PLEASE HELP 50 POINTS
Use matrices A, B, and C to find the following:
A+B
C-B
A+B+C
Answers
By solving matrices we get,
[tex]A+B= \left[\begin{array}{ccc}13&10\\4&7\\7&5\end{array}\right] , C-B=\left[\begin{array}{ccc}-8&1\\-7&4\\3&-5\end{array}\right] \\\\\\\\A+B+C = \left[\begin{array}{ccc}13&14\\2&12\\14&-6\end{array}\right][/tex]
A matrix is a rectangular array or table that contains numbers, symbols, or expressions that are arranged in rows and columns to represent a mathematical object or a characteristic of such an entity. As an illustration, consider a matrix with two rows and three columns.
Adding matrices, subtracting matrices, and multiplying matrices are the three algebraic operations that make up the majority of matrix operations. Array of numbers or expressions arranged in rows and columns is called a matrix. The field of mathematics has several useful uses for matrices.
Here the matrices A, B and C are given in the question, so we use matrix addition and matrix subraction operations to solve the question.
When solving by using the matrices solving method we get
[tex]A+B=\left[\begin{array}{ccc}5&7\\-1&6\\3&-9\end{array}\right] +\left[\begin{array}{ccc}8&3\\5&1\\4&4\end{array}\right]= \left[\begin{array}{ccc}5+8&7+3\\-1+5&6+1\\3+4&-9+4\end{array}\right]=\left[\begin{array}{ccc}13&10\\4&7\\7&5\end{array}\right] \\[/tex]
[tex]C-B = \left[\begin{array}{ccc}0-8&4-3\\-2-5&5-1\\7-4&-1-4\end{array}\right] =\left[\begin{array}{ccc}-8&1\\-7&4\\3&-5\end{array}\right][/tex]
[tex]A+B+C= \left[\begin{array}{ccc}5+8+0&7+3+4\\-1+5+-2&6+1+5\\3+4+7&-9+4+-1\end{array}\right] = \left[\begin{array}{ccc}13&14\\2&12\\14&-6\end{array}\right][/tex]
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Related Questions
For each set of points below, determine the distance between them using the distance formula. each answer in this problem will be an integer
Answers
Distance between two coordinates:
[tex]\text{ Distance=}\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]Given point: b) (10, -5) and ( -6, 7)
[tex]x_1=10,y_1=-5,x_2=-6,y_2=7[/tex]Substitute the value in the expression of distance formula
[tex]\begin{gathered} \text{ Distance=}\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2} \\ \text{Distance}=\sqrt[]{(-6-10)^2+(7-(-5))^2} \\ \text{Distance}=\sqrt[]{(-16)^2+(12)^2} \\ \text{Distance}=\sqrt[]{256+144} \\ \text{Distance}=\sqrt[]{400} \\ \text{Distance = 20 unit} \end{gathered}[/tex]The distance between coordinates (10,-5) & (-6,7) is 20 unit
This math question please
Answers
Find all possible values of the expression 1/a
1/2
__<1/a<__
Answers
The possible values of the expression 1/a = 1/2 is 2
The expression is the simple fraction form = 1/a
The expression is the defined as the a sentence with a minimum of two variables and at least one math operation.
The simple fraction is fraction that contains the numerator and denominator as whole number. The term one the top of the simple fraction called as the numerator and bottom term is called as the denominator.
Here it is given that
1/a = 1/2
Therefore the value of a = 2
Hence, the possible values of the expression 1/a = 1/2 is 2
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|x + 6| < or equal to 1
8
x < or equal to 2
x < or equal to ?
Answers
Answer: -14
Step-by-step explanation:
[tex]\frac{1}{8}|x+6| \leq 1\\\\|x+6| \leq 8\\\\-8 \leq x+6 \leq 8\\\\-14 \leq x \leq 2[/tex]
10. Evaluate (14-2)÷3(2-3) - 2²Mark only one oval.A. OB. 2C. 20D. 22
Answers
Order of the operations: parentheses, exponentials, division and multiplication, addition and subtraction.
1. Solve operations in parentheses:
[tex]=12\div3\cdot6-2^2[/tex]2. Solve exponentials:
[tex]=12\div3\cdot6-4[/tex]3. Solve division:
[tex]=4\cdot6-4[/tex]4. Solve multiplication:
[tex]=24-4[/tex]5. Solve subtraction:
[tex]=20[/tex]Then, the solution for the given expression is 20Answer: Answer is 20( please make me brainliest i just did this all in my head)
Step-by-step explanation: soo (14-2) =12 12divided by 3=4 so (2*3)= 6 so 4x6=24 24-2*2 =20 (2*2)=4 so 24-4=20 well this is confusing but i tried my best so hope my answer wasn't toooo confusing lol :)
Complete the equation so that it has no solution 9(x-4)-5x=
Answers
Answer:
9(x-4)-5x=
open brackets
9x-36-5x=0
relate with similar expressions
note,when negative crosses the equal sign,it becomes positive
9x-5x=36
4x=36
x=9
3|y|+(y-x²)
if x = -1 and y = -5
Answers
Parentheses first
-1^2= 1
-5-1=-6
Then we do |-5|
(the absolute value of -5 is 5)
So then we’re left with 3 x 5 - 6
Which would equal 8
Answer: 9
Please help ASAP starting to fall behind! This equation really confuses me and if someone could help that would be amazing!
Given the function:
f(x) = x² - 4x - 2
Find the following values.
a) f(2)
f(2)=
b) f(4)
f(4)=
c) f(-3)
f(-3)=
Answers
The values of the functions is ,
(a) f(2) = -6
(b) f(4) = -2
(c) f(-3) = 19
In the question ,
it is given that the function is f(x) = x² - 4x - 2
we have to find the value of f(2) , f(4) , f(-3)
Part(a)
to find f(2) , we substitute x = 2 in the function
On substituting , we get
f(2) = 2² - 4*2 - 2
= 4 - 8 - 2
= 4 - 10
= -6
Part(b)
to find f(4) , we substitute x = 4 in the function f(x)
On substituting , we get
f(4) = 4² - 4*4 - 2
= 16 - 16 -2
= 0 - 2
= -2
Part(c)
to find f(-3) , we substitute x = -3 in the function
On substituting , we get
f(2) = (-3)² - 4*(-3) - 2
= 9 + 12 -2
= 9 + 10
= 19
Therefore , The values of the functions is , (a) f(2) = -6 , (b) f(4) = -2 , (c) f(-3) = 19
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If the measures of two angles of a triangle are 96° and 29°, what is the measure of the third angle?
Answers
Answer: measure of the third angle is 55 degrees
Step-by-step explanation: the sum of all interior angles in a triangle is always 180 so, 96+29+x=180.
125+x=180
x=55
(8.59×10 4 )−(3.2×10 3 )
Answers
Answer:
The answer is 8.27×10^4
Answer: 8.27×10^4
Step-by-step explanation:
Simplify using the properties of exponents: (x^4 y^-3)^4/x^0y^2
Answers
Answer:
Rewrite using the commutative property of multiplication.
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Rewrite the expression using the negative exponent rule
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Simplify the denominator.
Tap for more steps...
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Simplify terms.
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I REALLLY would like to ACTUALLY understand how to solve this. Please tell me how you got the steps. So far, this was my thinking:
[tex]\frac{4x+2}{x^{2} -9+8} = \frac{2(x+1)}{(x-1)(x-8)}[/tex]
Please let me know what comes next?????
Answers
The empty boxes of the numerators for the given rational expression is to be filled with 4x and 2 respectively.
What is a rational expression?Rational expression is a division of two polynomials. Which implies that the numerator and denominator of the fraction consists of polynomials.
To solve this, we will first factorise the expression of the denominator as follows;
x² - 9x + 8 = x² - 8x - x + 8
x² - 9x + 8 = x(x - 8) -1(x - 8)
x² - 9x + 8 = (x - 1)(x - 8)
Hence, we can rewrite the rational expression as:
(4x + 2)/[(x - 1)(x - 8)]
we can break the expression further by dividing each term of the numerator with the expression (x - 1)(x - 8) as follows;
(4x + 2)/[(x - 1)(x - 8] = [4x/(x - 1)(x - 8)] + [2/(x - 1)(x - 8)]
Therefore, 4x and 2 will be the appropriate values to be filled in the empty boxes equated to the rational expression.
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State if there appears to be a positive correlation, negative correlation, or no correlation. When there is a correlation, identify the relationship as linear or nonlinear.
Answers
Answer:
Negative Correlation:
Linear relationship
Explanation:
We can draw the line of best fit through the points given, and this indicates that the relationship is linear. Furthermore, the line of best fit has a negative slope (which tells us that if one variable increases, the other decreases); therefore, the data set has a negative correlation
in the diagram below the lager angle is 4 times bigger than the smaller angle.find larger angle
Answers
Let the smaller angle be
[tex]=x[/tex]The larger angle is 4 times bigger than the smaller angle means
[tex]\begin{gathered} \text{larger angle =y} \\ \text{Therefore,} \\ y=4\times x \\ y=4x \end{gathered}[/tex]Concept:
The sum of two or more angles on a straight line is always 180°
Therefore,
[tex]x+y=180^0[/tex]By substituting the value of y=4x in the equation above, we will have
[tex]\begin{gathered} x+4x=180^0 \\ 5x=180^0 \\ \text{divide both sides by 5} \\ \frac{5x}{5}=\frac{180^0}{5} \\ x=36^0 \end{gathered}[/tex]substitute the value of x= 36° in y=4x to find the value of the bigger angle
[tex]\begin{gathered} y=4x \\ \text{when x=36} \\ y=4\times36 \\ y=144^0 \end{gathered}[/tex]Hence,
The larger angle is =144 °
OPTION D IS THE CORRECT ANSWER
Please be quick!
Clare has been working to save money and wants to have an equation to model the amount of money in
her bank account.
She has been depositing $175 a month consistently. She doesn't remember how much money she
deposited initially; however, on her last statement she saw that her account has been open for 10 months
and currently has $2475 in it.
Write an equation for the amount of money in Clare's bank account after x months. Which equation form
did you choose?
Answers
The initial amount that was deposited by Clare is $725.
The equation for the amount of money in Clare's bank account after x months will be 725 + 175x
What is an equation?An equation is the statement that illustrates that the variables given. In this case, two or more components are taken into consideration to describe the scenario. It is vital to note that an equation is a mathematical statement which is made up of two expressions that are connected by an equal sign.
Let the amount deposited initially be x.
Based on the information, this will be illustrated as:
x + 175(10) = 2475
x + 1750 = 2475
Collect like terms
x = 2475 - 1750
x = 725
The initial amount is $725.
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The Beta club is selling chocolate to raise money for Beta convention. Chocolate bars sell for $1.25 each and chocolate covered almonds sell for $2.00 each. The Beta club needs to raise more than $375 for all members to attend the convention. The students can sell up to 500 bars and covered almonds altogether.
1. Write a system of inequalities that can be used to represent this situation.
2. The club sells 100 chocolate bars. What is the least number of chocolate covered almonds that must be sold to cover the cost of attending Beta convention? Justify your answer.
Answers
(1) The system of inequalities that can be used to represent this situation is 1.25x + 2y > 375 and x+y ≤ 500 .
(2) The least number of chocolate covered almonds that must be sold to cover the cost of attending Beta convention is 126 .
In the question ,
Part(1)
let the number of chocolates be "x" .
let the number of chocolates with covered almonds be "y"
price of each chocolate bar = $1.25
price of each chocolate covered almonds = $2
Beta club needs more than $375
So , according to the question
1.25x + 2y > 375
and also the students can sell up to 500 bars and covered almonds altogether.
So , x+y ≤ 500 .
Part(2)
Given , the club sells 100 chocolate bars.
substituting x= 100 in the inequality 1.25x + 2y > 375 , we get
1.25(100) + 2y > 375
125 + 2y > 375
2y > 375-125
2y > 250
y > 125
least number of chocolate covered almonds to be sold is 126 .
Therefore , (1) The system of inequalities that can be used to represent this situation is 1.25x + 2y > 375 and x+y ≤ 500 .
(2) The least number of chocolate covered almonds that must be sold to cover the cost of attending Beta convention is 126 .
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Will and Sarah are racing across the playground. Instead of running, they are hopping. During the race, they must both hop at the same time. In one hop, Will can travel 5 feet, and Sarah can travel 4 feet.
The playground is 200 feet wide. Will wins the race after hopping 40 times. How far had Sarah hopped when Will finished the race?
I know the answer i just need explanation.
Answers
Sarah has hopped for 160ft when Will finished the race.
What is basic arithmetic?
Specific numbers and their computations employing a variety of fundamental arithmetic operations are at the center of arithmetic mathematics. Algebra, on the other hand, deals with the limitations and guidelines that apply to all other types of numbers, including whole numbers, integers, fractions, functions, and so on. Arithmetic math serves as the foundation for algebra, which always adheres to its definition. A large range of subjects fall within the broad definition of mathematics, which encompasses a very broad range of topics. Beginning with the fundamentals like addition, subtraction, and division of numbers, they then move on to more complicated topics like exponents, variations, sequence, progression, and more. This part does touch on some of the mathematical formulas and mathematical sequence. Four essential mathematical operations—addition, subtraction, multiplication, and division—are covered in basic arithmetic.
For Will
5 × 40
= 200 feet
For Sarah
4 × 40
= 160 ft
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Consider the density curve plotted below:1.63.24.86.480.050.10.150.20.25XPDF(X)Density CurveFind P(X<1.6) : Find P(X>4.8) :
Answers
Given:
There is a density curve given in the question
Required:
We need to find for
[tex]\begin{gathered} P(X<1.6) \\ P(X>4.8) \end{gathered}[/tex]Explanation:
Part a
We want to find P(X<1.6)
For this we just need to find the area below the curve until x=1.6, since we have a triangle we can do this:
[tex]P(X<1.6)=\frac{1}{2}*1.6*0.05=0.04[/tex]Part b
For this case we want to find this probability:
P(X>4.8)
and we can complement rule and we got
[tex]P(X>4.8)=1-P(X<4.8)=1-\frac{1}{2}*4.8*0.15=0.64[/tex]Final answer:
0.04
0.64
A. 2x-1+3x=0 B. 5x-1=0 How can we get Equation B from Equation A ?
Answers
By taking x as a common factor we get:
2x - 1 + 3x = 0
(2 + 3)*x - 1 = 0
5x - 1 = 0
How to get equation B from equation A?Let's start with equation A, it is:
2x - 1 + 3x = 0
If we group like terms, we will get:
(2x + 3x) - 1 = 0
Now we can take x as a common factor in the left term, so we get:
(2x + 3x) - 1 = 0
(2 + 3)*x - 1 = 0
Now we simplify the sum in the left term:
(2 + 3)*x - 1 = 0
5x - 1 = 0
This is equation B.
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Find the area of 2x-9 + x+5
Answers
Hope this helps :)
Answer: 3x-4
Step-by-step explanation: First Simplify, add the numbers 2x-9+x+5=2x-4+x Then combine like terms, 2x-4+x= 3x-4
Astronomers use a light year to measure distance. a light year is the distance light travels in one year. The speed is approximately 300,00km/sec. how long will it take a rocket traveling 63,000km/hr to reach Alpha Centauri (the ⭐ closest to Earth other than the ). Note: Alpha Centauri is approximately 4.34 light years from Earth. which is 4.11 x 10^13 km away (when using scientific notation). one light year is 9.46 x 10^12 km.
Answers
Speed of light = 300,000 km/sec
Rocket's speed = 63,000 km/hr or 6.3 x 10⁴ km/hr
Alpha Centauri distance from Earth = 4.11 x 10¹³ km
One light year (distance) = 9.46 x 10¹² km
To solve for the time it takes it travel, we can manipulate the speed formula.
[tex]\begin{gathered} \text{speed}=\frac{dis\tan ce}{\text{time}} \\ \text{time}=\frac{dis\tan ce\text{ }}{\text{speed}} \end{gathered}[/tex]We already have the distance of Alpha Centauri from Earth written above. We also have the speed of the rocket written above too. We will substitute those values to the formula.
[tex]\begin{gathered} \text{time}=\frac{4.11\times10^{13}\operatorname{km}}{6.3\times10^4\operatorname{km}\text{ /hr}} \\ \text{time}=0.6523809524\times10^9 \\ \text{time}=6.52\times10^8\text{ hr} \end{gathered}[/tex]Graph the Linear equation: y = - 3/4x + 5
Answers
Based on the given linear equation of y = - 3/4x + 5, the graph is shown attached.
How to graph an equation?When given a linear equation, you graph it by coming up with x values and then using the equation to find the corresponding y values.
The linear equation is y = - 3/4x + 5.
If the value x = -1, then y would be:
y = - 3/4x + 5
= -3/4(-1) + 5
= 5.75
If the value x = 0, then y would be:
y = -3/4(0) + 5
= 5
If the value x = 1, then y would be:
= -3/4(1) + 5
= 4.25
If the value x = 2, then y would be:
= -3/4(2) + 5
= 3.5
If the value x = 3, then y would be:
= -3/4(3) + 5
= 2.75
The points would be:
(-1, -5.75) (0, 5) (1, 4.25) (2, 3.5) (3, 2.75)
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a standard poker deck of cards contains 52 cards, of which four are kings. suppose two cards are drawn sequentially, so that one random circumstance is the result of the first card drawn and the second random circumstance is the result of the second card drawn. find the probability that the first card is a king and the second card is not a king. (round your answer to four decimal places.)
Answers
The probability that the first card is a king and the second card is not a king is 0.0045
Suppose two cards are drawn sequentially so that one random circumstance is the result of the first card drawn and the second random circumstance is the result of the second card drawn. To find the probability that the first card is a king and the second card is not a king.
In the first case let's find the probability of drawing a king from the deck of cards,
A = ( 4/52 )
In the second case the probability of drawing a card that is not a king from the deck is,
B = ( 3/51 )
At last, to get the final probability to draw that the first card is a king and the second card is not a king we need to multiply the above two cases as,
A x B = ( 4/52 ) ( 3/51 )
= 1/221
= 0.0045
The probability that the first card is a king and the second card is not a king is 0.0045
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Beth is planning a playground and has decided to place the swings in such a way that they are the same distance from the jungle gym and the monkey bars. if beth places the swings at point d, how could she prove that point d is equidistant from the jungle gym and monkey bars? if segment ad ≅ segment cd, then point d is equidistant from points a and b because congruent parts of congruent triangles are congruent. if segment ad ≅ segment cd, then point d is equidistant from points a and b because a point on a perpendicular bisector is equidistant from the endpoints of the segment it intersects. if m∠acd = 90° then point d is equidistant from points a and b because congruent parts of congruent triangles are congruent. if m∠acd = 90° then point d is equidistant from points a and b because a point on a perpendicular bisector is equidistant from the endpoints of the segment it intersects.
Answers
The angle bisector theorem states that a triangle's opposite side is divided into two halves by an angle bisector that is proportional to the triangle's other two sides.
A point on a perpendicular bisector is equidistant from the endpoints of the segment it intersects, therefore if mACD = 90°, point D is equidistant from points A and B.
Any point on the perpendicular bisector is simply equal distance from both endpoints of the line segment on which it is drawn, according to the perpendicular bisector theorem.
The answer is that point is equidistant from points A and B because a point on a perpendicular bisector is equidistant from the endpoints of the segment it makes up. Therefore, if a pillar is stationed at the middle of a bridge at an angle, all the points on the pillar will be equidistant from the end points of the bridge intersects.
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What sets does -√3,1 and 0 belong to
Answers
√2 and -√3 belong to the set of Irrational Numbers.
1 belong to the following sets:
• Rational
,• Whole
,• Natural
,• Integers
0 belongs to the following sets:
• Rational
,• Whole
,• Integers
The vertical distance is
. The horizontal distance is
. So the slope can be represented by the ratio
. The ordered pair for the red point on the line is
. If we substitute the numbers from the ordered pair in for x and y in the ratio, it will equal
please help ill give brainly
.
Answers
Answer:
. The horizontal distance
Step-by-step explanation:
The vertical distance is
. The horizontal distance is
. So the slope can be represented by the ratio
. The ordered pair for the red point on the line is
. If we substitute the numbers from the ordered pair in for x and y in the ratio, it will equal
please help ill give brainly
.
The coordinates of rhombus abcd are a(-4,-2) b(-2,6) c(6,8) d(4,0). What is the area of the rhombus
Answers
First, graph the rhombus:
Area of a rhombus = Product of diagonals / 2
Find the length of the diagonals:
Distance between points:
[tex]\sqrt[\placeholder{⬚}]{(x2-x1)^2+(y2-y1)2^}[/tex]Diagonal AC
[tex]AC=\sqrt[\placeholder{⬚}]{(6-(-4))^2+(8-(-2))^2}[/tex]AC= 10√2
Diagonal BD
[tex]BD=\sqrt[\placeholder{⬚}]{(4-(-2))^2+(0-6)^{^2}}[/tex]BD=6√2
Area= AC x BD / 2
Area = [(10√2) x (6√2)]/2
Area = 60
30. Solve for x: 7^/10 = 2, approximate to 4 digitsa. 6.325 b. 3.256 c. 3.265 d. 3.652 e. 3.562
Answers
• Solution
[tex]7^{\frac{x}{10}}=2[/tex]
To solve for x, we take the logarithm of both sides.
[tex]\log 7^{\frac{x}{10}}=\log 2[/tex]Applying the law of logarithm to the equation above;
[tex]\log a^b=b\log a[/tex][tex]\begin{gathered} \log 7^{\frac{x}{10}}=\log 2 \\ \frac{x}{10}\log 7=\log 2 \\ \text{Dividing both sides by log 7;} \\ \frac{x}{10}=\frac{\log 2}{\log 7} \\ \frac{x}{10}=\frac{0.3010}{0.8451} \\ \frac{x}{10}=0.3562 \\ \text{Cross multiplying the equation;} \\ x=0.3562\times10 \\ x=3.562 \end{gathered}[/tex]Therefore, the approximate value of x is 3.562
The correct option is E.
Evelyn is 2.5 years younger than James. Two times the sum of their age is 57. Write and solve an equation to find Evelyn age.
Answers
The age of Evelyn is 10.5 years finding by the properties of linear equation.
What is linear equation?
A linear equation in algebra is one that only contains a constant and a first-order (linear) component, like y=mx+b, where m is the slope and b is the y-intercept.
Let the age of James is x years.
The age of Evelyn is x - 2.5 years
Sum of age of Evelyn and James are x + x - 2.5 = 2x - 2.5
According to question,
2 x (2x - 2.5) = 57
=> 4x - 5 = 57
=> 4x = 57 - 5
=> 4x = 52
=> x = 52/4
=> x = 13
Age of James is 13 years and the age of Evelyn is 13 - 2.5 = 10.5 years.
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Which equation has the solution x = 5? Select each correct answer. Responses
A) 11 + 6x = 22
B) 3x + 1 = 9
C) 18−2x=9
D) 25/x+4=9
E) x/5 + 5 = 6
F) 32−4x=12
Answers
The equation that has the same solution as x = 5 are as follows:
25 / x + 4 = 9x / 5 + 5 = 6 32 - 4x = 12 How to solve equation?An equation is a mathematical statement with an 'equal to' symbol between two expressions that have equal values.
In other words, an equation is a mathematical statement that is made up of two expressions connected by an equal sign.
The equation can be solved as follows:
The equation will have the same solution as x = 5.
Therefore,
25 / x + 4 = 9
subtract 4 from both sides of the equation
25 / x + 4 = 9
25 / x + 4 - 4 = 9 - 4
25 / x = 5
cross multiply
5x = 25
divide both sides by 5
x = 25 / 5
x = 5
x / 5 + 5 = 6
x / 5 = 6 - 5
x / 5 = 1
cross multiply
x = 5
32 - 4x = 12
- 4x = 12 - 32
- 4x = - 20
divide both sides of the equations by - 4
x = -20 / - 4
x = 5
Therefore, the equation with same solution are 25 / x + 4 = 9, x / 5 + 5 = 6 and 32 - 4x = 12
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