Answers
Each time 5 sticks are added. So pattern 6 would have 25 stickers added to the original 7 sticks equaling 32 sticks
B)n=5x+7
Related Questions
show that the roots of the quadratic equation given by(x-a)(x-b)+(x-b)(x-c)+(x-c)(x-a)=0
are rea land they can not be equal unless a=b=c.
Answers
Expanding out the equation, we get
[tex]x^2 - ax - bx+ab+x^2 -bx-cx+bc+x^2 -ax-cx+ac=0 \\ \\ 3x^2 -x(2a+2b+2c)+(ab+bc+ac)=0[/tex]
Considering the discriminant,
[tex](2a+2b+2c)^2 - 4(3)(ab+bc+ac) \\ \\ =4a^2 + 4b^2 + 4c^2 + 8(ab+bc+ac)-12(ab+bc+ac) \\ \\ =4(a^2 + b^2 + c^2 - ab - bc - ac) \\ \\ =2((a-b)^2 + (b-c)^2 + (c-a)^2)[/tex]
This is always non-negative, meaning the roots are real.
The roots are equal if and only if the discriminant is 0, which is when a=b=c.
adam has $800 invested in two accounts. one pays 6% annual interest and the other pays 10% interest. the amount of annual interest is the same as he would earn if the entire $800 was invested at 8.25%. How much does he have invested at each rate?
Answers
Adam invested $350 at 6% and $450 at 10%
Amount invested by Adam = $800
Interest paid by one account = 6%
Interest paid by another account = 10%
Let the amount invested in one account be x and the other be y
The formula for simple interest is given by:
Simple interest = (P*R*T)/100
where P = Principal
R = rate of interest
T = number of years amount is invested
Substituting the value in the formula we get:
Simple interest in one account = (x*6*1)/100-------(1)
Simple interest in another account = (y*10*1)/100--------(2)
The question states that interest earned would be the same when $800 is invested at 8.25%, therefore
Simple interest = (800*8.25*1)/100
= 66----(3)
Equating (1), (2) and (3) we get:
x + y = 800-----(4)
6x/100 + 10y/100 = 66
6x + 10y = 6600-----(5)
Multiplying (4) with 6 and equating it with (5)
6x + 6y = 4800
6x + 10y = 6600
4y= 1800
y = 450
x = 350
So, Adam invested $350 at 6% and $450 at 10%
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HELP PLEASE DUE TODAY
Answers
12) Z ∪ N = {Set of Integers}
13) H ∪ Q = R which is a set of real numbers
How to classify numbers?
We are told that;
R = U represents the set of real numbers
N is the set of natural numbers
W is the set of whole numbers
Z is the set of integers
Q is the set of rational numbers
H is the set of irrational numbers
12) We want to find Z ∪ N. This is a set union of the set of integers and the set of natural numbers.
A rational number is a number that is expressed as the ratio of two integers, where the denominator should not be equal to zero. Thus, an integer is also a rational number and all natural numbers are positive integers and as such;
Z ∪ N = {Set of Integers}
13) We want to find H ∪ Q. This is a set union of the irrational numbers and the set of rational numbers. Now, we know that all real numbers are classified as either rational or irrational numbers
Thus; H ∪ Q = R which is a set of real numbers
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Please help I will give anyone brainliest
Answers
Answer:
1672.50 = 37.75x + 1068.50
x = 16
There were 16 players brought to the tournament.
Step-by-step explanation:
y = mx + b
y= the total cost
m = cost of each meal
x = the number of players
b = cost of the bus
Plug in what you know and solve for x
1672.50 = 37.75x + 1068.50 Subtract 1068.50 from both sides.
604 = 37.75x Divide both sides by 37.75
16 = x
Equation: 1068.50 + 37.75x =1,672.50
Answer: X= 16
If 1,672.50 is our total it will go behind the equal sign. 37.75x and 1068.50 must be added together to help us receive our total.
Our written equation should look like this
1068.50 + 37.75x =1,672.50
X is the number of players on the team.To find out we must first subtract the amount of money spent on the bus, from the total amount spent.
1,672.50-1068.50 is 604. This means our equation now looks like this
37.75x=604. The next and final step is to divide 37.75 into 604.
604/ 37.75 is 16. Which means that there are 16 players on the team.
I hope this helps & Good luck.
XZ is the perpendicular bisector of segment WY. Solve for m. Enter a NUMBER only.
Answers
2(14m-8)=180
24m-16=180
24m=196
m= 8 and 1/6
Can someone explain this pls
Answers
Answer:
Step-by-step explanation:
( g ° f )(x) = ( x + 7 )² = x² + 14x + 49
20 + 3(x² + 14x + 49) = - 34
20 + 3x² + 42x + 147 = - 34
3x² + 42x + 201 = 0 ⇔ x² + 14x + 67 = 0
D = 196 - 268 = - 72 < 0
There is no any roots in set of real numbers.
The values of x in set of complex numbers are:
[tex]x_{12}[/tex] = [tex]\frac{- 14 }{2}[/tex] ± [tex]\frac{6\sqrt{2}i }{2}[/tex]
[tex]x_{12}[/tex] = - 7 ± 3√2 i
How much should Roman invest today in order to withdraw $22450.15 in exactly 3.7 years from now if interest rate is 5.65 % compounded monthly?
Answers
Roman should invest $18,223.97 in order to withdraw $22450.15 in exactly 3.7 years from now if interest rate is 5.65 % compounded monthly.
First, convert R as a percent to r as a decimal
r = R/100
r = 5.65/100
r = 0.0565 per year,
Then, solve the equation for P
P = A / (1 + r/n)^(nt)
P = 22,450.15 / (1 + 0.0565/12)^{(12)(3.7)}
P = 22,450.15 / (1 + 0.0047)(44.4)
P = $18,223.97
The principal investment required to get a total amount of $22,450.15 from compound interest at a rate of 5.65% per year compounded 12 times per year over 3.7 years is $18,223.97.
Therefore, Roman should invest $18,223.97 in order to withdraw $22450.15 in exactly 3.7 years from now if interest rate is 5.65 % compounded monthly.
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Choose the measurement closest to 180 cm: 6 ft, 180 in. or 450 in
Answers
Answer:
6ft
Step-by-step explanation:
180cm=5ft10in=70in
So it's closer to 6ft
The point G(-5, -1) is reflected over the line y= -3. What are the coordinates of the resulting point, G’
Answers
The coordinates of the resulting point after the reflection are (-5, -5)
What are the coordinates of the resulting point?
When we do a reflection over a given line, the perpendicular distancee between the line and the point is invariant.
In this case, we want to reflect the point (-5, -1) over the line y = -3
The distance between the y-value of the point and the line is:
D = |-1 - (-3)| = | -1 + 3| = 2
The point is at 2 units (above) from the line, then after the reflection, the point will be 2 units below the line.
So the new y-value is:
y = -3 - D = -3 - 2 = -5
The coordinates of the resulting point are (-5, -5).
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Best answer is ready to give gift prize?
Answers
Step-by-step explanation:
but please where is the question I'm eager to answer and win the pizza
Select the correct answer. What is the solution for x in the equation? -x + 3/7=2x-25/7
Answers
Answer:
x + 3/7=2x-25/7
X=4
What is the sum of 2 3/4 and −2 3/4 ?
A. 0
B. 3/4
C. 5 1/2
D. I don't know.
Answers
Answer:
A. 0
Step-by-step explanation:
[tex]2 \frac{3}{4} + ( - 2 \frac{3}{4}) \\ = \frac{11}{4} - \frac{11}{4} \\ = \frac{11 - 11}{4} \\ = \frac{0}{4} = 0 \\ hope \: this \: would \: help[/tex]
Answer:
A. 0
Explanation:
Given:
[tex]2\dfrac{3}{4} +(-2\dfrac{3}{4} )[/tex]
In improper fractions:
[tex]\dfrac{11}{4} +(\dfrac{-11}{4} )[/tex]
Simplify:
[tex]\dfrac{11}{4} -\dfrac{11}{4}[/tex]
Evaluate:
[tex]0[/tex]
Tip:
As the integers are alike, when subtracted they simplify to zero as a result.
a line skew to AT (in image attatched)
Answers
The line skewed to AT is HB
How to determine the line skewed to AT?As a general rule, skew lines are nonparallel lines that do not intersect
This means that the lines are in different planes
From the given figure, we can see that lines HB and AT do not intersect and they are not parallel
Hence, the line skewed to AT is HB
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The annual attendance at the amusement park is initially 2 million people and is increasing at 3% per year. The park’s annual food supply is initially adequate for 4 million people and is increasing at a constant rate adequate for an additional 0.2 million people per year.
a. Write the equation that represents the food supply. Write the equation represents the park attendance.
The equation that represents food supply is
b. Based on these assumptions, in approximately what year will the amusement park first experience shortages of food?
c. If the park doubled its initial food supply and maintained the rate of increase of 0.2 million people per year, would shortages still occur? In approximately which year?
d. If the park doubled the rate at which its food supply increases, in addition to doubling its initial food supply, would shortages still occur? After how many years would the food supply run out?
Please show work. I will mark brainliest.
Answers
Answer:
[tex]\textsf{a)} \quad f(t) = 4+0.2t \:\: \textsf{ and }\:\:A(t)=2(1.03)^t[/tex]
b) 77 years
c) 86 years
d) 110 years
Step-by-step explanation:
Part (a)Given:
Initial food supply adequacy = 4 million peopleConstant annual growth rate = 0.2 million peopleAs the food supply grows at a constant rate of being adequate for an additional 0.2 million people per year, it can be expressed as a linear function:
[tex]f(t) = 4+0.2t[/tex]
where:
f(t) = annual food supply (in millions of people).t = time (in years).Given:
Initial attendance = 2 million peopleAnnual growth rate = 3%As the annual attendance increases by 3% per year, it can be expressed as an exponential function:
[tex]A(t)=2(1.03)^t[/tex]
where:
A(t) = annual attendance (in millions of people).t = time (in years).Part (b)Graph the two functions (see attached) and locate the value of t for which A(t) > f(t) for the first time.
From inspection of the graph, the two functions intersect at t ≈ 77. So after approximately 77 years the food supply will not be enough for the number of people attending the amusement park. Therefore, after approximately 77 years, the park will first experience shortages of food.
Part (c)If the park doubles its initial food supply and maintains the rate of increase of 0.2 million people per year, the new equation would be:
[tex]f(t) = 8+0.2t[/tex]
Again, graph the new function against A(t) and find the point where the two functions intersect. A(t) = f(t) at approximately t = 86 so the park will first experience food shortages after 86 years. So doubling the initial food supply delays the eventual food shortage by only c. 9 years.
Part (d)If the park doubled the rate at which its food supply increases in addition to doubling its initial food supply, the new equation would be:
[tex]f(t) = 8+0.4t[/tex]
Again, graph the new function against A(t) and find the point where the two functions intersect. A(t) = f(t) at approximately t = 110 so the park will first experience food shortages after 110 years. So doubling the initial food supply and doubling the rate delays the eventual food shortage by only c. 33 years compared to the initial parameters. Shortages would still occur, but it would be later in approximately 110 years' time.
Will y=3x+5 pass throught the (0,5) or will it not pass the (0,5) ?
Answers
(0,5) is that equations y intercept so it WILL pad through that point.
[tex]Answer:\ y=3x+5\ pass\ throught\ the\ (0,5)[/tex]
Step-by-step explanation:
[tex]y=3x+5\ \ \ \ \ (0,5)\\5=3*0+5\\5=0+5\\5\equiv5\\Hence,\\y=3x+5\ pass\ throught\ the\ (0,5)[/tex]
Ileana wants to know the mean number of pets owned by students in her
grade. She conducts a survey of 20 of her classmates to see how many pets
they own. The results are shown in the dot plot.
Number of Pets In the Home
::::::
0
1 2 3 4 5 6
●●
7
H
8 9 10
Which is the best estimate of the mean number of pets owned by students in
her grade?
Answers
Based on the results shown in the dot plot on the number of pets owned by students in Ileana's grade, the mean number of pets owned by students is 2.5 pets
What is the mean number?The number of pets owned per student home according to the dot plot is:
= 0, 0, 0, 1, 1, 1, 1, 1, 2, 2, 2, 3, 3, 3, 4, 4, 4, 5, 5, 8
The total number of pets owned is:
= 0 + 0 + 0 +1 + 1 + 1 + 1 + 1 + 2 + 2 + 2 + 3 + 3 + 3 + 4 + 4 + 4 + 5 + 5 +8
= 50 pets
The mean number of pets owned is:
= 50 / 20 students
= 2.5 pets
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HELP PLEASE!!!!!!! A zookeeper wrote down the number of fish each of the ten dolphins in the aquarium ate per day. His results were as follows: 18, 15, 25, 17, 13, 15, 23, 27, 30, and 27. Find the mean absolute deviation of this data set. What does the mean absolute deviation tell you about the dolphins at the aquarium?
Answers
The mean absolute deviation is 5.4.
The mean absolute deviation tells us that the variance of each data set is 5.4.
What is the mean absolute deviation?The mean absolute deviation is a measure of variance that determines the average distance between each data point in the dataset and its mean.
The mean absolute deviation = 1/n ∑ l x - m(x) l
The first step is to determine the mean of the data set: (18 + 15 + 25 + 17 + 13 + 15 + 23 + 27 + 30 + 27) / 10
= 210 / 10
= 21
The second step is to determine the absolute difference between the mean and each data point. Then add the result together.
|(18 - 21) + (15 - 21)+ (25- 21) + (17- 21) + (13- 21) + (15- 21) + (23- 21) + (27- 21) + (30- 21) + (27- 21)| = 54
Now, divide the sum by the total numbers in the data set : 54 / 10 = 5.4
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Which lists all the factors of 78?
Answers
Answer:
1, 2, 3, 6, 13, 26, 39, and 78
Step-by-step explanation:
:)
I got one final question... What is -1/3x + 1 = -7
Answer Formula: x =
Answers
Answer: x=24
Step-by-step explanation:
-1/3x+1= -7
you move the negative one to the other side of the equation to get x by itself and get -1/3x= -8
then you divide both sides by -1/3 and get 24
Given:
p: x-5= 10
q: 4x+1 = 60
Which is the inverse of p→q?
If x-5 ≠ 10, then 4x+1≠61.
If 4x+1 ≠61, then x-5≠10.
If x-5=10, then 4x+1=61.
If 4x+1=61, then x-5=10
Answers
Answer:
Step-by-step explanation:
what is the answer to 17^2-286
Answers
The answer for the given expression, 17²-286 will be 3.
What is the equation?An equation is a statement that two expressions, which include variables and/or numbers, are equal. In essence, equations are questions, and efforts to systematically find solutions to these questions have been the driving forces behind the creation of mathematics.
It is given that,the expression is,
17²-286
The expression is solved by the arrthmetic operation in which we do the addition of numbers, subtraction, multiplication, and division. It has a basic four operators that is +, -, ×, and ÷.
=17²-286
=289-286
=3
Thus, the answer for the given expression, 17²-286 will be 3.
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A total of 200 and a difference of 72
Answers
According to the solving the total and the difference of the numbers:
total = 136 + 64
difference = 64
Difference in Math Definition?Mathematical difference is the outcome of one of the key operations, which is the subtraction of two numbers. It reveals the margin of difference between two numbers.
How do we find the difference?Subtract the largest number from the lowest number to determine the difference between two integers. The difference between these two numbers is the product of this sum. As a result, there are 55 between the numbers 45 and 100.
According to the given data:Let the numbers be x and y
Given,
x+y = 200_____(1)
x-y = 72_____(2)
Add above 2 eq.
2x= 272
x= 136
Substitute the value of x in eq 1,we get
136+y = 200
y = 64
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The coordinate point (-5, 18) is a point on the graph of f. Write this point in function notation.
f(-5) = 13
f(-5) = 18
f(18) = -3.6
f(18) = -5
Answers
The function notation of the coordinate point where the coordinate point is given as (-5, 18) is f(-5) = 18
What are coordinate points?Coordinate points are mathematical statements that are used to represent the location of points on a coordinate plane
How to rewrite the function notation of the coordinate point?The coordinate point is given as
(-5, 18)
The above coordinate point can be represented as
(x, y) = (-5, 18)
The above coordinate point can further be rewritten as
(x, f(x)) = (-5, 18)
So, we have
x = -5
f(x) = 18
Substitute x = -5 in the equation f(x) = 18
f(-5) = 18
Hence, the function notation of the coordinate point where the coordinate point is given as (-5, 18) is f(-5) = 18
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A sum of money is shared in the ratio 3:4:7.
The smallest share is £210.
What is the total amount of money shared?
Answers
Answer:
£980
Step-by-step explanation:
3 portions = 210
1 portion = 70
so 70
70 × 4 = would be 280
70 × 7 = 490
490 + 280 + 210 = 980
hope this works : )
A t-shirt requires 1 3/8 yards of material. How many t-shirts can be made from 41 1/4 yards of material?
Answers
Applying the knowledge of fractions, the number of t-shirts that can be made is: 30 t-shirts.
How to Divide Fractions?In the problem given, we have the following information:
Material needed for one t-shirt = 1 3/8 yards
We want to find how many 1 3/4 we would find in 41 1/4.
Applying the knowledge of fraction, we are to divide 41 1/4 by 1 3/8. Convert both mixed fractions to improper fractions then divide:
41 1/4 ÷ 1 3/8
165/4 ÷ 11/8
165/4 × 8/11
165/4 × 8/11
15/1 × 2/1
= (15 × 2)/(1 × 1)
= 30/1
= 30.
Therefore, applying the knowledge of fractions, the number of t-shirts that can be made is: 30 t-shirts.
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The height above ground of a cannon is a function of the time since it was shot.
Question: When time equals 0, why is the height of the cannon ball not equal to 0? Describe the domain of this function. Describe the range.
Answers
Given is the quadratic function by its graph..
At the start point, when time is zero, the height is not zero because the cannon was shot above the ground level.
The domain is the time from the point the cannon was shot and to the point the ball lands.
The range is the height from zero to the maximum height the ball reaches.
Determine the value of cscθ given that the terminal side of angle θ intersects the unit circle in the first quadrant at (7/17,y).
Answers
The value of cscθ is 1/y
In this question, we have been given that the terminal side of angle θ intersects the unit circle in the first quadrant at (7/17, y).
We know that the point on the unit circle is of the form (cosθ, sinθ)
Comparing (cosθ, sinθ) with point (7/17, y) we get,
cosθ = 7/17, and sinθ = y
also, we know that cscθ = 1/sinθ
So, cscθ = 1/y
Therefore, the value of cscθ is 1/y
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Solving quadratics factoring G CF, solving equations by factoring
Answers
Answer: k=0,-5
Step-by-step explanation:
Your GCF is 5k, as you're able to take it out of both terms.
Once you've taken out a 5k, this will leave you with an equation that looks like this;5k(k+5)=0.
Set your 5k equal to 0 and divide to get k=0
Set your k+5 equal to 0 and subtract on both sides to get k=-5
Hope this helps you, dawg.
The company made a partial payment of $600 cash on the equipment purchased in transaction d.
Answers
Answer: can u finish the question
Step-by-step explanation:
Help :)
Evaluate the following expression
|−3d−6|+|−5−d2| for d=−3
Answers
|-3(-3)-6|+|-5-(-3)^2|
All we did was input -3 for d in the original equation because they are equal.
Step 2.) We now need to follow PEMDAS (orders of operations) to evaluate the expression. In PEMDAS, parentheses are 1st, exponents are 2nd, multiplication and division are 3rd and are worked left to right (whichever operation comes first), and addition and subtraction are 4th and are worked left to right. *REMEMBER: Multiplication and division are not separate steps; they are step 3 and done at the same time, so you work left to right. The same applies for addition and subtraction, except they are step 4, so they come after multiplication and division. But, addition and subtraction are also the same step, not desperate steps.
So we look at the expression:
|-3(-3)-6|+|-5-(-3)^2|
We can view the absolute value symbols as a form of parentheses, so we must simply what’s in them first.
To the left, we see multiplication and subtraction, but we must multiply first before we subtract:
-3(-3) = 9
|(9)-6|+|-5-(-3)^2|
9-6=3
|3|+|-5-(-3)^2|
Now, we can look at the right expression. We see exponents, so we do that first:
-(-3)^2= -(-3 • -3) = -(9) = -9
|3|+|-5-9|
-5-9= -14
|3|+|-14|
Step 3.) Absolute value is the distance from 0, and distances are never negative, so whenever there is a negative number in absolute value symbols, it ALWAYS equals that number in positive form.
|3|+|-14|
3+14=17.
-14 is not -14 from 0, but it is 14 units from 0. 3 is 3 units from 0. Then, we just added them.
The value of the expression |−3d − 6| + |−5 − d²| when d = -3 is 17.
Given expression: |-3d - 6| + |-5 - d²|, and d = -3
Substitute the value of d: |-3(-3) - 6| + |-5 - (-3)²|
Calculate the values inside the absolute value signs:
|-(-9) - 6| + |-5 - 9|
Simplify the inside calculations:
|9 - 6| + |-5 - 9|
Continue simplifying:
|3| + |-14|
Calculate the absolute values:
3 + 14
Add the values together:
3 + 14 = 17
So, the value of the expression |−3d − 6| + |−5 − d²| when d = -3 is 17.
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