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2 years ago

Solve for x: 7x-3/5x-2 = -2

Mathematics

1 answer:

VMariaS [17]2 years ago

4 0

Step-by-step explanation:

<h3>★ Solution:-</h3>

$\sf \leadsto \dfrac{7x - 3}{5x - 2} = -2$

$\sf \leadsto 7x - 3 = -2(5x - 2)$

$\sf \leadsto 7x - 3 = -10x + 4$

$\sf \leadsto 7x + 10x = 4 + 3$

$\sf \leadsto 17x = 7$

$\sf \leadsto x = \dfrac{7}{17}$

Hence the value of x is 7/17

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Kareem wants to find the number of hours the average sixth-grader at his school practices an instrument each week. Which is the

Klio2033 [76]

This question is incomplete because the options are missing; here is the complete question:

Kareem wants to find the number of hours the average sixth-grader at his school practices an instrument each week. Which is the best way Kareem can get a representative sample?

A. He can randomly survey 50 boys in the school.

B. He can survey 30 students in the school band.

C. He can randomly survey 50 6th graders in the school.

D. He can survey 20 friends from his neighborhood.

The correct answer is C. He can randomly survey 50 6th graders in the school.

Explanation:

A representative sample is a portion of a population that shows the characteristics of all the population. In this context, for a sample to be representative it needs to include only individuals of the population that is studied. Also, ideally, individuals should be selected randomly as this guarantees the sample is not influenced by the researcher. According to this, option C is the best as this is the only one that focuses on the target population (6th graders) and the sample is random, which contributes to the sample being objective and representing the behavior of 6th-graders.

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3 years ago

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Norma-Jean [14]

Answer:

2a: (c)

5o: (1, 3) and (1,1)

3a: (b)

1a: (d)

4o: (b)

Step-by-step explanation:

2a: the equation of a circle circumference needs to be transformable to the form $(x-x_C)^2 + (y - y_C)^2 = r^2$ where $C(x_C; y_C)$ is the center and r is the radius. (a) and (d) can’t be it because they contain non-zero factors on xy. (b) isn’t an equation.

5o: just put the given (x, y) into the equations and see if it holds. (2, 3) isn’t on the circumference of (1) because $2^2+3^2-2\cdot 2 -4\cdot 3 + 4 = 1 \neq 0$ , (3, 1) isn’t on it either because $3^2 + 1^2 - 2\cdot 3 - 4\cdot 1 + 4 = 4 \neq 0$ .

3a: calculate the value of the left-hand side term of the equation using (x, y) from the given point M. That’s the difference of square distance to the center to the square radius $r^2$ . Thus it’s 0 if the point is on the circumference, negative if inside and positive if outside. You get $3^2 + 4^2 - 6\cdot 3 -2\cdot 4 + 8 = 7$ , positive, so it’s outside the circle.

1a: see definition from 2a. Here, $r^2 = 9$ .

4o: insert the y from the straight line equation (r) (which can be equivalently transformed to $y = x+1$ ) into the circumference equation. If it yields no solution, that’s outside, it there’s exactly one solution, that’s a tangent and if there are two solutions, it’s a secant. $x^2+(x+1)^2+2x - 4(x+1) = x^2 + x^2 + 2x + 1 + 2x - 4x + 4 = 2x^2 + 5 = 0 \iff x^2 = 2.5 \iff x \in \{-\sqrt{2.5}, \sqrt{2.5}\}$ There are two solutions, so it’s a secant.