The way to convert the vertex form to factored form is explained below.
The term vertex is defined as a special point of a mathematical object, and is usually a location where two or more lines or edges meet.
Here we have to write down the steps to convert the vertex form to factored form.
The very first steps is to expand the vertex form into standard quadratic form and then use the quadratic root formula to determine the roots.
Here as we all know that factored term is the product of a constant and two linear terms and they are the roots of the function.
So, now we have to use the quadratic formula to convert them into factor form.
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What is the solution of pair of equation 2x y 5 and 3x 2y 4?
The solution of the system of linear equations 2x + y = 5 and 3x - 2y = 4 is x = 2, y = 1.
To find the solution of the pair of equations, 2x + y = 5 and 3x - 2y = 4, we can use different methods.
You can use elimination method to solve the system of linear equations. The elimination method consists of eliminating one of the variables by adding or subtracting the equations.
Multiply the first equation by 3 and the second equation by 2.
6x + 3y = 15
6x - 4y = 8
Subtract second equation from first:
7y = 7
y = 1
Substitute this value of y in the first equation:
2x + (1) = 5
2x = 4
x = 2
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Explore Part 1
Complete the puzzle so that each row, column, and diagonal adds up to the same total.
Answer:
hope I'm right-
Step-by-step explanation:
first row: 0.3
second row: 0.2
last row: 0.1
in a year group of 113 student 60 liked hockey 45 liked rugby and 18 liked neither. calculate the number of students who liked both rugby and hockey
Answer: 10
Step-by-step explanation:
Total number of students = 113
we require to find the number of students who like both hockey and rugby.
number of students who like game = total number of students - students who doesn't like either one
= 113 - 18 = 95 = A ∪ B
So equation become
A ∪ B = A + B - A ∩ B
95 = 60 + 45 - A ∩ B
A ∩ B = 105-95 = 10.
Error Analysis Elijah says ABC and ADEF
are congruent by SAS. Explain Elijah's
error.
The error made by Elijah is ABC Triangle has one included angle between two sides but in triangle DEF Angle is not included between two sides, so that triangles is not similar .
What is side angle side congruent triangles?
If all three corresponding angles and all corresponding sides are equal, two triangles are said to be congruent.
Triangles are said to be congruent according to Side Angle Side if any pair of corresponding sides and their included angle are also congruent.
Here in given triangles ΔABC and ΔDEF,
The error made by Elijah is that for two triangles are congruent there must be two sides and one included angles are needed .
But in that case ABC Triangle has one included angle between two sides but in triangle DEF Angle is not included between two sides .
Hence the error made by Elijah is ABC Triangle has one included angle between two sides but in triangle DEF Angle is not included between two sides, so that triangles is not similar .
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the area of trapezoid abcd is 164 cm2 . the altitude is 8 cm, ab is 10 cm, and cd is 17 cm. what is bc, in centimeters?
The area of trapezoid abcd is 164 cm2 with an altitude is 8cm, ab is 10 cm, and cd is 17 cm and bc=10cm
The area of a trapezoid can be calculated if the length of its parallel sides and the distance between them are given. The formula for the area of a trapezoid is expressed as,
A = ½ (a + b) h
where (A) is the area of a trapezoid, 'a' and 'b' are the bases and 'h' is the height.
Given that Area of trapezoid A=164 and the altitude is 8 cm, ab is 10 cm, and cd is 17cm.
Substitute these values in the formula:
164=8(BC+AD)/2
8(BC+AD)=328
BC+AD=41
Drop perpendiculars from B to AD and from C to AD and let them hit AD at E and F respectively. Note that each of these perpendiculars has a length of 8.
From the Pythagorean Theorem, AE=6 and DF=15 thus AD=BC+21. Substituting back into our original equation we have
BC+BC+21=41
2BC=20
BC=10cm.
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Show ur step for x and Y
2
The solution to the system of equation y = 9x + 2 and 7y = 63x + 14 is x = -1 and y = -7
What is an equation?An equation is an expression showing the relationship between two or more numbers and variables. An equation can either be linear, quadratic, cubic and so on depending on the degree.
Given the equations:
y = 9x + 2
multiply the equation by 7:
7y = 63x + 14
-63x + 7y = 14 (1)
And:
-2x + 7y = -47 (2)
To solve by elimination method, subtract equation 2 from 1 to get:
-61x = 61
x = -1
Put x = -1 in the equation:
y = 9x + 2
y = 9(-1) + 2 = -9 + 2 = -7
The solution to the equation is x = -1 and y = -7
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Unit 4 homework 7 part 2
Please help
Therefore ,light of this, the solution to the triangle issue given is ABC, which is equivalent to XYZ.
Describe the triangle.A triangular is a polygon since it has number of sides and three vertices. This geometric form is essential. Triangle ABC is still a triangles whose corners are located at points A, B, then C. In geometric shapes, a single planar and triangle are produced when four components are not coherent. Due to their three sides and top right corner, triangles are included in polygons.
Here.
Given :
ABC and XYZ are the same, hence ∠ A = ∠ X.
∠ B and ∠ Y mean the same thing.
"∠ Z" = "∠ C," and
The value of line ab matches that of xy.
Both line bc and yz can be substituted.
XZ corresponds to line ac.
To come up with a solution, Cpct was used.
Triangle segments that match each other are congruent.
The solution to the triangle problem is ABC is equal with XYZ as a result.
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Is y-intercept always 1?
The Y intercept of a straight line is simply where the line crosses the Y axis. In the above diagram the line crosses the Y axis at 1. The Y intercept is equal to 1 and the point is written as (0,1). Notice that for the y-intercept the x-coordinate of the point is always zero
Now, According to the question:
Y-Intercepts:
An intercept is a point on the y-axis, through which the slope of the line passes. It is the y-coordinate of a point where a straight line or a curve intersects the y-axis. This is represented when we write the equation for a line, y = mx+c, where m is slope and c is the y-intercept.
Is the y-intercept 0 or 1?
The Y intercept of a straight line is simply where the line crosses the Y axis. In the above diagram the line crosses the Y axis at 1. The Y intercept is equal to 1 and the point is written as (0,1). Notice that for the y-intercept the x-coordinate of the point is always zero.
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-
Given ƒ(x) = 4x² – 4x – 20, find ƒ(10)
The value of function ƒ(10) is 340 if given ƒ(x) = 4x² – 4x – 20.
What is function?The concept of a function is used by mathematicians to describe a variety of operations, including addition and multiplication, transformations of geometric figures, relationships between variables, and many other things.
A function is a set of guidelines for matching things with one another. A function pairs the inputs with the outputs and has inputs and outputs. This pairing is subject to a crucial limitation: Each input can only be coupled with one output.
The value of x = 10
4x² – 4x – 20
Lets solve
ƒ(10) = 4(10)² – 4(10) – 20
ƒ(10) = 400 – 40 – 20
ƒ(10) = 340
Thus, The value of function ƒ(10) is 340 if given ƒ(x) = 4x² – 4x – 20.
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Solar system
Star cluster
Galaxy
Galaxy cluster
While both star clusters and galaxies are assumed to have formed simultaneously from a collapsing ball of gas as linear equation .
what is linear equation ?A linear equation is one that satisfies the algebraic formula y=mx+b. m is the y-intercept, while B is the slope. The foregoing sentence is sometimes referred to as a "linear equation with two variables" because y and x are variables. Bivariate linear equations are two-variable linear equations. Examples of linear equations include 2x - 3 = 0, 2y = 8, m + 1 = 0, x/2 = 3, x + y = 2, and 3x - y + z = 3.
Here,
Given:
Both contain stars that are held together by gravity. Part of the Local Group of galaxies is the Milky Way galaxy, which houses our solar system.
The Milky Way, the Magellanic Clouds (big and small), and the Andromeda Galaxy are the largest. The average galaxy is also bigger than a star cluster. The cities where star clusters reside are like galaxies, according to Geller.
"Galaxies can contain thousands or more star clusters, numerous molecular clouds, dark matter, and other things," the author writes.
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The complete question is "Establish a linear equation between the following Solar system, Star cluster, Galaxy and Galaxy cluster. "
What is the equation of the line shown in the graph?
Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse.
Drag and drop the expressions to write the equation of the line in slope-intercept form.
The given line passes through points (0,4) and (-2,0) . So firstly we can find the slope of the line as ,
[tex]\longrightarrow m =\dfrac{y_2-y_1}{x_2-x_1}\\ [/tex]
[tex]\longrightarrow m =\dfrac{4-0}{0-(-2)}\\ [/tex]
[tex]\longrightarrow m =\dfrac{4}{2}\\ [/tex]
[tex]\longrightarrow m = 2 [/tex]
Now we may use point slope form of the line as ,
[tex]\longrightarrow y - y_1 = m(x-x_1)\\ [/tex]
[tex]\longrightarrow y - 4 = 2(x-0)\\ [/tex]
[tex]\longrightarrow y -4 = 2x \\ [/tex]
[tex]\longrightarrow \underline{\underline{ y = 2x +4}}[/tex]
And we are done!
Answer:
The given line passes through points (0,4) and (-2,0) . So firstly we can find the slope of the line as ,
Now we may use point slope form of the line as ,
And we are done!
Step-by-step explanation:
Compare the rates to find which is greater
15 laps in 12 seconds or 12 laps in 10 seconds
Answer: 15 laps in 12 seconds
Step-by-step explanation:
15 divided by 12 is 5/4 which is also 1.25
12 divided by 10 is 6/5 which is also 1.2
1.25 is greater then 1.2
jordan created a scale drawing of the school cafeteria in his art class. In the scale drawing, the length of the cafeteria is 14 centimeters. the length of the actual cafeteria is 210 feet. what scale did jordan use to create the scale drawing of the school cafeteria? how many feet does 1 centimeter represent on the scale drawing?
The number of feet in 1 centimeter is 14 feet.
What is scale factor?A scale factor is defined as the ratio between the scale of a given original object and a new object, which is its representation but of a different size (bigger or smaller).
The basic formula to find the scale factor of a figure is expressed as,
Scale factor = Dimensions of the new shape ÷ Dimensions of the original shape.
Given that, in the scale drawing, the length of the cafeteria is 14 centimeters. the length of the actual cafeteria is 210 feet.
Here, 14 centimeters = 210 feet
1 centimeter =210/14 feet
1 centimeter =14 feet
Therefore, the number of feet in 1 centimeter is 14 feet.
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answer 5 please answer
the answer is 7x I'll save you some time by not explaining
Gradiant of line y= -3x - 2
X = - (y + 2)/3 dividing the difference in the -coordinates by the difference in the -coordinates is a gradient of line.
What is a line’s gradient?The gradient of a line is a measure of how steep a straight line is. A line’s gradient might be positive or negative and does not have to be a whole integer.
Y=-3x-2
Y+2=(-3x-2)+2
Y+2=-3x-2+2
Y+2=-3x
-3x= y +2
3x/3=-y+2/3
X = - (y + 2)/3
A line’s gradient is computed by dividing the difference in -coordinates by the difference in -coordinates. This is also known as the vertical divided by the horizontal, or the change in divided by the change in. Choose two points on the graph for a straight-line graph. Line gradient = (change in y-coordinate)/(change in x-coordinate). Of course, we can use this to determine the equation of the line. Because the line crosses the y-axis at y = 3, the graph’s equation is y = 12x + 3.
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if Josh were two years older than 25 times his current age ,he would be the age of his grandfather. If his grandfather is 77 years old, how old is Josh?
Answer: 3
Step-by-step explanation: 77 - 2 = 75, 75/25 = 3
what is the value of the expression 8c - d when c = -6 and d = -12
Answer: -36
Step-by-step explanation:
so when a variable and a number are together you multiply, 8 times c, c is found equal to -6, so 8 x -6 would be -48 so then its -48 minus d d is found equal to -12 so -48 minus -12 would equal -36 hope this helped ^^
A farmer wants to plant three rectangular fields so that the widths are the same. The areas of the fields, in square yards, are given by the expressions 10x2y, 6xy4 , and 14xy. What is the greatest possible width of the fields if x=3 and y=2
The greatest possible widths of the fields will be -
W₁ = 180/L₁ & W₂ = 288/L₂ & W₃ = 84/L₃
What are algebraic expressions?In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.Given is that a farmer wants to plant three rectangular fields so that the widths are the same. The areas of the fields, in square yards, are given by the expressions 10x²y, 6xy⁴ and 14xy.
Rectangle { 1 } -
L₁ x W₁ = 10x²y
W = 10x²y/L₁
If x = 3 and y = 2, we can write that -
W₁ = (10 x 9 x 2)/L₁
W₁ = 180/L₁
Rectangle { 2 } -
L₂ x W₂ = 6xy⁴
W₂ = 6xy⁴/L₂
If x = 3 and y = 2, we can write that -
W₂ = (6 x 3 x 16)/L₂
W₂ = 288/L₂
Rectangle { 3 } -
L₃ x W₃ = 14xy
W₃ = 14xy/L₃
If x = 3 and y = 2, we can write that -
W₃ = (14 x 3 x 2)/L₃
W₃ = 288/L₃
W₃ = 84/L₃
The greatest possible widths of the fields will be -
W₁ = 180/L₁ & W₂ = 288/L₂ & W₃ = 84/L₃
Therefore, the greatest possible widths of the fields will be -
W₁ = 180/L₁ & W₂ = 288/L₂ & W₃ = 84/L₃.
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Eighteen of susans muffins weigh the same as 15 of Toms muffins. How many of susans muffins weigh the same as 7 of Toms muffins
8.4 of Susan's muffins weigh the same as 7 of Tom's muffins.
We can begin solving the problem by using the proportion:
(18 muffins) / (15 muffins) = (x muffins) / (7 muffins)
where x represents the number of Susan's muffins that weigh the same as 7 of Tom's muffins. To solve for x, we can cross-multiply and then divide:
18 muffins * 7 muffins = 15 muffins * x
x = (18 * 7) / 15
x = 8.4
Therefore, 8.4 of Susan's muffins weigh the same as 7 of Tom's muffins.
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If a=2³x3, b=2x3x5, c-3"x5 and LCM [a,b,c] = 2x32x5 then, n=?
Answer:
Step-by-step explanation:
The lowest number that is a multiple of two or more numbers is known as the least common multiple (LCM). To calculate the LCM of a, b, and c, we must first determine the greatest power of each prime number that appears in any of the integers.
Assume a = 23x3, b = 2x3x5, and c = 32x5.
As a result, the LCM of a, b, and c is 23x32x5.
Given that the LCM [a,b,c] = 2x32x5,
So, n= 2x3²x5
n=180
The angle from a point on the ground to the top of a 168-foot tower is 30 degrees. About how long is a wire that reaches from the top of the tower to the point on the ground
The wire that connects the top of the tower to the point of the ground is thus the hypotenuse and its length is 84 foot.
What are trigonometric ratios?Trigonometric ratios are based on the value of the ratio of sides of a right-angled triangle and contain the values of all trigonometric functions. The trigonometric ratios of a given acute angle are the ratios of the sides of a right-angled triangle with respect to that angle.
Given that the height of the tower is 168 foot, and the angle is 30 degrees.
The wire that connects the top of the tower to the point of the ground is thus the hypotenuse.
To find the hypotenuse, we use the trigonometric ratios as follows:
Sin 30 = 168 / Hypotenuse
0.5 = 168 / Hypotenuse
Hypotenuse = (168)(0.5)
Hypotenuse = 84.
Hence, the wire that connects the top of the tower to the point of the ground is thus the hypotenuse and its length is 84 foot.
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Draw a line of best fit for the
graph.
Based on the line your drew,
what is the likely test score of a
student who does not study for
the test?
Half of the data points, or a straight line, are on either side of a line of best fit.
What is meant by straight line?A line is a geometric object that is defined as being straight, thin, one-dimensional, zero width, and extending in both directions to infinity. An uncurved line is simply what a straight line is. We can also state that every line that connects any two specific places on the same plane will be distinct.
A student who doesn't study for the test is expected to receive a test score of 38, according to this line of best fit.
It is equivalent to doing no homework to not study for an exam (doing homework is considered studying).
Half of the data points, or a straight line, are on either side of a line of best fit.
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Solve for j
A = 4 j k
Answer:[tex]a=4jk\\isolate J: divide 4 and k\\= \frac{a}{4k} =J[/tex]
Step-by-step explanation:
Answer:
[tex]a = 4jk \\ akj = a \\ \frac{akj}{4k} \: = \frac{a}{ak} \\ j = \frac{a}{4k} \\ [/tex]
Here ur ans.
By:- Utsav Xettri
What is the HCF of the polynomials x6 3x 3x² 1 and x³ 3x² 3x 1?
The HCF of the polynomials x6 - 3x4 + 3x2 - 1 and x3 + 3x2 + 3x + 1 as calculated from the data given is found to be as (x + 1)3.
We will solve the given functions, to get their HCF.
f(x) = x6 - 3x4 + 3x2 - 1
⇒ x6 - x4 - 2x4 + 2x2 + x2 - 1
⇒ x4(x2 - 1) - 2x2(x2 - 1) +1(x2 + 1)
⇒ (x2 - 1)(x4 - 2x2 + 1)
⇒ (x + 1)(x - 1)(x4 - 2x2 + 1)
⇒ (x + 1)(x - 1)(x2 - 1)2
⇒ (x + 1) (x - 1) (x + 1)2 (x - 1)2
⇒ (x + 1)3(x - 1)3
Similarly ,
g(x) = (x + 1)3
Therefore,
The HCF of f(x) and g(x) is the common factor of equations obtained by solving these functions which is , (x + 1)3.
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What value of x is in the solution set of 3 x 4 ⥠5x 2?
The value of x in the solution set of 3x 4 ⥠5x 2 is x = -2.
3x 4 ⥠5x 2
3x 4 - 5x 2 = 0
3x - 5x = -2
-2x = -2
x = -2
The solution set of 3x 4 ⥠5x 2 is the set of all values of x that when substituted into the equation, make it true. To find the value of x, we must start by rearranging the equation to make the variable x the subject, or the thing that we are trying to find. To do this, we subtract 3x 4 from both sides of the equation, leaving us with 5x 2 = 0. We then subtract 5x from both sides of the equation, leaving us with -2x = -2. To solve for x, we divide both sides of the equation by -2, which gives us the answer x = -2. Therefore, the value of x in the solution set of 3x 4 ⥠5x 2 is x = -2.
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A scale model of a house uses a scale 14
inch = 3 feet. If the model is 4.25
inches tall, what is the actual height of the
house?
Answer:
A scale model of a house uses a scale of 14 inches = 3 feet, this means that for every 14 inches in the model, it represents 3 feet in the actual house.
If the model is 4.25 inches tall, we can use this proportion to find the actual height of the house:
4.25 inches / 14 inches = x / 3 feet
To find the actual height of the house, we can cross-multiply and then divide:
(4.25 inches * 3 feet) / 14 inches = x
x = 1.5 feet
So the actual height of the house is 1.5 feet
Please Help me
Question
Which relation is a function?
Responses
{(1, −7), (2, −8), (−2, 7), (1, 8)}
{(−2, 1), (−7, −1), (2, 8), (−7, −8)}
{(−2, 2), (−7, 7), (−1, 1), (−8, 8)}
{(−2, 1), (−2, 2), (−2, 7), (−2, 8)}
{(−2, 2), (−7, 7), (−1, 1), (−8, 8)} it is a function as every input has a single output. Therefore, option C is the correct answer.
What are relations in Math?In math, a relation defines the relationship between sets of values of ordered pairs. The set of elements in the first set are called domain which is related to the set of the element in another set, which is called range.
A) {(1, −7), (2, −8), (−2, 7), (1, 8)}
Since the element 1 corresponds to two different images i.e., -7 and 8. So, this relation is not a function.
B) {(−2, 1), (−7, −1), (2, 8), (−7, −8)}
Since the element -7 corresponds to two different images i.e., -1 and -8. So, this relation is not a function.
C) {(−2, 2), (−7, 7), (−1, 1), (−8, 8)}
It is a function as every input has a single output.
So, -2, -7, -1 and -8 are the elements of the domain of the given relation.
D) {(−2, 1), (−2, 2), (−2, 7), (−2, 8)}
Since the element -2 corresponds to different images i.e., 1, 2, 7 and 8. So, this relation is not a function.
Therefore, option C is the correct answer.
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Kristine has $150 to spend on school clothes. The store is having a sale for 25% off, and Kristine has an additional coupon for 10% off her entire purchase. She wants to buy 3 shirts that cost $35 each, a pair of jeans for $40, and a pair of shoes that cost $70. Part A – Does she have enough money to make the purchase? Part B – How much money would she have left over after the purchase? Or, how much more money would she need to make the purchase?
A) Kristine have enough money to make the purchase.
B) She have left over $10.25 after the purchase.
What is Percentage?To determine the quantity or percentage of something in terms of 100, use the percentage formula. Per cent simply means one in a hundred. Using the percentage formula, a number between 0 and 1 can be expressed. A number that is expressed as a fraction of 100 is what it is. It is mostly used to compare and determine ratios and is represented by the symbol %.
Given:
Kristine has $150 to spend on school clothes.
The store is having a sale for 25% off.
Coupon= 10% off
So, Cost of three shirts = 3 x 35 = 105
Cost of pair of jeans = $40
Cost of pair of shoes = $70
So, She have to spend total = 105 + 40 + 70 = $215
After discount she have pay = 215 - 215 x 0.35
= $139.75
Thus, Kristine have enough money.
Now, She would left with = 150- 139.75 = $10.25.
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Divide:
7,448 + 6 =
submit
PO
Answer:
ffggggggggggytdcuihgr
Among all rectangles that have a perimeter of 174, find the dimensions of the one whose area is largest. White your answers as fractions reduced to the lowest terms
The rectangle of perimeter 174 unit that encloses the largest area is a square. [tex]\frac{87}{2}[/tex] unit on a side.
The perimeter of rectangle is 174, let the length of rectangle is x and the width of rectangle is y.
so, the perimeter of rectangle is.
Perimeter=2(x+y)
174=2(x+y)
x+y=87
y=87-x
now the area of rectangle is.
A=x × y
substitute value of y,
[tex]A=87x-x^2[/tex]
This is a quadratic equation whose graph is parabola. because the value of a is negative. the vertex is always located at the point x=-b/2a.
[tex]x=\frac{87}{2}[/tex] unit
[tex]y=87-\frac{87}{2}[/tex]
[tex]y=\frac{87}{2}[/tex]
the rectangle of perimeter 174 unit that encloses the maximum area is a square 87/2 unit on a side.
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