Substitute the values
1/4 + 1/8 = 1/t
1/4 + 1/8 = 2/8 + 1/8 = 3/8
Therefore
3/8 = 1/t
Doing cross multiplication
3*t = 1 * 8
3t = 8
Dividing both sides by 3
3t/3 = 8/3
t = 8/3 hours
t =2 \frac{2}{3}t=2
3
2
hours or 2 hours and 40 minutes
4x -2 + 5x +6
What does this equal
Answer:
9x+4
Step-by-step explanation:
The circus had 43,475 guests last year. The fair had 8,034 fewer guests
than the circus. How many guests did the fair have?
Answer:
This year, the circus had 35,441 guests.
Step-by-step explanation:
You just subtract 8,034 from 43,475.
I really hope this helped you!
Confused PLEZZZZZ HELLLPPPP
Answer:B
Step-by-step explanation:
Answer:
believe it is the last one because the room is decreasing at 4 per minute so it would be -4x. Then the room is a 300 capacity so you would minus the -4x from the 300 leaving the formula as p(x)=300-4x
PLEASE HELP!!!
For the quadrant in which the following point is located, determine which of the functions are positive
(5. 7)
sin
sec
cos
cot
csc
tan
Step-by-step explanation:
The given point is
(5,7)
This is a point in the first quadrant.
In this quadrant all are positve.