Answer:
x=-5
Step-by-step explanation:
Set up the rational expression with the same denominator over the entire equation.
2x-2/6=3x+3/6
Since the expression on each side of the equation has the same denominator, the numerators must be equal.
2x−2=3x+3
Move all terms containing x to the left side of the equation.
−x−2=3
Move all terms not containing x to the right side of the equation.
-x=5
Multiply each term in x=−5 by −1
x=−5
The composition of the transformation is (b) A rotation of 90° and then a translation left 2, up 4.
<h3>How to determine the transformation?</h3>
The transformation rule is given as:
r (90, 0) T(−2,4)
The r(90,0) represents a rotation of 90 degrees.
The other part of the transformation rule can be rewritten as:
T(-2,4) => (x - 2,y + 4)
This means a translation right by 2 units and up by 4 units
Hence, the composition of the transformation is (b)
Read more about transformation at:
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Answer:
x=-2
Step-by-step explanation:
2(3x – 1) = 4x - 6
Distribute
6x-2=4x-6
Moving like terms (4x)
2x-2=-6
Moving like terms (-2)
2x=-4
Divide both sides by 2 to isolate x
x=-2
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Annie's Attic does not have a proportional relationship but Bettie's Boutique does. The constant of proportionality at Betty's Boutique is 0.8.
Step-by-step explanation:
Step 1; To have a proportional relationship, if x's value varies, the y's value should also vary. If x increases, y increases correspondingly while if x decreases, y should also decrease.
Step 2; For Annie's Attic, the sale price = Original price - $5.
No matter what the value of the original price, there is only a difference of $5. Even if the price is increased to $100 the discount will only be $5. So this is not a proportional relationship.
Step 3; At Bettie's Boutique, they are having a 20% off sale. Whatever the cost, 20% is reduced. If bought for $15, price is $15 - 20% = $12. If bought for $25, the price will be $25 - 20% = $20.
If the original price is taken as x as the sale price is y, the relationship is given by; y = (100% - 20%) × x = 80% × x = 0.8 × x. So y = 0.8x. Here the constant of proportionality is 0.8.
(p>64) divided by 4 is less than or equal to w
