The rule(s) of algebra illustrated by the statement is the identity property of algebra
How to identify the rule(s) of algebra illustrated by the statement.?The statement is given as:
1 · (1 + x) = 1 + x
The identity property of algebra states that:
1 * a = a or a * 1 = a
In the above (given) statement, we can see that the expression 1 + x is multiplied by 1 to given 1 + x
This can be illustrated as
1 * a = a
The rule(s) of algebra that illustrates the above equation is the identity property of algebra
Hence, the rule(s) of algebra illustrated by the statement is the identity property of algebra
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Systems of equations with graphing
The correct option is A. x = 1(1/3) and y = 2(1/3) in the mixed fractions.
What is defined as the system of equations?A system of equations is a collection of equations that all have the same variables.
If all of the equations are linear, you get a system of linear equations! To fix a system of equations, you must first determine the variable values that will solve all of the equations involved.A solution to an equation system is a set of variable values that satisfy all of the equations at the same timeNow, the given equation in the question are-
7x - y = 7 ........(equation 1)
and x + 2y = 6 ........(equation 2)
Multiplying both side of equation 1 with 2, we get
14x - 2y = 14 ........(equation 3)
Add equation 2 and 3.
x + 2y + 14x - 2y = 6 + 14
15x = 20
x = 4/3
x = 1(1/3)
Substitute the value of x in equation 1.
4/3 + 2y = 6
2y = 6 - 4/3
2y = 14/3
y = 7/3
or y = 2(1/3)
Therefore, the values for variables x and y are calculated as:
x = 1(1/3) and y = 2(1/3).
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answer please !!!!!!!
Answer: 32, but I'm not sure
Step-by-step explanation:
State whether the slopes would represent parallel lines, perpendicular lines, or neither.
-4 and 1/4
8 and -8
7 and 17
2 and 2
Answer:
neither
Step-by-step explanation:
i am goung to assume that the quarter really is just a quarter unit on the y-axis
Answer:
The line with a slope of [tex](-4)[/tex] is perpendicular to the line with a slope of [tex](1/4)[/tex] since the product of the two slopes is [tex](-1)[/tex].
Slope of [tex]8[/tex] and slope of [tex](-8)[/tex]: neither parallel nor perpendicular.
Slope of [tex]7[/tex] and slope of [tex]17[/tex]: neither parallel nor perpendicular.
The line with a slope of [tex]2[/tex] is parallel to the other line of slope [tex]2\![/tex] since the two lines have the same slope.
Step-by-step explanation:
Two lines in a cartesian plane are parallel to one another if and only if their slopes are equal. Two lines in a cartesian plane are perpendicular to one another if and only if the product of their slopes is [tex](-1)[/tex].
For example, a line with a slope of [tex]m[/tex] is parallel to another line of the same slope, [tex]m\![/tex].
Since [tex](-m)\, (1/m) = -1[/tex], a line with a slope of [tex](-m)[/tex] would be perpendicular to a line of slope [tex](1/m)[/tex].
Help me with this please , picture above
Write a simplified expression for the area of the rectangle below.
The simplified expression for the area of the given rectangle is 12x + 40
As per the given figure:
The length of the rectangle given in the question: 3/5x + 2
The breadth of the rectangle given in the question: 20
The formula for the area of a rectangle is given by:
Area of rectangle = Length of the rectangle * Breadth of the rectangle
Area of rectangle = (3/5x +2)*20
=(3x + 10)/5 * 20
= (3x + 10) * 4
= 12x + 40
Area of rectangle = 12x + 40
So, the simplified expression for the area of the rectangle with the given length and breadth is 12x + 40
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a bee flies at 20 feet per second directly to a flowerbed from its hive. the bee stays at the flowerbed for 14 minutes, and then flies directly back to the hive at 16 feet per second. it is away from the hive for a total of 19 minutes.
Distance, D = 5,760,000/2,160 = 2666.67 (approx)
What is time function?The Excel DATE/TIME capabilities include the TIME Function. We can construct a time using distinct hour, minute, and second components with the aid of TIME.
We might want to date a report while performing financial analysis. In these circumstances, TIME can be used to transform a text string into a format that indicates the time in decimal form. Additionally, the function can be used to combine different values into a single time value.
formula= TIME (hour, minute, second)
distance = rate X time
D = RT
T = D/R
20 feet per second = 1200 feet per minute
16 feet per second = 960 feet per minute
[of minutes to flowerbed] + 14 minutes + [of minutes back to hive] = 19 minutes
(D/R) + 14 + (D/R) = 19
(D/R) + 14 + (D/R) = 19
(D/1200) + 14 + (D/960) = 19, This is the equation we can use to find the distance from the flowerbed to the hive.
(D/1200) + (D/960) = 5
(D(1200)(960))/1200 + (D(1200)(960))/960 = 5(1200)960
960D + 1200D = 5(1200)960
2,160D = 5,760,000
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the names of 0 employees are written on 0 cards. the cards are placed in a bag, and three names are picked from the bag. what sampling technique was used?
The names of 0 employees are written on 0 cards. the cards are placed in a bag, and three names are picked from the bag - here simple random sampling technique was used.
What is simple random sampling?Basic irregular testing can provide you with an extremely precise image of how your motto performs with the typical individual, yet it won't give you nitty gritty data about unambiguous gatherings. Utilizing straightforward irregular testing permits scientists to make speculations about a particular populace and leave out any inclination. This can assist with deciding how to settle on future choices. It has been expressed that "the rationale behind straightforward arbitrary examining is that it eliminates predisposition from the choice method and ought to bring about delegate tests".
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b. For mixing a spray to kill weeds, Howard is to
use 2 1/2 tablespoons for each gallon of water.
How many tablespoons of the spray will he
need to use for 5 gallons of water.
The 12.5 tablespoons of the spray will he need to use for 5 gallons of water.
What is arithmetic?
Arithmetic is the branch of mathematics that deals with the study of numbers using various operations on them. Basic operations of math are addition, subtraction, multiplication and division. These operations are denoted by the given symbols.
Given:
For mixing a spray to kill weeds, Howard is to use 2 1/2 tablespoons for each gallon of water.
We have to find How many tablespoons of the spray will he need to use for 5 gallons of water..
According to given question we have
2 1/2 =5/2 tablespoons for each gallon of water.
5/2 tablespoons =1 gallon of water.
1 gallon of water=5/2 tablespoons
5 gallons of water=5/2*5 tablespoons
5 gallons of water=25/2 tablespoons=12.5 tablespoons
Therefore, the 12.5 tablespoons of the spray will he need to use for 5 gallons of water.
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the median of 6 consecutive integers is 9. what is the largest number
If the median of 6 consecutive integers is 9, the largest number is equal to 8.5.
Given the following data:
Median, M = 9.Number of consecutive integers, n = 6.What is a median?In Mathematics, a median can be defined as the middle number (center) of a sorted data set, which is when the data set is arranged in from the greatest to least or the least to greatest.
In Mathematics, the median of a data set is generally considered to be a better measure of center than the mean when there's an outlier in the data set.
For the largest number, we have:
Since consecutive integers must follow each other sequentially with a difference of 1, so the largest number is given by:
Largest number = Median + (n - 1)/2
Substituting the given parameters into the formula, we have;
Largest number = 6 + (6 - 1)/2
Largest number = 6 + (5)/2
Largest number = 6 + 2.5
Largest number = 8.5.
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If m ∠ F L G = ( 14 x + 5 ) ° and m ∠ H L G = ( 17 x − 1 ) ° , find m ∠ F L H .
The value of m ∠ F L H is 57°
How to determine the valueFrom the information given, we have that
m ∠ F L G and m ∠ H L G are congruent angles
Note that congruent angles are angles are equal or equivalent to each other
Given that;
m ∠ F L G = ( 14 x + 5 ) ∠ H L G = ( 17 x − 1 ) °Equate the expression for both angles
14x + 5 = 17 x − 1
collect like terms
14x - 17x = -1 - 5
Subtract like terms
-3x = -6
Make 'x' the subject of formula
-3x/-3 = -6/-3
x = 2
But we know that;
m ∠ F L G = ( 14 x + 5 ) = 14(2) + 5 = 28 + 5= 33°
m ∠ F L H = 90 - 33 = 57°
Thus, the value of m ∠ F L H is 57°
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whats the transformation
Answer:translation
Step-by-step explanation:
a man and a woman, both with brown eyes (bb), have a child. what is the percentage chance that the child will have blue eyes?
How do you evaluate a function?
Answer:
evaluating a function means finding the value of f(x) or f(y).......
Answer:
replace all the x variables with whatever x has been assigned
Step-by-step explanation:
evaluating a function means finding the value of f (x) = or y equals that corresponds to a given value of x to do this simply replace all the x variables with whatever x has been assigned for example if we are asked to evaluate f (4) then x has been assigned the value of 4
Round 1.496 to the place value of the underlined digit.
Rounding off the given decimal to the nearest hundredth, tenth and ones place are 1.50, 1.5 and 2 respectively.
The given decimal number is 1.496.
We need to round off the given decimal number.
How to round off the decimal number?There are some basic rules that need to be followed for rounding numbers.
We first need to know what our rounding digit is. This digit is the one that will ultimately be affected.After this, we need to check the digit to the right of this place which will decide the fate of the rounding digit.If the digit to the right is less than 5, we do not change the rounding digit. However, all the digits to the right of the rounding digit are changed to 0.If the digit to the right is 5 or more than 5, we increase the rounding digit by 1, and all the digits to the right of the rounding digit are changed to 0.Now, rounding off 1.496 to the hundredth place is 1.50
Rounding off 1.496 to the tenth place is 1.5
Rounding off 1.496 to the ones place is 2
Therefore, rounding off the given decimal to the nearest hundredth, tenth and ones place are 1.50, 1.5 and 2 respectively.
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EVALUATING EXPI
Evaluate the expression below
when g = 10
6g²
Answer:
600Step-by-step explanation:
Expression given:
6g²Find its value when g = 10:
6g² = 6(10²) = 6(100) = 600consider the value of t such that the area to the left of −|t|−|t| plus the area to the right of |t||t| equals 0.10.1.
We want to find the value of t such that the area to the left of −|t| plus the area to the right of |t| equals 0.1.
That is level of significance (α) = two-tail area = 0.1
what is a level of significance in research?
The significance stage (also called kind I mistakes rate or the extent of statistical importance) refers back to the chance of rejecting a null hypothesis that is in truth true. This amount stages from 0 (0.0) to at least one (1.zero) and is generally denoted through the Greek letter alpha (a).
What are the three levels of significance?
commonplace importance stages are 0.10 (1 risk in 10), 0.05 (1 risk in 20), and zero.01 (1 hazard in one hundred). The result of a speculation check, as has been seen, is that the null hypothesis is both rejected or now not.
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What is the equation of a line that has slope of -4/3 and passes through the point (12,-4)
Answer:
y = -4/3x + 12
Step-by-step explanation:
y - y1 = m (x - x1)
the y1 and x1 are where your coordinates go. The m is the slope.
So now we just plug it in.
y - (-4) = -4/3 (x - 12)
we can clean it up some more to make it into the y = mx + b format.
y + 4 = -4/3x - (-4/3)12
y + 4 = -4/3x + 16
y = -4/3x + 12
lillian drew a scale drawing of a county park. the scale she used was 1 inch : 4 yards. the picnic area is 80 yards wide in real life. how wide is the picnic area in the drawing?
The picnic area is 20 inches wide in the drawing in her scale of 1 inch : 4 yards.
What is unitary method ?Unitary method is a technique for first solving the value of a single digit unit and from there we can find the value of any given unit.
According to the given question lillian drew a scale drawing of a county park. the scale she used was 1 inch : 4 yards.
The picnic area is 80 yards wide in real life.
∴ The width of the picnic area in here drawing in inches will be
= 80/4 inches.
= 20 inches.
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charlene levington operates an oil change and tune-up service. she charges $33.95 per oil change. tune-up is $72.50 for a four-cylinder engine, $82.50 for a six-cylinder engine, and $92.50 for an eight-cylinder engine.
The charges for a week in which Charlene's facility did 35 oil changes and tuned 5 four-cylinder engines, and 7 six-cylinder will be $2313.25.
What is an expression?Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.
Given that charges per oil change are $33.95, charges for a four-cylinder engine $72.50, charges for a six-cylinder engine $82.50, and, charges for an eight-cylinder engine $92.50.
The total charges will be calculated as below:-
No oil changes done by Charlene = 35
price of 5 - four-cylinder engines = 5 × 72.50
= 362.50 .....(1)
Price of 7 - six cylinder engines = 7 × 82.50
= 577.50 ........(2)
Price of 2 - eight-cylinder engines = 2 × 92.50
= 185 ...........(3)
Now, adding (1), (2),(3)
= 362.50 + 577.50 + 185
= 1125 ...........(4)
Total charges for oil = 33.95 × 35
= 1188.25 ..........(5)
Add equations (4) and (5) to get the total charges.
= 1125 + 1188.25
= 2313.25
Therefore, the total charges will be $2313.25.
The complete question is given below:-
Charlene operates an oil change and tune-up service. she charges $33.95 per oil change. a tune-up is $72.50 for a four-cylinder engine, $82.50 for a six-cylinder engine, and $92.50 for an eight-cylinder engine. what are the charges for a week in which Charlene's facility did 35 oil changes and tuned 5 four-cylinder engines, and 7 six-cylinder?
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Find the derivative of the function by the limit process.
f(x)=(3)/(x-2)
Functions are expressed by writing a variable in terms of other variables known as the independent. The derivative of the given function is -3/(x-2)².
Derivative of a functionGiven the function below;
f(x) = 3/x-2
Since it is a quotient, we can use the quotient rule to express the equation as shown:
let u = 3 and v = x -2
du/dx = 0 and dv/dx = 1
According to the rule;
dy/dx = (x-2)(0) - 3(1)/(x-2)²
dy/dx = 0-3/(x-2)²
dy/dx = -3/(x-2)²
Hence the derivative of the given function is -3/(x-2)²
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Triangle HIJ, with vertices H(-9,-8), I(-5,-5), and J(-7,-3), is drawn on the
coordinate grid below.
what is the area, in square units, of triangle HIJ?
The area of triangle HIJ is 7 square units.
Given that, the vertices of triangle HIJ are H(-9,-8), I(-5,-5), and J(-7,-3) respectively. By using the vertices of triangle HIJ we have to evaluate its area in square units. So, let's procced to solve the question.
Area of ΔHIJ = 1/2|x₁(y₂-y₃)+x₂(y₃-y₁)+x₃(y₁-y₂)|
So, x₁ = -9, x₂ = -5, x₃ = -7 and y₁ = -8, y₂ = -5, y₃ = -3
Put all the listed values in the formula of area of triangle HIJ.
By using the above formula, we get
=1/2|-9(-5+3)+(-5)(-3+8)+(-7)(-8-(-5))|
=1/2|-9(-2)-5(5)+(-7)(-3)|
=1/2|18-25+21|
=1/2|14|
= 1/2 x 14
= 7
Therefore, the area of triangle HIJ is 7 square units.
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HELP! 25 POINTS
Factorise: √ab(x² +1) + x(a+b)
A bird flies from the bottom of a canyon that is 51 3/10 feet below sea level to a nest that is 737 1/10 feet above sea level.
685.8 feet
Sea level is a reference to elevation of the ocean or land interface called the shoreline.
Land that is above this elevation is higher than sea level and lower is below sea level.
The bottom of the canon is at 51 3/10 below the sea level which is also written as -51 3/10 ……(1)
The nest is at 737 1/10 feet above the sea level so it is expressed as
737 1/10 ….(2)
To find the distance between the bottom of the canyon and the bird’s nest we subtract (2) from (1)
737.1 – 51.3
= 685.8 feet
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Test each number with substitution to see which one is the correct solution for the equation.
Is -0.5, 0.5 or 4.5 the correct solution for the equation -6x+15=-12
the correct solution for the equation is 4.5
Lenny makes 55,000 per year and gets annual raises of 20,000 how many years why will it take lenny and kenny to make the same annual salary
Answer:
14,987
Step-by-step explanation:
Question 10: Andrew is going to fill an empty swimming pool.
Andrew fills the swimming pool with water at a constant
rate of 2.1 litres per second.
Given 1m³= 1000 litres, estimate how long it takes to fill the pool.
7.15m
21m
1.9m
The swimming pool will take 135850 seconds to fill with water.
Given the dimensions of the pool are:
7.15 m
21 m
1.9
The swimming pool is being filled with water at a constant rate of 2.1 liters per second.
hence the volume of the swimming pool is :
volume = 7.15 × 21 × 1.9
volume = 285.285 m³
convert from meters to liters.
volume = 285.285 × 1000
= 285285 liters.
to find out the time required to fill the pool, we need to divide the volume by the flow rate.
⇒ 285285 ÷ 2.1
= 135850
hence the swimming pool will take 135850 seconds to fill with water.
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The length of a rectangle is twice the width. The area of the rectangle is 90 square unites
A Which irrational number represents the length of each side of the square?
B Estimate the length and width of the rectangle
a) Both the length and the width of the rectangle are square roots of integers.
b) The length and the width of the rectangle are 6√5 units and 3√5 units, respectively.
How to analyze irrational numbers
Irrational numbers are numbers that not rational, that is, numbers that not of the form m / n, where m and n are integers and n is different of zero. Rational numbers may be integers or not.
Now, the statement indicates that the length and the width of rectangle have measures of 2 · x and x, respectively, and that the area of the rectangle is equal to 90 square units. The area formula is presented below:
90 = (2 · x) · x
90 = 2 · x²
x² = 45
x = √45
x = √(9 × 5)
x = √9 × √5
x = 3√5
a) Both the length and the width of the rectangle are square roots of integers.
b) The length and the width of the rectangle are 6√5 units (approx. 13.416 units) and 3√5 units (approx. 6.708 units), respectively.
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Please help me someone
Answer:
See the table below
For n, the answer is 2n+1
Step-by-step explanation:
The number of trees in each figure represents an arithmetic sequence where the difference between subsequent figures is 2 (caled the common difference)
So the sequence is
Figure(n) Number of Trees
1 3
2 5
3 7
4 9 (7+2)
5 11 (9+2)
n 2n + 1
In general, for any arithmetic sequence we can write an equation for the nth term as [tex]a_n = a_0 + d(n-1)[/tex] where [tex]a_0[/tex] is the first term and d is the common difference
So for this example, we have [tex]a_0 = 3[/tex] and d=2 giving
[tex]a_n = 3 + 2(n-1) = 3 + 2n -2 = 2n + 1[/tex]
This is
In the diagram below AB||CD what measure of ECF
Answer:
Step-by-step explanation:
135.8 minus 47.5
Can someone help me with the radius? please and thank you
Answer:
r=7cm
Step-by-step explanation:
the diameter (distance from one side of the circle to the opposite side) is given in the picture. the radius is 1/2 the diameter, so r=7cm
*i'm assuming the 14cm given is referring to the straight line in the circle and not the circumference