Paige claims that the solution to the systems of linear equations y=2x-1 and -12x+3y=9 is (-2,-5). Which 3 methods could be used to verify Paige claim?

Answers

Answer 1

Answer:

Final answer:

Paige's claim can be verified through three methods: substitution, elimination, and graphing. Each method involves using the potential solution (-2,-5) to determine if it is a valid solution to the given systems of linear equations.

Explanation:

The verification of Paige's claim that the solution to the systems of linear equations y=2x-1 and -12x+3y=9 is (-2,-5), can be achieved by using three distinct methods. These methods include: 1. Substitution; 2. Elimination; and 3. Graphing.

Substitution: You substitute the x and y values of the proposed solution into both equations to verify whether both are true. In this case, substituting x=-2 and y=-5 into both equations should confirm whether Paige's claim is correct.

Elimination: You can add or subtract the two equations in order to eliminate one of the variables and solve for the other. You then confirm if the solution matches Paige's claim.

Fianlly, Graphing: You graph both equations on the same axes and determine their point of intersection. If the point of intersection is (-2,-5), then Paige's claim is verified.

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What is an advantage of consuming natural foods instead of dietary supplements?

Answers

Answer with explanation:

Dietary supplements don't have all the nutrients you need that a natural food has .

Natural food has beneficial nutrients such as flavonoids and antitoxidants, that aren't in most supplements.

The fresh food is loaded with nutrients that are necessary for good health, such as magnesium,calcium ,and Vitamin A and C etc.

Whereas the dietary supplements in much amount can actually harm us.

for example: Extra Vitamin A supplements can lead to dangerous,toxic levels if taken too frequently.

Natural foods contain substances that protect the body against diseases, and are often more satisfying than supplements.

The measures of the exterior angles of a heptagon are x°, 2x°, 3x°, 4x°, 7x°, 9x°, and 10x°. Solve for x.

Answers

The value of x in the for an heptagon with exterior angles as x°, 2x°, 3x°, 4x°, 7x°, 9x°, and 10x° is 10.

What are heptagon:

Heptagons are polygons with seven sides.

The sum of exterior angles of a polygon is equals to 360 degrees.

Therefore,

x + 2x + 3x + 4x + 7x + 9x + 10x = 360°

36x = 360

divide both sides by 36

36x / 36 = 360 / 36

x = 10

Therefore, the value of x is equals to 10

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Final answer:

The heptagon's exterior angles sum up to 360 degrees. Given the angles are x°, 2x°, 3x°, 4x°, 7x°, 9x°, and 10x°, summing and setting equal to 360 yields a value of 10 for x.

Explanation:

The subject of this question is Mathematics, specifically pertaining to angles and geometry. The question pertains to a heptagon, or a seven-sided polygon, and its exterior angles. We know that the sum of the exterior angles of any polygon is 360 degrees.

The question provides the measures of the exterior angles of a heptagon in terms of x: x°, 2x°, 3x°, 4x°, 7x°, 9x°, and 10x°. Therefore, to find the value of x, we need to solve the equation x + 2x + 3x + 4x + 7x + 9x + 10x = 360. That results in 36x = 360, and so .

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Which expression is equivalent to 2 + 3?A) 3 - 2
B) 3 + 2
C) 3(2)
Eliminate
D) 6

Answers

B) 3+2 is the expression equivalent

B) 3 + 2 would be the answer to this question because they are both equivalent.

A store is offering a 20% discount on all sales over $50. If you purchase a shirt and a pair of jeans for $62.50, what is the amount of the discount you would receive?

Answers

If I purchase a shirt and a pair of jeans for $62.50, I would receive a $12.50 discount and the total price would now be $50.

What is the perimeter of triangle ABC with vertices A(-1,-2), B(2,-6), and C(-3,-6)?

Answers

find the distance between the points and that is perimiter

find
A to B
B to C
C to A
we need the distance formula
D= $\sqrt{(x2-x1)^(2)+(y2-y1)^(2)}$
where D is the distance between points (x1,y1) and (x2,y2)

A to B
(-1,-2) to (2,-6)
D= $\sqrt{(2-(-1))^(2)+(-6-(-2))^(2)}$ =5

B to C
(2,-6) to (-3,-6)
since the y value stayed the same, find the distance betwen the x values
2 to -3 is distance of 5

C to A
(-3,-6) to (-1,-2)
D= $\sqrt{(-1-(-3))^(2)+(-2-(-6))^(2)}$ =2√5

add everybody

5+5+2√5=10+2√5 units

During the Age of Exploration, stretching from the 1400s to the 1900s, which of the following regions was the focal point for global trade and exchange of culture? A Option A: Pacific B Option B: Atlantic C Option C: African D Option D: Asian

Answers

Answer:

The correct answer is Option B: Atlantic

Step-by-step explanation:

During the Age of Exploration, stretching from the 1400s to the 1900s, the Atlantic region was the focal point for global trade and exchange of culture.

During the Age of Exploration, the European ships traveled extensively overseas around the world to search new trading routes.

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