Answer:
July
Step-by-step explanation:
Took terst
1
Select the correct answer.
Which expression in factored form is equivalent to this expression? 4(x² - 2x)2(x² - 3)
O A. 2(x - 1)(x - 3)
O B.2(x + 1)(x + 3)
O C.(2x+3)(x + 1)
O D. (2x - 3)(x + 1)
This expression of is identical to the statement in factored form of
4 (x² - 2x) 2 (x² - 3) is 2 (x - 1) (x – 3)
What is meant by equivalent?When two or more fractions can be reduced to one another, they are said to be equivalent. As an illustration, the equivalent fractions of 1/5 are 5/25, 6/30, and 4/20, which when simplified yield the same fraction, i.e. 1/5. Equivalent expressions are those that, despite appearing differently, perform the same operations. When the same value of the variable is entered, the results of two algebraic expressions that are equal have the same value.When writing equivalent fractions, the numerator and denominator are both multiplied or divided by the same number. This explains why these fractions combine to equal one number.Given,
4(x² – 2x) – 2(x² – 3)
We would first of all expand the expression given
This becomes
= 4x² - 8x - 2x² + 6
Rearrange to enable us simplify
4x² - 2x² - 8x + 6
= 2x² - 8x + 6
Factorize
2 (x² - 4x + 3)
factorizing further using the factors of 3 that add up to -4
2(x² - x - 3x + 3)
pick out the common factors
2 (x (x - 1) - 3 (x - 1)
2 (x - 1) (x - 3)
Hence, the correct answer is A) 2(x - 1) (x – 3)
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What are the 5 types of expression?
The 5 types of expression include:
monomial, polynomial, binomial, trinomial, multinomialWhat is an expression?The concept of algebraic expressions is the use of letters or alphabets to represent numbers without providing their precise values. We learned how to express an unknown value using letters like x, y, and z in the fundamentals of algebra. Here, we refer to these letters as variables.
Variables and constants can both be used in an algebraic expression. A coefficient is any value that is added before a variable and then multiplied by it. They include monomial, polynomial, binomial, trinomial, multinomial.
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How do you find the height of a rectangle when given the area and the base?
Answer:
Heigh of rectangle: Area divided by base
Step-by-step explanation:
Area of rectangle: Base x Height
So, to find the height, we need to take the Area divided by the Base, and we will get the height of a rectangle!
What is the area of a 10x10 square?
Answer: The answer is 100 :)
Step-by-step explanation:
you multiply L x W and that would be 10 x 10 and if you do the math right you should get an answer of 100
Someone pls help me answer this question and give a thorough explanation!!!!!
Answer:
The boats cross paths at the points (1,8) and (4,11)
Step-by-step explanation:
First, we want to find the points of intersection between the two paths. We are given two equations, both in the form y=(equation). Since we want to find the intersection points, we set the two equations equal to each other (since both equal y we can plug one of the equations in for y into the other equation) to get
-x^2+6x+3=x+7
From here, we solve this like a normal quadratic equation, move all variables to one side first
-x^2+5x-4=0
This factors to -(x-1)(x-4)=0, giving us x=1 and x=4
Now we plug these back into one of the original equations (in this case the linear equation is much more simple) to give us the points (1,8) and (4,11)
A shop charges `\$4. 95` for a large `9`-ounce frozen yogurt. What is the cost per ounce of the frozen yogurt?.
Answer:
$0.55/ounce
Step-by-step explanation:
The problem gives us the ratio of cost to ounce. We need to create a proportion (when you set two ratios equal to each other) to solve for one variable of the second ratio.
⭐ The first ratio is [tex]$4.95/9 ounces[/tex], which means that it costs $4.95 for 9 ounces.
⭐ The second ratio is [tex]x/1 ounce[/tex], where x is the cost for 1 ounce of frozen yogurt.
. . . . . . . "per ounce" means "for every 1 ounce"
⭐ We need to set these two ratios equal to each other and solve for x.
. . . . . . . In proportions, keep the units of the numerators and denominators the same. In this case, we'll keep the cost as the numerators and the ounces as the denominators.
. . . . . . . [tex]\frac{4.95}{9} = \frac{x}{1}[/tex]
. . . . . . . [tex]\frac{4.95}{9}(1) = x[/tex]
. . . . . . . ∴ x = $0.55/ounce
Help me please on this IXL
Answer:
61
Step-by-step explanation:
Using the exterior angle theorem,
[tex]c-15+c-18=c+28 \\ \\ 2c-33=c+28 \\ \\ c-33=28 \\ \\ c=61[/tex]
What graph is best for comparing change over time?
Bar graph is best for comparing change over time.
What is a Bar Graph ?Using rectangular bars with heights or lengths proportionate to the values they represent, a bar chart or bar graph displays categorical data. Both a vertical and a horizontal bar plot are possible. A column chart is another name for a vertical bar graph.
The visual display of data (often grouped) in the shape of vertical or horizontal rectangular bars, with the length of the bars corresponding to the measure of the data, is called a bar graph. Bar charts are another name for them. One tool used in statistics for processing data is the bar graph.
Bar graph components
Title: The graph's topic is covered in the title.Scale: The numbers that represent the units used in the bar graph's scale.Labels: The bottom and side of the bar graph each include a label indicating the type of data displayed.The data number is measured by the bar.To learn more about Bar Graph refer to :
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When comparing data between groups or monitoring changes over time, bar graphs are utilized.
What is a bar graph?A bar chart, often known as a bar graph, is a diagram that displays categorical data as rectangular bars with heights or lengths proportional to the values they stand for. You can plot the bars either vertically or horizontally. A vertical bar chart may also be referred to as a column chart.Comparing different discrete categories is displayed in a bar graph. The chart's other axis depicts a measured value, while the first axis displays the specific categories under comparison. Some bar graphs show clusters of more than one bars, displaying the values of multiple measured variables.Bar charts have clear categories within their domain and are often scaled to accommodate all the data. Bars on the chart may be placed in any order if there is no obvious hierarchy among the categories being compared. Pareto charts are bar graphs that display incidence in order from highest to lowest.Hence, When comparing data between groups or monitoring changes over time, bar graphs are utilized.
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identify the ordered pair that has the same slope as the equation y = 1/2x
a. (4,3) and (1,2)
b. (1,2) and (2,4)
c. (1,1) and (2,2)
d. (2,1) and (4,2)
Answer:
d. (2,1) and (4,2)
Step-by-step explanation:
Slope is rise/run or (y2 - y1) / (x2 - x1)
We see option D, the y increase by 1, and the x increase by 2
So, the slope of this equation is 1/2, and it matches our question.
So, D is the answer!
If you can, please give me a Brainliest! Thank you, and have a good day!
Answer:
d. (2,1) and (4,2)
y = 1/2x
2y = x
x = 2y
CHECKING
x = 2y (substitute (2,1) and (4,2)
2 = 2(1)
2 = 2 correct
x = 2y
4 = 2(2)
4 = 4 correct
Therefore, d. (2,1) and (4,2) is the correct answer
Step-by-step explanation:
heart and star pls <3 brainliest will be appreciated <3(っ◔◡◔)っ -{ elyna s }-How do you graph xy =- 4?
The formula for a horizontal line at y=4 is as follows: There is no slope. 4.0 is the y-intercept.
What are the Slope and intercepts ?
In mathematics, a line's slope, also known as its gradient, is a numerical representation of the line's steepness and direction.
The slope expresses how quickly the dependent variable changes when the independent variable changes. The Greek capital letter D or D is frequently used by mathematicians and economics to represent change. Slope contrasts the change in the vertical axis, y, with the change in the horizontal axis, x.
On the x-axis, negative numbers are below the origin, and on the y-axis, they are to the left of the origin. If the x-value is negative, begin at the origin and go to the left; if the y-coordinate is negative, move downward.
Line graphs, also known as XY graphs, are used to visually represent data (the outcomes of an experiment) in order to demonstrate the link between various factors, such as the severity of the disease and time.
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A stock lost 8 3/8 points on Monday and then another 1 5/8 points on Tuesday. On Wednesday, it gained 13 points. What was the
net gain or loss of the stock for these three days?
a. a gain of 6 1/2 points
b. a loss of 1 points
c. a gain of 17 1/2 points
d. a gain of 23 points
Answer:
A gain of 3 points
Step-by-step explanation:
I'm not sure the options are correct. But normally, you add up the lost points on the both days. Then you compare it to the gained point on Wednesday.
Is this right?
I dont know whether the 3 or the y should be negative
Answer:
You are correct
This is my answer: -3x^a y^f+b z^g+c
Step-by-step explanation:
(3x^a y^b z^c) (-y^f z^g)
-3x^a y^f+b z^g+c
Because both have the same base is y, so we add both f and b
Same with z, both have the same base is z, so we have z^g+c
My answer is different in order, but both are correct!
Find the inverse of the following functions. Show all work
f(x) = 2√x+7
Answer:
the inverse of f(x)=2x−7 f ( x ) = 2 x - 7 .
Step-by-step explanation:
check if f−1(f(x))=x f - 1 ( f ( x ) ) = x and f(f−1(x))=x f ( f - 1 ( x ) )
Answer:
f(x) = 1/4 x² - 7
Step-by-step explanation:
x + 7 ≥ 0
x ≥ -7
y/2 = 2 /2 √(x+7)
y/2 = √(x+7)
y ≥ 0
(y/2)² = √(x+7)²
y²/4 = x +7
x = y²/4 - 7
f(x) = x²/4 - 7
if x is binomial with n = 5 and p = 0.05, the chance that x is at least 1 is 0.6240
In a case of binomial distribution of of x where n = 5 and p = 0.05, the probability that x is at least 1 is not 0.6240, it is 0.2262.
Therefore, the answer is False.
The formula for binomial distribution is
P = nCx × pˣ × (1 - p)⁽ⁿ⁻ˣ⁾
where P is the probability
n is the total number of trials
x is the number of success trial
p is the probability of success in a single trial
From given details
n = 5
p = 0.05
P( x is at least 1) = 1 - P( x is less than 1)
P( x is at least 1) = 1 - P( x is 0)
P( x is at least 1) = 1 - 5C0 × 0.05⁰ × (1 - 0.05)⁽⁵⁻⁰⁾
P( x is at least 1) = 1 - 1 × 1 × 0.95⁵
P( x is at least 1) = 1 - 0.7738
P( x is at least 1) = 0.2262
--The question is incomplete, answering to the question below--
"If x is binomial with n = 5 and p = 0.05, the chance that x is at least 1 is 0.6240. True or False."
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What does changing the base of a log function do to the graph?
The larger the base of a log function, the closer the graph approaches the asymptote of x = 0.
We know that for a exponential function b^x = y, b is the base, y is the exponent to which the base b is raised and x is the result obtained.
We can write this in logarithmic form as:
log_b(x) = y
A logarithm base is the subscript of the logarithm that carries or raises the exponent.
For example in case of log_(3) 9 = 2, the base here is 3.
The change of base formula is:
log_b(x) = log_c(x) / log_c(b)
Also as we know the bigger the logarithm base, the smaller the curve on the graph. This means, the larger the base of a log function, the closer the graph approaches the asymptote of x = 0.
The log function may increase at a slower rate if the base increases.
Therefore, if the base of a log function is large, the graph approaches the asymptote of x = 0.
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Write the product (2x - 5)² in the form az²+bx+c and identify the values of a, b, and c. Type numerical values only. No variables
ANSWER FAST FOR LOTS OF POINTS
The product of (2x - 5)² can be written in the form az²+bx+c as follows:
(2x - 5)² = (2x)² - 2(2x)(5) + (5)²
= 4x² - 20x + 25
In this expression, a = 4, b = -20, and c = 25.
What is the coefficient of x² in 3x² 5 )( 4 4x²?
The Coefficient of x² in the equation (3x²-5)(4+4x²) after simplification is -8 .
The Equation is given as : (3x²-5)(4+4x²)
To simplify , we first multiply the terms inside the bracket ;
So , given equation can be written as (3x²-5)×(4+4x²)
⇒ 12x² + 12x⁴ - 20 - 20x²
Adding the like terms of the equation ,
we get ;
⇒ (12 - 20)x² + 12x⁴ - 20
Simplifying further , we get
⇒ 12x⁴ - 8x² - 20 .
In the equation above we see that the numerical term with the x² is (-8) .
Therefore , the required coefficient is -8 .
The given question is incomplete , the complete question is
What is the coefficient of x² in the equation after simplification ; (3x²-5)(4+4x²) ?
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find the market and the selling price of the following item. Roundup answers to the nearest sent blank chemistry say costs and 27.5 marked up 32% on cards what is the markup
Arya knows that if they need to add antifreeze to their car's radiator the mixture used must contain 50% antifreeze. How many gallons of a mixture containing 70% antifreeze must be added to a 3-gallon mixture containing 20% antifreeze to obtain the mixture they need?
Arya needs to add 2 gallon of 70% antifreeze must be added to a 3-gallon mixture containing 20% antifreeze to obtain the mixture they need.
What is antifreeze?
Antifreeze is an additive that lowers a liquid's freezing point that is made of water. For cold environments, freezing-point depression is accomplished using an antifreeze mixture. Additionally, common antifreezes raise the liquid's boiling point, enabling higher coolant temperatures.
Let x be the amount of 70% antifreeze to be added, in gallons.
In terms of percentage of antifreeze, we write:
20% of 3 gallons + 70% of x gallons = 50% of (3 + x) gallons
0.2(3) + 0.7x = 0.5(3 + x)
0.6 + 0.7x = 1.5 + 0.5x
0.7x - 0.5x = 1.5 - 0.6
0.2x = 0.4
x = 2
Hence, Arya needs to add 2 gallon of 70% antifreeze must be added to a 3-gallon mixture containing 20% antifreeze to obtain the mixture they need.
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The diagrams show the position of a tap when off and fully on. When fully on, water flows out of the tap at 15 litres per minute. The rate at which water flows out is in direct proportion to the angle of turn. The tap is turned 123° 123 The water flows into a tank with a capacity of 90.2 litres. How long, in minutes, will it take to fill the tank?
Answer:
8.8 mins
Step-by-step explanation:
to find how long in mins it would take to fill the tank
at 180 degrees the speed of water is 15 liters/min at 123 degrees
so [tex]\frac{15}{180} *123[/tex] = 10.25 liters/min
the capacity of the tank is 90.2 liters
[tex]\frac{90.2}{10.25} \\[/tex] = 8.8 mins
How do you graph the function y =- 5x 3?
The required graph of the given function y = -5x + 3 which has been attached below.
What is a graph?A graph can be described as a visual representation or a diagram that represents data or values.
To graph the function y = -5x + 3, you can start by making a table of values.
Here's an example:
x y
-2 -11
-1 -6
0 3
1 -2
2 -7
To plot these points, start by graphing the point (0,3). This is the y-intercept, where the line crosses the y-axis.
Then, use the slope of the line (-5) to find the next point. For example, if you go one unit to the right on the x-axis (from 0 to 1), the y-value decreases by 5 (from 3 to -2).
Continue graphing points in this way until you have plotted enough points to see the shape of the line. You should see that the line has a negative slope, meaning it goes down from left to right.
The required graph of the given function y = -5x + 3 has been plotted.
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The graph of the given function is a straight line.
What is straight line?A straight line is an endless one-dimensional figure that has no width. It is a combination of endless points joined on both sides of a point and has no curve.
Equation of straight line ( slope-intercept form) is, y= mx+ c
Where, m= slope of the line & c= y-intercept.
Here, given function is, y=-5x+3 , which is an equation of straight line.
So, here, m= -5 & c=3
That is the line will passes through the point (0,3)
Now, if we put, y=0 then, x= 3/5=0.6
i.e., the line will also passes through the point (0.6,0)
So, we get, the required graph of the function ,
Hence, the graph of the function is a straight line.
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In 2005, Cory put $5,000 in an account that grows in value by 3.7% per year. what is the value of the account in 2020?
The value of the account in 2020 is given as $8622.86.
What is compound interest?The compound interest is a form of interest where the rate of interest is applied on the amount obtained after every interval of time.
The amount of one interval of time becomes the principal to the next one.
Suppose in 2005 t = 0.
Then, in the year 2020 t = 15.
Now, the given question can be solved by finding the Amount using the expression as below,
P(1 + r/100)ⁿ
Where p, r and n are the principal, rate and time for the compounding.
Substitute all the corresponding values to obtain,
A = 5000(1 + 3.7/100)¹⁵
= 5000 × 1.037¹⁵ = 8622.86
Hence, in 2020 the money invested in the account becomes as $8622.86.
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Marvin is playing a solitaire game with marbles. There are n bowls (for some positive integer n), and initially each bowl contains one marble. Each turn, Marvin may eitherremove a marble from a bowl, orchoose a bowl A with at least one marble and a different bowl B with at least as many marbles as bowl A, and move one marble from bowl A to bowl B.The game ends when there are no marbles left, but Marvin wants to make it last as long as possible.Prove that the game must end after at most n(n+1)/2 turns.Prove that for every positive integer k, there is an n such that Marvin can make the n-bowl game last for at least kn turns.Marisa comes along and asks to join the game. Marvin and Marisa revise the rules: they will alternate taking turns, starting with Marisa. When the game ends, whoever took the last turn is the winner.Prove that among any three consecutive values of n, there is at least one value for which Marvin has a winning strategy.
There is always at least one consecutive value of n for which Marvin has a successful approach.
By induction, we can demonstrate that the game must conclude after a maximum of n(n+1)/2 turns for the first half of the issue, Here Induction Means a method for demonstrating that a statement P(n) is true for every natural number n, and that the infinitely numerous examples P(0), P(1), P(2), P(3), etc. all hold, is mathematical induction. Informal analogies, such a ladder or a falling domino, are used to explain this technique .
Base case: If there is just one bowl, Marvin can get rid of it in one turn, ending the game after one.
Step one of induction: Assume that there are k bowls and that the game terminates after no more than k(k+1)/2 turns. When there are k+1 bowls, we shall demonstrate that the game terminates after at most (k+1)(k+2)/2 turns. The number of bowls lowers by one if Marvin takes a marble out of one, and the game must terminate after no more than k(k+1)/2 turns through induction hypothesis
When Marvin transfers a marble from bowl A to bowl B, where bowl A contains at least one marble and bowl B contains an equal number of marbles, bowl A loses one marble and bowl B gains one marble. The number of bowls stays the same because bowl B has at least as many marbles as bowl A. As a result, the game must still terminate after k(k+1)/2 turns at the latest.
In any scenario, the game ends after at most k(k+1)/2 turns, thus when there are k+1 bowls, the game must end after at most (k+1)(k+2)/2 turns. For the second component of the issue, we can demonstrate that for every positive integer k, there exists a n such that Marvin can devise a plan to extend the n-bowl game for at least kn turns.
Let's say Marvin wants the n-bowl match to go at least kn turns. He can accomplish this by ensuring that each bowl always contains at least k marbles. Marvin can start by putting k marbles in the first bowl, k-1 marbles in the second bowl, and so forth, down to 1 marble in the nth bowl, to accomplish this.
For the second component of the issue, we can demonstrate that for every positive integer k, there exists a n such that Marvin can devise a plan to extend the n-bowl game for at least kn turns.
Let's say Marvin wants the n-bowl match to go at least kn turns. He can accomplish this by ensuring that each bowl always contains at least k marbles. Marvin can start by putting k marbles in the first bowl, k-1 marbles in the second bowl, and so forth, down to 1 marble in the nth bowl, to accomplish this.
Marvin can select a bowl containing at least k marbles on each turn and transfer one marble to a bowl containing fewer than k marbles .Marvin can transfer one marble from the first bowl to the second bowl, for instance, if there are k+1 marbles in the first bowl and k marbles in the second bowl. This guarantees that there are at least k marbles in each bowl. The game will go for at least kn turns because Marvin can take at least one turn every bowl.
For the third component of the issue, we can demonstrate that there is always at least one value of n for which Marvin has a successful strategy.
Assume that n is a positive integer. We shall demonstrate that either Marvin or Marisa has a winning strategy for the game of n bowls or the game of (n+1) bowls.
If Marvin has a winning strategy for the N-bowl game, he can use that method to win the N-bowl game.
If Marisa has a winning strategy for the n-bowl game and Marvin does not, then Marisa does as well. In this scenario, Marvin can use Marisa's successful approach to the n-bowl game as his own successful approach to the (n+1)-bowl game.
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Makayla is decorating the outside of a box in the shape of a triangular prism. The figure below shows a net for the box.
11.4 cm
11.4 cm
7 cm
9 cm
12 cm
7 cm
What is the surface area of the box, in square centimeters, that Makayla decorates?
The surface area of the triangular prism box Makayla decorates is 454.8 square centimeters
What is the surface area of a solid?The surface area of a solid is obtained by adding together the surface areas of the faces or boundaries that encloses the solid.
The dimensions of the triangular prism are;
Rear rectangle;
Length = 12 cm
Width = 7 cm
Area of rear rectangle = 12 cm × 7 cm = 84 cm²Dimensions of side triangles;
Base length = 9 cm
Height = 7 cm
Area of each side triangle = 9 cm × 7 cm = 63 cm²
Sum of the area of both triangles = 2 × 63 cm² = 126 cm²The dimensions of the rectangle at the bottom of the rectangular prism
Length = 12 cm
Width = 9 cm
Area of the rectangle at the bottom of the prism = 12 cm × 9 cm = 108 cm²Dimensions of the slant surface rectangle at the top of the triangular prism are;
Length = 12 cm
Width = 11.4 cm
Area of the top slant rectangle = 12 cm × 11.4 cm = 136.8 cm²The surface area of the box, A, is the sum of the individual surface areas, which can be found as follows;
A = 84 + 126 + 108 + 136.8 = 454.8
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Reasoning 54.8 x 7.29 = 399.492
A) Write down three more calculations that have the same answer.
B)Write down a division that has an answer of 54.8.
C)Write down a division that has an answer of 0.729.
D)Charlie says that 54.8 x 72.9 = 3989.44. Explain why Charlie must be wrong.
Answer:
B)Write down a division that has an answer of 54.8.
What is the median of the data 78 56 22 34?
Median of the data 78 , 56 , 22 , 34 is 45.
The middle value of the observations in a data set , arranged in the order of size is known as the median.
It is calculated differently for odd and even number of observations.
1. For odd no. of observations, it is the middle value .
2. For even number of observations, it is calculated as the average of the middle two values.
In this problem , first we arrange the observations in the order of size i.e. 22 , 34, 56, 78.
Since, here the no. of observations is even , 4. So, the median is the average of middle two values.
The middle two values are 34 and 56 , and their mean is 45.
So, the median of the given data is 45.
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Julie wanted to match Lisa's obstacle course record of 74.6 seconds. She has already spent forty and one-fourth seconds on wall climbing and 10.56 seconds on the ropes. How much time did she have left to match the record?
23.79 seconds
29.69 seconds
34.35 seconds
64.04 seconds
Julie has only 23.79 seconds left to match the record.
How to calculate time left?
We know that times deals with a continued sequence of existence and events that occurs in an apparently irreversible succession from the past
From the question, the given times are:
Time to match Lisa's record = 74.6 seconds
Time to clin the wall = 10.56 seconds
Time already spent on climbing wall = 4.025 seconds
Time left is calculated thus
74.600 seconds =(40.025+10.56) seconds
=74.600-50.585
=23.79 seconds
Therefore time left is 23.79 seconds
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solve:
y=x-4
y=6x-10
Answer:
x=6/5
Step-by-step explanation:
x-4=6x-10
-5x=-6
x=6/5
y=6/5-4=-14/5
Answer:
x = 1.2
y = -2.8
Step-by-step explanation:
y = x - 4 and y = 6x - 10
so x - 4 = 6x - 10
x - 6x = 4 - 10
-5x = -6
x = -6/-5
x = 1.2
y = x - 4 = 1.2 - 4 = -2.8
What is the inverse of 16?
Additive inverse of 16 is -16.
Multiplicative Inverse of 16 is 1/16.
What is Inverse ?To produce a result equal to 0, add the original number and the additive inverse by simply reversing the sign of the integer. On the basis of negation of the original number, the characteristics of additive inverse are listed below. For instance, if x is the starting number, then -x is x's additive inverse.
A multiplicative inverse or reciprocal for a number x is a number that, when multiplied by x, produces the multiplicative identity, or 1. It is represented by 1/x or x/1. A fraction a/b has a multiplicative inverse of b/a. Divide 1 by the real number to obtain the multiplicative inverse of the number.
A function that "undoes" another function is called an inverse. In other words, if f(x) generates y, then y entered into the inverse of f creates x. An invertible function is one that has an inverse, and the inverse is indicated by the symbol [tex]f^{-1}[/tex].
Additive inverse of 16 is -16.
Multiplicative Inverse of 16 is 1/16.
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Write a point-slope equation for a line containing the points (-3,-1) and (5,2)
Answer:
Point-slope form: y + 2= 0.5(x + 3)
Slope-intercept form: y = 0.5x - 0.5
Step-by-step explanation: