1/4(7+3g)=-g/8
Please help, algebra homework!?!!!

Final answer:

To interpret algebraic expressions contextually, students should grasp the meaning behind each symbol and the relationships within equations rather than just substituting numbers. Understanding the conceptual basis for equations and checking the reasonableness of solutions aids in developing a deeper comprehension and ability to solve complex problems.

Explanation:

Interpreting Algebraic Expressions

To interpret algebraic expressions in terms of their context, it's essential to understand what each symbol represents within a given problem. Instead of rushing to substitute numerical values for symbols, students should focus on understanding the underlying concepts and relationships that the equation models. For example, consider the equation w = A/h, which relates the width of a rectangle to its area (A) and height (h). Instead of viewing it as a mere formula, recognizing it as a rearranged version of A = wh allows one to comprehend that if the height (h) decreases while the area (A) remains constant, the width (w) must increase. This understanding is crucial when working with equations, as it transforms them from abstract symbols to meaningful representations of physical quantities or logical relationships.

To further contextualize equations, students are encouraged to eliminate unnecessary terms to simplify the algebra, and upon finding a solution, to check if the results are reasonable within the context of the problem. This not only aids in solving the problem correctly but also in developing a deeper intuitive understanding of the subject matter.

In sum, interpreting algebraic equations requires a balance between the abstract manipulation of symbols and the practical reasoning about what these symbols represent in the real world. This applied understanding forms the basis of problem-solving in many scientific and engineering fields and empowers students to tackle more complex problems with confidence.

Answer: $1200

Step-by-step explanation:

To find the total distance walked by the four students, add their individual distances together.

To find the total distance walked together, you need to add up the distances each student walked. The distances given are represented as fractions. To add fractions, first make sure the denominators are the same. In this case, the denominators are already the same, so you can add the numerators together. So, 3/4 + 1/2 + 2/3 + 3/4 = 15/12.

Simplify the resulting fraction by finding the greatest common divisor of the numerator and the denominator, which is 3. Divide both the numerator and denominator by 3 to get the final answer: 15/12 ÷ 3/3 = 5/4.

Therefore, the students walked a total distance of 5/4 or 1 1/4.

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All three candles will be 6 centimeters tall after 4 hours of burning.

To determine when all three candles will be 6 centimeters tall, we can set up equations for each candle and solve for the time it takes to reach the desired height.

For the taller candle, we can set up the equation:

16 - 2.5t = 6,

where t represents the number of hours.

Similarly, for the shorter candle:

12 - 1.5t = 6.

And for the middle candle:

15 - 2.25t = 6.

Simplifying each equation, we have:

-2.5t = -10,

-1.5t = -6,

-2.25t = -9.

Solving for t in each equation, we find:

t = 4 for the taller candle,

t = 4 for the shorter candle,

t = 4 for the middle candle.

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The slope of the line is "4".

Given:

As we know the formula for finding the slope will be:

→ [tex]m = \frac{y_2-y_1}{x_2-x_1}[/tex]

By substituting the values, we get

→     [tex]= \frac{-61-(-37)}{-32-(-26)}[/tex]

→     [tex]= \frac{-61+37}{-32+26}[/tex]

→     [tex]= \frac{-24}{-6}[/tex]

→     [tex]=4[/tex]

Thus the answer above is right.  

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The name of Triangle is Isosceles Triangle.

Any triangle with (at least) two equal sides is said to be isosceles. The remaining side in the illustration has length in addition to the two equal sides. This characteristic equates to the triangle's two angles being equal. Therefore, an isosceles triangle has two equal sides as well as two equal angles.

Given:

From the figure we can see that the triangle is have two of its line segment is equal.

As, we know that the triangle which have two of its sides and angles are equal is an Isosceles Triangle.

Thus, the Triangle is Isosceles Triangle.

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I'm pretty sure that the answer is three inches PER YEAR because think, there is 12 months in a year so if he grows 3 inches per month for 4 year he/she would be taller than an 8 year old, so per year makes more sense.

The larger number will be 22 and the smaller number will be 16.

Determine the known quantities and designate the unknown quantity as a variable while trying to set up or construct a linear equation to fit a real-world application.

In other words, an equation is a set of variables that are constrained through a situation or case.

Let's say the larger number is L and the smaller number is s

Given the larger of the two numbers is 10 less than twice the smaller number

So,

L = 2s - 10

And

The Sum of the two numbers is 38

So,

L + s = 38

By substitution

38 - s = 2s - 10

s = 16

By again substitution

L = 2(16) - 10

L = 22

Hence "The larger number will be 22 and the smaller number will be 16".

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Answer:

The answer is 5

Step-by-step explanation:

x/2y = 10/2*1 = 10/2 =5

So basically you do the 10 on top and on the bottom you do 2*1 which equals 2 then you got 10/2 then you would see how many times 2 goes into 10 which is 5 so 5 is your answer hoped this helped! :)

Answer:

Adam travels total 415 miles.

Step-by-step explanation:

The distance Adam travels on Monday = 248 miles

The distance Adam travels on Tuesday = 167 miles

We have to calculate the total number of miles Adam travels.

Total number of miles Adam travels = distance traveled on Monday + distance  traveled on Tuesday

                                                           = 248 + 167

                                                           = 415 miles

Adam travels total 415 miles.

[tex]\text{Hey there!}[/tex]

[tex]17\dfrac{5}{6}=17\times6 + 5 =17\times6 \rightarrow102+5 = 107\\\\\text{107  would be your numerator \& 6 would be your denominator.}[/tex]

[tex]17\dfrac{5}{6} = \dfrac{107}{6}[/tex]

[tex]-\dfrac{3}{5}\times\dfrac{107}{6}\\\\5 + 6 = 10\\\\\text{Your new equation is: }\dfrac{-107}{10}\text{Which the mixed number fraction is: }-10\dfrac{7}{10}[/tex]

[tex]\boxed{\boxed{\bf{Answer(s): -10\dfrac{7}{10} \ or \dfrac{-107}{10}}}}\checkmark\\\\\text{Good luck on your assignment and enjoy your day!}\\\\\frak{LoveYourselfFirst:)}[/tex]

(1)negative x (2)negative = positive x (3)negative = negative x (4)positive = negative

negative divided by negative = positive

odd number were negative

The required solutions are as follows,
(a) Evelyn's answer is Too low, Option B is correct.

(b) Evelyn's answer is correct, and Option C is correct.

(c) Evelyn's answer is Too high, Option A is correct.

In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication and division,

Here,
According to the question,
Evelyn evaluated 1 and 6/7 - 3/4 as,
= 1 6/7 - 3/4  and add 3/4 later,
= 1 6/7 -3/4 + 3/4
= 1 6/7

So,
If the sum of her answers is 3/4 is 1,
Evelyn's answer is Too low, Option B is correct.

If the sum of her answer and 3/4 is 1 and 6/7
Evelyn's answer is correct, and Option C is correct.

If her answer is minus 3/4 is 1 and 6/7,
Evelyn's answer is Too high, Option A is correct.

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