The numbers -7, -5, -3, 3, -1, and 1 can be arranged into three pairs with the same total (-7, 7), (-5, 5), (-3, 3), (-1, 1).
To arrange the numbers -7, -5, -3, 3, -1, and 1 into three pairs with the same total, we need to find a combination of pairs that will give us the same sum for each pair.
Let's start by examining the numbers:
-7, -5, -3, 3, -1, 1
To find pairs with the same total, we can start by pairing the numbers with their additive inverses (numbers that sum to zero). In this case, -7 and 7, -5 and 5, -3 and 3 can be paired up. This leaves us with -1 and 1.
We have three pairs now: (-7, 7), (-5, 5), (-3, 3). However, we still have -1 and 1 remaining. To make the sum of the pairs equal, we can pair -1 with 7 and 1 with -5.
The three pairs with the same total are:
(-7, 7), (-5, 5), (-3, 3), (-1, 1).
Each pair sums up to zero, resulting in the same total for each pair. For example, (-7 + 7 = 0), (-5 + 5 = 0), and so on.
Therefore, the numbers -7, -5, -3, 3, -1, and 1 can be arranged into three pairs with the same total:
(-7, 7), (-5, 5), (-3, 3), (-1, 1).
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What is (fg)(x)?
f(x)=2x
g(x)=2x2+3x
Write your answer as a polynomial or a rational function in simplest form
Given statement Function Multiplication Simplified solution is :- (fg)(x) = [tex]4x^2[/tex] + 6x.
To find (fg)(x), we need to first find the product of f(x) and g(x) and simplify the expression.
f(x) = 2x
g(x) = [tex]2x^2[/tex] + 3x
To find (fg)(x), we substitute g(x) into f(x):
(fg)(x) = f(g(x)) = f([tex]2x^2[/tex] + 3x)
Now we substitute f(x) = 2x into the expression above:
(fg)(x) = 2([tex]2x^2[/tex] + 3x)
Distribute the 2:
(fg)(x) = [tex]4x^2[/tex] + 6x
So, (fg)(x) = [tex]4x^2[/tex] + 6x.
Function Multiplication Simplified solution is :- (fg)(x) = [tex]4x^2[/tex] + 6x.
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De los 12 jugadores del equipo 2/8 son delanteros
There are a total of 3 forwards on the team.
How many forwards are there on the team?A fraction represents a part of the whole or group of objects.In a fraction, numerator and denominator are separated by a horizontal bar known as the fractional bar
Given:
2/8 of the players are forwards.
Total number of players on the team = 12
We will determine the total number of forwards on the team by multiplying the total number of players by the fraction representing the forwards.
Fraction representing the forwards:
= 2/8
= 1/4
Total forwards on the team:
= 12 * (1/4)
= 3.
Translated question:
Of the 12 players on the team, 2/8 are forwards. What are the total forward in the team?
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what is a Pythagoras theorem
The Pythagoras theorem states that in a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides.
What is mathematical representation of Pythagoras theorem?From the given Pythagoras theorem above, the mathematical representation of the theorem would be written below as follows;
C² = a²+b²
Where:
'C' represents the hypotenuse which is the longest part of the triangle and is always diagonal connecting the two other points.'a' represents the perpendicular length that forms the angle 90° of the right angle triangle.'b' represents the base of the triangle.Learn more about Pythagorean formula here:
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The sum of 18 and a number, x, equals negative 40. Part A Which equation represents this situation? x-18=-40. x-18-40 18+x=-40. 18 + x = 40
Answer:
18+x = -40
Step-by-step explanation:
The sum of 18 and a number x is translated to "18+x"
Equals means "="
Negative forty is "-40"
Put them all in order and you get 18+x = -40
what is an example of "an extension of a function f"?
An example of an extension of a function f is adding additional input-output pairs beyond the original domain and range of f.
What is an example of "an extension of a function f"?The extension of a function f means new function that preserves the properties and behavior of the original function on its domain while adding new values or expanding its domain.
For example, we will consider the function f(x) = x^2 defined on the interval [0, 1]. An extension of this function could be g(x) = x^2 for x in [0, 1] and g(x) = 0 for x outside [0, 1].
This extension maintains the quadratic behavior of f on [0, 1] while assigning a constant value of 0 to points outside that interval.
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What means killogram?
Answer:
1,000 grams
noun. a unit of mass equal to 1,000 grams: the basic unit of mass in the International System of Units (SI). Up until 2019 the kilogram was defined as equal to the mass of an international prototype, a platinum-iridium cylinder kept in Sèvres, France.
The graph of � = ∣ � ∣ y=∣x∣y, equals, vertical bar, x, vertical bar is shifted down by 9 99 units and to the right by 4 44 units. What is the equation of the new graph? Choose 1 answer: Choose 1 answer: (Choice A) � = ∣ � − 9 ∣ − 4 y=∣x−9∣−4y, equals, vertical bar, x, minus, 9, vertical bar, minus, 4 A � = ∣ � − 9 ∣ − 4 y=∣x−9∣−4y, equals, vertical bar, x, minus, 9, vertical bar, minus, 4 (Choice B) � = ∣ � − 4 ∣ − 9 y=∣x−4∣−9y, equals, vertical bar, x, minus, 4, vertical bar, minus, 9 B � = ∣ � − 4 ∣ − 9 y=∣x−4∣−9y, equals, vertical bar, x, minus, 4, vertical bar, minus, 9 (Choice C) � = ∣ � − 4 ∣ + 9 y=∣x−4∣+9y, equals, vertical bar, x, minus, 4, vertical bar, plus, 9 C � = ∣ � − 4 ∣ + 9 y=∣x−4∣+9y, equals, vertical bar, x, minus, 4, vertical bar, plus, 9 (Choice D) � = ∣ � − 9 ∣ + 4 y=∣x−9∣+4y, equals, vertical bar, x, minus, 9, vertical bar, plus, 4 D � = ∣ � − 9 ∣ + 4 y=∣x−9∣+4
An equation of the new graph is: A. y = ∣x - 4∣ - 9.
What is a translation?In Mathematics and Geometry, the translation of a graph to the right simply means a digit would be added to the numerical value on the x-coordinate of the pre-image:
g(x) = f(x - N)
Conversely, the translation of a graph downward simply means a digit would be subtracted from the numerical value on the y-coordinate (y-axis) of the pre-image:
g(x) = f(x) + N
Since the parent function y = ∣x∣ was translated 4 units to the right and 9 units down in order to produce the graph of the image, we have:
y = ∣x - 4∣ - 9
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Missing information:
The question is incomplete and the complete question is shown in the attached picture.
Acylinder has a volume of 400 cubic feet. If the height of the cylinder is 25 feet, what is the radius of the cylinder? Use 3.14 for me and round to the nearest hundredth
adius hype your answer...
1
The radius of the cylinder is 2.25 feet.
To find the radius of the cylinder, we can use the formula for the volume of a cylinder:
V = πr²h
Given that the volume V is 400 cubic feet and the height h is 25 feet, we can substitute these values into the formula and solve for the radius r.
400 = 3.14 r² x 25
Dividing both sides of the equation by (3.14 * 25) to isolate r^2, we have:
r² = 400 / (3.14 x 25)
r² ≈ 5.08
Taking the square root of both sides to solve for r, we get:
r ≈ √5.08
r ≈ 2.25
Therefore, the radius of the cylinder is 2.25 feet.
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Graph the image of this quadrilateral after a dilation with a scale factor of 2 centered at the origin. Use the polygon tool to graph the quadrilateral.
The new coordinates of the quadrilateral ABCD after the dilation is:
A' = (-6, 6)
B' = (-8, -4)
C' = (4, -8)
D' = (0, 0)
We have,
To find the coordinates of the new quadrilateral after a dilation with a scale factor of 2 centered at the origin, we multiply the x and y coordinates of each point by the scale factor.
Given the original coordinates of the quadrilateral ABCD:
A = (-3, 3)
B = (-4, -2)
C = (2, -4)
D = (0, 0)
To dilate the coordinates with a scale factor of 2, we multiply each coordinate by 2:
A' = 2 x (-3, 3) = (-6, 6)
B' = 2 x (-4, -2) = (-8, -4)
C' = 2 x (2, -4) = (4, -8)
D' = 2 x (0, 0) = (0, 0)
Thus,
The new coordinates of the quadrilateral ABCD after the dilation is:
A' = (-6, 6)
B' = (-8, -4)
C' = (4, -8)
D' = (0, 0)
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in long division what is the working and answer for 348 divided by 4?
4 will divide the 348 is 8 and 2 left, so you will write the two and move the 8 down, which is now 28, then divide the 28 by 4. It will be 7.
Find the equation of a parabola with focus (3, 4) and directrix y = 1.
The equation of the parabola with focus (3, 4) and directrix y = 1 is [tex]x^2 - 6x - 12y + 57 = 0.[/tex]
To find the equation of a parabola with a given focus and directrix, we can use the standard form of the equation of a parabola:
[tex]4p(y - k) = (x - h)^2[/tex]
where (h, k) represents the coordinates of the vertex, and p is the distance between the vertex and the focus or directrix.
In this case, the focus is given as (3, 4), which means the vertex of the parabola will also be located at (3, 4).
The directrix is given as y = 1.
First, let's find the value of p, which is the distance between the vertex and the focus (or the vertex and the directrix). In this case, p will be the distance between the vertex (3, 4) and the directrix y = 1.
Since the directrix is a horizontal line, the distance between the vertex and the directrix is the vertical distance, which is |4 - 1| = 3.
Now that we have the value of p, we can substitute it into the equation:
[tex]4p(y - k) = (x - h)^2[/tex]
Plugging in the values (h, k) = (3, 4) and p = 3, we get:
[tex]4(3)(y - 4) = (x - 3)^2[/tex]
Simplifying further:
[tex]12(y - 4) = (x - 3)^2[/tex]
Expanding the equation:
[tex]12y - 48 = x^2 - 6x + 9[/tex]
Bringing all terms to one side:
[tex]x^2 - 6x - 12y + 57 = 0[/tex]
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Best way to solve this type of equation Ax+by=c
The best way to solve an equation of the form Ax+by=c could be either substitution, completing the squares or graphical method depending on the type of equation given.
Quadratic equation
The equation in the form Ax+by=c is a quadratic problem which could be approached in different ways depending on the specific equation given and the information provided.
The methods of approach are substitution, completing the squares or graphical method which all have proven to be suitable ways to arrive at the solution.
Hence, either of the three methods are good ways to solve such equation.
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A cheetah's speed was timed over a 50-yard distance. The cheetah was clocked running 60 miles per hour. Write an equation to represent this situation. (If your answering please show how you solved this)
The equation that represents this situation is:
⇒ 60t = 0.0284091
where t is the time in minutes.
We have to given that,
The speed of the cheetah is 60 miles per hour
The distance timed was 50 yards
Now, We have to convert the distance to miles, because the speed is in miles per hour.
Since, 1 yard = 0.000568182 miles
Hence, 50 yards = 50 x 0.000568182 miles
50 yards = 0.0284091 miles
Now we can use the formula:
distance = speed x time
We know that,
The distance is 0.0284091 miles, and the speed is 60 miles per hour.
Hence, the time it took the cheetah to run the 50-yard distance.
So, the speed from miles per hour to miles per minute, since we want the time in minutes:
60 miles per hour = 1 mile per minute
Now we can plug in the values we know:
0.0284091 miles = (1 mile per minute) x time
Solving for time:
time = 0.0284091 / 1
time = 0.0284091 minutes
time = 0.0284091 minutes x 60 seconds per minute
time = 1.704546 seconds
Thus, the equation that represents this situation is:
⇒ 60t = 0.0284091
where t is the time in minutes.
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The room is 20 feet by 25 feet. The walls are 8 feet tall. You will be painting all 4
walls, but not the ceiling.
The paint costs $13.98 per gallon and covers 400 square feet per gallon.
1. What are the dimensions of the 4 walls?
2. What is the total area to be covered? Show your computations here.
3. How many gallons of paint will you need? (remember each gallon covers 400 sq ft)
1) The dimensions of the 4 walls are:
Two walls are 20 feet long and 8 feet tall.
Two walls are 25 feet long and 8 feet tall.
2) Total area to be covered:
= 720 square feet.
3) You will need 1.8 gallons of paint to cover all four walls of the room.
Now, The dimensions of the 4 walls are:
Two walls are 20 feet long and 8 feet tall.
Two walls are 25 feet long and 8 feet tall.
And, The total area to be covered is:
For the two 20 feet long walls:
A = 20 feet x 8 feet
A = 160 square feet each.
And, For the two 25 feet long walls:
A = 25 feet x 8 feet
A = 200 square feet each.
Hence, Total area to be covered:
= (160 + 160 + 200 + 200) square feet
= 720 square feet.
For the number of gallons of paint needed, divide the total area to be covered by the area covered by one gallon of paint:
Number of gallons of paint needed = Total area to be covered / Area covered by one gallon of paint
Number of gallons of paint needed = 720 square feet / 400 square feet per gallon
Number of gallons of paint needed = 1.8 gallons
Therefore, you will need 1.8 gallons of paint to cover all four walls of the room.
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Which of the following shows a 90° counterclockwise rotation of the blue figure
En uno de los corrales de la granja de mi abuela hay gallinas y conejos. Aún cuando todos se mueven, logré contar 40 cabezas y 106 patas.
a) Explica cuáles son las incógnitas del problema.
b) Escribe una ecuación que represente el número de animales que hay en el corral.
c) Escribe una ecuación que represente el número total de patas.
d) ¿cuántos conejos y cuántas gallinas hay en el corral?
There are 27 chickens and 13 Rabbits in the pen on your grandmother's farm, based on the given information of 40 heads and 106 legs.
a) The unknowns in the problem are the number of chickens and rabbits in the pen. We don't know the exact quantities of each animal, which is what we need to determine.
b) Let's denote the number of chickens as "C" and the number of rabbits as "R." To represent the total number of animals in the pen, we can write the equation: C + R = total number of animals.
c) The total number of legs can be represented by the equation: 2C + 4R = total number of legs. This equation accounts for the fact that chickens have two legs, while rabbits have four.
d) To find the solution, we can use the given information: 40 heads and 106 legs. Since each animal has one head, the total number of animals is equal to the total number of heads, which is 40.
Using the equation C + R = 40, we can solve for one variable in terms of the other. For example, if we solve for C, we get C = 40 - R.
Substituting this value of C into the equation 2C + 4R = 106, we can solve for R:
2(40 - R) + 4R = 106
80 - 2R + 4R = 106
2R = 26
R = 13
Therefore, there are 13 rabbits in the pen.
To find the number of chickens, we can substitute the value of R into the equation C = 40 - R:
C = 40 - 13
C = 27
Hence, there are 27 chickens in the pen.
In conclusion, there are 27 chickens and 13 rabbits in the pen on your grandmother's farm, based on the given information of 40 heads and 106 legs.
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What is the sum of 104, 25, -11 to come of it
Answer:
118
Step-by-step explanation:
104+25+(-11)
129-11
118
Therefore, our answer is 118
11. Which one of the following is unique? b. mode a. Mean c. Median d. A and B
Among the mean, mode, and median, the unique one is the b. mode.
What is the mode?The mode is the data value that occurs many times more than other data values.
Unlike the mean that shows the average value of all the data values, the mode occurs more. While we compute the mean by dividing the total data value by the number of data items, the mode is not computed but found as the most frequent data value.
Similarly, the median can be computed when two values occur as the middle values.
Thus, among the three measures of central tendency, the mean, the median, and the mode, the mode is the most unique since it is not computed.
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log base 4 of 9
HELPPPPPPPP
Answer:
1.58 ish
Step-by-step explanation:
For a logx y = z, x^z = y
So here, log4 9= 1.58 or so
1.5849625007
These shapes are similar.
Find X.
5
X
5
30
24
30
The value of x is 4.
To determine the value of x, we can use the concept of similarity between shapes.
Similar shapes have corresponding sides that are proportional to each other.
Given the dimensions of the first shape as 5, x, and 5, and the dimensions of the second shape as 30, 24, and 30, we can set up the following proportion:
5/x = 30/24
To solve for x, we can cross-multiply:
30 · x = 5 · 24
30x = 120
Dividing both sides of the equation by 30:
x = 120 / 30
x = 4
Therefore, the value of x is 4.
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Find the number that belongs
in the green box.
[?]
37°
64°
21.1
30
Round your answer to the nearest tenth.
The value of x is 33.4
How to determine the valueTo determine the value in the green box, we need to know that there are six different trigonometric identities.
These identities are enumerated as;
sinecosinetangentcotangentsecantcosecantUsing the sine identity, we have;
sin θ = opposite/hypotenuse
We have that;
θ = 64 degrees
Opposite = 30
Hypotenuse = x
Substitute the values, we have;
sin 64 = 30/x
cross multiply
x = 30/0. 8987 = 33. 4
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pls help me with this
The term 9b represents the cost to rent a bike.
We have,
Rentals
Bike $9/h
Electric scooter $10/h
Kayak $18/h
Canoe $20/h
Paddleboard $22/h
Helmet Add $6
Here, the term 9b represents the cost to rent a bike.
In the provided rental options, the cost of renting a bike is $9 per hour.
The term "9b" indicates that the cost is calculated by multiplying the hourly rate of $9 with the number of hours (b) the bike is rented for.
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Answer Question 11 please
Answer:
increasing exponential function.
Step-by-step explanation:
We can see from the table that the function is not increasing by the same amount as it goes up by 1 in x, so it is not linear.
It must be exponential.
It is increasing at it increases in x, so it is an increasing exponential function.
URGENT!! ILL GIVE BRAINLIEST! AND 100 POINTS
PLEASE ANSWER!!
Answer:
Step-by-step explanation:
a. 2r + 5 = b because you have you have 5 more blue marbles than double the red *r= red and b=blue
b. to do the substitution you know that the red marbles plus the blue marbles add up to 77 so
b + r=77
now we can isolate for b and then substitute that value into the first equation
b=77-r and then this goes to 2r+5=77-r
c. now you just have to get like terms to their side of the equal sign
add r to both sides: 2r+r+5=77-r+r= 3r+5=77
and then you subtract 5 from both sides which makes 3r=72
to find r, divide both sides by 3
r=24
there are 24 red marbles
Decide whether pairs of angles <1 and <2, <6 and<1 , and <5 and <6 are alternate interior angles, same-side interior angles, corresponding angles, or alternate exterior angles. Question content area bottom Part 1 Choose the statement that correctly describes angles 1 and 2.
*PLEASE ANSWER EACH QUESTION. IN ALL 3 PICS. THANKS
<1 and <2 are same-side interior angles. Option D
<1 and <5 are same-side interior angles. Option B
<6 and <8 are corresponding angles. Option C
How to determine the anglesTo determine the angles, we need to know the following;
Corresponding angles are angles formed in matching corners with the transversal when two parallel lines are intersected by any other lineSame side interior angles are two angles that are found on the interior of two lines and exactly on the same side of the transversal. Adjacent angles are equalNow, from the information given, we have that;
1. <1 and <2 are same-side interior angles because they are found on the same side of the transversal
2. We can see that < 1 and <5 are also same-side interior angles because they are two angles found on the exact same side of the transversal
3. Since corresponding angles are angles on matching corners of a transversal, < 6 and < 8 are corresponding angles
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Linear equations linear equations
A graph of the linear equation y = 2x - 1 in slope-intercept form is shown in the image attached below.
What is the slope-intercept form?In Mathematics and Geometry, the slope-intercept form of the equation of a straight line is given by this mathematical equation;
y = mx + b
Where:
m represent the slope or rate of change.x and y are the points.b represent the y-intercept or initial value.Based on the information provided above, we have the linear equation:
y = 2x - 1
Lastly, we would use an online graphing calculator to plot the given linear equation as shown in the graph attached below.
In conclusion, the slope of this linear equation is equal to 2 and it does not represent a proportional relationship.
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Complete Question:
Plot the linear equation on the coordinate axis shown on the right.
Find the number that belongs
in the green box.
[?]
37°
64°
21.1
30
Round your answer to the nearest tenth.
The number that belongs in the green box is 32.8
How to find the number that belongs in the green boxFrom the question, we have the following parameters that can be used in our computation:
The triangle
The third angle in the triangle is calculated as
Third angle = 180 - 37 - 64
Evaluate
Third angle = 79
If the number that belongs in the green box is x, then we have
x/sin(79) = 30/sin(64)
This gives
x = sin(79) * 30/sin(64)
Evaluate
x = 32.8
Hence, the number that belongs in the green box is 32.8
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What is the circumference of the circle if the radius is 10 cm?
The circumference of the circle is 62.8cm.
The Circumference of the circle is given by the formula,
Circumference = 2*[tex]\pi[/tex]*r cm.........equation 1
Given, r = 10cm
On substituting the radius value in equation 1
Circumference = 2*[tex]\pi[/tex]*10
Circumference = 62.8 cm
Therefore, the circumference of the circle is 62.8cm.
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A merchant has 1500 kg of sugar part of which he sells at 8% profit and the rest at 18% profit. He gains 14% on the whole. The quantity sold at 18% profit is
Answer:
900 kg
Step-by-step explanation:
Let's assume the cost price (C.P.) of sugar is Rs. x per kg.
The total quantity of sugar is 1500 kg.
Let the quantity of sugar sold at 8% profit be represented by y kg.
The quantity of sugar sold at 18% profit would then be (1500 - y) kg.
Using the rule of alligation, we can set up the following proportion:
(8% profit) y kg
-------------- = ------
(18% profit) (1500 - y) kg
Simplifying the proportions, we find that the difference in percentages is 4% (18% - 14% = 4%) and 6% (14% - 8% = 6%).
The ratio of these differences is 2:3.
This means that for every 2 kg of sugar sold at 8% profit, 3 kg of sugar is sold at 18% profit.
Since y represents the quantity sold at 8% profit (2 kg), we can calculate the quantity sold at 18% profit (3 kg) as follows:
(2 kg) * (3/2) = 3 kg
Therefore, the quantity sold at 18% profit is 900 kg.
Please Help
8x + 1
115⁰