A student solved the given equation and justified every step except one. What is the missing reason? A) Associative property of
addition B) Commutative property of addition C) Multiplicative property of equality D) Distributive property of multiplication over addition
1 answer:
Given:
The statements and reasons to solve an equation.
To find:
The missing reason.
Solution:
If a, b and c are three real number, then
Associative property of addition :
Commutative property of addition :
Multiplicative property of equality :
Distributive property of multiplication over addition :
In the given step, is written as
.
It means, only parenthesis are changed, which is possible by Associative property of addition.
So, the missing reason is Associative property of addition.
Therefore, the correct option is A.
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Refer to the diagram shown below.
Let x = m∠ADB.
Because m∠BDC is 32° greater than m∠ADB, therefore
m∠BDC = x + 32°
Each angle of a rectangle is 90°, therefore
x + (x+32) = 90
2x + 32 = 90
2x = 58
x = 29°
x+32 = 61°
Answer:
m∠BDC = 61°
m∠ADB = 29°
Let x = m∠ADB.
Because m∠BDC is 32° greater than m∠ADB, therefore
m∠BDC = x + 32°
Each angle of a rectangle is 90°, therefore
x + (x+32) = 90
2x + 32 = 90
2x = 58
x = 29°
x+32 = 61°
Answer:
m∠BDC = 61°
m∠ADB = 29°
Answer: The correct option is second, a rotation clockwise about the origin followed by a reflection across the x-axis.
Explanation:
From the given figure it is noticed that the vertices of ΔABC are A(-6,4), B(-4,6), C(-2,2) and vertices of ΔA'B'C' are A'(4,-6), B(6,-4), C(2,-2).
It means if the point is P(x,y) then after transformation it will be P'(y,x).
If a point P(x,y) reflection across the y-axis followed by a reflection across the x-axis, then the image of point after transformation will be P'(-x,-y), therefore it is not the correct option.
If a shape is rotated clockwise about the origin then the point P(x,y) will be P'(y,-x) and after that reflect across the x-axis, so the point after transformation will be P'(y,x), therefore it is the correct option.
If a shape is rotated clockwise about the origin then the point P(x,y) will be P'(-y,x) and after that reflect across the x-axis, so the point after transformation will be P'(-y,-x), therefore it is not the correct option.
If a point P(x,y) reflection across the x-axis followed by a reflection across the y-axis, then the image of point after transformation will be P'(-x,-y), therefore it is not the correct option.
Hence, the correct option is second, a rotation clockwise about the origin followed by a reflection across the x-axis.
Answer: $ 4,515
Step-by-step explanation:
The cost of the car she wanted to buy = $35,550
Her savings = $20,700
That means she needs( $35,550 - $20,700) more in order for her to buy the car.
Amount borrowed from the finance company = $35,550 - $20,700
= $ 14,850
Since she now owes the financial company a total of $19,365, then the interest accrued by the loan she borrowed is given by:
$19,365 - $ 14,850
= $4,515