so if we take the area of the whole square that's shaded, and then subtract from it the area of the square that's not shaded, what's leftover is the area we never subtracted, namely the shaded region.
On Solving equation in one variable 0.4x = 5.2, we found that the clerk returned 13 dimes, 34 quarters and4 nickels in change of $10 bill.
What is an linear equation in one variable?
Linear equation is an equation containing one variable with power one and constants.
Standard form of an linear equation in one variable x is :
ax + b= 0 , a, b are constants
x= -b/ a is solution if this equation. Linear equation can be solved by adding or subtracting , multiplying , division same number to both sides.
A clerk need a change of $10 bill
Let the clerk returned x dimes and y nickels and z quarters to pay $10
Value of one nickel = $ 0.05, one dime = $ 0, one quarter = $ 0.25
Value of x dimes becomes 0.1x
Value of y nickels becomes 0.05 y
value of z quarters becomes 0.25 z
Total value of given dimes, quarters and nickels , 0.1 x + 0.05 y + 0.25z = 10
Number of dimes = Number of nickels + 9
∴ x = y +9 ⇒ y = x- 9
Number of quarters = Number of dimes +21
∴ z = x + 21
Put y = x-9 and z = x + 21 in 0.1 x + 0.05 y + 0.25z = 10
Then,
0.1 x + 0.05 ( x-9) + 0.25 (x +21) = 10
⇒ 0.1 x +0.05x -0.45 + 0.25 x + 5.25 = 10
⇒ 0.4x +4.8 = 10
⇒ 0.4 x = 10- 4.8
⇒ 0.4x = 5.2
⇒ x = 5.2/0.4 = 13
Thus , y = x-9 = 13 -9 = 4
z = x + 21 = 13 + 21 = 34
Therefore, the clerk returned 13 dimes , 4 nickels and 34 quarters for $10 bill.
Also, learn more about linear equation from the link below:
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Answer:
See Below.
Step-by-step explanation:
Let:
If we multiply both sides by 10, we get:
Now, we will subtract n from both sides:
On the left, we can replace the n:
Subtract:
Divide both sides by 9:
Hence:
Algebraically, 0.5 does not equal to 5/9. Instead, when 5/9 is converted to a decimal it equals approximately 0.56. The correct fraction representation of 0.5 is 1/2.
I'm sorry, but there seems to be a misunderstanding in your question. The algebraic representation of 0.5 is not equal to 5/9. If you convert 5/9 to a decimal, using division on a calculator or by hand, it doesn't equate to 0.5, but rather approximately 0.56. Let's go through the conversion step by step:
1. Divide the numerator (5) by the denominator (9).
2. This will give you a decimal approximation for the fraction.
So, 5 ÷ 9 = 0.56 (rounded to two decimal places).
This clearly shows that algebraically 0.5 does not equal 5/9. The valid algebraic equivalent of 0.5 in terms of fraction is 1/2.
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City M: −9° F
Which statement about the temperatures at the two cities is true?
City M was warmer than City L because −9° F < −8° F.
City M was warmer than City L because −9° F > −8° F.
City M was colder than City L because −9° F > −8° F.
City M was colder than City L because −9° F < −8° F.
Answer:
The 3rd one, -9 F > -8 F.
Step-by-step explanation:
B.commutative
C.distributive
D.reflexive
Which answer is right !
Leila used the distributive property in the first step to solve the given equation, multiplying both terms in the parentheses by the fraction 2/3.
In this step, Leila applied the distributive property. The distributive property states that a(b + c) = ab + ac. This property allows us to multiply a single term by two or more terms within a parenthesis. In this case, Leila multiplied the fraction 2/3 by both 'x' (the variable) and '5' (the constant), inside the parentheses.
So, the equation went from 2/3 (x + 5) to (2/3 * x) + (2/3 * 5), which follows the rule of distributive property ab + ac when applied to the given equation.
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Answer:
Step-by-step explanation:
-3