The explicit equation for the table is,
f(n) = n² + 4
Given, the values of an explicit function,
Let the function be,
f(n) = an² + bn + c
f(1) = a(1)² + b(1) + c
5 = a + b + c
f(2) = a(2)² + b(2) + c
8 = 4a + 2b + c
f(3) = a(3)² + b(3) + c
13 = 9a + 3b + c
On subtracting the equations, we get
5 = 5a + b
3 = 3a + b
Again, on subtracting we get
2 = 2a
a = 1
On putting the values we get,
b = 0.
a + b + c = 5
1 + 0 + c = 5
c = 4
Hence, the explicit equation for the table is,
f(n) = n² + 4
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A giant tortoise moves at a slow but steady pace. It takes the giant tortoise 1 hour to travel 2 miles. ¿How many miles (mi) a tortoise travels in ¼ hour? Use the bar diagram to help you.
The distance travelled by the tortoise in 1/4 hour is 0.5miles
What is rate?A rate is a more general measure in which one quantity is divided by another quantity, where both quantities don't necessarily need to have the same unit of measure. For example , Tayo typed 500 words in 50 minutes. This means that the rate of Tayo in typing is 500/50= 10words per minutes.
The tortoise travels 2miles in 1hour. There are two terms of different unit, which are distance in miles and time in hours
if the tortoise travels 2miles in 1hour
then in 1/4 hours,
the tortoise will travel 2×1/4
= 0.5mile
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CARD #8:
For community service, Ben is picking
up litter along Avondale and Bedford
Way. Adam is picking up litter along
Oakley Street.
Avondale
39 yds
Oakley Street
52 yds
Bedford Way
How many more yards of roadside is
Ben cleaning than Adam?
Samson says Ben is
cleaning 65 more
yards than Adam.
Sheridan says Ben
is cleaning 26 more
yards than Adam.
The yards of roadside that Ben is cleaning more than Adam is 26 yards. Sheridan is correct.
Who is correct?The first step is to determine the length of Oakley Street. Pythagoras theorem would be used to determine the length. Oakley Street is the hypotenuse of the right triangle that is formed by the streets.
The Pythagoras theorem: a² + b² = c²
where:
a = lengthb = basec = hypotenuse39² + 52² = c²
1,521 + 2704 = c²
c² = 4,225
c = √4225
c = 65 yards
Total yards Ben picked = 39 + 52 = 91 yards
Yards picked by Adam = 65 yards
Difference in the yards of litters picked = 91 - 65 = 26 yards
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Richard bought 3 slices of cheese pizza and 2 sodas for $8.75. Jordan bought 2 slices of cheese pizza and
4 sodas for $8.50. How much would an order of 1 slice of cheese pizza and 3 sodas cost?
• $3.25
O $5.25
• $7.75
• $17.25
The cost of 1 slice of cheese pizza and 3 sodas cost will be;
⇒ $5.25
What is an expression?
Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
Richard bought 3 slices of cheese pizza and 2 sodas for $8.75.
And, Jordan bought 2 slices of cheese pizza and 4 sodas for $8.50.
Now,
Let the cost of 1 slices of cheese pizza = x
And, The cost of 1 slices of soda = y
Since, Richard bought 3 slices of cheese pizza and 2 sodas for $8.75.
Hence, We get;
⇒ 3x + 2y = $8.75 ..(i)
And, Jordan bought 2 slices of cheese pizza and 4 sodas for $8.50.
So, We get;
⇒ 2x + 4y = $8.50 ..(ii)
Multiply by 2 with (ii);
⇒ 2 (3x + 2y) = 2 × $8.75
⇒ 6x + 4y = $17.5
Subtract from (ii), we get;
⇒ 6x + 4y - 2x - 4y = $17.5 - $8.50
⇒ 4x = $9
⇒ x = $2.25
And, ⇒ 2x + 4y = $8.50
⇒ 2 × $2.25 + 4y = $8.50
⇒ $4.5 + 4y = $8.50
⇒ 4y = $8.50 - $4.5
⇒ 4y = $4
⇒ y = $1
Thus, The cost of 1 slice of cheese pizza and 3 sodas cost will be;
⇒ $2.25 + 3 × $1
⇒ $2.25 + $3
⇒ $5.25
Therefore, The cost of 1 slice of cheese pizza and 3 sodas cost will be;
⇒ $5.25
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Graph the point on the graph.
Answer:
see below
Step-by-step explanation:
To graph this equation, start at the origin (0,0) since there is not y-intercept.
Because slope is characterized by rise/run ( i.e. how many units up or down depending on whether it is positive or negative and then however many units to the right.
Because the rise (up and down, numerator) is 1, we know that we will go up one unit.
The run (side to side, denominator) is 4, so we will go to the right 4 units.
This makes the first point (4, 1).
Continue doing this until you get an idea of the line and connect the points to get the graph
Answer:
Info down in Explaination
Step-by-step explanation:
To graph this equation, start at the origin (0,0) since there is not y-intercept.
Because slope is characterized by rise/run ( i.e. how many units up or down depending on whether it is positive or negative and then however many units to the right.
Because the rise (up and down, numerator) is 1, we know that we will go up one unit.
The run (side to side, denominator) is 4, so we will go to the right 4 units.
This makes the first point (4, 1).
Continue doing this until you get an idea of the line and connect the points to get the graph
Find the unknown term in the geometric proportion x = 4 :: 8 : 2
Arithmetic proportions are those whose means are not equal and are called discrete arithmetic proportions. On the contrary, if the means of the arithmetic proportion are equal, it is called continuous.
[tex]\bf\large{\underline{\fcolorbox{blue}{aqua}{Problem:}}}[/tex]
[tex] \sf x = 4 :: 8 : 2[/tex]
Since the unknown term is an extreme and as we have seen, it is equal to the product of the means divided by the other extremes, we will have:
[tex]\boxed{\: x = \frac{4 \times8}{2} = \frac{32}{2} = 16 }[/tex]Therefore, the resulting geometric proportion would be:
[tex] \: \: \: \: \: \: \: \: \: \: \: \: \: \red\longmapsto \sf \orange{16 : 4 :: 8 : 2}[/tex]
A farmer plans to build a rectangular garden behind his house such that he only needs fencing on 3 sides of the garden. If he wants the second side of the garden to be 30 feet longer than the back of his house, and the area of the garden is going to be equal to 400 square feet, how much fencing dose he need to buy?
The amount of fence the farmer will need to buy is 90 ft
What is Area of Rectangle?The area of rectangle is the product of its length to its width.
i.e., Area of Rectangle= length x width
let the length of the back of his house be x ft.
Thus, if the second side of the garden to be 30 feet longer than the back of his house,
then the length of the second side is; (x + 30) ft.
Now,
Area = Length × width
400 = x (x + 30)
400 = x² + 30x
x² + 30x - 400 = 0
Solving the quadratic equation:
x = -40 or 10
Thus, length of second side = 10 + 30 = 40 ft
Now, Perimeter of 3 sides = 10 + 2(40)
Perimeter of 3 sides = 90 ft
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An element with a mass of 800 g to Cave by 28% per minute. To the nearest minute how long will it take until they were 140 g of the element remaining?
Please help on two geometry questions!!!
Considering the two figures the value of x is
8) x = 12degrees9) x = 8.25 degreesHow to determine the value of xThe value of x is found by the external angle theorem which states that the sum of the two opposite internal angels of a triangle gives the external angle
The value of x is calculated as below
8) 70 + 5x = 9x + 22
70 - 22 = 9x - 5x
48 = 4x
x = 12
9) 65 + 8x + 11 = 16x + 12
65 + 11 - 12 = 16x - 8x
66 = 8x
x = 8.25
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y = 3x + 18
y = 15
..............................
Answer: " x = 1 ".
The answer for this 'system of equations' is: " [1, 15] ".
_________
Step-by-step explanation:
To solve for x :
Given:
y = 3x + 18
y = 15 ;
_________
We know that:
3x + 18 = 15 ; Now, subtract 18 from Each Side of the equation:
3x + 18 − 18 = 15 − 18 ;
to get:
3x = 3 ; Now, divide Each Side of the equation by 3 ;
to isolate x on one side of the equation;
and to solve for x :
3x / 3 = 3 / 3 ;
to get: x = 1
_________
The answer is: " x = 1 " ;
The answer for this 'system of equations' is:
" [1, 15] " <== { written as: " [x, y] "} ;
in which: " y = 15 " ; is given in the problem.
_________
Hope this answer is helpful.
Best wishes!
_________
There are 30 members in a committee. On a certain day.
[tex] \frac{11}{15} [/tex]
of the total members were present. How many members were present? How many were absent?
22 members were present and 8 members were absent.
There are 30 members in a committee.
On a certain day 11/15 of the total members were present.
Let x be the number of members who were present.
So, we get an equation,
x = 11/15 * 30
We solve above fraction.
x = 11 * 2
x = 22
So, 22 members were present.
And 30 - 22 = 8 members were absent.
Therefore, 22 members were present and 8 members were absent.
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Circle Centered at (5,-3)
Radius=9
Standard form:
general form:
The standard form of the equation of the circle is (x-5)² + (y+3)² = 9² and the general form is x² + y² + 10x + 6y - 47 = 0 .
We know that the general form of the equation of a circle is given by the following equation:
(x-h)² + (y-k)² = r² . Where r is the radius of the circle and (h, k) is the center of the circle.
So the general equation of the circle is (x-5)² + (y+3)² = 9² .
Let's first define a circle in order to determine its equation. A circle is formed by every point in a plane that is uniformly spaced from another point.
The constant point is located at the center of the circle. The radius of a circle is the separation between its center and any point along its circumference.
(x-5)² + (y+3)² = 9²
or, x² + 10x + 25 + y² + 6y + 9 = 81
or, x² + y² + 10x + 6y - 47 = 0
Hence the general form of the circle is x² + y² + 10x + 6y - 47 = 0.
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There are a Total of 11 bicycles and tricycles altogether in the shop window. They have a total of 29 wheels. How many bicycles are there ?
Please answer very correctly
The number of bicycles that are there is 4.
How to find the number of bicycles?There are a Total of 11 bicycles and tricycles altogether in the shop window.
They have a total of 29 wheels.
Therefore, the number of bicycles that are there can be calculated as follows;
Bicycles has 2 wheels and tricycles has 3 wheels.
Therefore,
let
x = number of bicycle
y = number of tricycle
2x + 3y = 29
x + y = 11
Multiply equation(ii) by 2
2x + 3y = 29
2x + 2y = 22
y = 7
x = 11 - 7
x = 4
Therefore the number of bicycle is 4.
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what are the two estimates of 1,624 divided by 3
A number is divisible by 3 it the sum of its digits is divisible by 3. In this case, we have
which is not divisible by 3. The nearest multiples of 3 are 1623 and 1626. If you divide these numbers by 3, you have
So, the result of our division is between 541 and 542.
If these numbers are too complex to divide, we have to choose easier numbers, but we will lose some accuracy. For example, we can see that 1624 is between 1500 and 1650, which are very easily divisible by 3. We have
So, the result of our division is between 500 and 550. This is still true, but as you can see it is a much looser approximation than the one before.
Could you guys please help?
The real roots of the function is {0,-2} and there are no repeated roots.
Given function:
f(x) = [tex]x^{2} +2x[/tex]
[tex]x^{2} +2x=0[/tex]
take x as common
x(x+2) = 0
x = 0 and x + 2 = 0
x+2 = 0
x = -2,0.
Therefore the real roots of the function is {0,-2} and there are no repeated roots.
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Draw the dilation of ABC with center P scale factor 2. label the dilation GHI
Using dilation rules, the dilated triangle whose coordinates of the vertices are as follows: A'(-2 , 2), B'(-1,0), C'(1 , 2).
What is the rule for a dilation?
To dilate a figure by a factor of a, each coordinate of each vertex of the image is multiplied by a, that is, the following rule is applied:
(x, y) -> (ax, ay).
suppose the coordinates of the vertices of ABC are given as follows:
A(-6,6), B(-3,0), C(3,6).
After a dilation with a scale factor of 1/3, the coordinates of the vertices of A'B'C' will be given as follows:
A'(-2 , 2), B'(-1,0), C'(1 , 2).
These coordinates are derived multiplying the coordinates of A, B and C by 1/3.
For the image of triangle DEF, each of the coordinates of D, E and F will be multiplied by 2 to generate the dilated triangle.
Learn at brainlyA sailboat is headed due north, and its sail is set perpendicular to the wind, which is from the south of west. The component of the force of the wind in the direction of the heading is 480N, and the component perpendicular to the heading (the drift component) is 650 N. What is the force exerted by the wind, and what is the direction of the wind?
The direction of force is [tex]53.6^0[/tex] South of West and force exerted by the wind is 596.4N.
What are the component of force?
If a force acting at some angle [tex]\theta[/tex] with respect to x axis then the force can be resolved into two perpendicular forces ([tex]Fcos\theta[/tex] and [tex]Fsin\theta[/tex]). These perpendicular forces are known as component of forces.
Consider the following diagram of the sialboat.
The component of force along the heading direction is 480N and the component of force perpendicular to the heading is 650N.
If F is the foce the direction of wind then then component of force in the East direction will be [tex]Fcos\theta[/tex] and the component of force in the heading direction is [tex]Fsin\theta[/tex]. Now, take the ratio of these two compnents to find the angle [tex]\theta[/tex] as follows:
[tex]tan\theta=\frac{Fcos\theta}{Fsin\theta}\\tan\theta=\frac{650N}{480N}\\\\\theta=tan^{-1}(1.354)\\=53.6^0[/tex]
Now, calculate the force exerted by the wind. Equate the force in heading direction to find the force.
[tex]Fsin\theta=480N\\F=\frac{480N}{sin\theta}\\=\frac{480N}{sin53.6^0}\\=596.4N[/tex]
Hence, the direction of force is [tex]53.6^0[/tex] South of West and force exerted by the wind is 596.4N.
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At the start of the year, the soup kitchen had v volunteers. During the year, 12 more
volunteers joined them. Write an expression that shows how many volunteers there are now.
V+12 is the expression that shows how many volunteers there are now
What is Expression?An expression is combination of variables, numbers and operators.
Given,
At the start of the year, the soup kitchen had v volunteers.
During the year, 12 more volunteers joined them
Joined them means added, it means 12 volunteers are added to the v volunteers
v plus twelve.
v+12
Hence v+12 is the expression that shows how many volunteers there are now
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An online streaming service charges a monthly fee as well as a one-time sign-up fee. The cost for this online streaming service is modeled by the following function where m represents the number of months the service is subscribed to and C(m) represents the total cost given that amount of time:
C(m) = 11.99m + 7
In the above function, what is the slope?
What is the y-intercept?
How do we interpret the slope of this function?
How do we interpret the y-intercept of this function?
The equation of a line is given by:
y = mx + c
where m is the slope of the line and c is the y-intercept.
C(x) = 11.99 + 7
The slope of the function is 11.99.
The y-intercept of the function is 7.
What is an equation of a line?The equation of a line is given by:
y = mx + c
where m is the slope of the line and c is the y-intercept.
Example:
The slope of the line y = 2x + 3 is 2.
The slope of a line that passes through (1, 2) and (2, 3) is 1.
We have,
C(m) = 11.99m + 7
The equation is in the form of y = mx + c
So,
m = 11.99
c = 7
The slope of the function is 11.99.
The y-intercept of the function is 7.
Thus,
The slope of the function is 11.99.
The y-intercept of the function is 7.
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Sally can paint a room in 6 hours while it takes Steve 8 hours to paint the same room. how long would it take them to paint the room if they work together
Answer:
It will take them 3.5 hours to paint the room.
Step-by-step explanation:
Step 1: Add the number of hours it takes them together
A. 6 + 8
Step 2: Divide the total number of hours by two (since two people are working together)
B. 12 / 2 = 7 hours
Step 3: Divide by two again since you now have twice the speed
C. 7 / 2 = 3.5 hours
An investor bought 500 shares of stock, some at $6.00 per share and some at $4.00 per share. If the total cost was $2550.00, how many shares of each stock did the
investor buy?
Answer: An investor bought 500 shares of stock , some at $ 3.50 per share and some at $6.00 per share. If the total cost was $ 2187.50, how many shares of each stock did the investor buy?
(a) How will you set up the problem?
Let # of 3.50 shares be "x" ; value is 3.5x dollars
# of 6.00 shares is "500-x" ; value is 6(500-x)=3000-6x dollars
EQUATION:
value = value = 2187.50
3.5x + 3000-6x = 2187.5
-2.5x = -812.5
x = 325 (# of 3.50 shares)
500-x = 175 (# of 6.00 shares)
Step-by-step explanation:
The scores of the students on a standardized test are normally distributed, with a mean of 500 and a standard deviation of 110. What is the probability that a randomly selected student has a score between 350 and 550? Use the portion of the standard normal table below to help answer the question. z Probability 0.00 0.5000 0.25 0.5987 0.35 0.6368 0.45 0.6736 1.00 0.8413 1.26 0.8961 1.35 0.9115 1.36 0.9131 9% 24% 59% 91%
Answer:
0.5867 (or 58.7%)
Step-by-step explanation:
The probability that a randomly selected student has a score between 350 and 550 is 59%.
What is z score?Standard score or z score in statistics is defined as the number of standard deviations by which that the value of a score is above or below the mean value.
Given that,
The scores of the students on a standardized test are normally distributed.
Mean, μ = 500
Standard deviation, σ = 110
z score = (x - μ) / σ
For x = 350,
z = (350 - 500) / 110 = -1.36
Probability = 1 - 0.9131 = 0.0869
For x = 550,
z = (550 - 500) / 110 = 0.45
Probability = 0.6736
Probability that a randomly selected student has a score between 350 and 550 is,
P = 0.6736 - 0.0869 = 0.5867 ≈ 59%
Hence the required probability is 0.5867 or 58.67%.
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Copy the triangle. Start at any vertex and label the triangle as WVU.
.
What sides include
Ashley has a $80 gift card to her favorite coffee shop. Each day, she uses her gift *
card to buy a coffee for $4.50, Aaron has a $60 gift card to the same coffee shop.
Each day, he uses his gift card to buy an iced tea for $2.50. For what number of
drinks purchased will Ashley's gift card balance be greater or equal to Aaron's?
Step-by-step explanation:
I assume this means that both purchase one item every day.
so, their number of purchases are the same (x).
80 - 4.5x >= 60 - 2.5x
20 - 4.5x >= -2.5x
20 >= 2x
10 >= x
our
x <= 10
after 10 purchased drinks their balances will be equal.
before that, Ashley's card balance will be greater than Aaron's.
after that, Aaron's card balance will be greater than Ashley's.
so, for up to 10 purchased drinks Ashley's card balance will be greater or equal to Aaron's.
How many liters of a 25% saline solution
must be mixed with 4 liters of a 40% saline
solution to make a 30% saline solution?
The required amount of 25% saline solution is 8 liters.
Finding unknown quantity using Linear equation:In mathematics, the equation that used to find an Unknow quantity is known as Linear Equation. Here we use different types of variables to represent the unknown value like x, y, z or a, b, c.. etc.
Here we have
4 liters of a 40% saline
we need to make it a 30% of saline solution by adding a mount of 25% saline solution
Let us assume that we added x L of 25% of saline solution
After adding x L of 25% saline into 4 liters of 40% saline to get 30% saline solution then the resultant solution is “x+4” liters of 30% saline.
The mathematical representation for the above line will be
⇒ x litres 25% saline + 4 litres 40% saline = (x+4) litres 30% saline
⇒ x(25%) + 4(40%) = (x+4)(30%)
⇒ 25x/100 + 4(40/100) = (x+ 4)30/100
⇒ 25x + 160 = (x +4)30
⇒ 25x + 160 = 30x + 120
⇒ 30x - 25x = 160 - 120
⇒ 5x = 40
⇒ x = 8
Therefore
The required amount of 25% saline solution is 8 liters
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5-1 Homework
1. An electronics store has a frequent
shopper program. The buyer earns
4 points for every movie purchased.
Draw a graph which models this
situation.
Answer:
f(x) = 4x
for graph see attachment
Step-by-step explanation:
when the buyer gets 4 points for each movie purchased, the equation for the graph is f(x) = 4x
x being the movies, 4 being the amount of points per movie granted.
Which parts of the triangles are congruent in the image? If you don’t know skip.
Answer:
angle LHJ is congruent to angle IKL
Answer:
segment JL is congruent to segment JK
segment HL is congruent to segment KI
Angle LJH is congruent to angle KJI
Step-by-step explanation:
we flip the triangles to look for the corresponding sides
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The number of students in nine faculties of a university are given as 168, 285, 397, 331, 383, 359, 366, 280 and 369 Find the mean number of students per Faculty
The mean number of students per Faculty is 326.
What is mean?Mean simply means the average of a set of numbers.
In this case, the number of students in nine faculties of a university are given as 168, 285, 397, 331, 383, 359, 366, 280 and 369. The mean will be:
= Total values / 9
= (168 + 285 + 397 + 331 + 383 + 359 + 366 + 280 + 369) / 9
= 2938 / 9
= 326.44
The mean is 326.
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find the slope line 2x + 5y = 21
Answer:
Slope [tex]\frac{-2}{5}[/tex]
Step-by-step explanation:
2x + 5y = 21 Subtract 2x from both sides of the equation
5y = -2x + 21 divide all the way through by 5
y = [tex]\frac{-2}{5}[/tex] x + [tex]\frac{21}{5}[/tex] The slope is the coeffience of the variable (the number before the x)
PLEASE ANSWER I CANT FAIL!
Answer:
D ,
Step-by-step explanation:
4cd(6-9c)
5(x+5)
The graph of y = f(x) is graphed below. What is the end behavior of f(x)?
Answer:
(a) as x → -∞, f(x) → ∞ and as x → ∞, f(x) → ∞
Step-by-step explanation:
You want to know the end behavior of the 4th-degree function shown in the graph.
Arrows on the graphThe graph has an arrow on each end of the curve shown in the figure. The left arrow points upward, indicating a tendency to +∞ as x gets more negative.
The right arrow also points upward, indicating a tendency to +∞ as x gets more positive.
As x → -∞, f(x) → ∞ and as x → ∞, f(x) → ∞.