Answer:
5..
Step-by-step explanation:
The equation is solved and the two numbers are x = 7 and y = 12
Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be represented as A
Now , the value of A is
Let's call the first number "x" and the second number "y"
x = y - 5 (the first number is 5 less than the second number)
2y = 4x - 4 (twice the second number is 4 less than 4 times the first)
We can use substitution to solve for one of the variables.
Substituting the first equation into the second equation, we get:
2y = 4 (y - 5) - 4
Simplifying this equation , we get
2y = 4y - 24
2y - 4y = -24
-2y = -24
y = 12
Now that we know that the second number is 12, we can use the first equation to find the first number:
x = y - 5
x = 12 - 5
x = 7
Hence , the two numbers are 7 and 12
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Answer:
9 and 14
Step-by-step explanation:
One number is 5 less than a second number.
a = b - 5
:
Twice the second number is 8 less than 4 times the first.
2b = 4a - 8
replace a with (b-5)
2b = 4(b-5) - 8
2b = 4b - 20 - 8
2b - 4b = -28
-2b = -28
b = 14
then
a = 9
Hi Mark
3x+y=4
2x+y=5
Solve 3x+y=4 for y
Add -3x to both sides
3x+y-3x=4-3x
y=-3x+4
Substitute -3x+4 for y in 2x+y=5
2x+y=5
2x-3x+4=5
Simplify both sides of the equation
-x+4=5
Add -4 to both sides
-x+4-4=5-4
-x=1
Divide both sides by -1
-x/-1= 1/-1
x=-1
Substitute -1 for x in y=-3x+4
y=-3x+4
y=(-3)(-1)+4
Simplify both sides of the equation
y=7
Answer: (-1,7)
I hope that's help ! Have a great weekend :)
Answer:
width is 14, length is 19
Step-by-step explanation:
let w represent the width of the rectangle.
"The length of a rectangle is 5 cm longer than its width."
You can take from this that you must add 5 to the width to get the length.
so, you can now write that L=w+5 .
The formula for perimeter is 2w+2L.
You can plug the values in.
2w+2(w+5) is the expression you get.
use distributive property on the 2(w+5) to get 2w+ 2w+10 . Add same terms together and get 4w+10, which represents the perimeter.
"..The perimeter of the rectangle is 66 cm."
Set the simplified expression 4w+10 to 66 to get
4w+10=66
Subtract 10 from both sides and get
4w=56
divide by four for both sides and get w=14 .
We are not done yet!
To find the length, plug the width back into our formula L=w+5 and get L=14+5. The length is 19.
Answer:
Step-by-step explanation:
The true purpose of homework is to reinforce and apply the concepts and skills learned in class, promote independent learning, and prepare students for future assessments.
The true purpose of homework is to reinforce and apply the concepts and skills learned in class. It provides an opportunity for students to practice and refine their knowledge, develop problem-solving skills, and improve time management and organizational skills. Homework also helps students prepare for future assessments and promotes independent learning.
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Homework in algebra assists students in developing an understanding and intuition for mathematics, aids students to apply classroom-learned concepts in solving problems, and allows teachers to gauge their progress. It involves independent practice and cooperative work through group activities, promoting deeper understanding, critical thinking, and self-efficacy among students.
The true purpose of homework, particularly in the field of mathematics and algebra, serves multiple beneficial objectives. One of the key purposes is helping students to develop an understanding and intuition for number relationships and algorithms, rather than seeking quick, short-term solutions. Homework functions as an essential tool that promotes the building of these necessary neural connections through problem-solving practice and reinforcement of classroom learning, which often requires some level of struggle and effort from the student.
Another role of homework is enabling students to apply math principles and concepts gleaned from classroom lessons and textbooks, essentially bringing equations to life. This often involves tackling mathematical questions, using algebra and arithmetic, and can be performed individually or through cooperative learning in group activities. This independent practice not only consolidates classroom learning but also empowers students to cross-verify facts and develop a sense of self-efficacy.
Lastly, homework provides teachers with the opportunity to monitor student progress, creating an understanding of the students' current skills and where there might be gaps in learning. This data collected from homework can guide future instruction and remedial help. Thus, while homework often gets a bad rap, it is indeed a critical pillar in the learning process, fostering a deeper understanding, critical thinking, and independent learning among students.
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