Answer:
(x+2)(4x-1)
For this problem, use the FOIL (first, outside, inside, last) method
You have x, 2, 4x, and -1. Start by multiplying x by 4x and -1. Then multiply 2 by 4x and -1. You should have four separate values to add together.
(x*4x)+(x*(-1))+(2*4x)+(2*(-1)) = 4x^2+(-x)+8x+(-2)
Once you have this, order each value by their exponents and combine like terms. The highest exponents always go to the left and lowest exponents go to the right.
4x^2+7x-2
Add these fraction
1) 2/3 + 6/3
2) 4/6+9/6
3) 6/6+6/6
The values of (2/3 + 6/3), ( 4/6 + 9/6 ) and ( 6/6 + 6/6 ) are 8/3, 13/6 and 2 respectively.
What is the value of the addition operation?Given that;
1) 2/3 + 6/3
We combine the numerators over the common denominators
= ( 2 + 6 ) / 3
= 8/3
2) 4/6 + 9/6
We combine the numerators over the common denominators
= ( 4 + 9 ) / 6
= 13/6
3) 6/6 + 6/6
We combine the numerators over the common denominators
= ( 6 + 6 ) / 6
= 12/6
= 2
The values of (2/3 + 6/3), ( 4/6 + 9/6 ) and ( 6/6 + 6/6 ) are 8/3, 13/6 and 2 respectively.
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Write the trig form of the complex number
18i
The trigonometric form of the complex number given in the task content is; 18(isin(π/2)).
What is the trigonometric form of the complex number?If follows from the task content that the complex number whose trigonometric representation is to be determined is; 18i.
Hence, It follows that the trigonometric form is;
= 18(cos(π/2) + isin(π/2)). where; cos(π/2) = 0.
Hence, we have;
= 18(isin(π/2)).
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Evaluate the limit, lim x -> 0 (x * cos theta - theta * cos x)/(x - theta)
The limit of
[tex]$\lim _{x \rightarrow 0}\left(\frac{x \cos (\theta)-\theta \cos (x)}{x-\theta}\right)=1$$[/tex].
What are limits?In Mathematics, a limit exists described as a value that a function approaches the output for the provided input values. Limits exist necessary in calculus and mathematical analysis and exist utilized to determine integrals, derivatives, and continuity.
Given:
[tex]$\lim _{x \rightarrow 0}\left(\frac{x \cos (\theta)-\theta \cos (x)}{x-\theta}\right)$$[/tex]
Substitute the value x = 0, then we get
[tex]$=\frac{0 \cdot \cos (\theta)-\theta \cos (0)}{0-\theta}$$[/tex]
Simplify the above equation, we get
[tex]$\frac{0 \cdot \cos (\theta)-\theta \cos (0)}{0-\theta}= 1$[/tex]
Therefore, the limit of
[tex]$\lim _{x \rightarrow 0}\left(\frac{x \cos (\theta)-\theta \cos (x)}{x-\theta}\right)=1$$[/tex]
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need help on this problem
Using an exponential function, it is found that:
For Country A, the doubling time is of 43 years.For Country B, the growth rate is of 1.9% per year.What is the exponential function for population growth?The exponential function for population growth is given as follows:
[tex]P(t) = P(0)e^{kt}[/tex]
In which:
P(t) is the population after t years.P(0) is the initial population.k is the exponential growth rate, as a decimal.t is the time in years.For Country A, we have that k = 0.016. The doubling time is t for which P(t) = 2P(0), hence:
[tex]P(t) = P(0)e^{kt}[/tex]
[tex]2P(0) = P(0)e^{0.016t}[/tex]
[tex]e^{0.016t} = 2[/tex]
[tex]\ln{e^{0.016t}} = \ln{2}[/tex]
[tex]0.016t = \ln{2}[/tex]
[tex]t = \frac{\ln{2}}{0.016}[/tex]
t = 43 years.
For Country B, P(36) = 2P(0), hence we have to solve for k to find the growth rate.
[tex]P(t) = P(0)e^{kt}[/tex]
[tex]2P(0) = P(0)e^{36k}[/tex]
[tex]e^{36k} = 2[/tex]
[tex]\ln{e^{36k}} = \ln{2}[/tex]
[tex]36k = \ln{2}[/tex]
[tex]k = \frac{\ln{2}}{36}[/tex]
k = 0.019.
For Country B, the growth rate is of 1.9% per year.
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a company has six employees.The salary of five of the employees are P2200,P1300,P800,P940 and P560.When the sixth employee is included,the total monthly salaries of the employees becomes P7000.
Calculate the salary of the sixth employees
The company is joined by two more employees whose salaries are of equal amounts.The mean salary of all 8 employees is P1100
Calculate the monthly salary of each of the new employees
Answer:
First answer is 1200
Second answer is 900 for each new employee
Step-by-step explanation:
First answer:
2200+1300+800+940+560+x = 7000
5800+x = 7000 subtract 5800 from both sides and you get your answer
x = 1200
Second answer:
x = 900. Each of the two employees made 900 a month or 1800 a month for both of them.
To find the average we take the total salaries and divide by the number of people to find the average salary. In this case, we know the average and we know all of the salaries, but two. We can figure this out.
(7000 + 2x)/8 = 1100 multiple both sides by 8 to clear the fraction/
7000 +2x = 8800 Subtract both sides by 7000
2x = 1800 Divide both sides by 2
x = 900
will give brainliest
The equation of a hyperbola is [tex]x^{2}[/tex]/9 - [tex]y^{2}[/tex]/4 = 1
What are the steps to Hyperbola equation ?
To find the equation of hyperbola, the following steps must be taken. You need to identify;
The coordinate of the centerThe coordinate of the verticesThe coordinate of the fociThe general equation of a hyperbola can be expressed as
[tex]x^{2}[/tex]/[tex]a^{2}[/tex] - [tex]y^{2}[/tex]/[tex]b^{2}[/tex] = 1
From the graph, we have the following parameters
a = 3
[tex]a^{2}[/tex] = [tex]3^{2}[/tex] = 9
b = 2
[tex]b^{2}[/tex] = [tex]2^{2}[/tex] = 4
The equation of a hyperbola can be expressed as
[tex]x^{2}[/tex]/9 - [tex]y^{2}[/tex]/4 = 1
The vertices = V(+/-a,0) = (+/-3,0)
The center = C(0,0)
The focus = F(+/-C, 0)
Where [tex]C^{2}[/tex] = [tex]a^{2}[/tex] + [tex]b^{2}[/tex]
C = [tex]\sqrt{9 + 4}[/tex]
C = [tex]\sqrt{13}[/tex]
Focus = F(+/- [tex]\sqrt{13}[/tex], 0)
The general equation for asymptote = +/- b/a X
= +/-2/3X
Therefore, the equation of a hyperbola can be expressed as
[tex]x^{2}[/tex]/9 - [tex]y^{2}[/tex]/4 = 1
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3. Luke, the furniture maker, knows that he has 54 stools in stock. Some of these stools have three legs and some have four legs. Luke, however, does not know how many of each type of stool he has in stock. Since the stools are stored upside down, he only counts the number of legs to find out how many of of stool he has in stock. He counts 200 legs. each type 3.1 If the number of four-legged stools is x, write an algebraic expression for the number of three-legged stools. 3.2 Now write algebraic expressions for the number of legs that the three- legged stools have altogether as well as the number of legs that the four- legged stools have altogether. 3.3 Use your answers to Question 3.2 to write an equation in x and then determine the number of four-legged and three-legged stools in stock.
The number of number of four-legged and three-legged stools in stock is 38 and 16 respectively.
Simultaneous equationlet
number of four-legged stools = xnumber of three-legged stools = yx + y = 54
4x + 3y = 200
From equation (1)
x = 54 - y
Substitute x = 54 - y into4x + 3y = 200
4(54 - y) + 3y = 200
216 - 4y + 3y = 200
216 - y = 200
- y = 200 - 216
-y = -16
y = 16
substitute y = 16 intox + y = 54
x + 16 = 54
x = 54 - 16
x = 38
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Explain how to graph the given piecewise-defined
function. Be sure to specify the type of endpoint each
piece of the function will have and why.
f(x)
X + 3, x < 2
3,
2 ≤ x < 4
4 - 2x,
X 2 4
The Piecewise -Defined function and how it is graphed is given below..
What is the explanation of how the Piecewise -Defined function is graphed?
Given the function in the attached image,
The Graph of f(x) = -x + 3 is drawn for x less than 2 because x is bounded.The Graph of f(x) = 3 is draw for x greater than and equal to 2 and less than 4 because x is bounded.The Graph of f(x) = 4 - 2x is draw for x greater than equal to 4 because x is bounded.See the attached Graph for better understanding.
f(x) = -x + 3 is coded purple.f(x) = 3 is coded orange.f(x) = 4 - 2x is coded green.Learn more about Piecewise -Defined function:
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The vertices of a triangle are P (-6,1), Q(-2,5) and R (8,1) - what is the slope of the median of the triangle that passes through point R?
What is the slope of the altitude of the triangle that passes through point Q?
The slope of the median of the triangle whose vertices are P(-6,1),Q(-2,5) R(8,1) and passes through R is -1/6.
Given that vertices of triangle is P(-6,1),Q(-2,5),R(8,1) and there is a median which passes through R.
Median of a triangle is a line segment which originates from a vertex of triangle and divides the opposite side in two equal parts. let median touches the line at L point.
When line passes through R then it must be a perpendicular on PQ. The coordinates of L is {(-2-6)/2,(5+1)/2}=(-4,3)
Now because median passes through R,it will be LR and we know that the formula of calculating slope of line from two points is [tex](y_{2} -y_{1} )/(x_{2} -x_{1} )[/tex] where [tex](x_{1} ,y_{2} ),(x_{2} ,y_{2} )[/tex] are the points of the end points of line.
Slope=(1-3)/(8+4)
=-2/12
=-1/6
Hence the slope of the median of the triangle whose vertices are P(-6,1),Q(-2,5) R(8,1) and passes through R is -1/6.
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za = a + b/m, solve for a
Answer: [tex]a=\frac{b}{zm-1}[/tex]
Step-by-step explanation:
Let's first multiply both sides by m to get rid of the denominator.
[tex]za=\frac{a+b}{m}\\zam=a+b[/tex]
Now, we have an a on both sides of the equation. It will be easier to solve if there is only one, so let's divide both sides by a.
[tex]\frac{zam}{a}=\frac{a+b}{a}\\zm=\frac{a}{a}+\frac{b}{a}\\zm=1+\frac{b}{a}[/tex]
The 1 on the right can be moved to the left to isolate the fraction.
[tex]zm-1=\frac{b}{a}[/tex]
We want to get a by itself, so let's multiply it on both sides to remove it from the denominator.
[tex]a(zm-1)=b[/tex]
Finally, we can divide zm-1 from both sides to get a by itself.
[tex]a=\frac{b}{zm-1}[/tex]
The number of bats in a colony is growing exponentially. After 3 years, there were 272 bats. After 5 years, there were 1088 bats.
If the colony continues to grow at the same rate, how many bats are expected to be in the colony after 11 years? Do not include units in your answer.
The number of bats are expected to be in the colony after 11 years if the colony continues to grow at the same rate is 69,632
Exponential functionLet
Number of bat at a time = n(t)exponential function;
y = ax^t
When t = 3
272 = ax³
when t = 5
1088 = ax^5
divide both equation272/1088 = ax^3 / ax^5
1/4 = x^3-5
1/4 = x^-3
1/4 = 1/x²
1 × x² = 4 × 1
x² = 4
x = 2
Substitute x = 2 into
272 = ax³
272 = a × 2³
272 = a × 8
272 = 8a
a = 272/8
a = 34
Number of bat expected at the colony after 11 years
y = ax^t
= 34 × 2^11
= 34 × 2048
y = 69,632 bats
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Question
If the length of the side of a square is 3x - y, what is the area of the square in terms of x and y?
3x² - 2xy + y²
3x² - 6xy + y²
09x² +6xy-y²
9x² - 6xy + y²
The area of the square is given by the quadratic expression:
[tex]A = 9x^2 - 6xy + y^2[/tex]
How to express the area of the given square?If we have a square whose side measures S, the area of said square is given by the equation:
[tex]A = S^2[/tex]
In this case, we know that the side length of our square is given by:
[tex]S = 3x - y[/tex]
Replacing that in the area equation we get:
[tex]A = (3x - y)^2[/tex]
Now we just need to expand that product, we will get:
[tex]A = (3x - y)^2 = (3x)*(3x) + (3x)*(-y) + (-y)*(3x) + (-y)*(-y) \\\\A = 9x^2 - 6xy + y^2[/tex]
Then we can see that the correct option is the last one.
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Ned and Sam are playing a game. Ned has -3 points. Sam has -8 points. How many more points does Ned have than Sam? Please provide an equation and an answer.
Answer:
5 points
Step-by-step explanation:
Subtracting their scores, we get (-3)-(-8)=5
On a number line, suppose point E has a coordinate of 4, and EG = 11. What are the possible coordinates of point G?
The possible coordinates for G are
(Type integers or decimals. Use
comma to separate answers as needed.)
Answer:
-7, 15
Step-by-step explanation:
The positive difference between E and G is 11.
SolutionG - E = 11
G = 11 + E = 11 + 4
G = 15 . . . . . . . . . . . . . when G is right of E
__
E - G = 11
E - 11 = G = 4 - 11
G = -7 . . . . . . . . . . . . when G is left of E
Possible coordinates for G are -7 and 15.
Part of your job as manager is to count the cash for the daily bank deposit. When you count the cash, you have 47 ones, 22 fives, 9 tens and 17 twenties. You also have 67 pennies, 12 nickels, 9 dimes and 15 quarters. What is the total amount of the deposit?
Answer:
$592.92
Step-by-step explanation:
Bills:
47 ones = 47*1 = $47
22 fives = 22*5 = $110
9 tens = 9*10 = $90
17 twenties = 17*20 = $340
Total Bills: 47+110+90+340 = $587
Coins:
67 pennies = 67*1 = $0.67
12 nickels = 12*5 = $0.60
9 dimes = 9*10 = $0.90
15 quaters = 15*25 = $3.75
Total Coins: 0.67+0.6+0.9+3.75 = $5.92
Total: $587+$5.92 = $592.92
two sides of a triangle are 5 and 55 cm complete the inequality to show the possible lengths of the third side _ < x < _
Answer:
50<x<60
Step-by-step explanation:
The triangle can only be formed with these two side lengths if the third side is bigger than (Subtract them)
55 - 5
...and smaller than (Add them)
55 + 5
55-5 < x < 55+5
50 < x < 60
PLSS HELPPPPP ASAPP
Answer:
Step-by-step explanation:
area=length×width
=(2x+3)(3x-5)
Area=6x²-10x+9x-15
=6x²-x-15
A parking garage bases its prices on the number of hours that a vehicle parks in the garage.
Graph of a piecewise function with one piece constant from 0 comma 2 to 2 comma 2 and another piece going from the point 2 comma 2 to 6 comma 10 and another piece going from 6 comma 10 through 7 comma 11 to the right
Based on the graph, what is the pricing scheme the parking garage uses for vehicles?
The first two hours cost $2, between two hours and six hours cost $2 per hour, and all hours after that cost $1.
The first two hours cost $2, between two and four hours cost $1 per hour, and all hours after that cost $0.50.
The first two hours cost $1 per hour, between two hours and six hours cost $2 per hour, and all hours after that cost $1.
The first two hours cost $1 per hour, between two hours and six hours cost $1 per hour, and all hours after that cost $0.50.
The pricing scheme of the function is (a) The first two hours cost $2, between two hours and six hours cost $2 per hour, and all hours after that cost $1.
How to determine the pricing scheme?The points are given as:
Constant = (0,2) to (2, 2)Another = (2,2) to (6,10)Another = (6,10) to (7,11)The constant interval implies that the first two hours cost $2
Next, we calculate the slope/rate of the other points.
This is done using
m = (y2 - y1)/(x2 - x1)
So, we have:
m1 = (10 - 2)/(6 - 2) = 2
m2 = (11 - 10)/(7 - 6) = 1
This means that:
The next 4 hours are charged for $2 per hourAll hours after that cost $1Hence, the pricing scheme of the function is (a)
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Work out the surface area.
Answer:
The surface area (SA) of the given triangular prism is 120m.
Step-by-step explanation:
Greetings !
B/c, SA=bh+(b₁+b₂+b₃)l
SA=4(3)+(4+3+5)9SA=12+(12)9SA=12+108SA=120mAnswer:
SA = 120 m2
Step-by-step explanation:
one 9×5 rectangle = 45 m2
one 4×9 rectangle = 36 m2
one 9×3 rectangle = 27 m2
two (4×3)/2 triangles = 6 + 6 = 12 m2
Add the areas:
surface area = 45 + 36 + 27 +12 = 120 square meters
Hope this helps
In a one tail hypothesis where you reject H0 only in the upper tail, what is the pvalue if Zstat = +2.10
The outcome P-Value is 0.0179 when Zstat = +2.10
According to the statement
we have given the value of Z-Stat which is +2.10
And we have to find the P value when H0 is rejected only in the upper tail
Z-stat is defined as the Z-score indicates how much a given value differs from the standard deviation. The Z-score, or standard score, is the number of standard deviations a given data point lies above or below mean.
And
we know that the relationship between Z-Stat and the p value is the P-Value is calculated by converting your statistic (such as mean / average) into a Z-Score.
So, the outcome p value is 0.0179
So, The outcome P-Value is 0.0179 when Zstat = +2.10
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In the drawing below, what choice shows the corresponding sides as equal ratios?
Considering the similarity of triangles, the corresponding sides are:
[tex]\frac{DE}{AB} = \frac{EF}{BC} = \frac{DF}{AC}[/tex].
What are similar triangles?If two triangles have the exact same angles, they are called similar, and the corresponding sides, that is, the sides adjacent to the same angles, have proportional lengths.
In this problem, the corresponding sides have equal ratios given as follows:
[tex]\frac{DE}{AB} = \frac{EF}{BC} = \frac{DF}{AC}[/tex].
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Can you help with this question? I'm not sure if the black highlighted choice is right
Answer:
See below
Step-by-step explanation:
Remember... when you square a negative number, you get a positive result
AND you cannot divide by zero AND you cannot have the sqrt of a negative number so:
-2 > x > 2 (looks like 'D' but there is a negative sign missing)
?
What is the equation of a parabola that has a vertical axis,
passes through the point (-1, 3), and has its vertex at (3, 2)?
X=
y=
y=
X =
уг
16
х2
16
+
+
бу
16
6x 41
16 16
41
16
x2 6х
41
+
16 16 16
уг бу
41
16 16 16
+
Answer: Option (3)
Step-by-step explanation:
Since the parabola has a vertical axis of symmetry, we can eliminate Options (1) and (4).
To see whether options (2) or option (3) is correct, we can substitute in [tex]x=-1[/tex] and see if we get y=3.
Doing this with option (2), we get y = -3, so it is wrong.
Doing this with option (3), we get y = 3, as required.
So, option (3) is correct.
Determine a limit for a piecewise function
The limit for the given piecewise function does not exist(DNE).
4th option is correct.
What is the limit of a function?In mathematics, limits are the points at which a function approaches the output for the specified input values. Calculus and mathematical analysis depend heavily on limits, which are required to determine integrals, derivatives, and continuity. It is applied during the analysis process and always focuses on the function's behavior at a certain time.
Unique real numbers are limits in mathematics.
According to the question,
Left hand limit of the function= -5(3)+4 = -15+4 = -11
Right hand limit of the function= (3)(3)+2 = 11
As the left and right-hand limits are not equal. Thus, the limit of the function does not exist.
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How do you work this equation? x² + x - 30 = 0
Answer:
x = 5 , x = - 6
Step-by-step explanation:
First we factor using factorisation method :
We need 2 numbers that multiply to give +1 and add to give -30 :
To find these numbers we write out all the factors of 30 :
1, 30
2 , 15
3 , 10
5 , 6 ----> These must be the numbers as -5+6 = 1
Now we split +x into -5x and +6x :
x² -5x + 6x -30 = 0
Factor the first 2 terms together and the last two terms :
x(x-5) + 6(x-5) = 0
Keep 1 bracket and terms outside the brackets collect them into one:
(x-5)(x+6) = 0
We know that 1 of these brackets must be equal to zero as anything multiplied by zero = 0
Either x - 5 =0 OR x + 6 = 0
So x = 5 x = - 6
These are our final answers
Hope this helped and have a good day
Answer:
(x-5) (x+6)
x=5
X=-6
Step-by-step explanation:
x²+x-30=0
factorizing
x²-5x+6x-30=0
x(x-5)+6(x-5) =0
(x-5)(x+6)=0
now solve individually
x-5=0
send 5 to the other side
x=5
x+6=0
send 6 to the other side
x=-6
hope you understand the procedure
what is the least common denominator of 1/2 5/6
Answer:
Multiples of 4:4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, …
Multiples of 6:6, 12, 18, 24, 30, 36, 42, 48, 54, 60, …
Answer: The least common denominator of 1/4 and 1/6 is 12.
Prime factorisations of 8= 2 × 2 × 2.
Prime factorisations of 12= 2 × 2 × 3.
More items...
Hi! ⋇
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
To find the least common denominator of [tex]\sf{\frac{1}{2}}[/tex] and [tex]\sf{\frac{5}{6}}[/tex], we should first find the least common multiple of 2 and 6, which is 6:
Multiples of 2: 2, 4, 6, 8, 10, 12, 14, 16... ∞
Multiples of 6: 6, 12, 18, 24... ∞
(all common multiples are in bold-face; all multiples of 6 are in bold-face because all multiples of 6 are also multiples of 2)
· In both sets, 6 is the least common multiple, and it's also the least common denominator.
Hope this made sense to you !!
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Olivia has made a pyramid model for her history project at school. The pyramid model has a square base. Each triangular side of the
model has a base length of 10 centimeters and a slant height of 8.9 centimeters. Olivia wants to wrap the pyramid in wrapping paper
before putting it into her school bag.
How much wrapping paper will Olivia need to cover the pyramid?
OA. 178 square centimeters
OB. 89 square centimeters
OC. 456 square centimeters
OD. 278 square centimeters
Answer:
278 square centimeters
Step-by-step explanation:
You need to use the Pythagorean Theorm. If you're pyramid is a perfect square, then to the middle the length is 5. Because 10/2 is 5. You then use the Pythagorean Theorm (a^2 + b^2 =c^2) to find the side length of the traingle. When you square the hypotenuse and subtract the bottom leg sqaured, you are left with 3.46274054 after square rooting it. (c^2-a^2=b^2) Plug these into the equation for a right, rectangluar pyramid. You then get 277.9, rounded, is 278.
Hope this helps!
a square foot has 16 tiles each tile is 1 square ft what is the length of one side of the square floor
Answer:
4 ft
Step-by-step explanation:
The area of each tile is tile is 1 square ft, so the total area of the floor is 16 square ft.
Therefore, the side length is 4 ft.
please answer this i have tried lots of answers but they are all wrong urgent
(a). All four sides are equal and the angles are right-angled (90 degrees).
(b). A quadrilateral has no pairs of parallel sides is a Kite and irregular trapezium.
(c). A triangle having one pair of equal sides and one pair of equal angles is an isosceles Triangle.
What is geometry?One of the first areas of mathematics is geometry, along with arithmetic. It is focused on spatial characteristics that relate to the proximity, size, shape, and relative placement of objects.
(a). Two features that make the shape square are all four sides equal and the angles are right-angled (90 degrees).
(b). A quadrilateral has no pairs of parallel sides is a Kite and irregular trapezium.
(c). A triangle having one pair of equal sides and one pair of equal angles is an isosceles Triangle.
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Complete the table by finding the missing equivalent form for each row. a = b = c =
Answer:
a=10%, b=25/100, c=1/2
Step-by-step explanation:
a: If the denominator is exactly 100, then the numerator represents a percentage.
b: when you change a fraction to have a greater denominator, an easy way to figure out how to change the numerator to match it and make the value of the rewritten fraction equal to the old version, is to divide the new value of the denominator by the old value (in this case being 100/4=25), and put the answer where the numerator goes.
c: When simplifying a fraction with a lesser numerator than denominator, find the greatest common factor (a factor is a whole number a number can be divided by without resulting in a negative or a decimal number) and divide both the numerator and denominator by it.