SOLUTION
From the question,
We have that the equation of the line is 5x + 2y = 9.
2y = - 5 x + 9
Divide both sides by 2, we have :
y = 1/ 2 ( -5x + 9 )
The slope of this line = -5 / 2
12. Check for Reasonableness Which of the quotients are equivalent to 2.5? Select all that apply.
10/-4
10/4
-10/-4
-5/-2
-5/2
5/2
HURRY Find all solutions to the equation 3x3 + 12x = 2x2 + 8.
Negative 2, negative two-thirds, 2.
Negative 2, two-thirds, 2.
Negative two-thirds, negative 2 i, 2 i.
Two-thirds, negative 2 i, 2 i.
4
Step-by-step explanation:
3×3+12x=2×2+8
9+12x=4+8
9+12x=12
12x=12-9
12x=3
x=4Find the value of x that makes line u parallel to line v
Answer:
x = 10
Step-by-step explanation:
the angles shown are corresponding angles
corresponding angles are equal
12x - 4 = 10x + 16
subtract 10x from both sides
2x - 4 = 16
add 4 to both sides
2x = 20
divide both sides by 2
x = 10
A party planner organized a dinner party. The party planner recorded the height of the candlesticks over time and graphed the relationship.
graph with the x axis labeled time in hours and the y axis labeled height of candlestick in inches and a line going from the point 0 comma 9 through the point 2 comma 6
Find and interpret the slope and y-intercept in this real-world situation.
The slope is negative two thirds, and the y-intercept is 9. The candle starts at a height of 9 inches and decreases two thirds of an inch every hour.
The slope is negative three halves, and the y-intercept is 9. The candle starts at a height of 9 inches and decreases three halves of an inch every hour.
The slope is 9, and the y-intercept is negative two thirds. The candle starts at a height of two thirds of an inch and decreases 9 inches every hour.
The slope is 9, and the y-intercept is negative three halves. The candle starts at a height of three halves of an inch and decreases 9 inches every hour.
The Slope of the line is 3/2 and the y-intercept is at (0,3)
Each solution in the two-variable scenario can be thought of as the Cartesian coordinates of a specific point on the Euclidean plane.
Each line in the Euclidean plane that is defined by a solution to a linear equation can be thought of as the sum of all solutions to a linear model with two variables.This is how equations in this class came to be referred to be "linear." A hyperplane of size n in Euclidean space is made up of all the solutions to an equation system with integer variables (a subdomain of dimension n1).The usage of linear equations is widespread throughout all fields of mathematics, physics, and engineering because they can commonly properly represent non-linear systems.The graph of the line passes through (0,9) and (2,6) .
Slope of the line = (6-9)÷(2-0) = 3/2
Hence the line will have the equation:
y - 6 = 3/2 ( x - 2 )
or, 2y - 12 = 3x - 6
or, 2y - 3x = 6
Now from the real world situation at y = 0, x = - 2
and at x = 0, y = 3
Hence the y-intercept is at (0,3)
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Answer:
A : The slope is negative two thirds, and the y-intercept is 9. The candle starts at a height of 9 inches and decreases two thirds of an inch every hour.
Step-by-step explanation:
I took the quiz and it was right
To keep Paul Senior from blowing a gasket, Paul Junior must deviate from the ideal area of the disk, which is 1000 in2, by less than ±4 in2. How close to the ideal radius must the Flowjet (the machine that cuts the disk) be to maintain tranquility at OCC? Use 3 significant figures to report your answer.
The area of a circle with radius r is given by the formula:
[tex]A=\pi r^2[/tex]If we change the value of r by a small amount Δr, the new value of the area will be:
[tex]\begin{gathered} A+\Delta A=\pi(r+\Delta r)^2 \\ =\pi(r^2+2r\Delta r+\Delta r^2) \end{gathered}[/tex]We can neglect the term Δr^2 since we are assuming that Δr is a very small quantity. Then:
[tex]A+\Delta A=\pi r^2+2\pi r\Delta r[/tex]Substitute A=πr^2 and isolate Δr from the equation:
[tex]\begin{gathered} \Rightarrow\pi r^2+\Delta A=\pi r^2+2\pi r\Delta r \\ \Rightarrow\Delta A=2\pi r\Delta r \\ \Rightarrow\Delta r=\frac{\Delta A}{2\pi r} \end{gathered}[/tex]Assuming that the ideal area of the disk is 1000in^2, calculate the ideal radius of the disk:
[tex]\begin{gathered} A=\pi r^2 \\ \Rightarrow r^2=\frac{A}{\pi} \\ \Rightarrow r=\sqrt[]{\frac{A}{\pi}} \\ \Rightarrow r=\sqrt[]{\frac{1000in^2}{\pi}} \\ \Rightarrow r=17.84124116\ldots in \end{gathered}[/tex]Substitute the value of r as well as the variation on the value of the area ΔA=4in^2 to find the variation in the value of the radius:
[tex]\begin{gathered} \Delta r=\frac{4in^2}{2\pi(17.84124116\ldots in)} \\ =0.03568248232\ldots in \end{gathered}[/tex]Up to 3 significant figures, the variation in the value of the radius must be less than:
[tex]0.0357in[/tex]If a triangle’s original dimensions are 24 cm by 40 cm, which triangle would be an enlargement of the original by a scale factor of 2.2?
The triangle’s enlargement dimensions will be 52.8 cm by 80 cm.
What is scale factor?The size by which the shape is enlarged or reduced is called as its scale factor.
Scale factor is defined as the number or the conversion factor which is used to change the size of a figure without changing its shape.
It is used to increase or decrease the size of an object.
The scale factor can be calculated if the dimensions of the original figure and the dimensions of the dilated (increased or decreased) figure are known.
For example, a rectangle has a length of 5 units and a width of 2 units. Now, if we increase the size of this rectangle by a scale factor of 2, the sides will become 10 units and 4 units, respectively. Hence, we can use the scale factor to get the dimensions of the changed figures.
Given:
A triangle’s original dimensions are 24 cm by 40 cm
scale factor=2.2
Thus,
enlarged dimensions= scale factor x original dimensions
[2.2] x 24 = 52.8 cm
[2.2] x 40 = 80 cm
Hence, the triangle’s enlargement dimensions will be 52.8 cm by 80 cm.
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find the value of 2/5 of 3 3/4 kg
Answer:
1.5
Step-by-step explanation:
2/5 of 15/4
1 of 3/2
1 1/2
1.5
Delaney's internet provider charges $14.95 per month plus $5.75 for each gigabyte of data she stores in the cloud a. write an equation to model the cost per month for the situation b. what will the dalneys bill for January be if she stores 8 gigabytes of data in the cloud that Month ?
Answer: (I know this is not college work, but whatever.) [tex]y=14.95x+5.75[/tex] is the answer.
One of the members of staff from the software organisation travels to Birmingham on a business trip. She pays for her ticket with three crisp £25 notes at the ticket office and is given £10.50 in change. Assuming that she bought a return ticket and that each leg of the journey cost the same amount, how much was one leg of the journey?
The cost of the one leg of the journey is 32.25 pounds.
Given that:-
Number of 25 pounds notes given by the member of staff travelling to Birmingham = 3
Change given to her = 10.50 pounds
It is assumed that she bought the return ticket as well and that each leg of the journey cost the same amount.
We have to find the cost of one leg of the journey.
Let the cost of one leg of the journey be x pounds.
Hence, we can write,
2x + 10.50 = 25*3
2x + 10.50 = 75
2x = 75 -10.50
2x = 64.50
x = 64.50/2
x = 32.25 pounds.
Hence, the cost of one leg of the journey is 32.25 pounds.
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A yoga studio charges a $140 yearly fee for membership plus $15 for each class. What is the average total cost per class if a studio member takes 50 classes per year?
The Average total cost per class if a studio member takes 50 classes per year will be 17.8$
What are average?The average can be calculated by dividing the sum of observations by the number of observations.
Average = Sum of observations/the number of observations
Given that A yoga studio charges a $140 yearly fee for membership plus 15 dollars for each class.
Yearly charge = 140 $
Charge per class = 15 $
The Number of classes attended by; studio members per year = is 50
We want to find the average total cost per class for this member for a year.
The Total charge = Yearly charge + Number of classes attended x Charge per class
Total charge = 140 + 50 x 15
Total charge = 140 + 750
Total charge = 890$
Than the Average total cost per class =890/ 50
= 17.8
Therefore, the Average total cost per class, if a studio member takes 50 classes per year, will be 17.8$
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h, the points A(−5, 6), B(2, 6), C(2, -1) and D(-5, -1) are the vert of a square. what is the area of the square?
Answer:
so find dots, then count how many sections are beetween them, so you will find lenght of every side and use formula to find area(S=a²+b²).
What steps would you need to take to graph the function:
f(x)=-3x^3-6x^2+3x+6
Name any x-intercepts and y-intercepts in the graph of the function.
Describe the end behavior of the function.
For extra credit, draw a sketch of the function by hand or in Paint.
The x-intercepts in the graph are ( - 2, 0 ), ( 1, 0 ) and ( - 1, 0 ) and the y-intercepts of the graph is ( 0, 6). The graph of the function tends to infinity in the negative y-axis direction after intersecting the x-axis at ( 1, 0).
Consider the function,
f(x) = - 3x³ - 6x² + 3x + 6
To find the x-intercept of the function we substitute y = 0.
f(x) = y = - 3x³ - 6x² + 3x + 6
- 3x³ - 6x² + 3x + 6 = 0
3x³ + 6x² - 3x - 6 = 0
3x²( x + 2 ) - 3 ( x - 2) = 0
( x + 2 )( 3x² - 3) = 0
Therefore,
x = - 2 and;
3x² - 3 = 0
3x² = 3
x = ± 1
Hence, the x-intercepts are ( - 2, 0 ), ( 1, 0 ) and ( - 1, 0 ).
Now, the y-intercept will be when x = 0,
y = - 3x³ - 6x² + 3x + 6
y = - 3(0)³ - 6(0)² + 3(0) + 6
y = 6
Hence, the y-intercept is ( 0, 6).
The graph of the function intersects the x-axis at ( - 2, 0) and ( - 1, 0 ) and then intersects the y-axis at ( 0, 6) then after intersecting the x-axis at ( 1, 0 ) the graph tends to infinity in the negative x-axis direction.
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List the angles in order from the largest to the smallest for triangle ABC AB=14AC=15BC=16
Explanation
An image of triangle ABC can be seen below;
The largest angles are the angles with the longest sides. Therefore from largest to smallest we will have
[tex]\angle A,\angle B,\angle C[/tex]Answer: Option A
Find the value of x and y need answers right now
○ x=15,y=12
○ x=14,y=11
○ x=14,y=12
○ x=15y=11
find the exact perimeter of hexagon ABCDEF plotted below
Perimeter Hexagon = 31.99
perimeter Hexagon = AB+BC+CD+DE+EF+FA
AB= [tex]\sqrt{58[/tex] =7.61
BC = 5
CD = 6
DE = [tex]\sqrt{29}[/tex] =5.38
EF =7
FA= 1
∴ perimeter Hexagon = 31.99
What is hexagon?Hexagons are six-sided polygons in geometry. A hexagon is said to be a regular hexagon if all of its sides and angles have identical lengths. To put it another way, a regular hexagon's sides are congruent.The area of a hexagon is calculated using the formula Area = (33 s2)/2, where s is the length of one of the regular hexagon's sides. The area of a hexagon can also be calculated using the apothem by using the formula Area of hexagon = (1/2) a P, where an is the apothem's length and P is the hexagon's perimeter.To learn more about : Hexagon
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What equation would you set up to solve for X?
the expression (x-6)² is equivalent to (1) x² - 36(2) x² - 12x +36 (3) x² + 36(4) x² + 12x +36
the expression (x-6)² is equivalent to
(1) x² - 36
(2) x² - 12x +36
(3) x² + 36
(4) x² + 12x +36
______________________
(x-6)²= ( x - 6) ( x - 6)= x^2 -6x - 6x + 36 = x² - 12x +36
______________________
Do you have any questions regarding the solution?
The price of an item has been reduced by 30% . The original price was $90 . What is the price of the item now?
THE PRICE AT WHICH THW ITEM IS REDUCED BY IS 30% OF $90
[tex] \frac{30}{100} \times \frac{90}{1} \\ = \frac{3}{10} \times 90 = 27[/tex]
THE PRUCE U BEING REDICED BY $27
TO GET THE NEW PRICE OF THE ITEM WE SUBTRACT THE PRICE IT WAS REDUCED BY FROM THE ORIGINAL SELLING PRICE.
[tex] = 90 - 27 \\ = 63[/tex]
NOW THE NEW PRICE OF THE ITEM IS $63
Describe the first step you would take to solve the system of equations 8x + y = -16 and - 3x + y = -5 using elimination and justify your answer.
8x + y = -16
3x + y = -5
The first to take is to subtract the second equation from the first equation
This will eliminate the y-variable leaving you with jus x-variable
That is;
5x = -11
x = -11/5
Find the value
-2+5/3
Answer: [tex]\Large\boxed{-\frac{1}{3} }[/tex]
Step-by-step explanation:
Given expression
[tex]-2+\dfrac{5}{3}[/tex]
Convert into fraction form
[tex]=-\dfrac{2}{1} +\dfrac{5}{3}[/tex]
Multiply 3 on both the numerator and denominator of 2
[tex]=-\dfrac{2\times 3}{1\times 3} +\dfrac{5}{3}[/tex]
[tex]=-\dfrac{6}{3} +\dfrac{5}{3}[/tex]
Add the numerator
[tex]=\dfrac{-6+5}{3}[/tex]
Simplify by addition
[tex]=\Large\boxed{-\frac{1}{3} }[/tex]
Hope this helps!! :)
Please let me know if you have any questions
3. The ratio of the amount of food that my cat Jade eats
to the amount of food that my cat Poe eats is 3 : 2.
If Jade eats 6 ounces of food, how many ounces of
food will Poe eat? (Your answer should be a whole
number.)
Answer: 4
Step-by-step explanation:
6/? = 3/2
3 x 2 = 6
2 x 2 = 4
Therefore; 4
The ounces of food that Poe eat is 4 ounces.
What is Ratio?Ratio is defined as the relationship between two quantities where it tells how much one quantity is contained in the other.
The ratio of a and b is denoted as a : b.
Given that,
ratio of the amount of food that my cat Jade eats to the amount of food that my cat Poe eats is 3 : 2.
For some constant k,
Ounces of food Jade eat = 3k
Ounces of food Poe eat = 2k
Jade eats 6 ounces of food.
3k = 6
k = 6 / 3 = 2
Ounces of food that Poe eats = 2k = 2 × 2 = 4
Hence Poe eats 4 ounces of food if Jade eats 6 ounces of food.
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need help on #3
picture attached
A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. The variables in the preceding equation are y and x, and it is occasionally referred to as a "linear equation of two variables."
What is a formula for linear equations?A linear equation has the slope-intercept form y = mx + b. Variables in the equation are x and y. When x is 0, the integers m and b provide the line's slope (m) and the value of y. (b).
How is a linear equation solved?Linear Equation Solvingclear decimals or fractions.Remove parentheses from each side of the equation and combine similar phrases to make it simpler.Remove the variable term from the equation's other side.Divide each side of the equation to find the solution.Verify your response.What are examples of linear equations?Ax+By=C is the usual form for two-variable linear equations. A standard form linear equation is, for instance, 10x+14y=50. When an equation is given in this format, finding both intercepts is rather simple (x and y).
What do a simple equation and a linear equation mean?When an equation of the form an x + b = 0, where a, b Q and, it is said to have one variable and be linear. A simple equation is a linear equation with a single variable. The solution of the equation is the value of the variables that makes the equation true, i.e., makes L.H.S. equal to R.H.S.
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A contractor completed five-ninths of a job before a second contractor completed an additional one-third. What fraction of the job is left undone?
[tex]\frac{1}{9}[/tex] fraction of the job is left undone.
What is fraction?Any number of equal parts is expressed by a fraction, which also represents a portion of a whole. A fraction, such as one-half, eight-fifths, or three-quarters, represents how many components of a suitable size there are when stated in ordinary English. fraction, A number that is stated mathematically as a quotient, where the numerator and denominator are divided. Both are integers in a simple fraction. A fraction occurs in the numerator or denominator of a complex fraction. The numerator of a proper fraction is less than the denominator. a week ago.
Given Data
A contractor completed five-ninths of a job before a second contractor completed an additional one-third.
Total work done is 1.
Contractor and second contractor completed:
= [tex]\frac{5}{9}[/tex] + [tex]\frac{1}{3}[/tex]
= [tex]\frac{5+3}{9}[/tex]
= [tex]\frac{8}{9}[/tex]
Total work done = 1
Work left undone:
= 1 - [tex]\frac{8}{9}[/tex]
= [tex]\frac{1}{9}[/tex]
[tex]\frac{1}{9}[/tex] fraction of the job is left undone.
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186+2947•4194(3.486)x=?
The value of x for the given equation will be -4.3×10⁻⁶.
What is a linear equation?It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.
Arithmetic operation is used to find the value of x in which we do the addition of numbers, subtraction, multiplication, and division. It has basic four operators that are +, -, ×, and ÷.
It is given that,
186+2947•4194(3.486)x
x=-186/2947•4194(3.486)
x=-4.3×10⁻⁶.
Thus, the value of x for the given equation will be 4.3×10⁻⁶.
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Hi dear! Can you help me to solve exercise #18 please!!!
Hello there. To solve this question, we'll have to remember some properties about dividing polynomials.
Given the polynomials, we want to evaluate the division:
[tex](1+3x+x^4)\div(3-2x+x^2)[/tex]Rewriting it the way we perform long division:
We start with the higher degree terms, namely x^4 and x².
Dividing x^4 by x², we get x². Now we multiply every term from the division by this factor and subtract from the term being divided.
Now, we have a 2x³ as the higher degree term from the term being divided. Dividing it by x², we get 2x. Multiply each term of the divisor and subtract from it.
Finally, the highest degree term from the term being divided is x². Dividing it by x², we get 1. Multiply each term of the divisor and subtract it from the dividend.
Now, the highest degree term from the dividend is -x, when the highest degree term from the divisor is x². We cannot proceed with the long division anymore.
It means that we have a quotient:
[tex]x^2+2x+1[/tex]And a remainder:
[tex]-x-2[/tex]Notice if we rewrite it as:
[tex]x^4+3x^2+1=(x^2-2x+3)\cdot(x^2+2x+1)-x-2[/tex]We have the division P(x)/D(x) written in the form:
[tex]P(x)=D(x)\cdot Q(x)+R(x)[/tex]Where Q(x) and R(x) are the quotient and remainder polynomials.
Determine the end behavior of the graph of the function. f(x)=(x+7)(x-6)^2
Using limits, the end behavior of the function f(x) = (x + 7)(x - 6)² is given as follows:
lim x -> -∞ f(x) = -∞.lim x -> ∞ f(x) = ∞.How to find the end behavior of a function?To find the end behavior of a function f(x), we have to find the limits of f(x) as x goes both to negative infinity and to positive infinity.
For this problem, the function is given as follows:
f(x) = (x + 7)(x - 6)²
As x goes to infinity, we consider only the highest exponent of the function, hence:
f(x) = x³.
Then the limits that define the end behavior of the function are given as follows:
lim x -> -∞ f(x) = (-∞)³ = -∞. (negative number with odd exponent, keeps the negative).lim x -> ∞ f(x) = (∞)³ = ∞.More can be learned about limits and end behavior at https://brainly.com/question/27165263
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Please help I’ll mark you as brainliest if correct!!
Answer:
23 remainder 13
Step-by-step explanation:
18 goes into 427 23 times with a remainder of 13
Answer:
The quotient of 427 and 18, the ratio of 427 and 18, as well as the fraction of 427 and 18 all mean (almost) the same:
427 divided by 18, often written as 427/18.
The number 427 is called the numerator or dividend, and the number 18 is called the denominator or divisor.
Welcome to 427 divided by 18, our post which explains the division of four hundred and twenty-seven by eighteen to you.
Step-by-step explanation:
f(x)=3x^6+4x^3-2x^2+4find all possible zeroes
Solution:
Given the function below
[tex]f\mleft(x\mright)=3x^6+4x^3-2x^2+4[/tex]For teh possible roots;
[tex]\begin{gathered} a_0=4,\:a_n=3 \\ \mathrm{The\:dividers\:of\:}a_0:1,\:2,\:4 \\ \begin{equation*} \mathrm{The\:dividers\:of\:}a_n:1,\:3 \end{equation*} \\ \mathrm{The\:following\:rational\:numbers\:are\:candidate\:roots:}\pm\frac{1,\:2,\:4}{1,\:3} \end{gathered}[/tex]From the deduction above,
The possible rational roots is
[tex]±1,\pm\frac{1}{3}\pm2,\pm\frac{2}{3},\pm4,\pm\frac{4}{3}.[/tex]Hence, all the possible zeros is
[tex][/tex]The standard form for a parabola with vertex (h,k) and an axis of symmetry of y=k is:(y-k)^2=4p(x-h)The description below is for a parabola. Write it in standard form. When answering the questions type coordinates with parentheses and separated by a comma like this (x,y). If a value is a non-integer then type is a decimal rounded to the nearest hundredth.Vertex is (2,2); directrix is x=2-\sqrt[]{2}, focus is (2+\sqrt[]{2},2)The value for p is: AnswerThe value for h is: AnswerThe value for k is: Answer
Given that a parabola has
[tex]\begin{gathered} Vertexis(2,2) \\ directrix\text{ }is\text{ }x=2-\sqrt[]{2} \\ focus\text{ }is\text{ }(2+\sqrt[]{2},2) \end{gathered}[/tex]And that the standard form of a parabola can be expressed as
[tex]\mleft(y-k\mright)^2=4p\mleft(x-h\mright)[/tex]We are asked to find the value of p, h and k. This can be seen below.
Explanation
Recall, If a parabola has a horizontal axis, the standard form of the equation of the parabola is this
[tex](y-k)^2=4p(x-h)[/tex]where p≠ 0. The vertex of this parabola is at (h, k). The focus is at (h + p, k). The directrix is the line x = h - p. The axis is the line y = k. If p > 0, the parabola opens to the right, and if p < 0, the parabola opens to the left.
Value of h and k
By comparison
[tex]\begin{gathered} \text{Vetex = (h,k) = (2,2)} \\ \therefore h=2;k=2 \end{gathered}[/tex]Answer: h = 2 and k =2
Value of p
Also, by comparison
[tex]\begin{gathered} focus=(h+p,k)=(2+\sqrt[]{2},2) \\ \therefore p=\sqrt[]{2}=1.41 \\ \end{gathered}[/tex]Answer : p =1.41
Writing the equation of the parabola in standard form
We can then use the given data to express the parabola in standard form as;
Answer
[tex](y-2)^2=4\sqrt[]{2}(x-2)[/tex]In a relation, the input is the number of people and the output is the number
of backpacks.
Is this relation a function? Why or why not?
A. No, because you do not know how many people there are.
B. No, because the same number of people might have a different
number of backpacks.
C. Yes, because each person has one backpack.
D. Yes, because a given number of people always has the same
number of backpacks.
If input is number of people and output is number of backpack then it is not a relation because same person can have different number of backpacks.
When the input is the number of people an the output is the number of backpacks, it is not a relation,
The reason is, Because same number of people might have a different number of backpacks.
A function is a relation in which each and every input has an output, and each and every input has a unique output.
In this situation, it is not compulsory that each person carry a backpack.
Even if each an everyone does have a backpack. It is not sure that if one person has only one backpack or not.
So, it is not a relation.
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