Answer:
the technical number depends on what you are including to be algebraic identities.
There are multiple forms of most identities (pos. / neg. and multiple ways of writing the same identity)
generally, you can consider there to be 10
Step-by-step explanation:
algebraic identity: an equality that holds true for any variable values
standard identities:
square of binomial:
(a+b)² = a² +2ab + b²
(a - b)² = a² - 2ab + b²
difference of squares:
(a + b)(a - b) = a² - b²
----
product of two binomials:
(x + a)(x + b) = x² + (a + b)x + ab
square of trinomial:
(x + y + z)² = x² + y² + z² + 2xy + 2yz + 2zx
(x - y - z)² = x² + y² + z² -2(xy + yz - zx)
cube of binomial:
(x + y)³ = x³ + y³ + 3xy (x + y)
(x - y)³ = x³ + y³ - 3xy (x - y)
(a - b)³ = a³ - 3a²b + 3ab² - b³
sum of cubes:
a³ + b³ = (a + b)(a² - ab + b²)
x³ + y³ = (x + y)(x² - xy + y²)
x³ + y³ = (x - y)(x² + xy + y²)
difference of cubes:
a³ - b³ = (a - b)(a² + ab + b²)
x³ - y³ = (x - y)³ + 3xy(x - y)
--
x³ + y³ + z³ - 3xyz = (x + y + z)(x² + y² + z² - xy - yz - zx)
= 1/2 (x + y + z) [(x -y)² + (y - z)² + (z - x)²]
(a + b + c)³ = a³ + b³ + c³ + 3(a + b)(b + c)(c + a)
--
and
if x + y + z = 0, then x³ + y³ + z³ = 3xyz
hope this helps!!
(this took me a while to write; there are also a few complicated identities also that I've left out)
[tex]( {a + b})^{2} = {a}^{2} + {b}^{2} + 2ab \\ \\ {(a - b)}^{2} = {a}^{2} + {b}^{2} - 2ab \\ \\ {a}^{2} - {b}^{2} = (a + b)(a - b) \\ \\ {a + b + c}^{2} = {a}^{2} + {b}^{2} + {c}^{2} + 2ab + 2bc + 2ca \\ \\ {a + b}^{3} = {a}^{3} + {b}^{3} + 3ab(a + b) \\ \\ {a - b}^{3} = {a}^{3} - {b}^{3} - 3ab(a - b) \\ \\ {a}^{3} + {b}^{3} + {c}^{3} - 3abc = (a + b + c)( {a}^{2} + {b}^{2} + {c}^{2} - ab - bc - ca).[/tex]
In 2005, an area vocational school had an enrollment of 325 men and 123 women. In 2006, there were 149 women. What was the percent increase of women students? Your final answer should be rounded to the nearest whole percent.
The percent increase of women students is 21.13%.
Given that, an area vocational school had an enrollment of 325 men and 123 women.
What is percentage?Percentage is defined as a given part or amount in every hundred. It is a fraction with 100 as the denominator and is represented by the symbol "%".
In 2006, there were 149 women.
Percentage increase = (New value - original value)/Original value × 100
= (149-123)/123 × 100
= 26/123 × 100
= 21.13%
Therefore, the percent increase of women students is 21.13%.
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Which of the following linear equations represents the data chart?
X Y
1 6
2 5
3 4
4 3
y=x+5
y=x+3
y = -x + 7
None of these choices are correct.
Answer: y = -x + 7
Step-by-step explanation:
The slope is [tex]\frac{5-6}{2-1}=-1[/tex], so we know the equation is of the form [tex]y=-x+b[/tex].
Substituting in the coordinates (1,6) to find b,
[tex]6=-1+b\\\\b=7[/tex]
Thus, the equation is y = -x + 7
If x/3 = 5/6 , then x =
Answer:
x = 5/2
Step-by-step explanation:
Given that,
[tex] \cfrac{x}{3} = \cfrac{5}{6} [/tex]
x = ?Solution:
Multiplying using criss-cross method;
[tex]x \times 6 = 5 \times 3[/tex][tex]6x = 15[/tex]Divide both sides by 6;
[tex] \cfrac{6x}6 = \cfrac{ \cancel{15} {}^{5} }{ \cancel6 {}^{2} } [/tex][tex]x = \cfrac{5}{2} [/tex]Done!
Hence x = 5/2.
Answer:
x = 2.5
Step-by-step explanation:
x = 3*(5/6)
Which graph represents the function
there are 2 more graphs but it won't add it
Answer:
[tex]f(x) = 9x^2+9x - 18/3x + 6\\= 9(x^2 + x - 2)/3(x+2)\\= 3(x^2+x-2)/x+2\\= 3(x+2)(x-1)/x+2\\= 3x - 3[/tex]
so y = 3x - 3
since 3x + 6 is on the bottom,
[tex]3x + 6\neq 0\\3x\neq -6\\x\neq -2[/tex]
so this means it should be the graph of y = 3x - 3, but with a hole at (-2, -9)
If m∠1 = 72º, then find the value of m∠2. vertical angles
If the angle 1 and angle 2 are vertical angles, hence they must be equal to each other, therefore m∠1 = m∠2 = 72º
What are vertical angles?Angles angle are angles that are equal to equal to each other in a line geometry.
Given the following parameters
m∠1 = 72º,
If the angle 1 and angle 2 are vertical angles, hence they must be equal to each other, therefore m∠1 = m∠2 = 72º
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Help !! I’ll mark brainliest !!
Answer:
9
Step-by-step explanation:
The opposite sides of a parallelogram are congruent.
Answer:
9
Step-by-step explanation:
Parallel sides are always equal. :)
Quadratic Functions graph
Answer:
y=-x^2-4x-1
Step-by-step explanation:
when it is an arch like an upside down U then its
-x^2
it passes through the y axis at -1
its vertex or high point is -2,3 so its
-4x
Answer:
See below
Step-by-step explanation:
Dome shaped parabola so 'a' is negative
'c' is determined where x = 0
this value is -1
Axis of symmetry is the x value of the vertex (which is the high point of the dome)
x = -2
A doctor's office schedules appointments in 30-minute time slots. All appointments are 30 minutes long. The office is open 8 hours per day, 5 days a week. How many appointments can they schedule, in total, for Thursday and Friday?
URGENT: Click on the graph to choose the correct answer to the equation. x > 2
The graph of x >2 is attached below
Clearly, the graph of x> 2 could be area beyond 2 on positive X axis
What is graph?
The graph is a demonstration of curves which gives the relationship between x and y axis.
The question seems to be incomplete, because options are missing.
so the option can be of several graphs.
Thus, The correct Graph of x >2 has been attached below.
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82% of what number is 94.3
Answer:
let the no. be X
82% of X = 94.3
82/100 *X = 94.2
X = 94.2 *100/82
X = 94.2/0.82
X = 114.8
Answer:
115
Step-by-step explanation:
82% = 82/10 = 0.82
94.3 / 0.82 = 115
Hope this helps
Which table shows a proportional relationship between x and y
Table second represents the proportional relationship between x and y the answer is the second table.
What is a proportional relationship?It is defined as the relationship between two variables when the first variable increases, the second variable also increases according to the constant factor.
As we know,
The proportional relation can be expressed mathematically:
y ∝ x
y = kx
Here k is the constant of proportionality.
k = y/x
From table second:
k = 3/2 = 6/4 = 9/6
Thus, the table second represents the proportional relationship between x and y the answer is the second table.
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What is the ratio of the weight of two castings that weigh 32 lbs. and 38 lbs
Answer:
16 : 19
Step-by-step explanation:
Given weights of the two castings : 32 lbs and 38 lbs respectively.
Now,
Ratio of the weights of the two castings ;
= 32 : 38
= 16 : 19
32:38
16:19
Answer:
this is my answer
If the sides of a square are increased by 2 inches, the area becomes 25 squares inches. Find the length of sides of the original square.
You know that the sides of a square are increased by 2 inches: the expression should be written as (x+2)
The area is 25 square inches
The area of a square is s×s or s²
so it can be solved as:
(x+2)²=25
[tex](\sqrt{x+2})^{2} =\sqrt{25}[/tex]
x+2=5
x=3
The length of the original side is 3 inches
Hope it helps!
If the center of a circle is at (5,-7)
and its radius is 6, complete its
equation:
The equation is:
(x-5)^2+(y-(-7))^2=36
I hope it helps!
Answer: [tex]\boldsymbol{(x - 5)^2 + (y + 7)^2 = 36}[/tex]
=========================================
Work Shown:
[tex](h,k) = (5,-7) = \text{center}\\\\r = 6 = \text{radius}\\\\(x - h)^2 + (y - k)^2 = r^2\\\\(x - 5)^2 + (y - (-7))^2 = 6^2\\\\\boldsymbol{(x - 5)^2 + (y + 7)^2 = 36}\\\\[/tex]
Help please!!! I will give 20 points to the correct answer !!!
Answer:
-3 and -7
Step-by-step explanation:
Factors of 21: 1, 3, 7, 21
3 and 7 add up to 10, but what about -10? Well, -3 * -7 is also 21, and -3 + -7 gives you -10.
Brainliest, please :)
3. When using set builder notation, what does it mean to 'Define a set'?
Answer:
A set is a well-defined collection of distinct mathematical objects.
Select the correct answer from each drop-down menu.
Are these lines perpendicular, parallel, or neither based off their slopes?
6x - 2y = -2
y = 3x + 12
The __ of the slope is __ so the lines are __ .
From the slope, it is possible to classify the lines as parallel.
Linear FunctionA line can be represented by a linear function. The standard form for the linear equation is: ax+b , for example, y=2x+7. Where:
a= the slope
b=constant term that represents the y-intercept.
The lines are classified as parallel when they have the same slope. You will have perpendicular lines when one line is the negative reciprocal of the second line. If the lines intersect, none of the previous conditions presented are met.
The given equations are:
6x-2y=-2 (1)
y=3x+12 (2)
First, you should write the equation 1 in the standard form.
-2y=-6x-2
-y=-3x-1
y=3x+1
Therefore, the slope for equation 1 is m=3.
After that, you should indicate the slope for equation 2. Thus, m also is 3.
As, both equations present the same slope (m=3). The lines are parallel.
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Answer: The Product(?) of their slopes is 3, so the lines are parallel
Step-by-step explanation:
summary of what the other person said
What is the domain of f(x) = 5x – 7?
{x | x > –7}
{x | x < –7}
{x | x > 0}
{x | x is a real number}
Answer:
all real number {x | x is a real number}
Drag each number to a box on the right to match each expression on the left with its product.
0.832 added to
Expression Product
83.2 × 0.1
832
8.32 × 102
8.32
83.2 × 102
8,320
832 × 0.001
0.832
The match has done below:
What is expression?An expression is a set of terms combined using the operations +, – , x or , /.
83.2*0.1= 8.32
8.32 × 102=848.64
83.2*102=8486.4
832 × 0.001=0.832
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2015-{2015÷5(x-5)÷5}=2014
Answer:
x=80.8
Step-by-step explanation:
follow BODMAS
2015-(2015÷5(x-5)÷5)=2014
2015-(2015÷5x-25÷5)=2014
2015-(405/x-5)=2014
2015-(405-5x)=2014
2015-405+5x=2014
1610+5x=2014
5x=2014-1610
(5x=404)1/5
x=80.8
Translate and solve using proportions what percent of 120 is15
Answer:
12.5%
Step-by-step explanation:
To find what percent of 120 15 is, we must find what 15/120 is.
15/120 = 0.125. To convert to a percent, we move the decimal two places to the right. So, the answer is 12.5%.
Brainliest, please :)
Answer:
12.5%
Step-by-step explanation:
Find the area of the following triangle. Round your answers to the nearest hundredth. b = 0.923 km, c = 0.387 km, A = 43.333°
O 0.26 km²
O 0.358 km²
O 0.06 km²
O 0.12km ²
Which of the following is the standard equation of the ellipse with vertices at (1, 0) and (11, 0) and an eccentricity of three fifths question mark
quantity x minus 6 end quantity squared over 100 plus y squared over 64 equals 1
quantity x plus 6 end quantity squared over 64 plus y squared over 100 equals 1
quantity x plus 6 end quantity squared over 16 plus y squared over 25 equals 1
quantity x minus 6 end quantity squared over 25 plus y squared over 16 equals 1
The equation fourth represents the ellipse that has vertices at (1, 0) and (11, 0), and an eccentricity of 3/5 option fourth is correct.
What is an ellipse?An ellipse is a locus of a point that moves in a plane such that the sum of its distances from the two points called focus adds up to a constant. It is taken from the cone by cutting it at an angle.
We have:
The vertices of the ellipse = (1, 0) and (11, 0)
Eccentricity of ellipse = 3/5
We have equations:
[tex]\rm \dfrac{\left(x-6\right)^{2}}{100}+\dfrac{y^{2}}{64}=1[/tex]
[tex]\rm \dfrac{\left(x+6\right)^{2}}{64}+\dfrac{y^{2}}{100}=1[/tex]
[tex]\rm \dfrac{\left(x+6\right)^{2}}{16}+\dfrac{y^{2}}{25}=1[/tex]
[tex]\rm \dfrac{\left(x-6\right)^{2}}{25}+\dfrac{y^{2}}{16}=1[/tex]
From the fourth equation:
The vertices of the ellipse:
(1, 0) and (11, 0)
The eccentricity:
c² = a² - b²
c² = 25-16
c = 3
e = c/a = 3/5
Thus, the equation fourth represents the ellipse that has vertices at (1, 0) and (11, 0), and an eccentricity of 3/5 option fourth is correct.
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The total cost of a tie and a pair of pants was $87.18. If the price of the tie was $2.12 less than the pair of pants, what was the price of the tie? Express your answer as a simplified fraction or a decimal rounded to two places.
work hours
frequency
0 - <10
45
10 - <20
33
20 - <30
20
30 - <40
7
40 - <50
8
Use your calculator to find the mean and standard deviation
The mean and the standard deviation are 16.15 and 12.03, respectively
How to determine the mean and the standard deviation?The table of values is given as:
Work hours Frequency
0 - <10 45
10 - <20 33
20 - <30 20
30 - <40 7
40 - <50 8
Start by rewriting the table using the midpoint of each class
x f
5 45
15 33
25 20
35 7
45 8
The mean is then calculated as:
[tex]\bar x = \frac{\sum fx}{\sum f}[/tex]
This gives
[tex]\bar x = \frac{5 * 45 + 15 * 33 + 25 * 20 35 * 7 + 45 * 8}{45 + 33 + 20 + 7 + 8}[/tex]
Evaluate the sum and the products
[tex]\bar x = \frac{1825}{113}[/tex]
Divide
[tex]\bar x = 16.15[/tex]
The standard deviation is:
[tex]\sigma =\sqrt{\frac{\sum f(x - \bar x)^2}{\sum f}}[/tex]
This gives
[tex]\sigma= \sqrt{\frac{45 * (5 - 16.15)^2 + 33 * (15 - 16.15)^2 + 20 * (25 - 16.15)^2 + 7 * (35 - 16.15)^2 + 8 * (45 - 16.15)^2 }{45 + 33 + 20 + 7 + 8}}[/tex]
Evaluate the sum and the products
[tex]\sigma= \sqrt{\frac{16350.4425}{113}}[/tex]
Divide
[tex]\sigma= \sqrt{144.694181416}[/tex]
Take the square root
[tex]\sigma= 12.03[/tex]
Hence, the mean and the standard deviation are 16.15 and 12.03, respectively
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Which products result in a difference of squares? Select three options. a (x minus y)(y minus x) b (6 minus y)(6 minus y) c (3 + x z)(negative 3 + x z) d (y squared minus x y)(y squared + x y) e (64 y squared + x squared)(negative x squared + 64 y squared)
Answer:
By comparing all the expressions with the formula (a - b)(a + b) = (a² - b²), we find that c, d and e options are correct.
Step-by-step explanation:
Concept: The condition is that, the product should result in a difference of squares. In mathematics, we have such a formula which is (a - b)(a + b) = (a² - b²). So, we need to compare all the options with this relation.
(x - y)(y - x) = -(x² - 2xy + y²)
(6 - y)(6 - y) = 36 - 12y + y²
(3 + xz)(-3 + xz) = (xz + 3)(xz - 3) = x²z² - 9 . This expression is correct
(y² - xy)(y² + xy) = [tex]y^{4} - x^{2} y^{2}[/tex]. This expression is correct
(64y² + x²)(-x² + 64y²) = (64y² + x²)(64y² - x²) = [tex]4096y^{4} -x^{4}[/tex]. This expression is correct.
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rewrite each pair of fractions to have the same denominator 1/3 and 1/4
Answer:
1/3 and 1/4
multiplying 1/3 by 1/4 and 1/4 by 1/3 we get
1/3 * 1/4
1 *1 /3*4
1/12
1/4 * 1/3
1*1 / 4*3
1/12
now, both have same denominator.
Use a calculator to graph the functions y=-3x-21 and y=x³-3x-3. How many points of intersection do the
functions share?
0
1
2
3
Answer:
1
Step-by-step explanation:
When you graph the functions they intersect at one point
(-3.368119, -31.10436)
Henry knows that the circumstance of a circle is 18pi inches. What is the area of the circle?
a. 36pi in²
b. 81pi in²
c. 162pi in²
d. 324pi in²
-------------------------------------------------------------------------------------------------------------
Answer: [tex]\textsf{Option B, 81}\pi\textsf{ in}^2[/tex]
-------------------------------------------------------------------------------------------------------------
Given: [tex]\textsf{Circumference = 18}\pi[/tex]
Find: [tex]\textsf{The area of the circle}[/tex]
Solution: We need to first determine the radius using the circumference formula and once we get the radius then we can plug in the value into the area formula and get our final answer.
Determine the radius
[tex]c = 2 \pi * r[/tex][tex]18\pi = 2 \pi * r[/tex][tex]\frac{18\pi}{2\pi} = \frac{2 \pi}{2\pi} * r[/tex][tex]\frac{18\pi}{2\pi} = r[/tex][tex]9 = r[/tex]Determine the area
[tex]A = \pi * r^2[/tex][tex]A = \pi * (9)^2[/tex][tex]A = \pi * (9 * 9)[/tex][tex]A = 81\pi[/tex]Therefore, the correct answer would be option B, 81π in2.
Tim go to school.His age is a cube number.His age is double 1 square number and half a different square number.How old is Tim?
Answer:
Tim is 8 years old.
Explanation:
8 is the cube number of 2, as 2 × 2 × 2 = 8. Additionally, 8 is double 4, which is the square number of 2, and half of 16, which is the square number of 4.
Tim who goes to school is 8 years old.
Why numerical ability is important ?Good numerical ability describes your ability to think and conclude logical thoughts in your daily life also in your working role how you handle data in form of numbers, graphs, statements etc.
According to the given question Tim goes to school.
His age is a cube number let that number be x therefore age of Tim would be x³.
His age can also be defined as double of 1 square number which is 2x² and half of a different square of a numbers.
Let us equate x³ = 2x² and by hit and trial we get to know that x = 2 satisfies this condition.
So, Age of Tim could be 8 years,Now lets check our third statement half a different square number 16 is square of 4 so half of 16 is also 8.
Thus Tim is 8 years old.
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