Discuss the history of algebra. Discuss some of the key developments in the field of algebra and discuss who the contributors were? Provide a timeline of these key developments 4 paragraphs plz i'll give branliest 50 points i need this plzz
History of algebra
Algebra can essentially be considered as doing computations similar to those of arithmetic but with non-numerical mathematical objects. However, until the 19th century, algebra consisted essentially of the theory of equations. For example, the fundamental theorem of algebra belongs to the theory of equations and is not, nowadays, considered as belonging to algebra (in fact, every proof must use the completeness of the real numbers, which is not an algebraic property).
This article describes the history of the theory of equations, called here "algebra", from the origins to the emergence of algebra as a separate area of mathematics.
You need to fence in a rectangular piece of land for your dog to run and play. The length is 3 times the width. If the perimeter is 120 ft, what are the dimensions of your very own dog park?
Answer:
Width = 15 feet
Length = 45 feet
Step-by-step explanation:
You need to fence in a rectangular piece of land for your dog to run and play. The length is 3 times the width. If the perimeter is 120 ft, what are the dimensions of your very own dog park?
Perimeter of a rectangle = 2L + 2W
The length is 3 times the width.
L = Length = 3W
W = Width
P = 120 ft
Hence:
120 = 2L + 2W
120 = 2(3W) + 2W
120 = 6W + 2W
120 = 8W
W = 120/8
W = 15 feet
Solving for Length
L = 3W
L = 3 × 15 feet
L = 45 feet
Therefore, the dimensions of your very own dog park is
Width = 15 feet
Length = 45 feet
plz help will give brainliest
CDE is reflected over the Y- Axis
Answer:
The answer to this question is A
The new coordinates will be C( 3 ,0), D( 7,1) , E(2,4) , Option A is the correct answer.
What is the meaning of Reflection ?When a object or a figure is reflected , it means an mirror image if the object is being created , the shape and size of the object remains same , Only the coordinates change on the basis of the axis used for Reflection.
The figure is given in the question.
The coordinates of the figure is
C( -3 ,0)
D( -7,1)
E(-2,4)
When reflection is done along any axis , the coordinates of the other axis change sign.
so in this case ( x,y ) -----> ( -x,y)
The new coordinates will be
C( 3 ,0)
D( 7,1)
E(2,4)
Therefore Option A is the correct answer.
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Solve each system by substitution y=-2
5x + 2y = 16
Answer:
the answer is 4
Step-by-step explanation:
5x=16+4
5x=20
X=4
Find the slope of the line that passes through (3, 11) and (10,8).
Answer:
-3/7
Step-by-step explanation:
Slope = [tex]\frac{y_{2}-y_{1}}{x_{2}-x_{1}}\\[/tex]
[tex]=\frac{8-11}{10-3}\\\\=\frac{-3}{7}\\[/tex]
Given: y= 2x + 1 and - 4x + y = 9,
solve the system by substitution
Answer:
x=-4 y=-7
Step-by-step explanation:
-4x+y=9 get y alone
add 4x both sides
y=4x+9
insert into y=2x+1
2x+1=4x+9
subtract 1 both sides
2x=4x+8
subtract 4x both sides
-2x=8
divide by -2
x=-4
y=2x+1
y=2(-4)+1
y=-8+1
y=-7
check
-4(-4)+(-7)=9
-16+(-7)=9
9=9
x=-4
y=-7
gl
Write an equation of the perpendicular bisector of the segment with endpoints
(−1, −5) and (3, −1).
HELP!!
Answer:
Step-by-step explanation:
Midpoint of line segment = (1,-3)
Slope of line segment = (-1-(-5))/(3-(-1)) = -3/2
Perpendicular bisector:
y+3 = ⅔(x-1)
y = ⅔x - 11/9
Determine the center and radius of the following circle equation: x² + y2 + 2x – 2y – 62 = 0
Step-by-step explanation:
x²+2x+y²-2y=62
using completing the square
x²+2x+1+y²-2y+1=62+1+1
(x+1)²+(y-1)²=64
(x+1)²+(y-1)²=8²
(x-a)²+(y-b)²=r²
by comparison
(a,b)=(-1,1)
a,b is the center of the circle
r=8unit
r is the radius
What is the equation for the axis of symmetry of the graph of this function?
F x = -3
G y = -3
H x = -5
J y = -5
Given ADE with AD= 5 centimeters, BD= 3 centimeters and DE= 10 centimeters
What is the length of BC?
A. 6 2/3 cm
B. 5 cm
C. 4 cm
D. 6 cm
Answer:
BC is 4
Step-by-step explanation:
Use a proportion to solve
AB is 2 (AD is 5 and BD is 3- so 5-3)
[tex]\frac{2}{x} = \frac{5}{10}[/tex]
[tex]5x=20\\x=4[/tex]
ANSWER QUICK BESTIES!! ty
Answer:
Option B
Step-by-step explanation:
Option A, C and D have x- values that repeat and you cannot have that.
Y values can repeat but not x-values.
Option B has all x values with different y-values
Answer:
B.
Step-by-step explanation:
an output can have more than one input but an input can only have one output
basically only one arrow can go from the input to the output and b is the only one who's graph thing is like that
hope this helps <3
20 is 80 percent of what number?
Answer:
20 is 80 of 25
Explanation:
20x10/8=25
A percentage is a way to describe a part of a whole. 20 is 80% of 25.
What are Percentages?A percentage is a way to describe a part of a whole. such as the fraction ¼ can be described as 0.25 which is equal to 25%.
To convert a fraction to a percentage, convert the fraction to decimal form and then multiply by 100 with the '%' symbol.
Let the number be x. Therefore, we can write,
80% of x = 20
0.80 × x = 20
x = 20/0.8
x = 25
Hence, 20 is 80% of 25.
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Which set of ordered pairs does not represent a function?
A\{(5, -1), (-3, -3), (8, 4), (4, -3)\}{(5,−1),(−3,−3),(8,4),(4,−3)}
B\{(-6, -7), (-3, -3), (-2, -8), (-6, 4)\}{(−6,−7),(−3,−3),(−2,−8),(−6,4)}
C\{(-2, 1), (-8, 0), (6, 7), (8, 7)\}{(−2,1),(−8,0),(6,7),(8,7)}
D\{(5, -3), (-6, 2), (-5, 3), (1, 2)\}{(5,−3),(−6,2),(−5,3),(1,2)}
Answer:
option B
Step-by-step explanation:
you cannot have one input and 2 outputs.
(-6,-7) and (-6,4), you have 2 Y for 1 X. therefore is not a fuction
Simplify
5т — п — 5п + 2
Answer:
5t-4n+2
Step-by-step explanation:
n-5n=-4n
5t-4n+2
Can Somebody help me real fast?
See attached an good explaination would be appreciated
Answer:
Y=X
Step-by-step explanation:
It depends on the context. No number besides 0 is given, so it can't really be the other ones with numbers.
identify 2 possible reasons for unemployment
Answer:
Pandemic, Loss In family
Step-by-step explanation:
The global pandemic has really hit small businesses and working Americans, which has caused millions of Americans to lose their jobs, but also small businesses to go out of business. Also during the pandemi, thousands of people have loved their loved ones to the pandemic, which can also lead to them not showing up to work, which could make the employed citize lose their job.
(Hope this helps)
Yours Truely, TheAnimeCatUwU
Given that sin 60° ≈ 0.866, write the
cosine of a complementary angle
Answer:
Step-by-step explanation:
Complement to 60° = 30°
cos(30°) = sin(60°) = 0.866
Answer:
0.866.
Step-by-step explanation:
We use the identity
sin x = cos (90-x)
So the cosine of the complementary angle is also 0.866.
The population of a certain bacteria doubles every 24 hours. How many times as great is the population after 5 days as the population was at the start?
Answer:
32 times as many bacteria after 5 days
Represente em uma reta numérica os conjuntos indicados abaixo (cada conjunto deve ser representado em uma reta numérica diferente). a) [1,2] [3, 17/2].
TURMA...
b) (-1, 1) U [1, +).
c) (-2, 3] n (3, 6).
d) [-3, -1) n -2, +0).
1.1
Consider the following pattern:
87; 84; 81 ...
1.1.1 Find an expression for the nth term of the
sequence
(3)
Answer:
The nth term of the arithmetic sequence is;
90 - 3n
Step-by-step explanation:
Here, we want to find an expression for the nth term of the sequence
Mathematically, let us determine the type of sequence
As we can see;
84 - 87 = 81-84 = -3
The difference between the terms is a constant; this means that the sequence is arithmetic
The nth term of an arithmetic sequence can be represented by;
Tn = a + (n-1)d
in this case, a is the first term of the sequence = 87
d is the common difference of the sequence = -3
The nth term is thus;
Tn = 87 + (n-1)-3
Tn = 87 - 3n + 3
Tn = 87 + 3 - 3n
Tn = 90 - 3n
Please answer correct its not 9 units
What is the probability that a number selected at random from interfere 3 to 30 inclusive is a multiple of 3
Answer:
5/14 is the probablity
byeeeeeeeeeeee
26x + 13y = 39
.
Rearrange this equation so it is in the form y = mx + b
After you have rearranged the equation, identify the slope and the y-intercept.
If x = 6, what should y =? Show all necessary work and steps. Round any decimals to
1 place as necessary.
If y = -1, what should x =? Show all necessary work and steps. Round any decimals
to 1 place as necessary.
Answer:
Rearrange: y=-2x+3
if x=6 then y = -9
if y=-1 then x = 2
Step-by-step explanation:
Algebra
to rearrange here are the steps
26x+13y=39
First move x to other side by subtraction
13y= -26x+39
to get y as just y divide everything by 13. Since 13/13=1 or 13y/13= y
y=-2x+3
are the ratios 4:1 and 20:5 equivalent? and if they are how are they equivalent and if they aren't why aren't they equivalent??!!
Answer:
They are equivalent.
Step-by-step explanation:
Please help me solve this!!!
V=1/3bh
Answer:
What?
Step-by-step explanation:
Okay, the formula, then what?
Answer:
the answer is v=bh/3
Step-by-step explanation:
I solve for V since you didn't put what letter you wanted the question to be solved for.
hope this helps.
Which set of measurements could not represent the side lengths of a right triangle?
A 16 ft, 30 ft, 34 ft
B 9 ft, 12 ft, 15 ft
C 7ft, 24 ft, 25 Ft
D 5ft. 7 ft, 12 ft
The set of measurements could not represent the side lengths of a right triangle is 5ft. 7 ft, 12 ft.
What is a right triangle?The right is a triangle with has one angle 90° and square of hypotenuse is equal to the sum of square of other two legs.
Given that, the set of measurements representing the side lengths of a right triangle,
We will check the measurements by seeing if they are following the Pythagoras theorem or not,
Option A)
16 ft, 30 ft, 34
16²+30² = 1156 = 34²
∴ 16²+30² = 34²
Option B)
9²+12² = 225 = 15²
9²+12² = 15²
Option C)
7²+24² = 625 = 25²
7²+24² = 25²
Option D)
5²+7² = 74 ≠ 12²
Since, 5ft. 7 ft, 12 ft set of measurements are not following the Pythagoras theorem.
Therefore, it's not a right triangle.
Hence, The set of measurements could not represent the side lengths of a right triangle is 5ft. 7 ft, 12 ft.
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PLZ PLZ PLZ PLZ HELP
Answer: -1/8 OR -0.125, -2^-3
Step-by-step explanation:
The first figure is dilated to form the second figure.
Which statement is true?
The scale factor is 0.4.
The scale factor is 0.9.
The scale factor is 2.1.
The scale factor is 2.5.
Answer:
The scale factor is 2.5
Step-by-step explanation:
took k-12 test
When a shape is dilated, the size of the shape changes
The true statement is (d) The scale factor is 2.5.
What is dilation?Dilation involves changing the size of a shape or figure
How to determine the scale factorIn figure A, we have:
Length = 0.6
In figure B, we have:
Length =1.5
The scale factor is then calculated as:
[tex]k = \frac{1.5}{0.6}[/tex]
Divide
[tex]k = 2.5[/tex]
Hence, the true statement is (d) The scale factor is 2.5.
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Given the point and its image, determine the scale factor. B(2,5) B'(1,2.5) 0 -1/2 02 0-2 O 1/2
Given:
The point is B(2,5) and its image is B'(1,2.5).
To find:
The scale factor.
Solution:
If a figure is dilated by the scale factor k and (0,0) is the center of then the scale factor is defined as
[tex]k=\dfrac{\text{x-coordinate of the point on image}}{\text{x-coordinate of the corresponding point on the original figure}}[/tex]
x-coordinate of point B' is 1 and the x-coordinate of point B is 2. So, the scale factor is
[tex]k=\dfrac{1}{2}[/tex]
Therefore, the scale factor is [tex]\dfrac{1}{2}[/tex] and the correct option is D.