The equation a²-4=0, which corresponds to the factorization of a²-4= (a+ 2)(a-2)
What is Factorization?Factorization refers to the process of breaking down a mathematical expression into simpler parts that can be multiplied together to give the original expression. For example, factorizing the expression x² + 4x - 12 would give (x - 3)(x + 4) as the factors.
In algebra, factorization is used to simplify expressions and to find the solutions of equations. For example, in the quadratic equation ax² + bx + c = 0, the first step in solving the equation is to factorize the quadratic expression ax² + bx + c. Once this is done, it becomes easier to find the solutions of the equation by setting each factor equal to zero and solving for x.
Factorization can also be used to simplify expressions in other branches of mathematics, such as number theory. For example, the prime factorization of a composite number is the representation of that number as a product of prime numbers.
Given:
The equation a²-4= (a+ 2)(a-2) is a factorization of a quadratic expression. It states that the expression a²-4 can be represented as the product of two binomials, (a+ 2) and (a-2).
This can be visualized as the graph of a parabola, where the x-intercepts of the parabola are -2 and 2. These are the solutions of the equation a²-4=0, which corresponds to the factorization of a²-4= (a+ 2)(a-2)
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What is the value FG?
FG is not a defined term, so there is no way to determine its value.
FG is not a defined term, so there is no way to determine its value. This means that we cannot assign a numerical or other value to it. In order to determine the value of FG, we would first need to identify the context in which it is being used, as different contexts may assign different meanings to the same term. Once the context has been established, we can then look up the definition of FG in order to understand what it means in that particular context, and then assign a value to it accordingly. For example, if FG stands for "Frequency Generator" in a physics context, then it would likely have a numerical value associated with it.
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O conjunto A é formado pelos números inteiros maiores que -5 e menores que 8. Marque a alternativa que representa esse conjunto
Alguém sabe a resposta dessas 2 questão?
Answer:
A opção 2. Para um número ser maior que -5,basta ele está mais perto do 0,na reta numérica.
Espero ter lhe ajudado!
Mhanifa please help! This is due tomorrow
Answer:
Use Pythagorean to confirm:
a² + b² = c²#43.1² + 1.6² = 12.173.4² = 11.5612.17 ≠ 11.56No#5√7² + (2√3)² = 7 + 12 = 19√19² = 1919 = 19Yes#636² + 15² = 152139² = 15211521 = 1521Yesthe perimeter of the trapezoid is 18x +18 find the missing length of the lower base
PLEASE HURRY
Answer:
Step-by-step explanation:
8x+18=2x+x+4x-3
8x+18=7x-3
perimeter = x+21
Graph the line with slope -8 and y-intercept 9.
Answer:
the coordinates will be (0,9) (-8,0) and the equation will be y=(9/8x)+9
Step-by-step explanation:
Im not 100% sure but if im right please mark me as brainliest
suppose you and three friends are each dealt 13 cards from a shuffled deck, and you observe that you were dealt a single ace; what is then the probably that your three friends also each have an ace
The probability of each of your three friends having an ace is 32%.
The probability of each of your three friends having an ace is calculated using the Binomial Probability Formula. The formula is P(x) = nCr * p^x * (1-p)^(n-x). Here, n = 13 (number of cards dealt to each person) , r = 1 (number of aces you want to calculate the probability of), p = 4/52 (probability of getting an ace from a deck of 52 cards) and x = 1 (number of aces each of your three friends have).
Therefore, the probability of each of your three friends having an ace is P(x) = 13C1 * (4/52)^1 * (48/52)^(13-1) = 0.32.
This means that the probability of each of your three friends having an ace is 32%.
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HELPPP 1. Write an equation of the ellipse with foci (0,14) and co-vertices at (±4,0).
The equation of the ellipse with foci (0,14) and co-vertices at (±4,0) is [tex]x^2/16+y^2/36[/tex].
Define ellipse.An ellipse is a geometric shape that is defined as the set of points such that the sum of the distances between the points and two fixed points (foci) is constant. It is a type of conic section and is defined by the equation:
[tex](x^2/a^2) + (y^2/b^2) = 1[/tex]
Where a and b are the semi-major and semi-minor axes, respectively. An ellipse can also be defined as the shape that results from the intersection of a plane and a cone at an angle that is not perpendicular to the base of the cone.
[tex]c=14, b=4, a²=b²+c²== > a=2√9\\x^2/b^2 + y^2/a^2\\x^2/16+y^2/36[/tex]
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HELP PLZ PLZ PLZZZZ I WILL MARK BRAINLYLIESF!!!!!!
Answer:
150.8
Step-by-step explanation:
The formula for soving cylinder is V=Bh or V=πr2hmso if you plug that in you should get this answer like I did.
Helppp please!!!!!!!!!!!
Answer:
C.
Step-by-step explanation:
If y=-3, then you substitute -3 into the equation every place that there is y, making it 4+(-3)/4(-3). This simplifies into 4-3/-12 which is 1/-12 or -1/12
In a class of 48 students, 24 of them do Arts, 22 do Chemistry and 20 do Biology. All the students do at least one of the three subjects. 3 do all three subjects while 4 do Arts and Biology only, 3 do Arts and Chemistry only and 5 do Chemistry and Biology only. Find the number of numbers of students that do two subjects only exactly one subject at least two of the subjects Represent the information on a complete Venn diagram.
Number of students that do two subjects are 12.
Number of students that do only exactly one subject are;
For Art;
⇒ 14
For Chemistry;
⇒ 11
For Bio;
⇒ 8
Number of students that do at least two of the subjects are 15.
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
In a class of 48 students, 24 of them do Arts, 22 do Chemistry and 20 do Biology.
All the students do at least one of the three subjects.
3 do all three subjects while 4 do Arts and Biology only, 3 do Arts and Chemistry only and 5 do Chemistry and Biology only.
Here,
Total students = 48
So, Number of students that do two subjects are = 4 + 3 + 5
= 12
And, Number of students that do only exactly one subject are;
For Art;
⇒ 24 - (3 + 4 + 3)
⇒ 14
For Chemistry;
⇒ 22 - (3 + 5 + 3)
⇒ 11
For Bio;
⇒ 20 - (3 + 4 + 5)
⇒ 8
Number of students that do at least two of the subjects are;
⇒ 3 + 3 + 4 + 5
⇒ 15
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In the right triangle below b = 18 and c = 20, solve for a in simplified radical form.
Answer:
a = 2 radical 19
Step-by-step explanation:
a^2 + 18^2 = 20^2
a^2 + 324 = 400
subtract 324 from both sides
a^2 = 76
square root both sides
a = radical 76
simplify radical to get 2 radical 19
PLEASE HELP! :/
The work of a student to solve the equation 4(3x − 4) = 8 + 4x + 8 is shown below:
Step 1. 4(3x − 4) = 8 + 4x + 8
Step 2. 7x − 8 = 16 + 4x
Step 3. 7x − 4x = 16 + 8
Step 4. 3x = 24
Step 5. x = 8
In which step did the student first make an error and what is the correct step?
A. Step 2, 12x − 16 = 16 + 4x
B. Step 2, 12x − 8 = 2(4 + 2x + 4)
C. Step 3, 7x − 4x = 16 − 8
D. Step 3, 7x + 4x = 16 + 8
Answer:
A
Step-by-step explanation:
4 times 3 and-4 is 12x and -16 not 7 and -8.
Please I need the 3 of them
The following operations are used to transform the quadratic equation y = x² into parabolas in standard form:
Case 1
Horizontal translation, vertical translation. Horizontal stretch.
Case 2
Horizontal translation, vertical translation. Reflection in the x-axis, vertical stretch.
Case 3
Horizontal translation, vertical translation. Horizontal stretch.
How to determine the magnitude of horizontal and vertical translations for quadratic equations
In this question we find three cases of parabolas in standard form, that is, quadratic equations of the form:
y - k = a · (x - h)²
Where:
a - Vertex constant(h, k) - Coordinates of the vertex.This parabola is translated both horizontally and vertically by using the following definitions:
Horizontal translation
x → x - a, where a > 0 for rightward translation.
Vertical translation
y → y - b, where b > 0 for upward translation.
Horizontal dilation
f(x) → f(k · x), where k is a non-negative real number.
Vertical dilation
f(x) → k · f(x), where k is a non-negative real number.
Reflection in the x-axis
f(x) → - f(x)
The procedure is summarize below:
Write the original function, that is, the equation of the parabola with vertex at origin.Apply dilation, translation and reflection definitions.Finally, we summarize the procedure for each case:
Case 1
g(x) = x²
g(x) = [(1 / 2) · x²]
g(x) + 4 = [(1 / 2) · (x - 2)]²
Horizontal shift: 2 units right, vertical shift: 4 units down. Horizontal stretch.
Case 2
f(x) = x²
f(x) = - (1 / 2) · x²
f(x) - 2 = - (1 / 2) · (x - 4)²
Horizontal shift: 4 units right, vertical shift: 2 units down. Reflection in the x-axis, vertical stretch.
Case 3
h(x) = x²
h(x) = 2 · x²
h(x) - 5 = [2 · (x + 2)]²
Horizontal shift: 2 units left, vertical shift: 5 units up. Horizontal stretch.
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Condense the following logarithmic expression.
2 ln(x) + 5 ln(y) - 7 ln(z) - In (5)
Answer:
Answer:
ln(x²y⁵/(5z⁷))
Step-by-step explanation:
You want to condense the logarithmic expression 2 ln(x) + 5 ln(y) - 7 ln(z) - In (5).
Rules of logarithmsThe relevant rules of logarithms are ...
a·ln(b) = ln(b^a)
ln(ab) = ln(a) +ln(b)
ln(a/b) = ln(a) -ln(b)
Application[tex]2\ln{(x)}+5\ln{(y)}-7\ln{(z)}-\ln{(5)}=\boxed{\ln\left(\dfrac{x^2y^5}{5z^7}\right)}[/tex]
Jasmine has $26 to spend on binders and one pack of pens. The pack of pens costs $4. 75. Each binder costs $5. Write an inequality to determine the maximum number of binders she can buy, (Define your variable. )
Jasmine can buy a average of 4 binders because the cost of the binders, multiplied by the number of binders she wants to buy, plus the cost of the pens, must not exceed her total budget of $26.
Step 1: Define the variable. Let x represent the number of binders Jasmine can buy.
Step 2: Write the inequality. 5x + 4.75 ≤ 26
Step 3: Solve the inequality. 5x ≤ 21.25
Step 4: Isolate the variable. x ≤ 4.25
Step 5: The maximum number of binders Jasmine can buy is 4.
Let x represent the number of binders Jasmine can buy
5x + 4.75 ≤ 26
5x ≤ 21.25
x ≤ 4.25
Jasmine has a total of $26 to spend on binders and one pack of pens. The cost of the pens is $4.75, and each binder costs $5. To determine the maximum number of binders she can buy. The inequality we need to solve is 5x + 4.75 ≤ 26. We can solve this inequality by first multiplying both sides of the equation by 5, which gives us 5x ≤ 21.25. We can then isolate the variable by dividing both sides of the equation by 5, which gives us x ≤ 4.25. This means that the maximum number of binders Jasmine can buy is 4.
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Plz, solve the question below! 20 pts!
Answer:
your answer would be c.
hope this helps (ツ)
Angle J and Angle M are base angles of isosceles trapezoid JKLM. If angle j= 23x+5, and angle m = 13x+15 , find measure k .
The angle K for the Isosceles trapezoid is a supplementary angle to the angle J and the measure of angle K = 152°
What is an Isosceles trapezoidThis is a trapezoid in which the base angles are equal and therefore the left and right side lengths are also equal. The opposite angles are supplementary which implies they sum up to 180°.
angle J and angle M are base angles for the Isosceles trapezoid and are equal, so:
23x + 5 = 13x + 15
23x - 13x = 15 - 5 {collect like terms}
10x = 10 {divide through by 10}
x = 1
angle J = 23(1) + 5 = 28°
Angle K and angle J are supplementary so:
K = 180 - 28
K = 152°
Therefore, the measure of the angle K for the Isosceles trapezoid JKLM is equal to 152°
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Please help!! I don't get it!
Answer:
64 times 7.5 and you will get your answer
Step-by-step explanation:
16*4=64
64*7.5=x
x is what you need to find
You are playing a game in which you randomly select one square tile and one round tile from the sets shown below. Before you select your tiles, you try to guess which combination you will pick.
20 green square tiles, 9 red square tiles, 16 pink square tiles, 10 yellow square tiles, 5 blue square tiles.Circle tiles: 5 purple, 6 orange, 10 blue, 1 white, 2 yellow, 4 red, 5 black, 3 green.
Of the four possible guesses listed below, which one will give you the greatest chance of success?
a.
green square tile and red round tile
b.
pink square tile and orange or yellow round tile
c.
red or blue square tile and black or green round tile
d.
blue square tile and blue or purple or white round tile
Answer:
b
Step-by-step explanation:
From the four possible guesses listed below, for the Terrence the highest chance of success is selecting black or pink square tile and blue or green round tile.
What is chain rule in probability?In probability theory, the chain rule describes how to calculate the probability of the intersection of, not necessarily independent, events or the joint distribution of random variables respectively, using conditional probabilities.
For two events A and B, by chain rule, we have:
P(A∩B) = P(B) P(A|B) = P(A) P(B|A)
Here P(A|B) is probability of occurrence of A given that B already occurred.
here, we have,
Terrence is playing a game in which he will randomly select one square tile and one round tile from the tile sets shown below.
Before he does so, he tries to guess which tiles he will draw.
Square tiles: 12 blue, 20 yellow, 8 red, 6 green, 4 pink, 5 black, 3 brown, 2 white, total 60.
Round tiles: 9 black, 4 green, 3 yellow, 2 white, 6 blue, 12 red, total 36.
Here, the event of choosing round tile and square tile is independent to each other.
a. black or pink square tile and blue or green round tile
The chance of black or pink square tile and blue or green round tile is,
P_1 = 0.65
b. yellow square tile and yellow round tile
The chance of yellow square tile and yellow round tile is,
P_2 = 0.42
c. green, brown, or white square tile and black or white round tile
The chance of green, brown, or white square tile and black or white round tile is,
P_3 = 0.49
d. red square tile and red or white round tile
The chance of red square tile and red or white round tile is,
P_4 = 0.52
Thus, from the four possible guesses listed below, for the Terrence the highest chance of success is selecting black or pink square tile and blue or green round tile.
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Is the y-intercept 0 or 1?
Coordinate (0,1) of y-intercept implies that a line or curve cross the Y axis
at 1.
What is y-intercept?
The location of a point on the cartesian coordinate plane where a straight line or curve line as well as a plane crosses the Y axis is called Y-intercept. The coordinate of y-intercept is expressed as (0, y). This y value is y-intercept. The X coordinate of y intercept is zero.
In case of an equation of line while writing in slope-intercept form it is denoted by b such as y = mx+ b
in the above equation, b is y-intercept and m is the slope.
What means y-intercept (0, 1)?The y -intercept given by coordinate (0, 1) defines that a straight-line or curve line cross the Y axis at 1. The x coordinate of y -intercept is always zero because over the Y axis there is no value of X.
The y-intercept can have negative or positive value.
Suppose we have an equation of line 4x + 8y + 10 = 0
we will write it in a slope-intercept form
8y = -4x - 10
y = - 4x/8 - 10/8
y = -1/2x - 5/4
In the above equation - 5/4 or -1.25 is the y-intercept that means the line crosses the Y-axis at -1.25
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can someone please help meee
Answer:
(-7,1)
Step-by-step explanation:
The vertex of a parabola is the maximum or minimum point on the graph. On this point, the maximum is at (-7,1).
Reduce 22/154
to its lowest form.
22/154=11/77=1/7
1/7 is the lowest form
What is the circumference of a
circle with a radius of 2.09 in
Answer:
The circumference formula is C=3.14d
Step-by-step explanation:
To find the diameter with the radius you need to multiply 2.09 x 2.
Now you have 4.18, this is your diameter, you're now going to multiply 4.18 with pi, which is typically 3.14, if it's not that it's 22/7.
Your answer would be 13.12
Which values of h make the relation {(-2,3), (4,7), (9, h)} a function?
Answer:
h can be any value.
Step-by-step explanation:
As long as each input as exactly one output, the value of h does not matter.
Find the volume of the pyramid. Write your answer as a fraction or mixed number. ft3
Answer:
Volume of pyramid = [tex]1\frac{1}{3}[/tex] feet³
Step-by-step explanation:
Given:
Length of base = 2 feet
Width of base = 1 feet
Height of pyramid = 2 feet
Find:
Volume of pyramid
Computation:
Area of base = Length x Width
Area of base = 2 x 1
Area of base = 2 feet²
Volume of pyramid = (1/3)(A)(h)
Volume of pyramid = (1/3)(2)(2)
Volume of pyramid = (1/3)(4)
Volume of pyramid = 4/3
Volume of pyramid = [tex]1\frac{1}{3}[/tex] feet³
Ron's car uses 12 L of gasoline per 100 km of highway driving. Asma's car as 5/6 as much fuel. How much fuel does Asma's car use per 100 km of highway driving?
10L fuel does Asma's car use per 100 km of highway driving
In this question, we have to use the unitary method
The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.
What is a unitary in math?
a unitary state. (mathematics, of an algebra) That contains an identity element. (mathematics, linear algebra, mathematical analysis, of a matrix or operator) Whose inverse is equal to its adjoint.
So from the unitary method, we can solve it
12 L of gasoline per 100 km
so for 5/6
12 L * 5/6
= 10 L
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Reggie made a scale drawing of a house. In real life, the garage is 3 meters wide. It is 6 millimeters wide in the drawing. What is the drawing's scale factor?
Answer:
1:50
Step-by-step explanation:
The drawing's scale factor is
1:50
Explanation:
In drawing, width of the garage is 6 cm and in actual width of the garage is 3m or 3×100=300 cm.
Hence, the drawing's scale factor is 6:300 and dividing by 6, it is 1:50
what is k if 1 1/3k=1/3
Answer: k = 11
Step-by-step explanation:
[tex]\frac{11}{3k} = \frac{1}{3} \\\\[/tex]
Cross multiply:
[tex]11 * 3 = 1*3k[/tex]
[tex]33 = 3k[/tex]
[tex]k = 11[/tex]
the length breadth and height of a cuboid are in the ratio 7:5:2 its volume is 35840cm³
[tex] \longmapsto \: 7x + 5x + 2x = 35820 \\ \\ x = \frac{35840}{14} = 2560[/tex] length equals to 7 into 2560 = 1792
Mrs. Campos is making cupcakes for a bake sale. She uses the equation c = 0. 55x to determine the cost, c, for x cupcakes. Which best represents the constant rate at which cupcakes are sold at the bake sale?
55 cupcakes per dollar
$0. 55 per cupcake
$4 per cupcake
4 cupcakes per dollar
Best represents the constant rate at which cupcakes are sold at the bake sale $0. 55 per cupcake
Mrs. Campos is making cupcakes for a bake sale. She uses the equation c = 0. 55x to determine the cost, c, for x cupcakes. Which best represents the constant rate at which cupcakes are sold at the bake sale?
55 cupcakes per dollar
$0. 55 per cupcake
$4 per cupcake
c = 0. 55x
to determine the cost, c,
for x cupcakes.
CASE 1
55 cupcakes per dollar
therefor x = 55
c = 0. 55x
c = 0. 55 × 55
= 30.25
case2
$0. 55 per cupcake
x = 1
c = 0. 55x
c = 0. 55 × 1
= 0. 55
case 3
$4 per cupcake
x = 1
c = 0. 55x
c = 0. 55 × 1
= 0. 55
therefor conclusion is best represents the constant rate at which cupcakes are sold at the bake sale $0. 55 per cupcake
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