Equation of the line
There are several forms to express the equation of a line.
The equation of the line in slope-intercept form is:
y=mx+b
Being m the slope and b the y-intercept.
The equation of a line passing through points (x1,y1) and (x2,y2) can be found as follows:
[tex]\displaystyle y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]The standard form of a line is:
Ax + By = C
We are given two points (1,2) and (3,10). The point-point equation is adequate according to the data we are provided.
[tex]\begin{gathered} \displaystyle y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1) \\ \text{Substituting:} \\ \displaystyle y-2=\frac{10-2}{3-1}(x-1) \end{gathered}[/tex]Operating:
[tex]\begin{gathered} y-2=\frac{8}{2}(x-1)=4(x-1) \\ \\ \text{Operating:} \\ y-2=4x-4 \end{gathered}[/tex]Subtracting 4x and adding 2:
y - 4x = -4 + 2 = -2
Rearranging:
-4x + y = -2
This is the required equation in standard form
A salsa recipe uses 14 ounces of peppers and 7 ounces of onions.which two statements correctly state the related unit ratio?A.Use 0.5 ounces of pepper for each ounce of onionB.Use 2 ounces of pepper for each ounce of onionC.Use 7 ounces of pepper for each ounce of onionD.Use 0.5 ounces of onion for each ounce of pepperE.Use 2 ounces of onion for each ounce of peppersF.Use 7 ounces of onion for each ounce of peppers
14 ounces of peppers ---------- 7 ounces of onions
wee need satisfy always this equivalence
B. satisfy the equivalence
2 ounces of peppers ---------- 1 ounce of onions
D. satisfy the equivalence
1 ounce of peppers ---------- 0.5 ounces of onions
we always need to have the relations 2:1
the correct statements are B and D
Solve the system by graphing and determine the number of solutions it has. (Hint: to graph find the y-intercept and slope of the line.)-4x + y = 5-2y = -8x + 4
Given the system of equations:
-4x + y = 5
-2y = -8x + 4
To solve the system of equations by graphing, apply the slope-intercept form:
y = mx + b
Where m is the slope and b is the y-intercept.
Rewrite each equation to slope-intercept form
Equation 1:
-4x + y = 5
Add 4x to both sides:
-4x + 4x + y = 4x + 5
y = 4x + 5
Equation 2:
-2y = -8x + 4
Divide all terms by -2:
[tex]\begin{gathered} \frac{-2y}{-2}=\frac{-8x}{-2}+\frac{4}{-2} \\ \\ y=4x-2 \end{gathered}[/tex]We have the equations in slope intercept form:
y = 4x + 5
y = 4x - 2
From the slope intercept form of both equatios, we can see both equations have the same slope.
Slope = 4
Since they have the same slope, they are parallel lines.
The solution will be the points of intersections, but parallel lines do not intersect.
Therefore, we can say the system has no solution.
We have the graph below:
From the graph above, both lines do not intersect. Therefore, there is no solution.
ANSWER:
No solution
2) Suve the following quadratic equations la, quadratic for naudas i) 2x²+7+3=0 ii) 6x²-5x=8
Answer: x = -1/2 and x = -3
Given the following quadratic function
[tex]2x^2\text{ + 7x + 3 = 0}[/tex][tex]\begin{gathered} \text{The standard form of a quadratic function is given as} \\ ax^2\text{ + bx + c = 0} \\ \text{a = 2 , b = 7 and c = 3} \\ \text{ find ac} \\ ac\text{ = 2 x 3} \\ ac\text{ = 6} \\ \text{ Find the factors of ac (6) when add that will give us 7x} \\ \text{The factor is 6 and 1} \\ 2x^2\text{ + 6x + x + 3 = 0} \\ 2x(\text{x + 3) + 1 (x + 3)} \\ (2x\text{ + 1) = 0 or (x + 3) = 0} \\ 2x\text{ + 1 = 0 or x+ 3 = 0} \\ \text{x = -1/2 or x = -3} \end{gathered}[/tex]The solution of the above quadratic function is x = -1/2 and x = -3
how do i find the markup price and retail price
Price = 72.87
The markup is 30% or 30/100 = 0.3
Let's find the markup of the price:
[tex]72.87\cdot0.3=21.861[/tex]The retail price, or selling price, is the price + markup.
Thus, retail price is:
[tex]72.87+21.861=94.731[/tex]Answers:
Markup = $21.86Retail Price = $94.73Help please if you can show your work
7
400 ÷ 64 = 6.25
This doesnt mean its 7 because if u multiply
6 x 64 =384
Multiply 64 x 7 it gives you 448 which means she has enough to go on the trip
3. How do these values relate to Max and Mary's ages?
The numbers of the intersections of the two lines represent the solution for the problem
for this, the point is (5,3) since they are the corresponding ages of them
Tucker is painting his pool deck over the weekend. The area of the deck is 76 1/2 square meters. He paints 2/3 of the deck before stopping to eat lunch. How many square meters does Tucker have left to paint after lunch?Write your answer as a whole number, fraction, or mixed number. Simplify any fractions.
Tucker is painting his pool deck over the weekend. The area of the deck is 76 1/2 square meters. He paints 2/3 of the deck before stopping to eat lunch. How many square meters does Tucker have left to paint after lunch?
Write your answer as a whole number, fraction, or mixed number. Simplify any fractions.
we have that
total area=76 1/2 m2
Convert to an improper fraction
76 1/2=76+1/2=153/2 m2
1-(2/3)=1/3
Multiply the total area by 1/3
(153/2)*(1/3)=51/2=25.5 m2 ------> 25 1/2 m2
the answer is 25 1/2 m2The graph of an equation drawn through which two points would best represent therelationship between the number of miles and the cost of the trip?
(10,5) and (250, 120)
1) Since we don't have the exact points, all we can do is a visual approximation of the line that best fits in.
2) So let's draw a line, like this on that graph also known as the eye-ball method. We are going to make it half, or almost half of it for each side.
3)Hence, examining the options we pick (10,5) and (250,120) as the best options that could represent the relationship between the number of miles ad the cost of that trip.
Since the line represents an average cost, and those points are approximately the same distance from the line.
What is the volume, to the nearest tenth of a cubic inch, ofthe plastic object?
In order to calculate the volume of a cylinder, we can use the formula below:
[tex]V=\frac{\pi d^2h}{4}[/tex]If the base diameter is 6 in and the height is 8 in, we have:
[tex]\begin{gathered} V=\frac{3.14\cdot6^2\cdot8}{4}\\ \\ V=226.2\text{ in^^b3} \end{gathered}[/tex]Therefore the volume is 226.2 in³.
Please help I need this for a text ASAP.
Two lines are 2linese intersect to form linear pairs with equal measures one angle measures 2x other measure 11y+2. x is 45 and y is 8.
The sum of a linear pair of angles is 180 degrees.
Now, we are given two pieces of information. We will use these to develop equations and then solve the equations simultaneously.
First, we know that the two angles are equal, therefore:
2x = 11y+2-------.> equation 1
Second, we know that the two angles form a linear pair of angles, therefore:
2x +11y+2 = 180 -------.> equation 2
Substitute by equation 1 in equation 2:
2x +2x = 180
4x = 180
x = 45
Substitute with the value of x in equation 1 to get y as follows:
2x = 11y+2
2 (45) -2 = 11y
88 = 11y
y = 8
Therefore:
the first angle = 2x = 2(45) = 90 degrees
the second angle = 11(8)+2 = 90 degrees
The two angles are equal and their sum is 180 .
What are linear pair of angle?Line pairs of angles occur when two lines intersect at a single point. Angles are considered linear if they are adjacent after the intersection of these two lines. The sum of the angles of a linear pair is always 180°. Such angles are also called supplementary angles.
If there is a pair of adjacent angles, the pair is a linear pair if the sum of the two angles (their measures) is 180°. Thus, linear pairs of angles always add up to 180°.
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Arrange the numbers 5^3, 6^2, and 2^7 in order from least to greatest.
5^3 = 5x5x5 = 125
6^2 = 6x6 = 36
2^7 = 2x2x2x2x2x2x2 = 128
From least to greatest
36 - 125- 128
6^2- 5^3 - 2^7
11) Solve the system by the addition method.
5x + 15y = -80
0.1x = -4.1 -0.3y
"5x + 15y = -80" + "0.1x = -4.1 -0.3y" using the addition method given equation "5.1x + 15.3y = -12.1".
What is the addition method of equations?A mathematical statement that has an "equal to" symbol between two expressions with equal values is called an equation. As in 3x + 5 = 15, for instance. Equations come in a variety of forms, including linear, quadratic, cubic, and others. Using the Addition Method to Solve Two-Variable Equation Systems The addition method, also known as the elimination method, is a third approach to solving systems of linear equations. In this method, the sum is zero by adding two terms with the same variable but opposite coefficients.So, "5x + 15y = -80" + "0.1x = -4.1 -0.3y" using addition method:
Change 0.1x = -4.1 -0.3y to: 0.1x + 0.3y = -4.1Now, "5x + 15y = -80" + "0.1x = -4.1 -0.3y" (refer to the image attached below for calculation)The resulting equation is: 5.1x + 15.3y = -12.1
Therefore, "5x + 15y = -80" + "0.1x = -4.1 -0.3y" using the addition method given equation "5.1x + 15.3y = -12.1".
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Melinda ate 3/5 of the cookies and left the rest for Suzanne. What fraction of the cookies are left for Suzanne?
The fraction of cookies left for Suzanne will be equal to 2/5 of the total number of cookies.
What is fraction?In Mathematics, fractions are represented as a numerical value, which defines a part of a whole. Example - 5/9. Here, (5) is called numerator and (9) is called denominator.
Given is Melinda who ate 3/5 of the cookies and left the rest for Suzanne.
Assume that the fraction of cookies left for Suzanne is represented by [x].
Fraction of cookies ate by Melinda = [y] = 3/5
The sum of the fractions representing the cookies eaten by both Suzanne and Melinda will be equal to 1. Mathematically -
x + y = 1
x + 3/5 = 1
x = 1 - 3/5
x = (5 - 3)/5
x = 2/5
Therefore, the fraction of cookies left for Suzanne will be equal to 2/5 of the total number of cookies.
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MATH PROBLEM HELP please make sure it correct
For the value of c = 0,c=1 then A is not invertible
For given matrix A is invertible if c≠ 0 and c≠ 1
[tex]Given \ $A=\left[\begin{array}{ll}1 & 1 \\ c & c^2\end{array}\right]$ \\A matrix $A$ is invertible if $|A|={det}(A) \neq 0$.\\Now consider $|A|={det}(A)=0$.[/tex]
[tex]$$\begin{aligned}&\Rightarrow\left|\begin{array}{ll}1 & 1 \\c & c^2\end{array}\right|=0 \\&\qquad \quad \text { If } A=\left[\begin{array}{ll}a & b \\c & d\end{array}\right] \text { then }|A|={det}(A)=a d-b c\end{aligned}$$[/tex][tex]$$\begin{aligned}&\Rightarrow c^2-c=0 \\&\Rightarrow c(c-1)=0 \\&\Rightarrow c=0, c=1\end{aligned}$If $c=0$ or $c=1$ then \A \is \\not \ invertible. \\$\therefore$ Given matrix $A$ is invertible iff $c \neq 0$ and $c \neq 1$. \\ie Given marix $A$ is invertible for $c \in \mathbb{R}-\{0,1\}$.[/tex]
What are matrix?Matrix, a collection of numbers arranged in rows and columns forming a rectangular array. The number is called the elements or entries of the matrix. Matrices have wide applications in engineering, physics, economics and statistics, as well as in various areas of mathematics. Matrices also have important applications in computer graphics, where they have been used to represent image rotations and other transformations.
Different types of matrices are
row matrixcolumn matrixzero matrixsquare matrixdiagonal matrix upper triple matrixlower triple matrixsymmetric matrix asymmetric matrix.To learn more about matrix, refer;
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According to Descartes's rule of sign, how many possible positive and negative roots are there for the equation 0=−4x6−3x5+2x2−4x+1?Drag the choices to the boxes to correctly complete the table.
According to Descartes’ Rule of Signs, if we let
[tex]f(x)=a_nx^n+a_{n-1}x^{n-1}+\cdot\cdot\cdot+a_1x+a_0[/tex]be a polynomial function with real coefficients:
then,
the number of positive real zeros is either equal to the number of sign changes of f(x) or is less than the number of sign changes by an even integer.
the number of negative real zeros is either equal to the number of sign changes of f(-x) or is less than the number of sign changes by an even integer.
In this case,
[tex]f(x)=-4x^6-3x^5+2x^2-4x+1[/tex]We will now check the number of sign changes of f(x)
There are 3 sign changes.
Therefore, f(x) has 3 or 1 positive real roots
Next we find f(-x),
[tex]\begin{gathered} f(-x)=-4(-x)^6-3(-x)^5+2(-x)^2-4(-x)+1 \\ \text{hence,} \\ f(-x)=-4x^6+3x^5+2x^2+4x+1 \end{gathered}[/tex]We will now check the number of sign changes of f(-x)
There are 1 sign changes.
Therefore, f(x) has 1 negative real root
Number of possible positive roots: 1 or 3
Number of possible negative roots: 1 only
Solve m (a – 5) = 12 for the variable a.
name the property illustrated by each statement if a=4.75 and 4.75 = b, then a=b
Answer:
Symmetric Property
Step-by-step explanation:
Find two circular objects. Measure the diameter and then make a prediction about the circumference of each circle. How could you check your predictions?
Let's say that the two objects have 5 centimeters and 7 centimeters of diameter.
The circumference of a circle is defined as
[tex]C=\pi d[/tex]Where d is the diameter. Using the measures above, we have
[tex]C_1=\pi(5cm)\approx5\cdot3.14\operatorname{cm}\approx15.7\operatorname{cm}[/tex][tex]C_2=\pi(7\operatorname{cm})=7\cdot3.14\operatorname{cm}=21.98\operatorname{cm}[/tex]Therefore, the circumferences of the measures obtained are 15.7 and 21.98 centimeters.Choose two pairs of alternate interrior angles.
D. <7 & <12
<6 & <9
The lines given by the equations y= 2x and y=-3x areA. neither perpendicularnorparallelB. parallelC. perpendicular
Consider that the general form of a line can be written as follow:
y = mx + b
where m is the slope and b the y-intercept.
Take into account that if two lines are parallel, then, the slopes of the line are equal. Based on the given equations, you can notice that the slopes are different, m1 = 2 and m2= -3.
Two lines are perpendicular if:
m1 = -1/m2
you can notice, based on the given equations that m1 is not equal to -1/m2, that is, 2 ≠ -1/(-3).
Hence, the lines are neither perpendicular nor parallel
Please help. Much Appreciated Please mark as a,b, & c. Thank you in advance.
a) We can see that an increase in the number of employees (x) also leads to an increase in the number of products produced monthly, thus we can say that there is a positive correlation between the number of employees in the plant and the number of products produced monthly.
A positive correlation occurs when one variable increases with respect to another variable.
b) The function that best fits.
Let's first Find the rate of change(slope).
Take the points;
(x1, y1) ==> (0, 120)
(x2, y2) ==> (10, 200)
Use the slope formula:
[tex]m=\frac{y2-y1}{x2-x1}[/tex]We have:
[tex]m=\frac{200-120}{10-0}=\frac{80}{10}=8[/tex]Use the form:
y = mx + b
Where m is the slope and b is the y-intercept
We have:
y = 8x + b
Substitue 0 for x and 120 for y, to solve for b.
120 = 8(0) + b
120 = b
Thus, we have the function:
y = 8x + 120
f(x) = 8x + 120
c) The slope, m is = 8
The slope indicates that the avearge rate of change between both variables is 8.
The y-intercept can be said to be the point where the line of the plot crosses the y-axis. This means when the number of employees are is zero, the number of products will be 120.
It can also be called the constant value.
Kayla notices that she can buy snacksandcandy in bulk at the grocery store.Write a formula that helps Kayla determinehow much she'll have to pay if she buys thefood in bulk.Let's lett = total pricep = price per kilogramk = number of kilograms of foodEnter the correct answer.
In this problem the total price (p) will be equal to the price per kilogram (p) times the number of kilograms of food (k) so the equation will be:
[tex]t=p\cdot k[/tex]1. AMNO with M(-5,2), NO. 4), and O(4.5): (-6, -2) /1 a. What kind of transformation is this? /3 b. What are the vertices of the image after the transformation?
Answer:
a. Translation
b. M'(-11, 0)
N'(-6, 2)
O'(-2, 3)
Explanation:
<-6, -2> indicates that the triangle MNO will be translated 6 units left and 2 units down, so <-6, -2> is a translation.
On the other hand, to know the new vertices, we need to apply the following rule:
(x, y) ----> (x - 6, y - 2)
So, the vertices of the image after the transformation are:
M(-5, 2) ----> (-5 - 6, 2 - 2) = M'(-11, 0)
N(0, 4) ----> (0 - 6, 4 - 2) = N'(-6, 2)
O(4, 5) ----> (4 -6, 5 - 2) = O'(-2, 3)
Therefore, the answers are:
a. Translation
b. M'(-11, 0)
N'(-6, 2)
O'(-2, 3)
The polynomial function f(x) is graphed below. Fill in the form below regarding the features of this graph.
Answer:
Step-by-step explanation:
degree 6 -- triple root, double root, single root
leading coefficient is negative -- it opens downward
3 distinct roots
3 relative extrema
divide (x3−8x2+2)÷(x−3)
Answer: -37
Step-by-step explanation:
standard: -13 -[tex]\frac{37}{x-3}[/tex]
quotient: -13
Remainder: -37
Answer:
[tex]x^{2} + \frac{-5x^{2} + 2}{x - 3}[/tex]
Step-by-step explanation:
Attached on file below.
1/2 ▾
8-10. Answer each multiple choice question to indicate which reason
corresponds to each missing statement in the 2 column proof (3
points).
Proof Diagram
A
Statements
1.2125 Given
Reasons
2.24 21 a
3.24 25 b.
4.pr
8. Choose the correct reason:
a. Linear Pair Postulate
C
b. Angle Addition Postulate
c. Vertical Angles Postulate
1 Pt
B
O Search the web
Given: 21 25
Prove: pr
*
9. Choose the correct reason:
a. Symmetric Property
b. Reflexive Property
c. Transitive property
1 Pt
hn
A
B
r
E
1) ∠4 ≅∠1
Vertically opposite angle
2) ∠4 ≅∠5
Alternate angle
Define angles.An angle is a figure in plane geometry that is created by two rays or lines that have a shared endpoint. The Latin word "angulus," which meaning "corner," is the source of the English term "angle." The shared terminus of two rays is known as the vertex, and the two rays are referred to as sides of an angle.
An acute angle is one that is smaller than 90 degrees. Right Angle: An angle with a 90 degree exactness. More than 90 degrees but less than 180 degrees is referred to as an obtuse angle. A straight angle is one that has a 180 degree angle. An angle that is more than 180 degrees but less than 360 degrees is called a reflex angle.
Given Data
∠1 ≅∠5
1) ∠4 ≅∠1
Vertically opposite angle
2) ∠4 ≅∠5
Alternate angle
3) p ║r
When a transversal cuts two lines so that the accompanying angles are congruent, the lines are said to be parallel. When a transversal cuts two lines so that their opposing interior angles coincide, the lines are said to be parallel.
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selected the ordered pair that represent solutions to the system of inequalities. A) (-6,3)B) (-3,3)C) (-5,0)D) (-4,2)E) (0,0)F) (-6,6)G) (-3,-6)H) (-4,0)PLEASE ANSWER FAST
To detremine the ordered pairs that represent the system of inequalities given, from the choices given, the corredct ordered pairs are:
(x, y) ==> (-6, 3), (-4, 2), (-6, 6), (-4, 0)
Prorate the following expenses and find the corresponding monthly expense.Lan pays a semiannual premium of $650 for automobile insurance, a monthly premium of $150 for health insurance, and an annual premium of $350 for life insurance.Question content area bottomThe monthly expense is $ (Round to the nearest cent as needed.)
Given:
Lan pays,
A semiannual premium of $650 for automobile insurance.
A monthly premium of $150 for health insurance.
An annual premium of $350 for life insurance.
To find:
The monthly expense.
Explanation:
According to the problem,
The amount paid for automobile insurance per year will be,
[tex]650\times2=1300[/tex]The amount paid for health insurance per year will be,
[tex]150\times12=1800[/tex]The amount paid for life insurance per year will be,
[tex]350\times1=350[/tex]The total expenses in a year are,
[tex]1300+1800+350=3450[/tex]So, the monthly expense is,
[tex]\frac{3450}{12}=\text{ \$}287.50[/tex]Therefore, the monthly expense is $287.50.
Final answer:
The monthly expense is $287.50.
Many bank accounts never go below zero. But some banks will allow a negative balance, at least for a short time, called an overdraft. It means someone has taken out, or 'drafted', more money than was in the account to begin with. Chloe's account went into overdraft. To get back to a positive balance, she deposited money at steady rate of $30.84 per week. After 3 weeks, she had $44.21 in the account. What was the balance when the account went into overdraft?
When the overdraft occurred, the balance was -48.31.
What happens if a bank account balance falls to zero?Major Takeaways. When your account balance drops below zero, you have an overdraft. If you have overdraft protection, your bank may permit a negative balance on your account or may provide one-time exceptions, but they may charge you for each transaction. Bank clients are required by federal regulations to choose to participate in overdraft protection schemes.
Let x represent the balance at the time the account entered overdraft.
He consistently made deposits totaling $30.84 a week in order to return to a positive balance.
Amount deposited per week = $30.84
Amount deposited 3 weeks = 30.84 × 3 = 92.52
Now amount in account after 3 weeks =x+ 92.52
We are given that After 3 weeks, he had $44.21 in the account.
So,x+92.52=44.21
x=44.21-92.52
x=-48.31
Hence The balance when the account went into overdraft was -48.31
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What is the value of y when x is 4/5 ?
According to the direct variation model, the value of the variable y is the mixed number [tex]3 \frac {1}{5}[/tex]. (Correct choice: C)
What is the value of a variable according to a direct variation model?If a variable y varies directly with the variable x, then we can derive the following relationship to find the missing value:
y₁ / x₁ = y₂ / x₂
Where:
x₁, x₂ - Value of the variable x.y₁, y₂ - Value of the variable y.If we know that x₁ = 3 / 5, y₁ = [tex]2 \frac{2}{5}[/tex] and x₂ = 4 / 5, then the value of y₂ is:
y₁ = 2 + 2 / 5 = 12 / 5
y₂ = (y₁ / x₁) · x₂
y₂ = [(12 / 5) / (3 / 5)] · (4 / 5)
y₂ = (12 / 3) · (4 / 5)
y₂ = 4 · (4 / 5)
y₂ = 16 / 5
y₂ = 15 / 5 + 1 / 5
y₂ = 3 + 1 / 5
y₂ = [tex]3 \frac{1}{5}[/tex]
The value of the missing variable is the mixed number [tex]3 \frac{1}{5}[/tex].
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