the solution of equation y=x+2 and y=3x-2 are x= 2 and y=4
y = x+2 ------------ equation 1
y = 3x -2 ------------ equation 2
in the first equation y = x +2
in the second equation y = 3x -2
this mean equation 1 = equation 2
then we can equate the two together to get one of the variable
remember, we have to unknown variables which are x and y, so we need to isolate y to get x
x + 2 = 3x -2
let collect the like terms
x - 3x = -2 -2
let us factorize out x on the right hand side of the equation
x(1 - 3) = -4
x(-2) = -4
-2x = -4
divide both sides by -2
-2x/-2 = -4/-2
x = 2
to find y put x in any of the above equations
let us use equation one
y = 2 + 2
y = 4
complete question
How do you solve, y=x+2 y=3x-2
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HELPPPP PLEAAAASE I HAVE NO IDEA WHAT IM SUPPOSED TO DOOOOO
Answer:
[tex]\mathrm{Factoring}\:4x^3-15x^2-31x+30:\quad \boxed{\left(x+2\right)\left(4x-3\right)\left(x-5\right)}[/tex]
Step-by-step explanation:
This is a particularly tough question. It involves polynomial division(a real laborious process) and solving using quadratic formula.
I presume your school has provided you the resources for both.
Anyways, here goes a brief explanation
To find the roots(zeros) of a polynomial, [tex]f(x)[/tex] , set [tex]f(x) = 0[/tex] and solve for values of [tex]x[/tex]
In general, if [tex]a[/tex] is a zero of [tex]f(x)[/tex], then [tex]f(x) \div(x-a)[/tex] will leave no remainder. In other words, it is a factor of the polynomial. It also means [tex]x - a = 0[/tex]
The given polynomial is [tex]4 x^{3} - 15 x^{2} - 31 x + 30[/tex]
We are given that [tex]- 2[/tex] is a zero of [tex]f(x)[/tex]. This simply means that [tex]f(-2) = 0[/tex]
Plugging [tex]-2[/tex] into the function gives
[tex]f(-2) = 4(-2)^3 -15(-2)^2 - 31x + 30\\\\ = 0 =4\left(-8\right)-15\cdot \:4-31\left(-2\right)+30[/tex]
Which indeed is 0
Here [tex]a = -2[/tex] , so [tex]x - (-2)[/tex] which is [tex]x + 2[/tex] is a factor of[tex]f(x)[/tex]. It also means that
[tex]x-(-2) = 0 \;or\; x + 2 = 0[/tex]
Steps to factor the polynomial [tex]4 x^{3} - 15 x^{2} - 31 x + 30[/tex] :
Divide [tex]4 x^{3} - 15 x^{2} - 31 x + 30[/tex] by [tex]x+2[/tex]Multiplying both sides of the above by [tex]4[/tex] gives [tex]4x -3 = 0.[/tex] So [tex]4x-3[/tex] is the third factor, replacing [tex]x - \dfrac{3}{4}[/tex]
The factors of [tex]4 x^{3} - 15 x^{2} - 31 x + 30[/tex]
are:
[tex]x+2, x-5 \;and \;4x-3[/tex]
Answer:
[tex]\mathrm{Factor}\:4x^3-15x^2-31x+30:\quad \boxed{\left(x+2\right)\left(4x-3\right)\left(x-5\right)}[/tex]
Use a polynomial division calculator which you can find on the web and a quadratic formula calculator (on the we or on your own calculator)
Convert this equation into standard form
The standard form of the given linear equation is; -x + 3y = 15
How to write the Linear Equation in standard form?The standard form of a linear equation is expressed in the form;
Ax + By = C
Now, we are given the equation as;
y - 4 = ¹/₃(x + 3)
Multiply through by 3 using multiplication property of equality to get;
3y - 12 = x + 3
Add 12 to both sides to get;
3y = x + 15
Subtract x from both sides to get;
-x + 3y = 15
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3/1107
Long division please show work! Tysm
cosec⁴A-cosec ²A=cot ⁴A-cot ²A
from the internet it's different and i did in in this way :
cosec ²A)²-cosec ²A
1+cot ⁴A-2cot²A-1+cot ²A(1-1=0)(2cot ²A-cot ²A=cot ²A)
cot ⁴A-cot ²A
Therefore , the solution of given trigonometric equation has been proved.
The trigonometric equation is what?A trigonometric equation is one that contains one or more ratios of unknown trigonometric angles. The ratios of sine, cosine, tangent, cotangent, secant, and cosecant angles are used to express it. A trigonometric equation is cos2 x + 5 sin x = 0, for instance.
Here,
Given :
Cosec A cosec²A cot A+ cot² A
LHS=(1+cot2A)2- (1 + cot2 A)
=1+2cot2A+cot A-1- cot2 A
= cot2A+ cot1A
= RHS
Hence, Cosec1A- cosec² A = cot ⁴A-cot ²A
Therefore , the solution of given trigonometric equation comes out to be it has been proved
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Two angles are complementary the difference between four times the measure of the smaller angle and the measure of the larger angle is 10 what is the measure of the larger angle
The measure of the larger angle is obtained as follows:
70º
What are complementary angles?Two angles are defined as complementary is the sum of their measures is of 90º.
The variables that represent each angle in this problem are given as follows:
x and y.
They are complementary angles, hence:
x + y = 90.
The difference between four times the measure of the smaller angle and the measure of the larger angle is 10, hence:
4y - x = 10.
x = 4y - 10.
Hence the value of y is obtained as follows:
4y - 10 + y = 90
5y = 100
y = 100/5
y = 20º.
Hence the measure of the larger angle is given as follows:
x + 20 = 90
x = 70º.
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what is equivlent to 4/9x7
Answer:
Step-by-step explanation:
The expressions that are equivalent to 4/9 x 7 are 28/9, 3¹/₉ and 3.11
As no options are included, I will include the expression that is equivalent to 4/9 x 7 in both fractions and decimal.
In fractions:
= 4/9 x 7
= 28/9
or,
= 3¹/₉
In decimals:
= 4/9 x 7
= 28/9
= 28 ÷ 9
= 3.11
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Question content area top
Part 1
Find the approximate side length of a square game board with an area of 162 in2.
The approximate side length of the square game board is 13 inches.
What is a square?A square is a two-dimensional figure that has four sides and all four sides are equal.
The area of a square is side².
We have,
Area of a square game board = Side².
Area of the square = 162 inches²
Now,
Side² = 162 inches²
Side = √162 inches
Side = 12.73 inches
Side = 13 inches
Thus,
The side length of the square game board is 13 inches.
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struggling please help I'll mark brainliest
What is the solution to the inequality |2x + 3| < 7?
4 < x < 10
–5 < x < 2
x < 4 or x > 10
x < –5 or x > 2
Answer:
its the second one: -5<x<2
Step-by-step explanation:
I did out the math
Josh collected 2 pounds of plastic during the park clean up. Sherri collected 1 ¾ times as much as Josh.
How many pounds of plastic did they collect together?
Therefore , the solution of the given problem of unitary method comes out to be 3.5.
A unitary method is exactly what?One can utilize the unit strategy to solve a problem by first multiplying the value of one unit by the quantity of units required. The unit function, to put it simply, is used to separate a single entity amount from just a given many. 400 pence, or the equivalent of one pen, would buy 40 needles. There might be a common approach to determining this. only one country. Anything has a distinguishing feature. Matrix logic, algebra, and its interpellation & inverse are all comparable terms.
Here,
Given : Josh gathered 2 pounds of plastic while cleaning up the park.
Josh received 1 ¾ times as much money from Sherri.
thus ,
To find the total plastic collected by both of them:
=> 1 ¾ * 2 + 2
=> 7/4 * 2
=> 14/4
=> 7/2
=>3.5
Therefore , the solution of the given problem of unitary method comes out to be 3.5.
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Which of the following equations have an -intercept of (-2, 0) and y-intercept of (0, 3)?
Select all that apply.
y=3/2x+3
y=3x-2
2y-3x=6
y=-2x+3
y-1=-2(x+3)
Answer:
The first and third choices
[tex]y = \dfrac{3}{2}x + 3[/tex]
and
[tex]2y-3x=6[/tex]
Step-by-step explanation:
(I cannot properly see the leading negative signs in choices 4 and 5, I copied/pasted your question choices from Brainly post and zoomed)
First understand what x and y intercepts are
The y-intercept is the value of y where the graph of the equation crosses the y-axis, It is the value of y when x = 0
The x-intercept is the value of x where the graph of the equation crosses the x-axis, It is the value of x when y = 0
We are given that the x-intercept is (-2, 0) and y = (0,3)
We can use a process of elimination to get rid of obviously incorrect choices and then work on the possible correct ones depending on whether we come up with the correct values of y first and eliminating those that do not match x =0, y =3 or (0,3) and then see if the x-intercept is (-2,0)
First choice let's find the y-intercept for the first choiceGwen can a photo that i 4inche wide by 6 inche long into her computer. If he cale the length down to 3inche how wide hould the imilar photo be?
The width of a similar photo will be 2 inches.
As per the given problem,
Width of original photo = 4 inches
Height of original photo = 6 inches
After scaling the photo,
Height of new photo = 3 inches.
Let’s understand about scale factor.
An amount that multiplies (or "scales") a quantity is called a scale factor.
Scale factor = height of the sized image/size of the original image.
Scale factor = 3/6 = 1/2.
Therefore, the scaled image's width = scale factor *the size of the original image.
The width of the scaled photo = (½)*4 = 2.
Hence, the width of a comparable image measures 2 inches.
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What is an equation that passes through the points (-6,1) and (6,7)
Considering the expression of a line, the equation of the line that passes through the points (-6,1) and (6,7) is y=1/2x +4.
What is a linear equationA linear equation o line can be expressed in the form y = mx + b
where
x and y are coordinates of a point.m is the slope.b is the ordinate to the origin.Knowing two points (x₁, y₁) and (x₂, y₂) of a line, the slope can be calculated using:
m= (y₂ - y₁)÷ (x₂ - x₁)
Substituting the value of the slope and the value of one of the points in y= mx + b, the value of the ordinate to the origin b can be calculated.
Equation in this caseIn this case, being (x₁, y₁)= (-6, 1) and (x₂, y₂)= (6,7), the slope can be calculated as:
m= (7 -1)÷ (6 -(-6))
m= (7 -1)÷ (6 +6)
m= 6÷ 12
m= 1/2
Considering point 2 and the slope m, you obtain:
7= 1/2×6 + b
7= 3 +b
7 -3= b
4= b
Finally, the equation of the line is y=1/2x +4.
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2\5+5\5 = 8\5 9\5 7\5 help
The value of the expression 2/5 + 5./5 is 7/5.
What is a fraction?A fraction is written in the form of a numerator and a denominator where the denominator is greater that the numerator.
Example: 1/2, 1/3 is a fraction.
We have,
2/5 + 5/5
= 2/5 + 1
= (2 + 5) / 5
= 7/5
Thus,
The value is 7/5.
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Prove that x² - 2px + 2p² is non-negative for all real values of x.
[tex]x^2-2px+2p^2 \\ \\ =(x^2-2px+p^2)+p^2 \\ \\ =(x-p)^2+p^2[/tex]
Assuming [tex]p \in \mathbb{R}[/tex], [tex](x-p)^2 \geq 0[/tex] and [tex]p^2 \geq 0[/tex], meaning that [tex](x-p)^2+p^2 =x^2-2px+2p^2 \geq 0 \forall x \in \mathbb{R}[/tex]
Find the rule and the graph of the function whose graph can be obtained by performing the translation 3 units right and 4
units up on the parent function f(x)=x²
a. f(x)=(x-5)² +4
8
6-
4
2+
864 -2
-2
L
19
do
+
Mark this and return
+
b. f(x) = (x+3)² + 2
2 4 6
C. f(x)=(x-3)² +4
N
864
d. f(x)=x²-4
2+
-2
4
Top
+
2 4 6
3+
Next
Submit
Answer:
C. f(x) = (x - 3)² + 4
Step-by-step explanation:
Given parent function:
[tex]f(x)=x^2[/tex]
When a graph is translated "a" units right, subtract "a" from the x-value of the function.
Therefore, the translation of the parent function 3 units right is:
[tex]\implies f(x-3)=(x-3)^2[/tex]
When a graph is translated "a" units up, add "a" to the function.
Therefore, the translation of the function 4 units up is:
[tex]\implies f(x-3)+4=(x-3)^2+4[/tex]
What is the formula of a triangular method?
The formula for a triangular method is: (x1 + x2 + x3) / 3
1. The triangular method is the average of three different values: x1, x2, and x3.
2. To calculate the average, add the three values together and divide by three.
3. The formula for a triangular method is therefore (x1 + x2 + x3) / 3.
The triangular method is a method used to calculate an average of three different values. This method is most useful when there is not enough information available to calculate a more accurate average. To calculate an average using the triangular method, the three values (x1, x2, and x3) are added together and then divided by three. The formula for a triangular method is (x1 + x2 + x3) / 3. This method is useful for finding an average when a more accurate average cannot be calculated due to a lack of data. It is also used when data points are not necessarily related, as the triangular method is less affected by outliers than other methods of calculating an average. The triangular method is a quick and easy way to find an average when more complex calculations are not possible.
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Which of the following are factors of 56? A.4 B.6 C.7 D.9 E.10
Answer:
Step-by-step explanation:
A and C will both work. 4 goes into 56 evenly and so does 7.
A garden in the shape of a square measures 15 feet on each side. A triangular paved patio is in the center.
The area occupied by the garden is 185 square feet.
What is Area?Area is the entire amount of space occupied by a flat (2-D) surface or an object's shape. On a sheet of paper, draw a square using a pencil. It has two dimensions. The area of a shape on paper is the area that it occupies.
Given:
Base = 10 feet, height = 8 feet
First, Area of Garden without patio
= 15 x 15
= 225 square feet.
Now, The patio is in the shape of a triangle which has a height of 8 feet and a base length of 10 feet.
So, Area of triangular patio
= 0.5 x 8 x 10
= 0.5 x 80
= 40 square feet.
Then, Actual Area of garden
= area of garden without patio - area of patio
= 225 square feet - 40 square feet
= 185 square feet.
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What is substitution method formula?
Particularly there is no formula for substitution just insert the given values in the equations.
One of the methods to solve a system of linear equations in two data algebraically is the substitution method. In this method, we find the value of any one of the variables by discordant it on one side and taking every other term on the other side of the equation.
This method is a simple way to resolve a system of linear equations algebraically and find the answer to the variables.
As the name suggests, it involves finding the value of the x-variable in terms of the y-variable from the first equation and then substituting or exchanging the value of the x-variable in the second equation.
The substitution method is one of the algebraic methods to solve coincident linear equations. It concludes by substituting the value of any one of the variables from one equation into the other equation.
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stressed bc test due tonight help plese ty
For 16-19, graph each equation or inequality.
16. 2y – 4x < 8
17. -4y > -x + 12
18. | x + 3 |= y
19. |2x – 6| + 2 = y
The solution is the set of all points (x,y) that satisfy the inequalities:
y < 2x + 4, y < x/4 - 3, x + 3 = y, and 2x - 6 + 2 = y.
What is the graph of a function?
The graph of a function is a visual representation of the relationship between the input values (x-coordinates) and the output values (y-coordinates) of the function. In other words, it is a visual representation of the function's rule.
The graph of a function can take many different forms, depending on the function's rule. Linear functions, for example, will produce a straight line on the graph.
i) 2y - 4x < 8 can be solved by adding 4x to both sides and then dividing by 2, giving:
y < 2x + 4.
ii) -4y > -x + 12 can be solved by adding x to both sides and then dividing by -4, giving: y < x/4 - 3.
iii) | x + 3 | = y, you can split this into two cases:
i. x + 3 = y
ii. -(x + 3) = y
iv) |2x – 6| + 2 = y, you can split this into two cases:
i. 2x - 6 + 2 = y
ii. -(2x - 6) + 2 = y
We can use these equations to plot the graph on a coordinate plane.
Hence, the solution is the set of all points (x,y) that satisfy the inequalities:
y < 2x + 4, y < x/4 - 3, x + 3 = y, and 2x - 6 + 2 = y.
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Find the area of a circle with a radius of 21 inches. Use
area: about
in.
22/7
for π.
Answer:
[tex]1386 in^2[/tex]
Circle Formulasr: radius
Circumference: [tex]2\pi r[/tex]
Area: [tex]\pi r^2\\[/tex]
In this case, we are using 22/7 as an estimation for pi.
Q)Plug into the area formula.
22/7 * (21)^2
22/7 * 441
[tex]1386 in^2[/tex]
The corresponding angles in these polygons are congruent.
What are the factors of 10m?
Answer:
1, 2, 5 and 10
Step-by-step explanation:
Step-by-step explanation:
1x10
2x5
4x5
.................
please help its for a test and I need these done so I can be free. its due tonight and I did this all day
For 16-19, graph each equation or inequality.
16. 2y – 4x < 8
17. -4y > -x + 12
18. | x + 3 |= y
19. |2x – 6| + 2 = y
An inequality is defined as an unfair comparison between two numbers or other mathematical expressions. When comparing the sizes of two numbers on a number line, it is most commonly used. The graph for each inequality or equation is included in the attachment.
What is graph?A graph is a visual representation of statistical data or a functional relationship between variables. Graphs are useful for forecasting because they can highlight broad trends in the quantitative behaviour of data. However, as mere approximations, they can be inaccurate and occasionally deceptive.
Most graphs have two axes: one for a set of independent variables and one for a set of dependent variables. The most common type of graph is a broken-line graph, with time serving as the independent variable.
16. 2y – 4x < 8
= 2y < 4x + 8
= y < 2x + 4
17. -4y > -x + 12
= y > x/4 + -3
18. | x + 3 |= y
y = | x + 3 |
19. |2x – 6| + 2 = y
y = |2x – 6| + 2
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I need help with this problem number 6
Answer: I can't see the question
Step-by-step explanation:
What are the 3 unit systems?
The International System of Units (SI) units, the British Imperial System, and the US Customary System are the three common systems of measurement.
Define 3 unit systems of measurements?Associating numbers with physical quantities and phenomena is referred to as a system of measurement. Measurement systems are groups of units of measurement and the rules that link them.Measurement systems that are metric.
The metric system uses three primary units: meters to measure length, kilograms to measure mass, and seconds to measure time.The unit of measurement for length is the meter. The letter (m) serves as the unit's designation. View the graph below. By successively multiplying by 10, we add "Deca," "Hecto," and "Kilo" to the base unit of "m" to measure large units.American National Standards Institute:
The US uses the imperial system of units, also known as the U, just like the metrics system. standard units of S. Things are measured in this place in feet, inches, pounds, ounces, and so on. In the sections that follow, let's examine them in more detail.Different Metric Systems of Measurement:
Although we are aware of the fundamentally defined metric systems for length, mass, and volume, there are many other physical quantities for which we need to define the base unit. Using the fundamental 7 quantities of the metric system of measurement as a starting point, units for quantities like force, power, area, and magnetic intensity were developed.To know more about the unit systems, here
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Answer:
The French system, British system and the Metric system.
Step-by-step explanation:
Three systems of unit and their fundamental units:C.G.S. system (or French system): In this system, the unit of length is centimeter (cm), unit of mass is gramme (g) and unit of time is second (s).
F.P.S. system (or British system): In this system, the unit of length is foot (ft), unit of mass is pound (lb) and unit of time is second (s).
M.K.S. system (or Metric system): In this system, the unit of length is meter (m), unit of mass is kilogram (kg) and unit of time is second (s).
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i forgot how to it can i please get some help2x+1 + x+6=
Answer:
3x+7
Step-by-step explanation:
You need to combine like terms. Add 2x + x. It is 3x add the six and the one to make seven \
Hope this helps
Answer:
3x+7
Step-by-step explanation:
First, you want to group the variables, which in this case, is x. You take the 2x and x and make it 3x.
3x+1+6
Now that you have this done, you want to group the numbers, by making the 1+6 to 7.
3x+7
This is your answer, 3x+7.
I’m The coordinate plane point A has coordinates of A(-5,8). Which is further from A, point B or point C given that they have the coordinates of B(1,0) and C(-10,16)
The answer is point C is further from point A than point B
what is the Cartesian co-ordinate system?A Cartesian coordinate system in a plane is a coordinate system that specifies each point uniquely by a pair of numerical coordinates,
Given here: The points A(-5,8) , B(1,0) C(-10,16)
length of AB= [tex]\sqrt{(-5-1)^2+(8-1)^2}[/tex]
=9.22 units
Similarly length of AC= [tex]\sqrt{(-5+10)^2+(8-16)^2}[/tex]
= 9.433 units
Hence, point C is further from point A than point B
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ninas garden is 4 1/5 meters long 3/10 meters wide . what is the area of ninas garden? please help asap
Based on the information provided, the area in Nina's garden is 0.26 square meters.
What is the area?The word area refers to the space occupied by a surface, in this case, the space of the garden. In a rectangle, this area can be calculated with the following formula, although for other shapes the formula might be different:
area = length x width
What is the area of the garden?To make this process easier, let's convert the fractions into regular numbers
4 1/5 = 4.2 (1/5 = 0.2)
3/10 = 0.3
4.2 x 0.3 = 1.26 square meters
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Is y² 5y 10 a quadratic equation justify?
Yes, y² = 5y - 10 is a quadratic equation.
In algebra, a quadratic equation is that which can be rearranged in standard form as
ax² + bx + c = 0,
where x is an unknown value, and a, b, and c are known numbers, where a ≠ 0. (If a = 0 and b ≠ 0 then the equation is linear). Quadratic equations are the polynomial equations of degree 2 in one variable of type f(x) = ax² + bx + c = 0 where a, b, c, ∈ R and a ≠ 0.
We have the equation
y² = 5y - 10
y² - 5y + 10 = 0
The highest degree of this equation is 2, therefore it is a quadratic equation.
-- The given question is incorrect, the correct form of equation is
"Is y² = 5y - 10 a quadratic equation justify?" --
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