When two negative numbers are joined together, the result is a positive number. −10−(−10) is not −20 but it's 20.
What are negative numbers?In mathematics, the opposite is represented as a negative number.
In the real number system, a negative number is one that is less than zero.
It is common to use negative numbers to describe how severe a loss or a shortage is.
The fact that the sum of two negatives is positive is related to the fact that the inverse of a positive number is that positive number back again.
When a negative number is subtracted from a negative number, a minus sign and a negative sign are merged to make a plus sign (-).
A negative number becomes a positive when two negatives are added together. −10−(−10) is not −20.
Instead, think about how one of the negative signs could be made to stand up so that it can cross over the other and become a plus.
10 + 10 = 0 would be the outcome.
Therefore, when two negative numbers are joined together, the result is a positive number. −10−(−10) is not −20 but it's 20.
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Complete the statement to explain how the lengths of the sides of the arrays shown on the grid are related. Enter your answer in the box.
Four arrays are shaded on a grid: an array with side lengths of 1 and 8, an array with side lengths of 4 and 2, an array with side lengths of 2 and 4, and an array with side lengths of 8 and 1.
The lengths of the sides of each array are factors of
The lengths of the sides of each array are factors of 8.
What is factors in math?A factor is a number that divides another number, leaving no remainder. In other words, if multiplying two whole numbers gives us a product, then the numbers we are multiplying are factors of the product because they are divisible by the product.
Given here: The dimensions of the four arrays as (1,8), (4,2), (2,4), (8,1)
Now factors of 8 are given by 8=2⁰,2¹,2²,2³
Thus clearly all the sides are factors of 8
Hence, The lengths of the sides of each array are factors of 8
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if a relation is not a function, then its inverse is sometimes, always, or never a function. explain your reasoning.
An inverse of a relationship that is never a function and can be a function itself.
An inverse function or an anti-function is defined as a function, which can reverse into another function, which undoes the action of another function. A function is the inverse of a function if whenever y=f(x) then x=g(y).
Every function has an inverse, but not every inverse will be a function. The inverse may fail the vertical line test. If the original function is a one-to-one function, then its inverse will be a function.
A one-to-one function not only passes the vertical line test, but it also passes a horizontal line test.
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math i need help with this question
I need help on my math work
When the slope of an equation or line is zero, the term "zero slope" is used.
How does a graph that has a negative slope behave?A line on a line graph with a negative slope is falling as it goes from left to right graphically. We shall discover that "price" and "quantity requested" have an adverse connection, meaning that when the price is greater, fewer people will buy the product.When the slope of an equation or line is zero, the term "zero slope" is used. Thus, a horizontal line is created. Because the slope of a vertical line is undefined rather than zero, it is not a line with zero slope.From a graph, we may write the slope-intercept equation. Our b-value is located at the location where the graph crosses the y-axis. Our m-value is the slope. Connect them to y=mx+b.To learn more about line graph refer to:
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I need help please!!!!
You must replace each variable with a number and carry out the arithmetic procedures to evaluate an algebraic expression. f(x) = -27.
What is meant by determine?research, analysis, or calculation to learn more about or reach a conclusion about. choose a solution to the issue. direct control over something, direct influence, or decision-making Depending on how much money we are permitted to spend, we will be able to hire a certain number of employees. What you consume affects your health in part. Genetics determines eye color. Determiners like decide, resolve, rule, and settle are frequently used interchangeably. In spite of the fact that all of these verbs indicate "to arrive to a conclusion or cause a conclusion to come to," the word "determine" refers to the process of determining the identity, character, scope, or direction of anything.f(x) = 3x - 9
determine f(x) = 9
f(9) = 3(9) - 9
f(9) = 27 - 9
f(9) = 22
Hence, the answer is 22.
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Help with this pls!!!
Use variables to write an equation that represents the relationships between the time and the distance.
An eagle flies 40 miles per hour.
The relation for time and distance will be written as D = 40t miles.
What is speed?Speed is defined as the ratio of the time distance travelled by the body to the time taken by the body to cover the distance. Speed is the ratio of the distance travelled by time. The unit of speed in miles per hour.
Given that the speed of the eagel is 40 miles per hour. The relationship between the distance and the time will be calculated as,
Distance = Speed x Time
Distance = 40 x Time
D = 40t miles
Here t, is in hours.
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The angle formed by two chords intersecting inside a circle has a measure equal to the arithmetic mean of the intercepted arcs' respective lengths.
What is meant by intersection of chords?The products of the measures of the segments of the chords are equal if two chords cross in a circle.
Theorem of intersecting chords. "The arithmetic mean of the measures of the two intercepted arcs is equal to the measure of an angle created by two chords that intersect inside a circle."
By intersecting the lines from two well-known ground landmarks, intersection is a technique for finding a location on a map. Fire lookouts employ a variety of techniques to locate fires, including intersections.
A tangent is a line that precisely crosses a circle at one point, and the junction is identified by the term "point of tangency" for the intersection. A radius drawn to the point of tangency always has the tangent perpendicular to it. A line that crosses a circle at precisely two different locations is known as a secant.
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what is the value of f(g(-3))
The two functions be[tex]$f(x)=3 x-7$[/tex] and [tex]$g(x)=\frac{x+1}{x-1}$[/tex] then the value of f(g(-3)) be -1.
What is meant by functions?An expression, rule, or law in mathematics that specifies the relationship between an independent variable and a dependent variable (the dependent variable). In mathematics and the sciences, functions are fundamental for constructing physical relationships.
A function is an equation with just one solution for every value of y in the equation. A function pairs each input of a particular type with exactly one output. Instead of y, it is typical to name functions f(x) or g(x).
If a function produces the same outcome regardless of how the input is represented without changing its value, it is said to be well defined.
Let the given two functions be
[tex]$$\begin{aligned}& f(x)=3 x-7 \\& g(x)=\frac{x+1}{x-1}\end{aligned}$$[/tex]
f(g(-3)) = f(g(x = 3)) = f(3 - 1) = f(4/2) = f(2)
f(x = 2) = 3 × 2-7 = 6 - 7 = -1
Therefore, the correct answer is option A. -1.
The complete question is:
Consider these functions:
[tex]$$\begin{aligned}& f(x)=3 x-7 \\& g(x)=\frac{x+1}{x-1}\end{aligned}$$[/tex]
What is the value of f g(3))?
A. -1
B. 0
C. 3
D. 5
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What is the equation of a line perpendicular to 3x+y=4 that passes through(-1,6)
Please help ASAP
The equation of the line perpendicular to 3x+y=4 that passes through(-1,6) is y = 1 / 3 x + 19 / 3.
How to find the equation of a line?The equation of a line can be represented in slope intercept form as follows:
y = mx + b
where
m = slopeb = y-interceptTherefore, the line is perpendicular to 3x + y = 4 that passes through(-1,6).
Perpendicular lines have slopes that are negative reciprocals of one another.
Therefore,
y = -3x + 4
The slope of the line will be 1 / 3.
Hence, let's find the y-intercept as follows;
using (-1, 6)
y = 1 / 3 x + b
6 = 1 / 3 (-1) + b
6 + 1 / 3 = b
b = 18 + 1/ 3
b = 19 / 3
Therefore, the equation is y = 1 / 3 x + 19 / 3
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Determine which numbers could not be used to represent the probability of an event. Select all that apply A. 0.0002, because probability values must be rounded to two decimal places. B. 33.3%, this is because probability values cannot be greater than 1 C. 0, because probability values must be greater than 0 D. 64/25, because probability values cannot be greater than 1 E. 320/1058, because probability values cannot be in fraction form. F. -1.5, because probability values cannot be less than 0.
The option D "64/25, because probability values cannot be greater than 1" and option F "-1.5, because probability values cannot be less than 0" could not be used to represent the probability of an event.
In the given question, we have to determine which numbers could not be used to represent the probability of an event.
Let P be the probability.
It can accept any value [0,1] (inclusive of 0, 1), as well as [0%, 100%] (inclusive of 0% and 100%).
It is unable to accept negative values.
Because probability values cannot be larger than one or less than one, 64/25 and -1.5, respectively, cannot be used to indicate the likelihood of an evens.
So, the option D "64/25, because probability values cannot be greater than 1" and option F "-1.5, because probability values cannot be less than 0" could not be used to represent the probability of an event.
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true or false: for categorical data, the mode is a particularly useful measure of central tendency, compared to mean or median
For categorical data, the mode is a particularly useful measure of central tendency it is a True statement.
A categorical variable in statistics is a variable that, based on some qualitative quality, can have one of a small, and typically fixed, number of potential values, designating each individual or other unit of observation to a certain group or nominal category.
Ordinal variables shouldn't be averaged because the gaps between the categories could not be uniform. Standard deviation and variance shouldn't be used to describe categorical data because they both depend on the mean. Instead, percentiles and range are used as metrics of spread for ordinal categorical data.
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1.03 solving compound inequalities
8 – 6x < −28 or 9x + 5 < −31
The solution of the inequalities is x > 6 or x < -4
How to solve compound inequalities?An inequality compares two values, showing if one is less than, greater than, or simply not equal to another value e.g 5 < 6, x ≥ 2, etc.
8 – 6x < −28 or 9x + 5 < −31
collect like terms and solve for x in both inequalities:
For 8 – 6x < −28:
8 – 6x < −28
-6x < -28 - 8
-6x < -36
-x < -36/6
-x < -6
x > 6
For 9x + 5 < −31:
9x + 5 < −31
9x < -31 - 5
9x < -36
x < -36/9
x < -4
Thus, the solution is x > 6 or x < -4
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2340, 3455,675,960 1350 . 1 . () () , ()
a) 8780
b) i) 1159 ii) 1990
c) 9611
a) The total number of workers at the beginning is 2340 + 3455 + 675 + 960 + 1350 = 8780 workers.
b)
i) The first two companies laid off 1 worker for every 5 workers, so for the first company (2340 workers) this means 2340/5 = 468 workers lost their job. For the second company (3455 workers) this means 3455/5 = 691 workers lost their job.
In total, 468 + 691 = 1159 workers lost their job.
ii) The other three companies recruited 2 new workers for every 3, so for the third company (675 workers) this means 6752/3 = 450 new workers were recruited. For the fourth company (960 workers) this means 9602/3 = 640 new workers were recruited. For the fifth company (1350 workers) this means 1350×(2/3) = 900 new workers were recruited.
In total, 450 + 640 + 900 = 1990 new workers were recruited.
c) The total number of workers finally is 8780 - 1159 + 1990 = 9611 workers.
The complete question is -
Five companies employed 2340, 3455, 675, 960, and 1350 workers. The first two companies laid off 1 worker for every 5 workers, while the other three recruited 2 new workers for every 3.
a) What was the total number of workers at the beginning?
b) How many people: i) Lost job ii) Got a job?
c) What was the total number of workers finally?
What is quotient rule in math?
Dividend ÷ Divisor = Quotient and Remainder
When a dividend is divided by a divisor, we get the value of the quotient in the result.
The quotient is the result of dividing one integer by another. For example, in 8÷ 4 = 2, the result of the division is 2, hence the quotient is 2. The dividend is 8 and the divisor is 4.
According to the Quotient Rule, the derivative of a quotient equals the denominator times the numerator's derivative minus the numerator times the denominator's derivative, all divided by the denominator's square.
This is the rule we employ when dividing one exponential equation by another. According to the quotient rule, we must subtract the exponent in the denominator from the exponent in the numerator, but the bases must be the same.
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The middle school chorus has 12 altos, 20 sopranos, 4 tenors, and 40 bass singers. What
is the ratio of sopranos to the entire chorus as a fraction?
Therefore , the solution of the given problem of ratio comes out to be
5/14 is the ratio of sopranos to the entire chorus as a fraction.
It defines a ratio.A pair of equivalent variables "a" and "b" can be defined using the straightforward formula "a / b," where "b" could also be bigger than zero. Two ratios are combined to make one ratio. The ratio would indeed be 1:1 if there were just one guy and three women. 3/4 of the group are girls, while 1/4 are boys. Parts can be a division between one or more items, a number, or a portion of the volume of a component.
Here,
given :
=>12 altos, 20 sopranos, 4 tenors, and 40 bass singers.
To find the ratio of sopranos to the entire chorus as a fraction
So,
Total singers leaving sopranos are :
=> 12 + 4 + 40 = 56
The ratio of sopranos and entire chorus is:
=> 20 /56
=> 10/28
=> 5/14
Therefore , the solution of the given problem of ratio comes out to be
5/14 is the ratio of sopranos to the entire chorus as a fraction.
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How do you graph parent quadratic functions?
The process of plotting the parent quadratic function is explained below.
The term parent function is known as a family of functions is a group of functions that have the same degree or the same form.
Here the examples of families of functions include linear functions, quadratic functions, square root functions, and absolute value functions.
And here we also know that the parent function of any family of functions is the simplest form of the function where the graph does not experience any transformations.
As for example here we have the linear parent function is y=x where the graph passes through the origin and has a slope of 1.
In order to plot the graph, then we must following the below steps:
1) Identify the points of the equation or function.
2) Make the table through it.
3) Now, plot the value on the graph
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multiplying polynomials is done by applying the ___ property when necessary.
Answer: Distributive property
Step-by-step explanation:
What is the quotient of 52 and 4?
Andre says, "We know that if
rectangle is scaled by a factor of k, the area
scales by a factor of k². Does this apply to other shapes?"
Jada says, "Here's a shape that's not a rectangle. Say its area is A square units.
Let's draw some rectangles on it that get smaller and smaller to fit the
remaining empty space. With enough rectangles we can come close to
covering the whole blob."
Andre says, "These rectangles start to make a nice approximation of the blob.
If we wanted to get closer, we could add even more rectangles. The sum of the
areas of all the rectangles would add up to the area of the blob. I think we're
almost there!"
2. What does this tell you about the area of the dilated image? Explain your
reasoning.
3. Suppose a circle has area 20 square inches and it's dilated using a scale
factor of 6. What is the area of the image? Explain or show your reasoning.
The above conversation suggests that the area of the dilated image can be approximated as the sum of the areas of rectangles. If the original shape is dilated by a factor of k, the area of the dilated image would scale by a factor of k².
The area of the image based on the information will be 720 square inches.
How to calculate the areaThe area of a circle with radius r is given by A = πr².
If the circle has an area of 20 square inches, then we can solve for the radius: 20 = πr² => r = sqrt(20/π). If the circle is dilated using a scale factor of 6, the radius would be 6 times larger, which means the area would be 6² times larger: A' = π(6r)² = 36πr²
= 36π(20/π)
= 720 square inches.
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-43 = x/5 - 47
solve for x:
Hey there!
Answer:
After solving for x, our final answer is x = 20.
Further Explanation1. Switch sides.
[tex]\frac{x}{5}-47=-43[/tex]
2. Move 47 to the right side.
[tex]\frac{x}{5}=4[/tex]
3. Multiply both sides by 5.
[tex]\frac{5x}{5}=4*5[/tex]
4. Simplify.
[tex]x=20[/tex]
___________________________
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PLEASE HELP !
one of the tables shows a proportional relationship. Graph the line representing the proportional relationship from this table.
Answer: The equation is y=2x
A picture of a school's mascot is 18 in. wide and 24 in. long. It is enlarged proportionally to banner size. If the width is enlarged to 63 in., what is the length of the banner?
The length of the banner is, 84 inch when the width is enlarged to 63 in.
What is Proportional?Any relationship that is always in the same ratio and quantity which vary directly with each other is called the proportional.
Given that;
A picture of a school's mascot is 18 in. wide and 24 in. long.
And, It is enlarged proportionally to banner size.
Now, Let the length of the banner when the width is enlarged to 63 in.
Hence, By definition of proportionality, we get;
⇒ Length / Width
⇒ 24 / 18 = x / 63
Solve for x as;
⇒ 24 × 63 / 18 = x
⇒ x = 84 inch
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10(b-6) as simplified expression
circuit optimation problem georgina orwell wants to build a rectangular pig pen along the side of a pre-existing barn, so she will only need fencing on three sides. she has 200 feet of fencing and will use all of it to maximize the pig pen. find the maximum area (in square feet) she can enclose.
The maximum area that Georgina Orwell can enclose is 10000 square feet.
The maximum area that Georgina Orwell can enclose with 200 feet of fencing is:
Let x be the length of the side of the pig pen along the barn and y be the width of the pig pen.
We know that:
x + 2y = 200
We can use this equation to find the value of one variable in terms of the other. For example, we can solve for y:
y = (200 - x) / 2
We can use this equation to find the area of the pig pen:
A = xy = x((200 - x) / 2)
= (200x - x^2) / 2
To find the maximum area, we need to find the value of x that maximizes A. To do this, we can take the derivative of A with respect to x and set it equal to zero:
A'(x) = (200 - 2x) / 2 = 0
200 - 2x = 0
x = 100
So the maximum area is:
A = (200x - x^2) / 2 = (200 * 100 - 100^2) / 2 = 10000 sq ft.
Therefore, the maximum area that Georgina Orwell can enclose is 10000 square feet.
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Could someone answer at least all the questions that are un-answered or just a couple or just the word problem, you can pick any of those options but you can try, also the last 3 aren’t actually answered I just re-wrote the equation.
Answer:
the answers are in the picture.. if you have any questions you can ask :)
Please help fill out!!!
0, becous A (-1x2) can't be negative.
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Part 3: Choose a proof method.
1. Use a paragraph, flow chart, or two-column proof to prove that is the perpendicular bisector of side .
The congruences given are the corresponding sides and angles of WZX and YZX. Segment ZX is congruent to itself, so SAS WZX YZX.
What is congruency?Two figures or objects are congruent in geometry if they have the same shape and size, or if one has the same shape and size as its mirror image.Then, by CPCTC, WXZ YXZ and WX YX. This means that X is a midpoint and ZX is a bisector of WY. Because they are both congruent and supplementary, the angles of the linear pair WXZ and YXZ must be 90°.The corresponding sides and angles of WZX and YZX are given as congruences. SAS WZX YZX because segment ZX is congruent to itself.As a result, ZX is perpendicular to WY and its bisector.To learn more about congruency refer to :
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given m n find the value of x(7x-4) and n(5 x+10)
The value of x for the given corresponding angles is, 7 degree.
What is corresponding angles?
In geometry, corresponding sides and corresponding angles of polygons are compared as part of the tests for congruence and similarity. In these tests, the order of adjacency is maintained by pairing each side and each angle of one polygon with a side or angle of the other polygon.
Given:
m || n
The angles (7x - 4) and (5x + 10) are corresponding angles.
We have to find the value of x.
Since, the angles are corresponding angles and corresponding angles are equal when the lines are parallel.
⇒ 7x - 4 = 5x + 10
Add 4 on both sides,
7x - 4 + 4 = 5x + 10 + 4
7x = 5x + 14
Subtract 5x on both sides,
7x - 5x = 5x + 14 - 5x
2x = 14
Divide both sides by 2
⇒ x = 7
Hence, the value of x for the given corresponding angles is, 7 degree.
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Brody and his children went into a movie theater and he bought $44.50 worth of drinks and pretzels. Each drink costs $6 and each pretzel costs $3.25. He bought a total of 12 drinks and pretzels altogether. Determine the number of drinks and the number of pretzels that Brody bought.
The number of drinks and the number of pretzels that Brody bought are 10 and 2 respectively.
What is a linear equation?
Linear equation can be defined as an algebraic equation of degree one. The variable or the variables in the case of a linear equation in two variables the variables are x and y.
Brody and his children went into a movie theater and he bought $44.50 worth of drinks and pretzels.
Assuming no. of drinks to be x and no. of pretzels to be y and drink costs $6 and each pretzel costs $3.25.
∴ 6x + 3.25y = 44.50...(i)
He bought a total of 12 drinks and pretzels altogether.
∴ x + y = 12...(ii)
multiplying eqn (ii) by 6 and subtracting from eqn (i) to cancel out the x term we get - 2.75y = - 27.5 ⇒ 2.75y = 27.5 ⇒ y = 10 and hence x = 2.
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The drama club is performing a musical. Tickets cast $5 for adults and $3 for students. The drama club wants to raise up to $450. What is an equation to find the number of each type of ticket they should sell?
5x+3y=450 is the equation to determine how many of each type of ticket they should sell.
What is equation?The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two expressions 3x + 5 and 14, which are separated by the 'equal' sign. A mathematical statement known as an equation is made up of two expressions joined together by the equal sign. A formula would be 3x - 5 = 16, for instance. When this equation is solved, we discover that the value of the variable x is 7.
Here,
Let x be the number of adult tickets and y be the number of student tickets.
5x+3y=450
The equation to find the number of each type of ticket they should sell is 5x+3y=450.
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