The value of x from the given linear equation is -1 and y = 1
A linear polynomial over a field, from which the coefficients are taken, can be equalized to zero to produce a linear equation.
A line in the Euclidean plane is formed by a linear equation's solutions, and every line may be thought of as the collection of all solutions to a linear equation with two variables. This is where the term "linear" for this class of equations came from
It is given that y = 3x+4 (i) and y = x+2 (ii)
Put equation i) = ii)
Then, we get 3x+4 = x+2
2x = -2
x = -1.
Put the value of x in equation ii)
y = -1+2
y = 1
Hence, the value of x from the given linear equation is -1 and y = 1
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Six times a number is at least four less than eight times the number. If x represents the number, which will help find the
number?
O6x<8x-4
O6x≤8x-4
O 6x28x-4
O 6x>8x-4
The number that represents Six times a number is at least four less than eight times the number is the expression 6x ≥ 8x - 4.
What is system of equations?
A system of equations, also referred to as a set of simultaneous equations or an equation system, is a finite set of equations for which we searched for the common solutions. Similar to single equations, a system of equations can also be categorised. In everyday life, systems of equations are used to model situations where the unknown values can be represented by variables.
A system of equations is made up of two or more equations with the same variables. A solution to an equation system is the point at which the lines intersect.
According to given question, x represents the number
So, The number would be 6x ≥ 8x - 4
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A store purchases rolling pins from
the manufacturer for $9 each.
Calculate the sticker price for the
pins in order to achieve a 60% gross
margin.
A. $20.00
B. $22.50
C. $15.67
D. $15.00
The store charges $12.65 for a 14 oz container of watermelon sugar scrub. How many ounces of watermelon sugar scrub do you get per dollar?
The ounces of the watermelon sugar scrub per dollars is 1.1 ounces per dollars.
How to find the ounces of watermelon per dollars?The store charges $12.65 for a 14 oz container of watermelon sugar scrub. The amount in ounces of watermelon sugar scrub per dollars can be calculated as follows:
12.65 dollars = 14 ounces
1 dollars = ?
cross multiply
Hence,
amount of ounces of watermelon sugar scrub per dollars = 14 × 1 / 12.65
amount of ounces of watermelon sugar scrub per dollars = 14/ 12.65
amount of ounces of watermelon sugar scrub per dollars = 1.10671936759
amount of ounces of watermelon sugar scrub per dollars = 1.1 ounces per dollars
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A 6 m tall ladder tanding next to tatue cat a 3m hadow if the tatue cat a hadow that i 7m long then how tall i it
The statue of the cat is 14 meters tall.
If the ladder is 6 meters tall and it casts a shadow that is 3 meters long and the statue of a cat casts a shadow that is 7 meters long, then we can use the concept of similar triangles to determine the height of the statue of the cat.
The ratio of the height of the ladder to the length of its shadow is 6/3 = 2.
We can also assume that the ratio of the height of the statue of the cat to the length of its shadow is also 2.
so, the height of the statue of the cat can be calculated by:
height of statue of the cat = (2 * shadow length of the statue of the cat) = (2 * 7) = 14 meters
Therefore the statue of the cat is 14 meters tall.
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The height, h, of a cylinder i 5 unit le than 3 it’ radiu, r. Which expreion repreent the height of the cylinder in term of it radiu?
The expression that represents the height of the cylinder in terms of its radius is 3r - 5.
The cylinder's radius is specified in "r" units.
So, In comparison to its radius, r, a cylinder's height, h, is five units less.
The radius times three will be denoted by the unit "3r."
and
The radius reduced by 5 units will be shown as "3r - 5" units.
The height "h" of the cylinder is equal to 5 units less than 3 times the radius, hence the final equation is,
h = 3r-5
Thus, the expression representing the height of the cylinder in terms of the radius is h = 3r-5
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What is the SSA theorem?.
The SSA theorem tells us that if two angles and a non-included side of one triangle are congruent to two angles and also the corresponding non-included side of another triangle, then it is claimed that the two triangles supplied are congruent to one another.
Similar triangles are triangles that have the same shape, but their sizes may vary. All equilateral triangles and squares of any side length are similar objects. To put it another way, if two triangles are similar, then their respective sides are proportionately equal and their corresponding angles are congruent.
The SSA congruence rule is not a reliable standard for determining if two triangles are congruent to one another.
Hence, there is no such SSA similarity from which you can make predictions that whether the two triangles are similar or not.
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what is the gcf of 36 and 69?
Answer:
The GCF of 36 and 69 is 3
Step-by-step explanation:
hope this helps
The number of bacteria in a lab experiment can be modeled by the function � ( � ) = 45 ( 3 ) � + 1 . S(t)=45(3) t+1 . Write an equivalent function of the form � ( � ) = � � � . S(t)=ab t .
The equivalent function when the number of bacteria in a lab experiment can be modeled by the function is P(t) = 1161(9)^t
How to calculate the function?A function illustrates the variables given. In this case, it is vital to note that two or more components are considered in order to be able to describe the situation.
Here, we are given that the number of bacteria in a lab experiment can be modeled by the function given as P(t) = 43(39^(2t + 3)
This will be:
= 43 × 3³ × 3(^2t)
= 1161 × 3²^t.
P(t) = 1161(9)^t
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today everything at a store is on sale. the store offers a 20% discount. the discount price of a hat is 18$. what is the regular price/price without the discount?
Answer: $22.5
Step-by-step explanation:
refer to the image to see the steps and explanation
Find the value of a in the triangle shown below.
·
102
48°
The value of third angle is 30 and we can find using angle sum property.
What is angle sum property?The triangle's angles can be added up to equal 180 degrees, according to the angle sum property of triangles. A triangle has three sides, one at each vertex, and three angles. The total of the interior angles in any triangle, whether acute, obtuse, or right, is 180 degrees.
One of the most commonly employed properties in geometry is the angle sum property of a triangle. Calculating the unknown angles is primarily done using this characteristic. When the values of the other two angles are known, the measure of an unknown interior angle can be determined using the angle sum property.
Given
The two angles are given as 102 and 48
we need to find the third angle
Let the third angle be a then
using the angle sum property we get
102 + 48 + a = 180
a = 30
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Triangle ABC was reflected over line m, then dilated by a scale factor between 0 and 1. Which diagram illustrates these transformations? Triangle A B C is reflected across line m and then is dilated to form smaller triangle A double-prime B double-prime C double-prime Triangle A B C is rotated about line m and then dilated to form smaller triangle A double-prime B double-prime C double-prime Triangle A B C is reflected across line m and then is dilated to form larger triangle A double-prime B double-prime C double-prime Triangle A B C is rotated about line m and then dilated to form larger triangle A double-prime B double-prime C double-prime Mark this and return
The reflection and after that the dilation of triangle ABC is correctly represented by,
⇒ Triangle ABC is reflected across line m and then is dilated to form smaller triangle A double-prime B double-prime C double-prime.
What is mean by Triangle?A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.
We have to given that;
Triangle ABC was reflected over line m, then dilated by a scale factor between 0 and 1.
Now, After the reflection, the triangle will be inverted and the measure of angle: A should be equal to A", B should be equal to B", and C should be equal to C".
Now, The dilation factor is less than 1 and greater than 0. So, the reflected triangle should shrink its size.
Therefore, The reflection and after that the dilation of triangle ABC is correctly represented by,
⇒ Triangle ABC is reflected across line m and then is dilated to form smaller triangle A double-prime B double-prime C double-prime.
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Given a polynomial and one of its factors, find the remaining factors of the polynomial.
x^3-9x^2+27x-27; x-3
The factors of the polynomial x^3-9x^2+27x-27 are (x -3), (x - 3) and (x - 3)
What is Factor of the PolynomialThe polynomial you provided is x^3-9x^2+27x-27. If you know one of the factors of this polynomial, we can use that to find the remaining factors.
One factor of this polynomial is (x-3) as it gives remainder zero when divided by (x-3)
quotient is x² - 6x + 9
remainder is zero
So the remaining factors are (x-3) and x² - 6x + 9
Alternatively, we can factor the remaining quadratic polynomial x² - 6x + 9
by using Factor theorem or by using difference of squares
x² - 6x + 9 = (x - 3)²
So the remaining factors are (x-3) and (x - 3)
So the original polynomial can be factored as (x-3)(x-3)(x-3) = (x-3)³
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The drawing below shows three squares joined at their vertices to form a right triangle. The area of square A is 9 ft2 and the area of
square B is 16 ft². What is the side length of square C?
25
7
8
5
Answer:
side length of square C is 5 ft
Step-by-step explanation:
A, B andC are the areas of the sides of a right triangle.
C is the square on the hypotenuse of the right triangle.
using Pythagoras' identity in the right triangle.
the square on the hypotenuse is equal to the sum of the squares on the other 2 sides, that is
C² = A² + B² = 9 + 16 = 25 ft²
the area of a square is s² , where s is the side length, then
s² = 25 ( take square root of both sides )
s = [tex]\sqrt{25}[/tex] = 5 ft
How many images will form when two mirrors are placed at 120 degree and 30 degree object is placed symmetrically with respect to both the mirrors?.
The number of images formed by using the angle 120° is 3 or 30° is 11.
Angle in math is defined as the image formed when two rays are joined together at a common point and the common point here is called node or vertex and the two rays are called arms of the angle.
Here we have given that 120 degree and 30 degree object is placed symmetrically with respect to both the mirrors.
As we all know that the formula number of images formed between two mirrors kept at some angles is written as,
=> n = (360 / θ) - 1
Here we have n is the number of images and θ is the angle between the mirrors.
The value of θ is 120 or 30.
If the angle is 120, then the number of image is calculated as,
=> n = (360 / 120) - 1
=> n = 3 - 1 = 2
Where as the angle is 30, then the number of image is calculated as,
=> n = (360 / 30) - 1
=> n = 12 - 1 = 11
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using trigonometric identities to decode a secret message
Using trigonometric identities to decode, the secret message is
2 20-14-25-12 4-19-17 20-14-11-14-25 23-2-21-14-5 23-26-5-7-2-21-14-5! A Nerd who never makes mistakes!
What is trigonometric identities?Trigonometric Identities are equality statements involving trigonometry functions that hold true for all values of the input variables in the equation.
The side length and angle of a triangle are both subject to a variety of distinctive trigonometric identities. Only for right-angle triangles do the trigonometric identities hold true.
All trigonometric identities are built upon the foundation of the six trigonometric ratios. It consists of sine, cosine, tangent, cosecant, secant, and cotangent. These right triangle sides—including the adjacent side, opposite side, and hypotenuse side—are used to define all of these trigonometric ratios. The six trigonometric ratios are the starting point from which all fundamental trigonometric identities are derived.
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How much of a circle is a 60 degree angle turn?.
A circle has a total degree of 360 so 1/6 is a circle is a 60 degree angle turn.
An irregular plane figure is a circle. Every point on the circle is equally distant from the circle's fixed center. It has a radius of 1, making it a 2D shape. The Latin word "circulus," which means "little ring," is the source of the English word "circle.
A total angle of circle is 360 degrees so if a turn is of a 60 degree so then 6 turns are possible to make a whole circle giving us 1/6 part as the total of which the only 60 degree turn is taken.
Angles can be measured using one of two standard units. Degrees are the most widely used unit of measurement. A straight angle is 90° since a circle has 360 equal degrees.
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19. A rectangular lawn is to be laid with turf. James measures the sides of the rectangle as 30 m by
40 m, with both values being given to the nearest metre. He sends his friend Toby to buy the
turf.
a. Find the area of the maximum area of turf that Toby needs to buy, giving your answers
to 2 decimal places.
b.
Find the area of the minimum area of turf that Toby needs to buy, giving your answers
to 2 decimal places.
A rectangle is a four-sided geometric shape with opposite sides that are parallel and equal in length. The opposite sides are called the length and width of the rectangle. Area = (30m - 0.5m) x (40m - 0.5m) = 29.5m x 39.5m = [tex]1162.75 m^2[/tex]
What is rectangle?a. The maximum area of turf that Toby needs to buy can be found by using the measurements given by James, which are the length and width of the rectangle.
The area of a rectangle is found by multiplying its length and width, so the maximum area of turf needed would be:
Area = length x width = 30m x 40m = [tex]1200 m^2[/tex]
b. The minimum area of turf that Toby needs to buy can also be found by using the measurements given by James, but this time taking into account the margin of error due to the measurements being given to the nearest metre.
If the true length and width of the rectangle are slightly less than the measurements given by James, the mini mum area of turf needed would be:
Area = (30m - 0.5m) x (40m - 0.5m) = 29.5m x 39.5m = [tex]1162.75 m^2[/tex]
So the minimum area of turf that Toby needs to buy would be [tex]1162.75 m^2[/tex]and the maximum area of turf that Toby needs to buy would be [tex]1200 m^2.[/tex]
In general, the measurements given by James could be off by half a meter in both directions, therefore the minimum area of turf that Toby needs to buy would be the area calculated by taking into account the margin of error, in this case, it's [tex]1162.75 m^2.[/tex]
The maximum area of turf that Toby needs to buy would be the area calculated using the measurements given by James, which is [tex]1200 m^2.[/tex]
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Which prefix means 10?
deci
centi
Deca
Milli
For the number 10, the prefix used is 10. The correct option is A.
What is a numeral prefix?Prefixes derived from numerals or other numbers are known as numeral or number prefixes. They are used to coin numerous series of words in English and many other languages.
The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
The given number is 10. The prefix used for the number 10 is deci.
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The ma of the blue copper ulfate crytal i two-third the ma of the red fluorite crytal. Write an equation you can ue to find the ma $m$ (in gram) of the blue copper ulfate crytal
The equation-CuSO4.5H2O(s)→CuSO4.3H2O(s)+2H2O(g) for blue copper sulfate crytal I two-thirds the ma of the red fluorite crytal.
The following steps are used to make copper sulfate crystals:
Add a few drops of diluted sulfuric acid to a beaker of water.
Water heating. Add the powdered copper sulfate gradually as it begins to boil.
Stirring is ongoing during this procedure.until no more copper sulfate powder can be dissolved, keep adding it.Filter the remedy.Allow it to cool.The copper crystals will gradually separate.The ma of the blue copper sulfate crystal I two-thirds the ma of the red fluorite crystal
The equation-
CuSO4.5H2O(s)→CuSO4.3H2O(s)+2H2O(g)
the ma (in grams) of the blue copper sulfate crytal
It is 30 divided by 1/3 or 3.
The answer is 10
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the measurements, to the nearest centimeter, of a box are given as 10cm x 7cm x 4cm. calculate the upper and lower bounds for the volume of the box.
In summary, the upper and lower bounds for the volume of the box are:
Upper bound: 382.125cm³
Lower bound: 238.375cm³
The volume of the box is calculated by multiplying the length, width, and height together. In this case, the measurements of the box are given as 10cm x 7cm x 4cm, so the volume of the box is:
volume = 10cm x 7cm x 4cm = 280cm³
However, since the measurements are given to the nearest centimeter, there is a slight degree of uncertainty in the exact measurements of the box. To calculate the upper and lower bounds for the volume of the box, we need to consider the possible variations in the measurements.
The upper bound for the volume would be calculated by taking the highest possible measurements for each dimension. So, if the length could be as much as 10.5cm, the width could be as much as 7.5cm and the height could be as much as 4.5cm. Then the upper bound for the volume would be:
Upper bound = 10.5cm x 7.5cm x 4.5cm = 382.125cm³
The lower bound for the volume would be calculated by taking the lowest possible measurements for each dimension. So, if the length could be as little as 9.5cm, the width could be as little as 6.5cm and the height could be as little as 3.5cm. Then the lower bound for the volume would be:
Lower bound = 9.5cm x 6.5cm x 3.5cm = 238.375cm³
In summary, the upper and lower bounds for the volume of the box are:
Upper bound: 382.125cm³
Lower bound: 238.375cm³
And the exact volume is 280cm³
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What is the rule for fg )( x?.
The notation "FG)(x" refers to the composition of two functions, "F" and "G", where the output of "G" is used as the input for "F". The notation for this is usually represented as "F(G(x))", where "x" is the input for both functions.
The rule for this notation is that the innermost function is applied first. In this case, the function "G" is applied to the input "x" first, and then the output of that function is used as the input for the function "F". The composition of the functions F and G is denoted by the notation F(G(x)) and the result of this notation is a new function obtained by applying F to the result of G on x.
The function "F" is applied to the output of the function "G", meaning that the output of the function "G" is used as the input for the function "F".. For example, if the function "F" is applied to the input "x" first, followed by the function "G", the notation would be represented as "G(F(x))", and the resulting function would be different.
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22. Four friends, Lerato, Jarrod, Ian and Tandeka, play a computer game in which they race a car around a circuit. Lerato takes 2 minutes, Jarrod takes 3 minutes, Ian takes 4 minutes and Tandeka takes 5 minutes to complete one circuit of the game. They play for a total of 12 minutes. a) If they play continuously and at the same rates, which one of the players will be in the middle of a circuit as the time runs out? b) After how many minutes did this player begin the last circuit? c) How many more games did Lerato play than Tandeka?
Answer:
a) Tandeka will be in the middle of a circuit as the time runs out.
b) Tandeka began the last circuit after 7 minutes.
c) Lerato played 2 more games than Tandeka.
Explanation:
a) To determine which player will be in the middle of a circuit when the 12 minutes are up, we need to figure out which player completes the most circuits in 12 minutes. We can use the formula: time available / time per circuit = number of circuits completed. In this case: 12 minutes / 2 minutes per circuit = 6 circuits for Lerato, 12 minutes / 3 minutes per circuit = 4 circuits for Jarrod, 12 minutes / 4 minutes per circuit = 3 circuits for Ian, 12 minutes / 5 minutes per circuit = 2.4 circuits for Tandeka. Tandeka completes 2 full circuits, and starts the third one, hence she will be in the middle of a circuit when the time runs out.
b) To determine when Tandeka began the last circuit, we need to figure out how many minutes were left when she completed the second circuit. We know that Tandeka completes 2 full circuits in 10 minutes (2 x 5 minutes). So, the last circuit starts after 12 minutes - 10 minutes = 2 minutes
c) To determine how many more games Lerato played than Tandeka, we can subtract the number of games Tandeka played from the number of games Lerato played: 6 games - 4 games = 2 games.
Step-by-step explanation:
How do you simplify polynomials and write in standard form?.
Polynomials can be simplified by applying the distributive property to multiply the term outside the parentheses by everything inside the parentheses.
The highest degree of terms is written first, followed by the next degree, and so on, to represent a polynomial in standard form. The standard form of the polynomial is f(x) = anxn + an-1xn-1+an-2xn-2+.....+a1x+a0
An expression made up of variables, constants, and exponents that are joined together via mathematical operations is referred to as a polynomial.
A polynomial must be simplified in two ways: Firstly, combine similarities, and secondly, rewrite the terms in descending order of exponent. A polynomial can be written in standard form. To write any polynomial in standard form, consider the degree of each term. Then, from highest to lowest, left to right, you write each term in order of degree.
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How do special right triangles theorems 45 45 90 and 30 60 90 differ from each other?.
The 45-45-90 triangle has two congruent sides and one right angle, with each angle measuring 45°. The sides are perpendicular to each other and the length of the hypotenuse is equal to the square root of 2 times the length of a leg.
The 30-60-90 triangle has one right angle and two sides that are proportional. The shortest side is half the length of the hypotenuse and the middle side is equal to the shortest side times the square root of 3. The two acute angles in the triangle measure 30° and 60°, respectively.
In conclusion, both 45-45-90 and 30-60-90 triangles are special right triangles with distinct relationships between their sides and angles.
A triangle is a polygon with three edges and 3 vertices. The terminology for categorizing triangles is more than two thousand years vintage, having been defined on the first actual page of Euclid's elements.
In Euclidean geometry, any three factors, while non-collinear, decide a completely unique triangle and simultaneously, a unique plane (i.e. a -dimensional Euclidean space). In different words, there's best one plane that consists of that triangle, and every triangle is contained in some plane. If the entire geometry is only the Euclidean plane, there is the best one plane and all triangles are contained in it; however, in higher-dimensional Euclidean spaces, this is not real. this text is ready triangles in Euclidean geometry, and in particular, the Euclidean plane, except wherein otherwise stated.
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How do you graph the equation XY 4?.
A horizontal line at y=4 has the following formula: Nothing slopes. The y-intercept is at 4.0.
What are the intercepts and slopes?
The slope or gradient of a line in mathematics is a numerical representation of the steepness and direction of the line.
The slope conveys how quickly the dependent variable shifts in response to changes in the independent variable. Mathematicians and economists frequently use the Greek capital D or D to denote change. The change in the horizontal axis, x, is contrasted with the change in the vertical axis, y.
Negative values are below the origin on the x-axis and to the left of the origin on the y-axis. If the y-coordinate is negative, go downhill; if the x-value is negative, start at the origin and travel to the left.
Line graphs, often referred to as XY graphs, are used to graphically display data (the results of an experiment) to show how multiple aspects, such as time and the severity of the disease, are related.
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What is the percent of decrease from 95 to 19?
The percent of decrease from 95 to 19 is 80%
What is percentage?A percentage is a number or ratio that can be expressed as a fraction of 100. If we have to calculate percent of a number, divide the number by the whole and multiply by 100. Hence, the percentage means, a part per hundred. The word per cent means per 100.
Given that, what is the percent of decrease from 95 to 19,
Percent of decrease = final value - initial value / initial value x 100
Here, final value = 95
initial value = 19
Therefore,
Percent of decrease = 19-95 / 95 x 100
= -76 / 95 x 100
= -0.8 x 100
= -80%
Here, - sign is representing the decrease,
Hence, the percent of decrease from 95 to 19 is 80%
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For what value of k does the pair of equations 3x y − 8 and 6x KY 16 0 have infinitely many solutions?.
The value of k for which the pair of equations 3xy - 8 = 0 and 6xky - 16 = 0 have infinitely many solutions is 4.
To solve this question, we need to find the value of k for which the two equations are equivalent. Equivalence means that the coefficients of x and y are the same and the constant terms are the same.
From the given equations, we can see that the coefficients of x and y are the same in both equations, which is 6x. The constant terms, however, are different. The first equation has a constant term of -8, while the second equation has a constant term of -16.
To make the equations equivalent, we need to make the constant terms the same. We can do this by dividing the second equation by 2. This gives us 6 ky - 8 = 0. We can see that the constant term is now the same as the first equation. Therefore, the value of k that makes the equations equivalent is k = 4.
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The complete question is:
For what value of k do the pair of equations 3xy - 8 = 0 and 6xky - 16 = 0 has infinitely many solutions?
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what is the slope of line A and B
Answer:
1/5
Step-by-step explanation:
You want the slope of line AB, given A(-2, 2) and B(3, 3).
SlopeThe slope is given by the formula ...
m = (y2 -y1)/(x2 -x1)
m = (3 -2)/(3 -(-2)) = 1/5
The slope of the line AB is 1/5.
__
Additional comment
You can also find the slope by counting the grid squares. Point B is 1 up and 5 over from point A, so the slope is rise/run = 1/5.
PLSSS HELP IF YOU TURLY KNOW
Answer:
14
Step-by-step explanation:
If d is 5
2(5) + 4(5) - 9 - 7
10 + 20 - 9 - 7
30 - 16
= 14
How do you find y and y intercepts?.
Substitute y = 0 and solve for x to find the x-intercept, and do the same for the y-intercept.
How do you find an example of the y-intercept?Examples on the Y Intercept Using the y-intercept formula, we can find the y-intercept of a function by substituting x = 0 and solving for y; consequently, the given function lacks a y-intercept. 2nd Example: Find the value of "a" if the y-intercept of a function y = a (x - 1) (x - 2) (x - 3) is (0, 12).
With two points, how do you find the y-intercept?We can solve for the y-intercept in the slope-intercept equation y=mx+b by first determining the slope between two points on a line and then writing an equation for that line.
How are the slope and y-intercept of Y determined?The slope-intercept form is used to write the line's equation, which looks like this: y is equal to mx + b, where m is the slope and b is the y-intercept. We can see that the line has a slope of 6 in our equation, which is y = 6x + 2.
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