Let n be a number of friends at the perty. If <span>dinner costs $30 per person, then it cost $30n for all friends.
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Robert has booked a banquet hall which costs <span>$200, then his total expenses are $200+30n.
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If the final bill is p, then p=<span>200+30n.
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Answer: p=<span>200+30n.</span>
Width of the rectangle is 12 cm.
Solution:
The length of a rectangle is 4 cm more than its width , and the area of the rectangle is 96 cm². Find the width of the rectangle.
Given data:
Let x be width of the rectangle.
Length of the rectangle = (x + 4) cm
Area of the rectangle = 96 cm²
length × breadth = 96
Subtract 96 from both sides.
Let us factor the polynomial.
Take x common in 1st two terms and -12 common in next two terms.
Now, take (x + 8) common in both terms.
x + 8 = 0 and x - 12 = 0
x = -8 and x = 12
Dimension cannot be in negative terms, so ignore x = -8.
Width = 12 cm
Width of the rectangle is 12 cm.
When all sides of a quadrilateral are equal (indicated by tick marks on the four sides) in length and connect the opposing vertices with a line, it will form four 90° angles. Therefore, each equation will equal 90.
10x= 90
x+y= 90
3z= 90
The measure of angles 1 and 3 can be solved as they are so:
10x= 90 ➡️ x=9
3z= 90 ➡️ z= 30
The value of x is needed to solve for the measure of angle 2 so plug in the value of x and solve:
x+y= 90
9+y= 90
y= 81
Therefore the answer is a.
Answer:
C. (x +1)(x +3)(x +4)
Step-by-step explanation:
The least common multiple is the product of the unique factors of each of the expressions. To find it, we need to factor each expression and identify the unique factors.
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<h3>factorization</h3>
x² +4x +3 = (x +3)(x +1)
x² +7x +12 = (x +3)(x +4)
<h3>LCM</h3>
The unique factors are (x +1), (x +3), (x +4). The LCM is their product:
LCM = (x +1)(x +3)(x +4)
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<em>Additional comment</em>
The positive sign of the constant (+3, +12) in each case tells you that the constants in the binomial factors will have the same sign. The positive sign of the linear term (+4x, +7x) in each case tells you the binomial factors will have constants with a positive sign. So, all of the answer choices that have negative constants can be eliminated.
