[tex](\stackrel{x_1}{3}~,~\stackrel{y_1}{-4})\hspace{10em} \stackrel{slope}{m} ~=~ - 6 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-4)}=\stackrel{m}{- 6}(x-\stackrel{x_1}{3}) \implies y +4= -6 (x -3) \\\\\\ y+4=-6x+18\implies {\Large \begin{array}{llll} y=-6x+14 \end{array}}[/tex]
How to do elimination with 3 variables?
Elimination is a method used to solve systems of linear equations with two or more variables. One possible method to solve a equation with 3 variables using elimination is solving algebraically.
To use elimination to solve a system of equations with three variables, you can follow these steps:
1. Write the system of equations. For example, if you have the equations:
3x + 2y - z = 5
2x - 4y + 2z = 6
5x - 2y + 3z = 10
2. Multiply one of the equations by a scalar (a number) so that one of the variables has opposite coefficients, say y in two of the equations.
3. Next, you can multiply one of the equations by a scalar (a number) so that one of the variables has opposite coefficients, say x in two of the equations.
4. Now substitute this value of z in the first or the second equation to solve for x
5. Now substitute this value of x and z in the second equation or any other equation to solve for y
This is one possible way to use elimination to solve a system of equations with three variables. Depending on the specific problem, there may be different ways to eliminate variables, but the general idea is to use scalar multiplication and addition or subtraction to create a new equation with one variable having the same coefficient but with opposite signs. One can also use Gaussian elimination or matrix inversion method.
To know more on Gaussian elimination
https://brainly.com/question/29004583
#SPJ4
find the values of X, Y, and Z
On applying the midpoint theorem the values of x, y, and z are 2, 10 and 8 respectively.
What is the mid-point theorem?
According to the midpoint theorem, the line segment connecting any two triangle sides' midpoints is parallel to and equal to half of the third side.
The outer triangle is ABC and the inner triangle is DEF.
It can be seen that sides AB, BC and AC are equally divided such that AD=DB,
BE=EC and
CF=FA.
So, this proves that point D, E and F are the middle points of AB, BC and AC respectively.
Now, according to the midpoint theorem -
DF = 1/2(BC)
Plugging in the values -
x = (5x-6)/2
2x = 5x-6
2x-5x = -6
-3x = -6
x = 2
Now, for side DE -
DE = 1/2(AC)
Plugging in the values -
12 = (2z+8)/2
24 = 2z+8
24-8 = 2z
16 = 2z
z = 8
Now, for side EF -
EF = 1/2(AB)
Plugging in the values -
y = 20/2
y = 10
Therefore, the values obtained are x=2, y=10 and z=8.
To learn more about midpoint theorem from the given link
https://brainly.com/question/26189487
#SPJ1
help ! find x and y
[tex]x + y = 2[/tex]
[tex]y - x = 2[/tex]
Answer:
[tex](x,y)\rightarrow(0,2)[/tex]
Step-by-step explanation:
[tex]\displaystyle \left \{ {{x+y=2} \atop {y-x=2}} \right.\\[/tex]
Combine system of equations on both sides:
[tex](x+y)+(y-x)=2+2\\2y=4\\y=2[/tex]
Thus,
[tex]x+y=2\\x+2=2\\x=0[/tex]
(x, y) <=>(0, 2)
Step-by-step explanation:
[tex]x + y = 2 \\ y - x = 2 \\ \\ x + (x + 2) = 2 \\ y = x + 2 \\ \\ 2x + 2 - 2 = 2 - 2 \\ y = x + 2 \\ \\ 2x = 0 \\ y = x + 2 \\ \\ x = 0 \div 2 \\ y = x + 2 \\ \\ x = 0 \\ y = 0 + 2 \\ \\ x = 0 \\ y = 2[/tex]
How do you write numbers more than 100?
The numerical figures are used to write numbers more than 100.
What is numbers?
An arithmetic value known as a number is used to represent a quantity and perform calculations. Numbers are represented by written symbols, such as "3," which are referred to as numerals. A number system is a method of writing that uses logically ordered digits or symbols to represent numbers.
To represent numbers greater than 100, use numeral figures; however, whole numbers, such as 300 or 1,000, should be written out.
When representing non-whole numbers like 1,239 or 603, use numerals.
Except for whole numbers combined with hundred, thousand, hundred thousand, million, billion, and beyond, the Chicago Manual of Style advises spelling out numbers from zero to one hundred and using figures after that (e.g., two hundred; twenty-eight thousand; three hundred thousand; one million).
Hence, the numerical figures are used to write numbers more than 100.
To know more about numbers, click on the link
https://brainly.com/question/24644930
#SPJ4
what number is in the same ratio to 64 as 5 is to 8
Answer: 102.4
Given ratio 5:8
Let's assume the answer to be x
5÷8 should be equal to 64÷x
∴ x= (64×8) ÷ 5
=102.4
The number that has the same ratio to 64 as 5:8 is gotten as; 40
How to Calculate Ratio?
We have the ratio 5:8.
Now, we want to find the number that has the same ratio to 64 as 5:8. Thus, we will use proportion to get this;
x/64 = 5/8
Cross multiply to get;
x = 64 * 5/8
x = 40
Need this question quick 20 points
On solving the provided question we can say that the rectangular form of the equation is y = -1
What is equation?An equation is a mathematical formula that connects two assertions using the equal sign (=) to denote equivalence. In algebra, an equation is a mathematical statement that establishes the equivalence of two mathematical expressions. For instance, an equal sign separates the components 3x + 5 and 14 in the equation 3x + 5 = 14. A mathematical formula is used to explain the connection between two sentences on either side of a letter. Frequently, there is just one variable, which is also the symbol. for example, 2x - 4 = 2.
Ф = [tex]\pi[/tex]/2
y = - 1
To know more about equation visit:
https://brainly.com/question/649785
#SPJ1
Find out the answer to 4x+12=63
[tex]12 \frac{3}{4} [/tex]
or 12.75
Answer:
x=12.75
Step-by-step explanation:
Follow the steps within the image.
-Hope this helped
A school is arranging chairs in rows for an assembly. $11$ chairs make a complete row, and right now there are $110$ chairs total. The school wants to have as few empty seats as possible, but all rows of chairs must be complete. If $70$ students will attend the assembly, how many chairs should be removed?
The number of chairs that should be removed, for there to be as few empty seats as possible but for all rows of chairs to be complete, is 33 chairs.
How to find the chairs to be removed ?The number of chairs that make up a row is 11 chairs and there are to be 70 students in attendance. The number of rows that would take the students is therefore:
= Number of students / Number of rows
= 70 / 11
= 6. 36
= 7 rows rounded up
The number of rows needed is 7 rows which means the number of chairs would be:
= 7 rows x 11 chairs per row
= 77 chairs
The number of chairs to be removed is:
= Total chairs - Chairs needed
= 110 - 77
= 33 chairs
Find out more on the number of chairs at https://brainly.com/question/27141775
#SPJ1
Solve the following quadratic equation, leaving your answer in exact form:
2e²-8e +7= 0
Pls can anyone help it would rrly help out
Answer:
The two answers would be 0 and ln (7)
Step-by-step explanation:
Hope it helps:)
Hello can someone please help me with this please What is the best possible geometric model for a set of rail tracks?
Ray ----Point ---- Line --- Plane
Fine the measure of an angle that is supplement to ABC if m < ABC is 82?
100 ---- 8---------278------
Fine the measure of an angle that is complementary to ABC is 32?
328------148------58------32
The intersection of two lines is a ?
Quadrilateral--------Point--------Line--------Plane
A rail track is composed by multiple lines, however all the lines are in the same plane, hence a plane is the best geometric model for the rail track.
How to obtain the supplement of an angle?Two angles are supplementary if the sum of their measures is of 180º, hence the supplement of an angle is obtained subtracting 180º by the angle measure.
This means that the supplement of ABC = 82º is given as follows:
180º - 82º = 98º.
How to obtain the complement of an angle?Two angles are complementary if the sum of their measures is of 90º, hence the complement of an angle is obtained subtracting 90º by the angle measure.
This means that the supplement of ABC = 90º is given as follows:
90º - 32º = 58º.
Where do two lines intersect?Two lines intersect at a single point, which is the solution to the system of equations involving the two lines.
More can be learned about complementary and supplementary angles at https://brainly.com/question/12067750
#SPJ1
What are the 3 triangles called?
The types of 3 triangles are called-
equilateral,isosceles, andscalene.Explain the classification of the 3 triangles?Scalene triangle:
The scalene triangle has sides that are all measured differently.In such a triangle, no side will be the same length as any other side.Every interior angle in a scalene triangle is also unique.Isosceles triangle:
The lengths for two of the sides in such an isosceles triangle are equal.The angles that are opposite their equal sides are therefore equal.An isosceles triangle, in other words, has two equal sides with two equal angles.Equilateral triangle:
Each side of an equilateral triangle has an equal length.Each internal angle in this scenario will be 60 degrees in length.An equilateral triangle is often referred as an equiangular triangle since its angles are equal.To know more about the classification of the 3 triangles, here
brainly.com/question/13509596
#SPJ4
Find the equation of the line that goes through ( 0, 2 ) and ( 3, 4 ).
Answer:
y = [tex]\frac{2}{3}[/tex] x + 2
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
calculate m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (0, 2 ) and (x₂, y₂ ) = (3, 4 )
m = [tex]\frac{4-2}{3-0}[/tex] = [tex]\frac{2}{3}[/tex]
the line crosses the y- axis at (0, 2 ) ⇒ c = 2
y = [tex]\frac{2}{3}[/tex] x + 2 ← equation of line
H)
find the exact value of sec 7pi / 4
Answer: sqrt(2)
Step-by-step explanation:
Remember that sec x = 1/cos x.
That means that sec 7pi/4 = 1/cos(7pi/4)
cos(7pi/4) = -cos(7pi/4 - pi)
= -cos(3pi/4)
cos(3pi/4) is a special angle which evaluates to -sqrt(2)/2.
Hence, -cos(3pi/4) evaluates to simply sqrt(2)/2
Since cos(7pi/4) is equal to -cos(3pi/4),
cos(7pi/4) is equal to sqrt(2)/2.
Lastly, sec 7pi/4 = 1/cos(7pi/4) , which is the reciprocal of sqrt(2)/2, that is 2/sqrt(2).
Rationalizing the answer 2/sqrt(2) gives sqrt(2)
How do you find the sides of a 45 45 90 triangle when given the hypotenuse?
The value of the legs of the triangle would be hypotenuse/√2 and trignometric angle are 45 degree
You can use basic trigonometry to solve this problem. We know that the sine of the angle made by the hypotenuse and the base is equal to the ratio of perpendicular height and the hypotenuse, given that the angle is 45° the perpendicular will be equal to ⇒ hypotenuse × sin(45°).
That is perpendicular=hypotenuse/√2
Similarly, the cosine of the angle made by the hypotenuse and the base is equal to the ratio of base length and the hypotenuse, given that the angle is 45° the base will be equal to ⇒ hypotenuse × cos(45°)
That is base=hypotenuse/√2
Therefore, the value of the legs of the 45°-45°-90° triangle would be hypotenuse/√2.
Learn more about Trigonometry on
brainly.com/question/29002217
#SPJ4
Lin is solving the inequality 15-x< 14. She knows the solution to the
equation 15 - x = 14 is x = 1
How can Lin determine whether x > 1 or x < 1 is the solution to the
inequality?
If Lin is solving the inequality [tex]15-x < 14[/tex] and she know the solution is x = 1 , then the solution of inequality is [tex]x > 1[/tex] .
The inequality that Line is solving is [tex]15-x < 14[/tex] ,
the solution of the equation [tex]15-x = 14[/tex] is given as x = 1 ;
we have to find the value of x for which the given inequality expression is true ,
Case(i) , let us take [tex]x > 1[/tex] ,
So , putting x = 2 , in the inequality ,
we get ; [tex]15-2 < 14[/tex]
= 13 < 14 , that is TRUE .
Case(ii) , let us take [tex]x < 1[/tex] ,
So , putting x = 0 in the inequality ,
we get ; [tex]15-0 < 14[/tex]
= 15 < 14 , that is FALSE .
Therefore , the solution of the inequality is x > 1 .
Learn more about Inequality here
https://brainly.com/question/21897111
#SPJ4
An office manager is planning to set up three computer workstations and a file cabinet in a space that is 27 feet wide. The file cabinet takes up 3 feet. What is the width of the space available for each computer station?
Answer:
The width of the space available for each computer station is 8 feet-------------------------------
The width of the space for computer stations is:
27 - 3 = 24 feetEach computer station has a space of:
24/3 = 8 feetFactor Completely 4q^6+8q^3
Answer:
4[tex]q^{3}[/tex]( q³ + 2)
Step-by-step explanation:
4[tex]q^{6}[/tex] + 8q³ ← factor out 4q³ from each term
= 4q³ (q³ + 2)
Answer:
4q^3(q^3 + 2)
Step-by-step explanation:
The GCF of the exponents is 3, and the GCF of the bases is 4q. So divide both numbers by 4q ^ 3 and get
4q ^ 6 / 4q ^ 3 = q ^ 3
8q ^ 3 / 4q ^ 3 = 2
so you get
4q^3 (q ^ 3 + 2)
At the movie theatre, child admission is $5.70 and adult admission is $9.60. On Monday, three times as many adult tickets as child tickets were sold, for a total sales of $1345.50. How many child tickets were sold that day
The total number of child ticket and adult ticket that were sold was: 270 and 810 respectively.
How many child tickets were sold that day?On Monday, three times as many adult tickets as child tickets were sold at the movie theatre.The adult admission was $9.60, and the child admission was $5.70.The total sales for the day were $1345.50.In order to find out how many child tickets were sold that day, the total sales for the adult tickets must first be calculated. Since three times as many adult tickets were sold, the number of adult tickets can be calculated by dividing the total sales by three. This results in $448.50.To calculate the total sales for the child tickets, the total sales must be subtracted from the adult ticket sales.This results in $897.00. Since the price of the child tickets was $5.70, the total number of child tickets sold can be calculated by dividing the total sales by this price.This results in 157 child tickets sold.To learn more about the application of linear equations refer to:
brainly.com/question/2030026
#SPJ4
A coordinate plane. The x- and y-axes each scale by one. A graph of a line intersects the points negative one, zero and zero, one. A coordinate plane. The x- and y-axes each scale by one. A graph of a line intersects the points negative one, zero and zero, one. What is the slope of the line?
The slope of the line on the given coordinate plane is equal to 1.
How to calculate the slope of a line?In Mathematics, the slope of a straight line can be calculated by using this this mathematical expression;
Slope, m = (Change in y-axis, Δy)/(Change in x-axis, Δx)
Slope, m = (y₂ - y₁)/(x₂ - x₁)
From the information provided in the graph, we have the following data points on the line:
Points on x-axis = (-1, 0).
Points on y-axis = (0, 1).
Substituting the given points into the slope formula, we have the following;
Slope, m = (y₂ - y₁)/(x₂ - x₁)
Slope, m = (1 - 0)/(0 - (-1))
Slope, m = 1/(0 + 1)
Slope, m = 1/1
Slope, m = 1
In conclusion, we can logically deduce that the slope of this line is equal to 1.
Read more on slope here: brainly.com/question/1884491
#SPJ1
GIVING BRAINLIEST AND 50 POINTS
Answer:
2x + 2
Step-by-step explanation:
Combine all the like terms:
-5x + 7x -12 + 14 = 2x + 2
Answer:
2x + 2
Step-by-step explanation:
(- 5x - 12) + (14 + 7x) ← remove parenthesis
= - 5x - 12 + 14 + 7x ← collect like terms
= (- 5x + 7x) + (- 12 + 14)
= 2x + 2
How do you create a function in forex?
A trader can create their own automated trading strategies in forex by writing a script or program in a programming language, such as MQL4 or Python. This script will contain instructions to execute trades according to specific criteria defined by the trader. They can then backtest the strategy to see how it performs.
1. Decide on a trading strategy. This could include things like setting entry and exit points, calculating position sizes, and setting stop losses and take profits.
2. Choose a programming language that is compatible with the trading platform you are using, such as MQL4 or Python.
3. Write the script or program that will contain the instructions for the trading platform to follow in order to execute the trading strategy.
4. Test the script or program to make sure it works properly.
5. Run a backtest to see how the trading strategy performs.
6. If the results of the backtest are satisfactory, you can deploy the trading strategy on the trading platform.
Learn more about forex here
https://brainly.com/question/799175
#SPJ4
A stone was thrown into a pond from 8 feet above the surface of the water in the pond. Justin wrote 8 feet to represent the height from which the stone was thrown. What does 0 represent in this situation
Solve for x and express the zeros in a + bi form x^2=6x-10
Solution of the equation is x = 3 ± i that is a complex number where 3 is the real part and i is the imaginary part.
What is quadratic equation?The equation of two-degree polynomial having one variable is called quadratic equation.
The solution of a quadratic equation is either real or complex. We use quadratic equation formula for solution whenever we cannot expand, and factoring a given two-degree polynomial equation.
How to solve the given equation?given equation, x² = 6x -10
x²-6x +10 =0
This equation cannot be expanded so we need to write the formula for quadratic equation to solve it.
we know that standard form of a quadratic equation is given by
ax² + bx +c = 0
where a is the coefficient of x², b is the coefficient of x and c is the constant.
the solution of the equation is given by x = -b ± √ (b² - 4ac) / 2a
Now, the solution for the above equation is x = 6 ± √ (6² - 4×1×10) / 2×1
x = 6 ± √ (36 -40) / 2
x = 6 ± √-4 / 2
as √-4 = √-1 ×2
x = 6 ± 2 √-1 /2
divide both numerator and denominator by 2
x = 3± i as √-1 = i
this is the solution in (a + bi) form a = 3 and b = 1
To learn more about quadratic equation visit:
https://brainly.com/question/29011747
#SPJ1
The point P(2k, k) is equidistant from A(-2, 4) and B (7,-5). Find the value of k.
If point P(2k, k) is equidistant from A(-2, 4) and B (7,-5), the numerical value of k is 3.
What is the numerical value of k?The distance formula used in finding the distance between two points is expressed as;
d = √( ( x₂ - x₁ )² + ( y₂ - y₁ )² )
The distance between P(2k, k) and A(-2, 4) is:
d = √((2k - (-2))² + (k - 4)²)
d = √((2k +2)² + (k - 4)²)
The distance between P(2k, k) and B(7, -5) is:
d = √((2k - 7)² + (k - (-5))²)
d = √((2k - 7)² + (k + 5)² )
Since the distances are equal, we can set the two equations for d equal to each other and solve for k.
√((2k +2)² + (k - 4)²) = √((2k - 7)² + (k + 5)² )
Square both sides
(2k +2)² + (k - 4)² = (2k - 7)² + (k + 5)²
(2k +2)² + (k - 4)² = 5k² - 18k + 74
5k² + 20 = 5k² - 18k + 74
Collect like terms
5k² - 5k² + 18k = 74 - 20
18k = 74 - 20
18k = 54
k = 54/18
k = 3
Therefore, the value of k is 3.
Learn more about the distance formula here: brainly.com/question/24509115
#SPJ1
What is the coefficient of x3y4 in 2x 3y2 5?
The coeficient of x^3+y^4 in the algebraic expression is the number 2
What is an algebraic expression?
An algebraic expression is a set of numbers and letters that make up an expression that has a meaning, the letters are variables and the numbers are coefficients or independent terms, algebraic expressions can be part of an equation and model mathematical processes.
In the given expression we have the following:
2x^3+ 2y^4
As we are asked for the coefficient of the variable "y" then we must take the number that is just before the letter which in this case is the number 2.
2 is the coefficient of x^3+y^4
Learn more about algebraic expression in:
brainly.com/question/21856579
#SPJ4
Write a statement to represent the expression h-9
expression h-9 is represented as statement 'h decreased by 9'.
What is subtraction?Subtraction is an operation used to find the difference between numbers. When you have a group of objects and you take away a few objects from it, the group becomes smaller. For example, you bought 9 cupcakes for your birthday party and your friends ate 7 cupcakes. Now you are left with 2 cupcakes. This can be written in the form of a subtraction expression: 9 - 7 = 2 and is read as "nine minus seven equals two".
Given expression
h-9
Here h is a variable, 9 is constant and - is the symbol of subtraction.
the phrase "decreased by" tells us to use subtraction.
Statement for the above expression
h decreased by 9.
Hence, the statement 'h decreased by 9' represents expression h - 9.
Learn more about subtraction here:
https://brainly.com/question/2346316
#SPJ1
Please help me find x and y. May you also tell me the steps in which to do so.
Answer:
x=
y=31
Step-by-step explanation:
hope this helps
Which of the following sets of numbers could not represent the three sides of a triangle? [12,17,26] [12,20,29} {7,20,25} {7,16,24}
Answer:
The fourth one could not represent the three sides of a triangle
Step-by-step explanation:
because the two sides of the triangle must be larger together than the third side and 7+16=23<24, so the fourth one could not represent the three sides of a triangle.
Answer:
C
Step-by-step explanation: The third one down. There are two ways you know this.
1. If you had two boards that where 6 cm and 20 cm and tried to make a triangle with the third side = 27, the two little boards would lie flat on the 27 cm board.
2. The other three answers all make the smaller two sides larger than the third larger side.
Write 6789 correct to 3 significant figures
Answer:
The answer is 679
Step-by-step explanation:
A significant figure is a number greater than zero so to 3 significant figures just count 3 from the front then round up 9 and it becomes 1 then add it to 8 to become 9 which equals 679
Hope it helps
Pls rate as brainliest answer
Simplify:-
[tex]x {}^{2} - 5x + 6 \div x {}^{2} +3x - 10 \\ [/tex]
Guys help me please.
Step-by-step explanation:
[tex] = {x}^{2} \div {x}^{2} + 3x - 5x + 6 - 10 \\ = 1 - 2x - 4 \\ = - 2x - 4 + 1 \\ = - 2x - 3 \\ = - 1(2x + 3)[/tex]
HI,HOPE THAT IS HELPFUL.