The solution of the simultaneous equation is given by (-7 , 4) .
A pair of simultaneous equations is the most common representation of a pair of straight lines in the cartesian plane.
For solving a pair of simultaneous equation we can use various procedures such as the matrix method, substitution or the method of elimination.
The given pair of simultaneous equation is given as:
x=−2y+1
3x+8y=11
Let us solve the equations by the method of substitution:
From the first equation we take the value of x and put it in the second equation:
3x + 8y = 11
or, 3 ( -2y + 1 ) + 8y = 11
or, -6y +3 +8y = 11
or, 2y + 3 = 11
or, 2y = 8
or, y = 4
Substituting the value of y as 4 in the first equation we get:
x = − 2y + 1
or, x = - 2 × 4 +1
or, x = -8 +1
or, x = -7
Therefore the solution set of the pair of equations is given by (-7 , 4) .
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Determine the probability of following event.
In Armando's senior class of 100 students, 91% went to the senior prom. If two people are chosen at random from the entire class, what is the probability that at least one of them did not go to prom?
According to the question, the probability of the event in which all the students went to prom except one. For this, the probability of the complement rule is used.
Out of [tex]100[/tex] students, [tex]91[/tex] went to prom.
So, the probability that students went to prom = [tex]\frac{91}{100} =0.91[/tex]
Now, P(both went to prom) = [tex](0.91)(0.91)=0.8281[/tex]
Using standard probability formula:
P(at least one did not went to prom) = 1-P(both went to prom)
[tex]1-0.8281=0.1719=17.2%[/tex]
The probability that at least one student did not went is [tex]17.2[/tex] percentage.
What is Probability?
The term probability means the study of the occurrence or the outcomes of the event. It is the measurement of the events that occurred during events. And many uncertain events cannot be measured.
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Expand & simplify:
4(× + 5) - 2(x - 3)
The Simplification of 2x +26
simplify:
4(× + 5) - 2(x - 3)
4x + 20 - 2x +6
2x +26
Making something simpler is making it less intricate or crowded. When you describe a complex mathematical idea to a youngster in words they can easily comprehend, you are simplifying. When you eliminate many of the tasks that were keeping you occupied and stressed out, you have simplified.
Making something simpler refers to making it simpler to accomplish or comprehend. Therefore, when we reduce or simplify a fraction, we aim for maximum simplicity. In order to do this, we divide both the numerator and the denominator by the biggest integer that can be divided precisely into both numbers.
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URGENT!! ILL GIVE BRAINLIEST! AND 100 POINTS Which expression is equivalent to 4 ^ 3
The expression that is equivalent to 4 ^ 3 would be an expression that equals 4 ^ 3
4 ^ 3 = 4 x 4 x 4 = 16 x 4 = 64
Answer:
4^3 =
4 x 4 x 4 x4 = 64
Find the distance between the points (1, 6) and (9, 0).
Answer:
You have to use the distance formula
d=√(x2-x1)^2 + (y2-y1)^2
replace the points and get 10
Point b is on line segment \overline{ac} ac . given ab=2x+10,ab=2x+10, bc=x,bc=x, and ac=5x,ac=5x, determine the numerical length of \overline{ac}. ac
The numerical length of line segment AC is 25.
A line segment refers to a straight line connecting two points.
If point B is on line segment AC, then point B divides the line segment into segments AB and BC.
AB + BC = AC
Given that AB =2x + 10, BC = x, and AC = 5x, substitute these expressions in the equation AB + BC = AC.
AB + BC = AC
2x + 10 + x = 5x
3x + 10 = 5x
5x - 3x = 10
2x = 10
x = 5
To determine the numerical length of line segment AC, substitute the value of x in the equation AC = 5x.
AC = 5x
AC = 5(5)
AC = 25
Hence, the numerical length of line segment AC is 25.
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A baker uses the equation y= 3.5x to find the number of cups ,y, of milk he needs to make a number ,x, of tres leches cakes. What is the constant of proportionality between y and x?
Answer:
Step-by-step explanation
Equation: y=3.5x
Constant of proportionality:
The constant ratio of one variable quantity to another to which it is proportional.
Answer: 3.5
The reason is for 3.5 cakes you need this amount of milk.
Use PEMDAS to solve the following. (17 - 6 divided 2) + 4 x 3
What is the anwser?
A. 54
B. 28.5
C. 21
D. 26
Answer:I used PEMDAS I Got D.26
Step-by-step explanation:
A customer wants to buy 0.4 pounds of mulch that cost $5.20 per pound. If the customer has a coupon for $0.50 off the total cost, how much will they pay for the mulch?
$1.04
$1.58
$2.08
$4.16
The amount paid for 0.4 pounds of much after deducting $0.50 coupon is $1.58. option B
DiscountCost of each pound of mulch = $5.20Number of pounds of mulch bought = 0.4 Coupon = $0.50Cost of 0.4 pounds of mulch = xCost of mulch : pounds of mulch
5.20 : 1 = x : 0.4
5.20/1 = x/0.4
5.20 × 0.4 = 1 × x
2.08 = x
Cost of 0.4 pounds of mulch = x = $2.08
Amount paid for 0.4 pounds of much after deducting $0.50 coupon
= $2.08 - $0.50
= $1.58
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Answer:
b) $1.58
Step-by-step explanation:
Now we have to,
→ find the amount the customer must pay.
One pound of mulch costs,
→ $5.20
Then 0.4 pounds of mulch costs,
→ $5.20 × 0.4
→ 5.20 × 0.4
→ $2.08
Total cost after reducing $0.50,
→ 2.08 - 0.50
→ $1.58
Hence, customer must pay $1.58.
Add. Write your answer as a fraction or as a whole or mixed number.
10 1/2 + 3 2/3
In basketball, teams can score by making two-point shots, three-point shots, and one-point free throws. What algebraic expression models the total number of points that a basketball team scores in a game? If a team makes 10 two-point shots, 5 three-point shots, and 7 free throws, how many points does it score in all?
The algebraic expression models the total number of points that a basketball team scores in a game is 2x+3y+z and If a team makes 10 two-point shots, 5 three-point shots, and 7 free throws then the total points scored by the team is 42 points
Given,
The team can score by making = 2 point ,3 point and one point free throw
Then,
Consider the number of 2 points = x
The number of 3 points =y
The number of one point free throw = z
Then then algebraic expression for the total number of points that a basket ball team scores in a game = 2x+3y+z
Then,
Number of 2 points =10
Number of 3 points = 5
Number of free throws = 7
Substitute the values in the equation
The total points scored by basketball = 2×10+3×5+7
=20+15+7
=42 points
Hence, the algebraic expression models the total number of points that a basketball team scores in a game is 2x+3y+z and If a team makes 10 two-point shots, 5 three-point shots, and 7 free throws then the total points scored by the team is 42 points
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Answer:
ADGJL
Step-by-step explanation:
HELP HELP HELP HELP HELP 4/9×4/5=
Answer: 16/45
Step-by-step explanation:
[tex]\displaystyle\\\frac{4}{9}*\frac{4}{5}= \\\\\frac{4*4}{9*5}=\\\\\frac{16}{45}[/tex]
Please, I'm desperate. 13 Questions. 1-11 have provided options, 12 and 13 are manual answers.
1. Perform the required operations on the following functions.
Given: f(x) = 3 - x; g(x) = -2x
Find g[f(x)].
Options:
A. -x - 6
B. 2x - 6
C. 2x + 3
2. Perform the required operations on the following functions.
Given: f(x) = 3 - x; g(x) = -2x
Find f[g(2)].
Options:
A. -1
B. 25
C. 7
3. Given: f(x) = 3 - x; g(x) = -2x
Find g[f(-1)].
Options:
A. -22
B. 8
C. -8
4. Given: F(x) = 2x - 1; G(x) = 3x + 2; H(x) = x^2
Find F[G(x)] - F(x).
Options:
A. 4x + 4
B. 4x
C. 4x + 2
5. Given: F(x) = 2x - 1; G(x) = 3x + 2; H(x) = x^2
Find G[H(1)].
Options:
A. 5
B. 35
C. 8
6. Given: F(x) = 2x - 1; G(x) = 3x + 2; H(x) = x&2
Find F{G[H(2)]}.
Options:
A. 121
B. 27
C. 71
7. Given: F(x) = 2x - 1; G(x) = 3x + 2; H(x) = x^2
Find H(x + a) - H(x)
Options:
A. a^2
B. a^2 + 2ax
C. 2a
8. Given: F(x) = 2x - 1; G(x) = 3x + 2; H(x) = x 2
Find [H(x + a) - H(x)] / a
Options:
A. 2x + a
B. a
C. a^2 + 2x
9. Given: F(x) = 2x - 1; G(x) = 3x + 2; H(x) = x^2
Find F(x) + G(x) + H(x).
Options:
A. 5x^3 + 1
B. x^2 + 5x + 3
C. x^2 + 5x + 1
10. If f(x) = 2x 2 - 3x + 1, find f(3) - f(2).
Options:
A. 0
B. 7
C. 17
11. If G(x) = 5x- 2, find G^-1 (x).
Options:
A. (x + 2)/5
B. (x/5) + 2
C. -5x + 2
12. What is the inverse of f(x) ? Show all work for full credit.
f(x) = 2 / [x - 6]
13. Use composition of functions to determine whether f(x) and g(x) are inverses of each other. Show all work for full credit.
f(x) = 4/5 x + 1
g(x) = [5x - 5] / 4
The evaluation of the given functions are as follows;
B. 2•x - 6C. 7C. -8A. 4•x + 4A. 5B. 27B. a² + 2•a•xA. 2•x + aC. x² + 5•x + 1B. 7A. (x + 2)/5(2/x) + 6The inverse of g(x) is f(x)How can the functions be evaluated?1. f(x) = 3 - x
g(x) = -2•x
Therefore;
g(fx) = -2 × f(x)
Which gives;
-2 × (3 - x) = -6 + 2•x = 2•x - 6
g(fx) = 2•x - 6
B. 2•x - 6
2. f(x) = 3 - x
g(x) = -2•x
f(g(x)) = 3 - (-2•x) = 3 + 2•x
f(g(x)) = 3 + 2•x
f(g(2)) = 3 + 2×2 = 7
The correct option is therefore;
C. 7
3. f(x) = 3 - x
g(x) = -2•x
Therefore;
g(fx) = 2•x - 6
g(f-1) = 2×(-1) - 6 = -8
C. -8
4. F(x) = 2•x - 1, G(x) = 3•x + 2, H(x) = x²
F(G(x)) = 2•(3•x + 2) - 1 = 6•x + 3
F(G(x)) - F(x) = 6•x + 3 - (2•x - 1) = 4•x + 4
A. 4•x + 4
5. F(x) = 2•x - 1, G(x) = 3•x + 2, H(x) = x²
G(H(x)) = 3•x² + 2
G(H(1)) = 3×1² + 2 = 5
A. 5
6. F(x) = 2•x - 1, G(x) = 3•x + 2, H(x) = x²
F(G(H(x))) = 2•(3•x² + 2) - 1 = 6•x² + 3
F(G(H(2))) = 6×2² + 3 = 27
B. 27
7. F(x) = 2•x - 1, G(x) = 3•x + 2, H(x) = x²
H(x + a) - H(x) = (x + a)² - x² = 2•a•x + a²
B. a² + 2•a•x
8. (H(x + a) - H(x))/a = (a² + 2•a•x)/a
(a² + 2•a•x)/a = a + 2•x = 2•x + a
A. 2•x + a
9. F(x) = 2•x - 1, G(x) = 3•x + 2, H(x) = x²
F(x) + G(x) + H(x) = 2•x - 1 + 3•x + 2 + x² = x² + 5•x + 1
C. x² + 5•x + 1
10. f(x) = 2•x² - 3•x + 1
f(3) - f(2) = 2×3² - 3×3 + 1 - (2×2² - 3×2 + 1) = 7
B. 7
11. G(x) = 5•x - 2
G^(-1)(x) = (G(x) + 2)/5
Which gives;
G^(-1)(x) = (x + 2)/5
A. (x + 2)/5
12. f(x) = 2/(x - 6)
The inverse is therefore;
(2/f(x)) + 6
The inverse of f(x) is therefore;
(2/x) + 6
13. g(x) = (5•x - 5)/4
(4•g(x) + 5)/5 = (4/5)•g(x) + 1
The inverse of g(x) is therefore;
(4/5)•x + 1 = f(x)
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Solve each equation using the Quadratic Formula. x(x-5)=-4 .
Answer:
x
2
−4x−5=0
All equations of the form ax
2
+bx+c=0 can be solved using the quadratic formula:
2a
−b±
b
2
−4ac
. The quadratic formula gives two solutions, one when ± is addition and one when it is subtraction.
x
2
−4x−5=0
This equation is in standard form: ax
2
+bx+c=0. Substitute 1 for a, −4 for b, and −5 for c in the quadratic formula,
2a
−b±
b
2
−4ac
.
x=
2
−(−4)±
(−4)
2
−4(−5)
Square −4.
x=
2
−(−4)±
16−4(−5)
Multiply −4 times −5.
x=
2
−(−4)±
16+20
Add 16 to 20.
x=
2
−(−4)±
36
Take the square root of 36.
x=
2
−(−4)±6
The opposite of −4 is 4.
x=
2
4±6
Now solve the equation x=
2
4±6
when ± is plus. Add 4 to 6.
x=
2
10
Divide 10 by 2.
x=5
Now solve the equation x=
2
4±6
when ± is minus. Subtract 6 from 4.
x=
2
−2
Divide −2 by 2.
x=−1
The equation is now solved.
x=5
x=−1
Marline Was playing basketball and made 8⁄10Of the shots he took what decimal Number repeat Number repeat represents done fraction of shots Merlin made
The fraction ( 8/10 ) when converted into a decimal number is equal to 0.8.
The decimal number system is frequently used to express both integer and non-integer quantities. The Hindu-Arabic numeral system has been expanded to include non-integer values. Decimal notation is the name for the method used to represent numbers in the decimal system.
The number of shots fired by Marlin should be expressed as a decimal number.
We know that,
Marlin made 8 shots out of 10 shots which is in fraction, it is 8/10.
However, since we are dividing by 10, we shall shift the decimal point of 0.8 to the left (the zero is not really important as it only represents a place value )
Or,
( 8 /10) = ( 4 / 5 ) = 0.8
Therefore, the fraction of the shots Marlin made is 0.8.
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Find the indicated measure. Round to the nearest tenth.
Find the diameter of a circle with an area of 79 square feet.
The diameter of circle is 10.0 feet.
We are given the area of circle. The formula of area with respect to diameter is as follows -
Area = 1/4πd², where d represents diameter of circle.
Taking the value of π as 3.14.
Rewriting the equation according to diameter -
d² = (area×4)÷π
Now, keep the values in formula to find the diameter of circle.
d² = (79×4)÷3.14
Performing multiplication on the Right hand side of the equation
d² = 316÷3.14
Performing division on the Right hand side of the equation
d² = 100.6
d = √100.6
Taking square root on the Right hand side of the equation
d = 10.03 feet
Rounding to nearest tenth -
d = 10.0 feet
Hence, the diameter of circle is 10.0 feet.
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m/KLM = 135º.
Find the value of y and m/MLN
L
M
K
47°
(16y)⁰
N
volume of a sphere(please hurry im in a test.
and can you also show the prosses of getting the anwser)
Answer:
The answer is 113.3
Step-by-step explanation:
We get this because he formula for the volume of a sphere is V = 4/3 πr³.
The radius is 7.
7^3 = 243
243*4 = 972.
So, the asnwer is 972 ft^3
Find the measure of the missing angles h,g and m,k
Give the degrees 119 and 121
The missing angles in degrees are-
∠k = 61°∠m = 119°∠g = 29°∠h = 151°What is defined as the vertically opposite angles?Vertically opposite angles are produced by two straight intersecting lines that are exact reverse one another at a specific vertex. Angles that are vertically opposite each other are equal. These are sometimes referred to as vertical angles.In the given figure;
∠g = 29°, as ∠g and ∠29° are vertically opposite to each other. Both will be equal.
Similarly,
∠k = 61°, as ∠k and ∠61° re vertically opposite to each other. Both will be equal.
What is defined as the linear pair?When 2 lines intersect at a single point, a linear set of angles is formed. If the angles are adjacent to one another after the two lines intersect, they are said to be linear. The sum of the angles of a linear pair is indeed 180°.From the linear pair;
∠h + ∠g = 180
∠h = 180 - 29
∠h = 151°
Similarly,
∠m + ∠k = 180
∠m = 180 - 61
∠h = 119°
Thus, the missing values of the angles are found.
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I think i know how to do this but i keep getting them wrong lol help
Answer:
no worry I'll help u out
Step-by-step explanation:
90+55=145
180-145=35
z=35°
also may I ask for u to mark brainlist?asking
Find the relationship between p and q if px*2+2x-q is a perfect square. please help me ASAP
[tex]\displaystyle\\Answer:\ p=-\frac{1}{q}[/tex]
Step-by-step explanation:
A perfect square has equal sides
Hence, px²+2x-q has equal roots (D(discriminant)=0)
[tex]\displaystyle\\D=2^4-4*p*(-q)\\D=2*2+4pq\\D=4+4pq\\D=0\\\Rightarrow\ 0=4+4pq\\Divide\ both\ parts\ of\ the \ equation\ by\ 4:\\0=1+pq\\0-1=1+pq-1\\-1=pq\\Divide\ both\ parts\ of\ the \ equation\ by\ q(q\neq 0):\\-\frac{1}{q}=p\\ Thus,\\p=-\frac{1}{q}[/tex]
At an electronics store, a smart phone is on sale for 35% off the original price of 679.if you use the store credit card,you can recive an additional 15% off the sale price.what is the final price of the smart phone if you use the store credit card?Round to the nearest cent.
The final price of the smart phone if you use the store credit card is $375.15.
What is the final price?A discount is when the price of an item is marked down. An item becomes cheaper when it is discounted.
Percentage is the fraction of an amount expressed as an amount out of 100. Percentage is a measure of frequency. The sign used to represent percentage is %.
Price of the smartphone after 35% is discounted : (1 - percentage decrease) x original price
(1 - 0.35) x 679
0.65 x 679 = $441.35
Purchase price after you buy with your credit card : (1 - percentage decrease) x discounted price
(1 - 0.15) x $441.35
0.85 x $441.35
= $375.15
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The product of two rational numbers is -14/7 if one of the numbers be 7/9 find the other
Answer:
The other number is (-18/7)
Step-by-step explanation:
Let the other rational number be 'x'.
[tex]\sf x * \dfrac{7}{9}= \dfrac{-14}{7}[/tex]
[tex]\sf x = \dfrac{-14}{7} \div \dfrac{7}{9}[/tex]
Now, use KCF method.
Keep the first fractionChange the division to multiplicationFlip the second fraction
[tex]\sf x = \dfrac{-14}{7}*\dfrac{9}{7}\\\\x = -2* \dfrac{9}{7}\\\\x = \dfrac{-18}{7}[/tex]
Answer:
-18/7
Step-by-step explanation:
let the unknown no be y
7/9×y= -14/7
7y/9= -14/7
cross multiply
-14×9=7y×7
divide both sides by 7
-2×9=7y
-18=7y
divide both sides by the coefficient of y which is 7
y= -18/7
hope this helps
please give brainliest
Solve each equation or inequality.
|3 x+9|=11
After solving the equation or inequality, x is equal to 2/3, -20/3 for the equation |3 x+9|=11
How to solve an equation?To solve linear equations, utilize the steps that are provided below.
Remove parentheses from each side of the equation and combine similar terms to make it simpler.To separate the variable term on one side of the equation, use addition or subtraction.To find the variable, use division or multiplication.The common denominator can be multiplied by each side of the equation to eliminate fractions.Lets take an example of solve z for 7z – (3z – 4) = 12
Here is no multiplication or division, so this will be easy to solve
⇒ 7z – (3z – 4) = 12
⇒ 7z – 3z + 4 = 12
⇒ 4z = 12 – 4
⇒ 4z = 8
⇒ z = 8/4
⇒ z = 2
See, that was so simple, using the mentioned methods, every linear equation can be solved easily.
⇒ |3 x+9| = 11
For positive case
⇒ (3 x+9) = 11
⇒ 3x = 11 - 9
⇒ 3x = 2
⇒ x = 2/3
For negative case
⇒ -(3 x+9) = 11
⇒ -3x -9 = 11
⇒ -3x = 20
⇒ x = -20/3
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F(x) = 5x + 6 evaluate f(-7)
[tex]\huge\text{Hey there!}[/tex]
[tex]\mathsf{f(x) = 5x + 6}\\\mathsf{f(x) = 5(-7) + 6}\\\mathsf{f(x) = -35 + 6}\\\mathsf{f(x) = -29}\\\\\\\huge\text{Therefore your answer should be:}\\\huge\boxed{\mathsf{f(x) = -29}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
Find the value of x to the nearest tenth. tan x° = 90 89.9 89.6 89.4
Answer:
89.4
Step-by-step explanation:
89.9,89.6 are more than five so we'll be using the lowest number as the nearest thenth
State whether each sentence is true or false. If false, replace the underlined word or phrase to make a true sentence.
The arithmetic mean of two numbers is the positive square root of the product of the numbers.
The statement "The arithmetic mean of two numbers is the positive square root of the product of the numbers." is False.
And the true sentence is "The geometric mean of two numbers is the positive square root of the product of the numbers."
Arithmetic Mean:
The arithmetic mean, is also called the average or average value, is the quantity obtained by summing two or more numbers or variables and then dividing by the number of numbers or variables.
Given,
Here they given the sentence, "The arithmetic mean of two numbers is the positive square root of the product of the numbers.".
We need to find this one is true or not and we also need to replace the underlined word or phrase to make a true sentence.
Based on the definition of arithmetic mean, the given statement is false.
And the correct sentence is
"The geometric mean of two numbers is the positive square root of the product of the numbers.".
Because geometric mean is average value or mean which signifies the central tendency of the set of numbers by finding the product of their values.
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Angle relationships and triangles
Three angles make compose a triangle.
They'll be known as a°, b°, c°.
If we total everything up:
a° + b° + c = 180
The triangle's horizontal line may be drawn farther to the right, creating a new angle. Call this angle "d°" for short.
a° + b° Equals d°
Give this some values:
a° = 60° b° = 70°
c° = 50°
Do should be 130° since c and d create 180° with c° 50°.
Additionally, because:
A + B + C Equals 180, and C + D = 180.
Because the cremains in both cases are the same, a + b = d.
Any of these fit the bill.
Let's call this f° if you will just extend the triangle's horizontal line to the left.
So, b + c Equals f.
So, if a F Equals 120° since f = 60° and a + f = 180.
We established that b + c Equals f in this instance.
Let's now make the line longer and give it the name angle g°.
B being equal to 70°, the angle next to it is 110°.
Consequently, a + c = g.
All inner angles added together equal 180 degrees.
Additionally, the total of the other two inside angles is equal to the outer angles.
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c. Will bought a tennis racket on sale for $24.60. If the sale was 20% off,
how much was the tennis racket originally?
Answer:
$30.75
Step-by-step explanation:
Since the sale was 20% off, the tennis racket is 80% of its original price.
[tex].8p = 24.60[/tex]
[tex]p = 30.75[/tex]
What is the annual percentage rate on a loan with a stated rate of 2.75 percent per quarter?
The annual percentage rate on a loan with a stated rate of 2.75 percent per quarter is 11%.
How to calculate the loan?It was given that the annual percentage rate on a loan with a stated rate of 2.75 percent per quarter.
It should be noted that quarter means that the value was divided by 4.
Therefore, the annual percentage will be:
= 2.75 × 4
= 11%.
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(3x
3
+4x
2
)−(2x
3
+3x
2
−x
On simplifying, x(x2 + 7x + 1) is the final expression.
The provided simplification expression can be solved, per the question, by moving the variable terms to one side and the normal terms to the other.
As a result, the phrase may be expressed more succinctly as:
(3x^3+4x^2) - (2x^3 + 3x^2 -x)
x^3 + 7x^2 + x
x(x^2 +7x + 1)
Consequently, x(x2 + 7x + 1) is the right solution via simplification.
How does simplification work?A technique to make the phrase less complex is simplification. And the variables' calculations became simple. Problems with simplification can be resolved by using mathematical characteristics.
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