The smallest whole-number value for x that works is 7. The triangle’s sides can be defined as: a = x, b = 2x, and c = 15. Recognizing c as the longest side leads us to the condition for an acute triangle: c^2 must be less than a^2 + b^2. Inputting the known values, we solve for x and find that x must exceed 6.708. As a result, the least integer that satisfies this requirement is 7.
Answer:
zero slope
Step-by-step explanation:
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The formula for the box's volume is V = (length)(width)(height). If we denote the side length of the cutouts as x, we establish V = (28 - 2x)(22 - 2x)(x). Explanation: We intend to excise x by x squares from each corner of a 28 by 22-inch poster board, leading to bottom dimensions of 28 - 2x and 22 - 2x, with a height of x. This expression can be left as is or multiplied and simplified if desired. If we select x = 2 (a random choice as you did not specify), the box's volume calculates to V = (28 - 2*2)(22 - 2*2)(2), rendering V = (24)(18)(2) cubic inches. Since x measures length, it must be greater than zero. Furthermore, the base width of the box can't fall below zero, establishing the inequality for x: 22 - 2x > 0, meaning 11 - x > 0, or x < 11. If we check with x = 10, then V = (28 - 20)(22 - 20)(10). Is this greater than zero? YES. Thus, x < 11 is indeed a reasonable domain in this context.
The original price stands at $450.
Step-by-step explanation:
Step 1:
Given information, Discount%, D% = 30 and Selling Price, SP = $315
Step 2:
Formulate the equation for determining the Original Price
Selling Price (SP) = Original Price (OP) - Discount (D)
Discount (D) = Original Price (OP) * (D%/100)
Step 3:
Plug in the known values into the formula
315 = OP - D
D = 
D = 0.3 OP
Step 4:
Insert the value of D back into the initial equation
315 = OP - 0.3 OP
315 = OP (1 - 0.3) = 0.7 OP
A resulting Original Price of OP = 315/0.7 = $450
Answer:
No solution
Step-by-step explanation:
Given:
and 
Handle each inequality separately.
Utilizing the subtraction property of inequalities




and
Utilizing the addition property of inequalities



Thus, the solution to the combined inequality is the overlap of both solutions.
Refer to the attached image for the number line representation.
No solution