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Svetlanka
6 days ago
10

If only two points are needed to determine a​ line, why are three ordered pair solutions or points found for a linear​ equation?

Mathematics
1 answer:
zzz [9K]6 days ago
7 0

To plot the graph of a linear equation, two points suffice to create a line.

Nevertheless, errors can occur; thus, when the line is drawn, it may seem accurate. Two points will always define a line, regardless of the correctness of those points.

To confirm that the points are accurate, we find a third point to verify that the two previously calculated points are correct and that all points align on the same line. If they don’t, an error has been made.

Option A) is the correct choice

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the shorter sides of an acute triangle are x cm and 2x cm. the longest side of the trinalge is 15 cm. what is the smallest possi
Leona [9271]
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.
3 0
1 day ago
Which number line represents the solution set for the inequality –negative StartFraction one-half EndFraction x is greater than
Leona [9271]

Answer:

zero slope

Step-by-step explanation:

Hope this information is helpful:)

5 0
1 month ago
Andre wants to make an open-top box by cutting out corners of a 22 inch by 28 inch piece of poster board and then folding up the
Svet_ta [9518]
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.
4 0
12 days ago
a sign says that the price marked on all music equipment is 30% off the original price you buy an electric guitar for sale price
PIT_PIT [9121]

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 = OP \times30/100

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

5 0
19 days ago
12x+7&lt;−11 AND5x−8≥4012
Svet_ta [9518]

Answer:

No solution

Step-by-step explanation:

Given: 12x+7 and  5x-8\geq 40

Handle each inequality separately.

12x+7              Utilizing the subtraction property of inequalities

12x

12x

x

x

and

5x-8\geq 40               Utilizing the addition property of inequalities

5x\geq 40+8

5x\geq 48

x\geq \dfrac{48}{5}

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

8 0
1 month ago
Read 2 more answers
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